i~ · measurements of the solar, twilight, a~d nightglow radiation spectra are presented. an...
TRANSCRIPT
o Research and Development Technical ReportECOM-7023
ATMOSPHERIC OPTICAL ENVIRONMENT
0
by
Mimhri L. Vatsia
i~ DDC-
September 1972 .• 1972
0
* Approved for public release; distribution wdimited.
leoraduced by
NATIONAL TECHNICALINFORMATION SERVICE
U S De~c'rtment of Commerce
Sor.'gfleld VA 22157
EICOMUNITED STATES ARMY ELECTRONICS COMMAND . FORT MONMOUTH, N. J.
N.
U NC LASSI WrFDSecurty Clmass""cation
DOCUMENT CONTROL DATA.- R & DfS~lcwjly elosaedftcAeon of Mtte. body' of abstract and indexing annatetion musei be entered when the oeratll. riprlto elsoel lid)
1. ORIGINA TING ACTIVIY.- (ootomtle mautho) Tam. REPORT SECURITY CLASSIFICATION
U. S. Army Electrontips Command UnclassifiedNight Vision L~aboratnry b~. GROUP
Fort Belvoir. Virginia,ýS. REPORT TITLE
ATMOSPHERIC OPTli(AL ENVIRONMNENT
4. DESCRIPTIVE NOTES (27'pe 0 report and Inclusive datea)
Technical ReportS. AU TNORISI (Firta nasme. julddluonitial. lost name)
Mishri L. Vathia
S. REPORT DATE 7.TTLN.O AE b O FRF
September 19721117O.CONTRA^CT OR GRANT NO. So. ORIGINATOR'S REPORT NUMSERISI
6. PROJEC T No.1IS662709D6 11' ECONI-7023
C. .. S. OTHER REPORT NOISt (Any other nM10be`1 Mst BaY b. sss01PInadthis report)
d.
10. DISTRINUTION STATEMENT
Approved for public release; di-4ributicin unlimited.
$I- SUPPLEMENTARY NOTES . 12. SPONSORING MAILITARY ACTIVITY
U. S. Army Electronics CommandNight Vision Laboratory, ATTN: AMSEL.NV-VIFort Belvoir, Virginia
IS. AINSTRACT
A knowledgc of the fundamer I al optical properties of the terrestrial atmospheric environment isessent~ial for solving various problerWýý in the multidisciplinary field of Visionics including thle areas of vision.psychology, atmospheric physics, ink-ared physics, simulation, astrogeophysics, and electro-optical technology.The aim of this report is to generaliz4 tile. recent work of the author and summarize thle data from otherworldwide sources published by the 4rst quarter of the year 1972. This report included a treatment orfitheatmospheric radiation, the atmosphctý transmission, and the transfer of contrast by the atm.osphere. Thefundamental characteristics of thle da~lime and nighttime radiation including some important recentmeasurements of the solar, twilight, a~d nightglow radiation spectra are presented. An extensive chapter onlatmospheric transmission includes, thic..%ndamental properties or the terrestrial atmosphere and( basicprinciples of atmospheric absorption "fid scattering. A fairly complete collection of the most important dataon atmospheric transmittance in the 084 pim to 15 pim spce-tral region is presented. The effects of atmosphericturbulence on the propagation of imao,',ry are described. A dctIailed( analysis of the transfer of contrast by tileatmosphere is presented, and its signiifiance on thle performance of eleclro-optical devices is emphasized.'
IV
DD INOV*9.1473 RELCSOPR'?. A d ~ SU-NCLASSIFIE.1Ir I /k Q - IC Uri Wy Clea -st Net t n
UNCLASSIFIED)Security Classlfieadlo_
LINK A LINK a LiNK C
14, KEY WOlDINO LE WT ROLE WT ROLIC WT
Solar RadiationF :Airglow
MoonlightAtmospheric TransmissionAtlwspheric AttenuationAtmospheric Contrast TransferNight Sky RadiationAtmospheric ScatteringAt mospheric AbsorptionAtmospheric OpticsAtmospheric Optical EnvironmentEnvironment
1UNCI,ASSIFIED1.cwtt- clas.afcstio1
1 4. 42.1.71-VtI~vot
Reports Control Symbol OSD-1366
RESEARCH AND DEVELOPMENT TECHNICAL REPORT
ECOM-7023
ATMOSPHERIC OPTICAL ENVIRONMENT
by
Mishri L. Vatsia
VISIONICS TECHNICAL AREA
NIGHT VISION LABORATORY
Project $6627091) 61 7
September 1972
Approved for public relcase; distribution u nlimnited.
U. S. ARMY ELECTRONICS CONUNIANi)iF'OR'FM NNMoUTII. NEW .E RSlE Y
-VC
SUMMARY
A knowledge of the fundamental optical properties of thc terrestrial atmosphericenvironment is essential for solving various problems in the multidisciplinary field ofvisionics including the areas of vision, psychology, atmospheric physics, infrared physics,simulation, astrogcophysics, and electro-optical technology. The aim of this report is togeneralize the recent work of the author and to summarize the data from other world-wide sources published by the first quarter of 1972. This report include's a treatment ofthe atmospheric radiation, the atmospheric transmission, and the transfer of contrast bythe atmosphere. The fundamental characteristics of the daytime and nighttime radia-tion including some important recent measurements of the solar, twilight, and nightglowradiation spectra are presented. An extensive chapter on atmospheric transmission in-cludes the fundamental properties of the terrestrial atmosphere and basic principles ofatmospheric absorption and scattering. A fairly compictc collection of the most import-ant data on atmospheric transmittance in the 0.4 pm to 15 ym spectral region is present-ed. The effects of atmospheric turbulence on the propagation of imagery arc described.A detailed analysis of the transfer of contrast by the atmosphere is presented, and itssignificance on the performance of clectro-optical devices is emphasized.
FOREWORD
It is my pleasant duty to acknowledge the general guidance and moral supportprovided by Mr. John Johnson, Director, Visionics Technical Area, and Mr. BenjaminGoldberg, Director, Night Vision Laboratory, during the course of this study. I am in-debted to many colleagues who provided constructive criticism and commncts duringthis study. I am especially grateful to Dr. Robert W. lFenn and Mr. John E. A. Selbyfor their critical reviewing of the manuscript and many helpful suggestions. I amgrateful to Mr. Harry Ribber who provided excellent artistic guidance on illustrationsand to Betty L. Dobson for her patience in typing the original manuscript. The readersare requested to forward their constructive criticism and comments addressed toDirector, Night Vision Laboratory, U. S. Army Electronics Command. Attn: AMSEL-NV VI (Dr. MI. L. Vatsia), Fort Belvoir, Virginia 22060.
III~o
CONTENTS
.4Section Title Page
SUMMARY ii
FOREWOiRl)
ILLUSTRATIONS vi
TABLES x IATMOSPlHERIC RADIATION
I. Daytime Radiation I2. Twilight Radiation 143. Nighttime Radiation 18
11 ATMOSPII ERIC TRANSMISSION
4. The Terrestrial Atmosphere 345. Atmospheric Attenuation and Emission 40o. Outdoor, H orizontal, Long- Path At mospheric I
Transmittance 447. Laboratory Studies of the Attenuation of Radiation
by Atmospheric Gases 688. Fundamental Principles of (;aous Absorption 69
a. The Shape and Width of a Spectral Line 72
b. The Rigorous Method for Coviputing GaseousSpectral Absorptance 74
c. Band Models for Computing Spectral Absorplanve 76d. Empirical Methods for Calculating Spectral
Transmittance 789. Scattering of Radiation by the Atmosphere 81
a. Rayleigh Scattering 811). Mie Scattering 82c. Atmospheric Turbulence 90d. Multiple Scattering 93
10. Tables of Attenuation Coefficients 95
III CONTRAST TRANSFER BY THE ATMOSPHERE 09
II. Definitions of Contrast 9912. The Alteration of Contrast by the Atmosphere I(0)0
iVl
CONTENTS (cont'd)
Section Title Page
H! 13. Optical Measurements for D)erivation of Atmospheric(cont'd) Contrast Tranferance 103
14. The Effect of Contrast on the Performanace of ViewingSystems 106
15. Meteorological Visibility of Objects Scen, Against theSky Background 108
I'
IiI
I! V
/S
ILLUSTRATIONS
Figure Title Page
The Solar Spectral Radiant Incidance (Irradiance) NASAStandard (Thekaekara) 3
2 The Annual Variation of Insolation for Different Latitudes
on the Earth (Adapted from Kondratyev) 5
3 The Solar Spectral Radiant Incidance (Irradiance) at SeaLevel for One Air Mass (Valley) 10
4 Natural Luminous Incidance (Illuminance) as a Functionof Solar and Lunar Altitude and for Various Phases of theMoon as Measured by Brown 12
5 Some Low Resolution Twilight Radiant Sterance Spectraof time Zenith Sky for Three Solar Zenith Angles. TheOrdinate Axis Numbers are to Be Multiplied by 10'12 forCurve I, x 10"1 for Curve 2. and x 10-15 for Curve 3(Rozenberg) 16
6 A lligh-Resolution Twilight Spectrum (from Chamberlain) 17
7 Night Sky Spectral Radiant Sterance at Kitt PeakObservatory (Adapted from Broadfoot and Kendall) 21
8 Night Sky Spectral Radiant Sterance for Various Phasesof the Moon as Measured by Vatsia, Stich, and Dunlap 22
9 Atomic Oxygen (01) Energy Levels 24
10 The Relative Radiant Sterance of the Moon as a Functionof Phase Angle after Russel and Rougier Measurements 31
II Night Sky Radiant Sterance Spectra for Various Altitudesof the Moon as Measured by Valsia, Stich. and Dunlap 33
12 Vertical 1)iLtribution of Atmospheric Constituents from13 0 to 250 Kilometers (Valley) 35
13 Vertical Distribution of Atmospheric Constitiuents from80 to 500 Kilometers (Valley) 36
vi '
ILLUSTRATIONS (cont'd)
Figure Title Pag!
14 Temperature-Altitude Profile to 100 km for U. S. StandardAtmosphere, 1962 (Valley) 39
15 Spectral Transmittance of Atmospheric Gases (LaboratoryMeasurements) and the Solar Radiant Incidance Spectrum(Valley) 49
16 Spectrum of Atmospheric Transmittance for 2.07 kmOptical Path Containing 1.7 cm of Precipitable WaterVapor Based upon Gebbie et al. Measurements 50
I 7a Atmospheric Transmittance Spectra for Selective Fogsas Measured by Arnulf et al. 51
I 7b Atmospheric Transmittance Spectra for Evolving Fogsas Measured by Arnulf er al. 52
17c Atmospheric Transmittance Spectra for Stable Fogs,Type I, as Measured by Arnulf et al. 53
I 7d Atmospheric Transmittance Spectra for Stable Fogs,Type 2, as Measured by Arnulf et al. 54
1 7c Atmospheric Transmittance Spectra for Haze as Measuredby Arnulf etal. 55
18 Atmospheric Transmittance Spectra Recorded by Taylorand Yates over 0.3, 5.5, and 16.2 km Long Optical Paths 57
19 Atmospheric Transmittance Spectrum Recorded by Yatesand Taylor on a 27.7 km Optical Path with 20 cmPr{ecipitable Water Vapor 58
20 Atmospheric Transmillanee Spectra for Various Amountsof Precipitable Water Vapor in 25 km Optical Path:(A) 21.5 cm, (B) 25.4 cm, (C) 36.2 cm, (D) 43.3 cm, and
(E) 26.7 cm, Recorded by Streete 59
21 Atmospheric Transmittance Spectra for Various Aniountsof Prcripitablle Water Vapor: (A) 0.105 m.!, (B) 0.27 cm,(C) 0.53 cm, (D) 1.05 cm, and (E) 0.78 cmi. Recorded byFilippov et al. 60
"vi ¶
ILLUSTRATIONS (cont'd)
Figure Title Page
22 Atmospheric Transmittance Spectra for Various Amountsof Precipitable Water Vapor: (A) 1.55 cm, (B) 2.05 cm,(C) 2.47 cm, (D) 3.0 cm, and (E) 3.5 cm, Recorded byFilippov et al. 61
2.3 Spectral Attenuation Coefficients for Winter lhaze in the0.59 to 5.0 pmn and 0.59 to 12.0 pim Regions Reportedby Filippov et at. 62
294 Transmittance of 0.63 ym, 3.5 M~m, and 10.6 pm LaserRadiation through Variable Haze over 2.6 kin OpticalPath as Measured by Chu and Hoegg 64
25 Transmittance of 0.63 p~m, 3.5 pm, and 10.6 pAm LatterRadiation through Variable Rain in 2.6 kmn OpticalPath as Measured by Chu and Ilogg 65
26 Transmittance of 0.63 pm, 3.5 p~m, and 10.6 pin LasterRadiation through Light Snow over 2.6 kmi OpticalPath as Measured by Chu and llogg 66
27 Relative Size Distribution of Fog Particles in the FogChamber as Reported by Perry and Layman 70
28 Relative Tranhmittance of Visible, 3 to 5 pm, and 8 to 12pm Radiation through Artificial Fog with Varying OpticalDensity as Measured by Pei ry and Loy man 71
29 D~oppler and Lorentz Spectral Line Shapes for SimilarStrengths (Intensities) and Line Widths 75
30 Computed Spectra of Atmospheric Transmittance forFive Model Atmospheres with 23 kmn Horizontal Visibility 79
31 Computed Spectra of Atmospheric Tranismittance for FiheModel Atmospheres with 5 km Hlorizontal Visibility It0
32 irn and 'r, Functions of Scattering Angle for n I to 6Used in Nlie Theory (After Van de Ilulst) 84
viii
ILLUSTRATIONS (cont'd)
Figure Title Page
33 Spectral Attenuation and Scattering Coefficients forVarious Haze (LM,1I) and cloud (C, 1 , :(3) Models(Adapted from Deirmendjian) 87
34 Spectral Attenuation Coefficients for Various Models ofContinental Haze: (A) Relative Ilumidity 4 0.90, and(B) Relative Humidity 2i 0.95 as Reported b) Rensch 88
35 Variatit-a of Attenuation Efficiency K with SizeParameter x for Various Values of Refractiwv Indices(Adapted from Van de llulst) 91
36 Variation of Photographic Resolution as a Function ofOptical Path Length for Various Values of ExposureTime as Measured by Smith, Saunders, and Vatsiu 92
37 Variation of Atmospheric Contrast Transferance(Transmittance) with Observer Altitude for Various Look(Nadir) Angles for Two Model Atmospheres (Adaptedfrom Wells et al.) 104
38 Atmospheric Contrast Transferance as a Function ofAltitude for Two Types of Background (Adapted fromDuntley et al.) 107
Iix
!.x
TABLES
Table Title Page
1 NASA Standard Solar Spectral Radiant Incidance(Irradiance) 2)
1l Relitive Optical Air Mas as a Function of Solar Altitude(F. Kasten)
III Vertical Atmospheric Transmittance for a Unit OpticalAir Mass 9
IV Spectral Luminous Efficiency for t[ie CIE StandardObserver I I
V Horizontal Luminous Incidance for Various Solar.Altitudes (Brown) 13
VI Major Nightglow Emissions (Adapted from McCormac) 27
Vita The Relative Radiant Sterance of the Moon as a Functionof Phase Angle Based upon Russel's Measurements 29
Vllb The Relative Radiant Sterance of the Moon as a Functionof Phase Angle Based upon Rougier's Measurements 30
VIII Compositior, of the Atmosphere (Dry) up to About 90 km 37
I X Major Horizontal Long.Path Atmospheric TransmittanceMeasurements 46
X Attenuation Coefficients for [laze for Variwui, Values ofHorizontal Visible Ranges (Adapted from Elterman) 96
X! Spectral Attenuation Coefficients for Fog for Visibilititcsof 0. 100 and 0.755 km (Adapted from Arnulf et al.) 97
Xil Spectral Attenuation by Haze and I ight Fog, VisibilityI km (Adapted from Chu and logg) 97
Xlll ipectral Attenuation Coefficients foi Coastal or Marin,[laze with lh zontal Surface Visibility of 2 Kilometers(Adapted from I)eirmendjian) 98
mihi : x
IIATMOSPH ERIC OPTICA L EN VIRON MENT
I. ATMOSPiiERIC RADIATION
1. Dayltne Radiation. During the day, the predominant radiation oni the earthis the solar radiation v ich is propagated to the earth through the intervening space andterrestrial atmosphere. The electromagnetic spectrum of the solar radiation extends inwavelengths from a fraction of an angstrom to hundreds of meters including the gammaand x-rays, and the ultraviolet, visible, infrared, micro, and radio waves. There are anumber of publications which present interesting features of the solar radiation." 3
The earlier measurements of solar radiation were made mainly with ground-based instru.mentation. However, recently, high-altitude aircraft, balloon, rocket, and space.borneinstruments have been used for solar energy studies. The solar radiation incident on theearth's surface varies in magnitude and spectral composition due to the fluctuations insolar emissions, the attenuation of the atmosphere, and the variations in solar distance.The solar-distance variation produces a maximum change of ± 3.5 percent during theyear in the solar irradiance on the earth's surface. The variations in the solar spectrumdue to fluctuations in solar activity are comparatively much smaller in magnitude. Thefluctuations in the incoming solar radiation, insolation, at a fixed location on the globeare mainly caused by the terrestrial atmosphere especially due to variations in the cloudcover, water vapor, and aerosols in the atmosphere.
The solar constant is the amount of total solar energy received per unit timeper unit area exposed normally to the solar rays at the average suit-earth distance in theabsence of the atmosphere. The spectral distribution of this energy as a function ofwavelength is the solar spectral radiant incidance* (irradiance). Thekackara has report-ed the latest state-of-the-art on the mea',,.rement and computation of the solar constantand the solar spectral radiant incidance. 4 5 Table I and Fig. I contain the NASA stand-ard, solar spectral radiant incidanee data as proposed by Thekaekara. The new NASA
-For radionetric nomenclature, the reader is referred to th.r prolpsed NII, Standard for InfraredTerms and Definitions, Part I, Appendix C, of Final Report QL.TR-71-7, NIICONI GCntractDAAII01-71-(.0433, Ford-Philco Corporation, Aeranutronic Division, Newport IBaclh, Calif.92663 (1971).
1 K. Ya. Kondraty.,v, Radiation in the Armnsphere, Academic Prebs, New York (1969).
2 N, Robirnson, editor, Solar Radiation, Elsevier Publishing Cotnpan%, New York (1900).
"3J. W. T. Walsh, The SNjienre of Daylight, Maedona'd & Co.. Iondon (1961).
h1. P. Thekarkara, j. na',ironmengal Sri. 13, (4) 6 (1970).
'M. P. Tlhekaekara and J. . 1)urntmond, Nature Ph yi(al•Sirnee 229, (1971).
Table 1. NASA Standard Solar Spectral Radiant Incidance (Irradiance)
0* - .1..spectral .tr.8,.nc.- A..raqrd u-er s-':1 ban.,~ddth cent~red ot .n m N a-
19t-ýI- Area nodelr thv solar spectfk.ral &r a,,~c- c rve In the ttaselirqtl, rangqe 0 to inn W 0-
OW-) - Percentage :1 :-. solar constant associated withn wavclgn.ths shnorter than
Soa - -oat -3S - - - - -
E33 (O-4) D6o--3 9n?3 Io-) blo-kl C(h) z10.3 D10'3
.3s0 Sog got .O03 .3, 10f 31 orb t6.71o2 1.1's Is*0 I 00.90?
.10 .07 .I,0 .0000 .0301 310.0to ff.oI4 1.40 100 37l.O.P 41I.S93too .PS .60400 .020046 .440 spot 370.07 P4.084 1.40 10.2 lt00.p0 of.100
.171 .63 .01330 .08800 .000 1700 386.621 160p3? 3.00 120 3203.00 02.644
.100 3.2t .02300 .90169 .%so Ins IIN.SoS M366. 1.4 110 1100.00i 43. #66
.:0 211 .1002 .00310 SS0 3770 *000.133 10.011 ?.to 101 00sf40 03.%69
. 302.91 ra7,03 IM",o '6.60 316 023.30 3. .0 1"..0 0002.720 02.0 .004 .000 .7 1712 0131.11, 11.40? P.90 00 12004.00 0.
OYZO 00. PS,0 Isis0 .01 1 4041.26t 22.S41 2.0 02.0 lt14~.00 0.0.70 1. .~0 e~ .000 Isis 400.4.1r 31.116 p. 00. 13062.00 90.2no3
6'0 3.0 t.93549 1. 11 .00 1 404%.1 0. .7 0.*?0 12.3 t. f?304, .11666 .5"0 is 300 ?40. %, 3S.21". P.0i 3.0.0 31.0 q.21333.?VP 10.% 2.63000 .1944 .000 10%6 002.70b 3S.443 P.9 0. 1320.10 07.0038
. it" I0 bb000 .220 .6- 1007 4141.6ro 36.291 3.8 31.6 t321.00 O'.0277to0 130 3.010 .26414 .030 13010 001.2to% 30.100z 1.1 246.0 1 326.00 00.0363
1.1% 140 4.63410 .1264 .020 1ose 030.000 30.000 1.? Z2.6 100 90.P170?'0 12 S.06160 .00 .' 1070 S31.329 30.210 3.3 10.2 13.0 0.12
.70 70 .0710 .%IS? .0.. 1000 0S0.604 00.1.21 1.0 10.0 1332.06 q0.0607??z P2 .6306 .5640 .4s 1011 S14.114 01.040 1.0I 10.0 1330.3? 00.0200
.0% Its 0.40M0 .6436 .00 1%60 W1.Ist %Z.65? 1.0 3 133%.1 3 3"0.770?.200 40* 16.9716 "04 .99100 01.46) 43.744 1.7 14.3 1337.02 10.010??4%0 000 13.3.0) 1.,1 P0 30? 060.M0 4%.616 1.0 11.1 1330.10 00.0000
*vj Sit O 16.316 &.M?0 .&I 1t.$? 070.020i 00.000 3.0 30.3 1330.71 00.0001* 31 03 30101 1.11 7 130t1.o 0 7 1. 9.5 1300.20 00.0010
S10 11 ? '7.0001 1.000 .7 1100 60100 07.02 0.1 0.? 1101.11 00.12s2to:0 ?0 .20300 1.02043 .72 111 00k 61.131 10.6.6 0.7t 1.6 130.1.00 00.10014' .10 8 01 ?.Zia& .?I 1200 0N. I" 00.0an. 0. 1 7.1 t1302.13 00.7012
!S 30 30031 2.5 *% 70 320 oo.O 3. 700 .0.0 0.0 131011 0.pq110
.10034 0.01 .1 .00 1100 707.0% ,0'.7 0', 3.03 13.10 00030
.. b. 113 1.0300 0.123 .?l 10009 110.000 S4.014 7.3 %.So 34S0.56.1 I0.01100
'SS I 130 61.610 %.O0 .0s 1130 705.0.11 56.231 0.0F 3.4 1341.3166 00.011723
.10110 0O 00.9100 7.3i3 .40 00ss 010.0301 116.00 63.3 Ws1 1107.1030 00.07221?
S4 1310 ??0.4366 It.0?3 .4? 0070 ?0.70% s1.31 ?7.1 .199 10.0 111.90100%
:,'?I list 120.130 I..20-t .00 0031 ?%@.3t% 0330 1.0 .000 312733 0.00010
.0 3 31 0 0 3. 3 0 0 1 0 0 1 1 ~ 0:00 0 :.0 7 3 . 0 0 30 .3 .0 3 3 1 1 0 3.01 013 0 0.0 0 0 0 0.021 307 1010301 1.72? .1 000 os~ooo oo.Jo 310.3 .2 3207 00,
.070 3001~~33 10.00 130 .is Sol? 00.0 00.0. 10. .04.0 1370 0.00.030s'. 117 0.01 17o1 .0 031 000 0 0 2. .3106 1107.0110 00.000035
.40S 3030 100.700§b 13.12 .40 003 01.00% 01.100 13.0 .00%9 1307.OiO M-6401111
.000 3022 300'.030 30.030 .00 Sao 020.100 00.300 306. .76300 137r.0I0736 00.0070.01
.00 710'n1 130.011, 10.00 3.00S 70 05.3 F000 00.0 9~30 17001 0.0.000 2000 220.1210 1SI330M00 000I2.6 00 .00010.02 000
.000 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ M I00 20000 3.1 .0 0 b13 1.3 00 .06730o 00 002
.04 30 07s. 2 2110 21 3.1 30.1 33 00 1 01. 0
.00 00 20.3 1.10 I .t 31 1303.6 00.1
"'So 3007 370.020 4 8 .01 1.0 %1 09 707 300 36 6 .
* %V403 0.311 ?0.911 3.00 '2) 1710.00 40.010 16.10026.4 - 468 - .-S -3 -o)$ - -
"Po 71.169 19 114.rs 1.62
4-4
1 ~Cý
C*4)
Lai
5044
wri~~ - 4)3NO3I NI
I
Standard of solar constant is 135.3 mW cm2 (1.940 calories em"2 min") with anz errorof ± 1%. The solar constant value of 139.5 mW cm"2 (2 cal cm"2 min') proposed byJohnson in 1954 is about 3% higher than ihe new NASA Standard.6 Tile wavelengthrange of 0.22 micrometer to 15.0 micrometers contains 99.98% of the solar energy outof which the 0.22. to 0.38-micrometer (ultraviolet) region contains 7.0%, the 0.38. to0.72-micrometer (visible) region contains 41.86%, and the 0.72- to 15.0-micrometer(infrared) region contains 51.12% of the total solar energy.
The spectral or total solar radiant incidance E at a horizontal plane at any
time at a given geographical location at a solar distance R is given by
E P.0 (Ro/R)' cosz (I)
where E. is the solar constant at normal incidence at the average solar distance Ro (oneastronomical unit), and z is the sola, zenith angle. The factor (Ro/R) 2 depends uponthe position of the earth in its orbit around the sun. McCullough suggests that to a goodapproximation (Ro/R)2 = I + 2e cos (2 w D/365) where e is the eccentricity of theearth's orbit (0.01675) and D is the day of the year.' The annual variation of factor(R0/R) 2 , the inverse squared solar distance measured in astronomical units, is small ascompared to the variations in cos z which is the principal factor determining the hori-zontal-plane solar radiant incidance. The zenith angle z may be expressed in terms ofthe astronomical coordinate variables using the spherical astronomy relation: s
coz z = sin 8 sill 0 + Cos 6 Cos 0 cos It, (2)
where 6 is the declination. 0 is the geographical coordinate latitude of the location, andh is the time of the day in hour angles.
The annual variation of daily totals (f solar radiation in the absence of atmo-sphere at different latitudes is presented in Fig. 2 on a 3-coordinate graph. The verticalcoordinates of the surface are proportional to the daily totals of incident solar energyfor the corresponding latitude and season of the year. The terrestrial atmosphere atlen.uates the incoming solar radiation even under "clear" conditions due to scattering andabsorption by atmospheric gaseous molecules and aerosols. Atmospheric transmissionof electromagnetic radiation is a wavelength-dependent function. (This subject will lrdiscussed in more detail in a later chapter.)
6F. S;. J ohnson, J. Veteorul. 11 43 ,11 (195-l).
'E. C. NtrCulhough ,.rch. MIet. GeophYs. Biokl. Ser. B 16. 12•") (196•).
81. I. luellehr and II. Eichhon-, Spherical and Practical ..tsronornv. rederiiL I ngar Publisihing Cj..
Nu York (196,9).
S. . . . .. . .. . . . . . . . . .. .. .. ... . . .. . . .. . . . . . . .. ,. . . = • . .. = - ' = = '- _. . . . .
000
ooC
op.V 40 0
opU00 op
.0. .0
10000V
* U.
d~p
'% b % b
In the presence of the terrestrial atmosphere, the spectral radiant incidancedue to direct solar radiation is reduced while the atmospheric gases and aerosols produce-diffuse sky radiation due to scattering of some of the direct solar radiation. The reduc.tion of direct incoming solar radiation depends upon the optical path which the radia-tion has traveled within the terrestrial atmosphere. When the solar radiation is incidentnormally on the earth's surface, the optical air mass is unity, if the earth were flat andno refraction took place, the effect of radiation incident on any ange z from the nor-mal would be to reduce the incident radiation by an air-mass factor equal to secant z.7This is a good approximation until z approaches 800. At greater zenith angles, the se-cant gives values which are increasingly too high because of errors due to atmosphericrefraction, curvature of the earth, etc. The air mass m has been calculated by F. Kastenusing corrections for the variations of refractive index.9 Table 11 gives values of opticalair mass as a function of solar altitude. In any transparent, homogeneous medium, theoptical transmittance T through an optical path length R is given by
TR =exp(- aR) (3)
where a is the attenuation coefficient per unit optical path length.
For R 1, T, exp(- a), (4)
therefore, Tt T1 R. (5)
In the case of the earth's atmosphere, if T, is the atmospheric transmissionfor a unit iir mass, then the atmospheric transmission Tm through a slant optical pathinvolving air mass m will be given by
Tm = (T,) m . (6)
The spectral radiant incidance (irradiance) EX due to the attenuation (of thedirect sunlight by the tcrre-trial atmosphere is given by
EX, = FOX IT, XI m, (7)
where Eo)" is the spectral radiant incidanee for zero air mass. T' X is tlhe vertical, atmo-spheric I raismittance for unit a;r mass, and m is thei air mass between the sun and thepoint of incidence. The vertical, integral, atmospheric transmittance for unit mass forthe visible range ;ý 0.796. 1",is is based upon the relation:'°9 F. Kasten. "A New Tab!P and Approximation Formula for the Relative O Ipti'al Air th,,," ..trhii.fur M[eteorologie, ,eoF ysik and Biioklimatologie, It- i4, 20W1 (1965).
I)J. W. T. W.1ah, nhe Srience of lavlight. Mlardmahl I &Co., London (1)6 1).
(6
1119 $ROMAR RAIP Ua 11O mill 9-1
aMa
7"qtq9~ OC C
CR1 210 IN :R A iW 0 1 p AN
~4 4 -- ------------------------ C~
C4 t
I
Tiv =1y EoX TX V /Z Eo• VA, (8)
where T, v is the integral, vertical, atmospheric transmittance for the visible solar radia-tion for unit air mass, V) is the spectral, luminous efficiency of radiation, and T) is tilevertical, spectral transmittance of the atmosphere. The spectral atmospheric transmit-tance for a unit optical air mas TX is a variable function dependent upon the composi-tion of the highly variable constituents of the atmosphere, namely water vapor, ozone,and aerosob at the time of measurement. Table III gives a typical set of atmospherictransmittance data based upon earlier measurements reported in the literature."Figure 3 shows the spectral distribution of solar radiant incidance at sea level for oneoptical air mass.12
The spectral luminous efficiency V), for photopic vivion (light-adapted vision)and Vj for scotopic vision (dark-adapted vision), is given in Table IV. These values arebased upon a "standard" observer.13 Interpolated values of spectral luminous efficiencyat 1-nanometer intervals are available in the literature.' 4 5 An actual normal observermay have significantly different spectral luminous efficiency.16
D uring the period 1943.1947, Brown made worldwide photometric measure-ments of daytime and nighttime natural illumination as a function of solar altitude.' 7
Figure 4 contains Brown's basic curves for horizontal luminous incidance (illuminance)as a function of solar and lunar altitude and various phases of the moon. These curvesgive average luminous incidance levels for "clear" environments. Table V gives valuesof average luminous incidance in footcandles for the entire range of solar altitudes ,rom-90° to +90*. At a particular geographic location, the altitude of the sun is calculateiusing the relation,
A = sin" [sin 6 sin 0 + cos 5 cos 0 cos h). (9)
l1j. W. T. Walsh, The Science of Daylight, Macdonald & Co., London (1961).
12S. L. Valley, Handbook of Geophysics and Space Environments, McGraw-Hill, New York (1965).
131-iternationnl Lighting Vocabulary, Third Edition, International Commission on Illumination (CIE),Paris (1970).
14 y. Le Grand, Light, Colour and Vuion, translated by R. W. G. Hunt, J. W. T. Walsh, and F. R. W.Hunt, Chapman and Hall Ltd., London (1968).
15J. W. T. Walsh, Photometry, Third Edition, Constable & Company Ltd., London (1958).
16 ,Y Le Grand, Loc. cit.
1 7 D. R. E. Brown, .Natural Illumination Charts, Report No. 374-1, Department of the Navy, Bureauof Ships, Washington, D. C. (1952).
8I
Table Ill. Vertical Atmospheric Transmittance lor a Unit Optical Air Mlas
WAVELENGTH TRANSMITTANCE WAVELENGTH TRANSMITTANCETRI CNSOMIIETI IMICIAOMIMIT
0.36 0.489 0.56 0.797
0.37 0.516 0.57 0.300
0.38 0.547 0.58 0.801
0.39 0.575 0.59 0.104
0.40 0.600 0,60 0.813
0.41 0.624 0.61 0.822
0.42 0.644 0.62 0.830
0.43 0.663 0.63 0.843
0.44 0.685 0.64 0.353
I 0.45 0.703 0.65 0.862
0.46 0.718 0.66 0.869
0.47 0.733 0.67 0.877
0.43 0.746 0.68 0.883
0.49 0.759 0.69 0.824
0.50 0.768 0.70 0188
C.51 0.777 0.71 0.884
0.52 0.783 0,72 0.789
0.53 0.788 0.73 0.160
0.54 0.795 0.74 0905
0.55 0.796 0.75 0.836 .
924
cl
0.4.
ciIqwI
4-4
=F C
cm4.
cc ZL
s Or
Cace C
(ai
CA ~WMI ca cl j
1000
Table IV. Spectral Luminous Efficiency for the CIE Standard Observer(From International Lighting Vocabulary)
WAVELENGTH LUMINOUS EFFICIENCY LUMINOUS EFFICIENCY{NAUSETE *s) FOR PHOTOPIC VISION FOR SCOTOPIC VISIONV___ __ __ _Vx
I- I IXV
380 100 0 0000 589390 0.0001 9002209400 0.0004 0.009 29410 1001 2 0.03484420 0.0040 0.09 6430 1011 6 0.199 !440 0.023 0.321I450 0.038 1L455460 0.060 0.567410 0.091 &676480 U139 0.793490 R208 0.904500 0.323 0.982510 1503 0,997520 1710 0.935530 1862 1811540 0.954 0.650550 0.995 0.481560 1995 0.3288570 1952 R2076580 0.870 0.1212590 0.757 0.0655600 0.631 0.03315610 0.503 0.01593620 1381 0.01737630 1265 0.003335640 1175 0.001427650 0.107 0.000677660 0.081 0.000 3129670 0.032 0.0001480680 0.017 0.0000715690 1008 2 0.00003533700 10041 1000 017 80710 0.0021 .000 00914720 1001 05 0.000 004 78730 0.00052 1000002546740 &000 25 0.000 001379750 0.00012 0106 000 760760 0.000106 01,00 000 425710 0.00003 0.000 000 241780 0.000015 10000000139
I I
90' ~4(rc T 2r I ff (r 1(r Ar X 4(r Wc A 7V7 W~ 90'
........... . .. ..... . .. .
* *9 *AAIiM BASIC CURVE,S LU CONDITIONS -0A
I I BLACK S¶ORUCLOUD1jxN EXTEME CONDITIONI 1~ TRE.Mw
e. -- Ax
r ()Lo:;f+.t M O M-_
z
~16
KArA Aw OA R7 S MAX -4.0 X10*
of D
I~~~ . .... m.... ftm
ALTITUDE
Fig. 4. Natural luminous inciclance (illuminance) as a function of solar and lunar alti-tude and for various phases of the moon as measured by Brown.
12
Table V. Horizontal Luminous Incidancc for Various Solar Altitudes (Brown)
29*10.3:~rv- 7 r;, 0, 4 a5T I W j~th 2o i5NY 54o 0'~ 4370 T4W' 620-50 7900 W0 9i-502 463 .V 4.73 .1 71.9 .1 10S .!a3 2555 .1 43901 .1 6220 .1 7920 .1 9460
.a4.6.652 .2 260. 1005 4410 .2 6230 27940.2 9470* .7 4.90 .75.73 .3 90.3 .3 1053 .3 2595 .3 4430~ .3 6250 .3 7950 3 9460
-6' .6 4,95 A6 6.32 A4 64.0 .4 1068 A4 2610 A 440 270 A 7970 .4 9500.5 S00 .5 6.97 .5 69.3 .5 1082 .5 2625 .5 4460 .5 6290 .5 7990 .5 9510.4 W 50 .4 7.70 .6 94.2 .6 1096 .6 2645 A 4410 J6 6300 £ 6000 Z 9520
13' 3 &11 .3 6.50 .7 99.3 .7 1102 .7 2660 .7 4500 .7 6320 .7 8020 .7 9530
V* 25.16 .2 9.40 .6 105 .8 1123 .8 2675 B 4520 .8 6340 A 6040 A 9540.1 522 .3 04.30 .2... 11 -9 1136 2 . 2II2D A.4.5A a &S 9 80502 255-s0' 19 j5j2j -9J* 1.3V16 1' 1150 21' 2705 31' 4560 41' 63751' 6070 6 V 95705.134 .9 1.20 .1 121 .1 1162 .1 2725 .1 4560 .1 6390 .1 6060 .1 9560A6 543 A 1.43 .2 126 2 1178 2 2745 2 4600 2 6410 .2 6100 2 9600
76 2-81-W A6 555 6 1.74 A o40 .4 1205 A 2760 .4 4640 A 64401 4 83140 4 962075 ' $62 .5 1363 .5 146 5 3220 .5 2795 .5 4660 .5 6460. .5 8360 5 963074 .4 17 A 2-13 .6 155 .6 1235 .6 2610 .6 4680 6 6460 .6 e180,.6 9640
-732 T .3 2.73 61 .7 1250 .7 2030 .7 4700 .7 6490 .7 03190ý , 660
722 587 2 2.63 .6 166 . 6 1262 .6 2845 .8 4 7 30 .8 6510 ,8 8 2 01 0 . 6 96707 81ffi. .32 21 292 2875 32 704 505,924 a*99
.A2 9 6.35 .9 3.62 .1 191 .1 1303 .1 2895 .1 4770' 1 6560 .1 8260 .1 9700.G: 2s 91 625 a 402 .2 SO9 2 31352: 21 2 4790 . 6580 2 8270 2 9710
.7636 .7 49 .3 206 .3 332 .3 2930 3 480.:50. 2901 .3 9720'263 .6 6.47 .6 siO .4 215 .4 3342 .4 2945 .4 4830 .4 6630 .A 3 101 A 973012-4. 5 IW0 -5 5.60 .5 222 .5 1356 .5 2960 .5 48350 .5 6630 .5 6330 .5 9750
A1 4 6.73 A 62? .6 231 .6 1370 .6 2980 .6 4670 .6 6640 .6 8340 .6 97603* r4 .3 G86 .3 7.03 .7 239 .7 13385 .7 3000 .7 4880j 7 660 7 8360' 7 970
-2*2ss 2 7.0 0 2 7.86 248 8 1400 6 3015 8 4900 8 667 .8 380 .8 9780lus 3B 715 .1 685 .J.j1 25 9 1415 9S 3035 .
9 49Oj.
9.j90. 9 8400 1.....9 .9 TI
-6 17 7,30 1Zto' 3- 263 13* 1 43o 23'T s 30 3 49 L4 6710 53' 8430 63- 9800-592e Z ?4 .9 3.32 1 274 .1 1446 3 3070 1 49601 A 6730 .1 6 430 .1 9810267 .6 765 .8 326 .2 262 .2 1460 2 3090 .2 4980! 2 6750 .2 8440 .2 9620
W 207 .7 763 7 141 3 290 3 1475 .3 3105 3 4990 3 6760 3 8460 .3 9830U :2.66 .6 603 6 356 .4 296 .4 3490 4 3125 .4 5010 .4 6780 .4 8460 .4 984015:2oo .5 8,23 .5 177 .5 307 5 3504 .5 3345 .5 5030, r5 680.5 8490 .5 9850-5*289 .4 645 ý4 398 .6 336 6 1! 18 .6 3165 6 550 .6 680 .6 8510 6 n860S290 3 869 3 223 7 324 7 3532 .7 3380 .7 5070 .7 6830,ý .7 8530, .7 9670~29 1 2 695 2 Z.51 8 33 6 54 8320 0 5080 6 68501 8 8540, .F 9860
-52.92 .2 924 1 2.6 3 34Z 9 1 560 . 3215 9 510 .9 85601 9 9890'*2.93 -is*95?. 1-fe36 V ýTF 56ZV3 Y3*52 -1 6:IT 0 54 85080 64* 9900*4:294 .9 ~90. 935 .1 3659 .1 1:090 .1 32650 .3 540, .1 6001 .1860 I90*2.a$5 a 3023 1c 3.97 .2 3 6 2 1604 2 3265 2 5360W .2 620 ý2 8:100 2 9920
47*206 7 306 7 447 .3 377 .3 1638 .3 3285 .3 5170' .3 69 30 3 830 3 99304'2.9? 6 330 .6 503 A4 386 .4 1635 .4 3305 4 5390 .4 6950 A ses50 4 9940'2.9 5 11t4 5 561 .5 396 S5 3650 5 3320 .5 5210; .5 6970 .5 86701 .5 9950
-4*299 4 316 4 630 .6 404 6 1665, .6 3340 .6 5230i .6 6980 .6 86801 .6 9960-3: 300 323 .3 708 .7 414 .7 160 .7 3360 .7 5250 ! 7 7000 .7 8700. 997042 301 23 3.28 2 7.94 .6 424 .8 16950 81 3380 .98 5260 f 70110 .6 8710 a .998041*302 171 3.3 TO 01 .9___ ______ 9____13. . .3.40 41 0 432I1 . 13 .9 3395 95280 9' 03, .9 8701 9 9990,40 304 15 .3 .00 3-?- 442 15'T 1725 5 3410 35' 5306 45700 5'8 4 65'100-39'306 9 46 9 .1 452 1 1740 .1 3430 .1 5320 13 7060 1 8750!'66 0103036 308 a 3.52 .8 1.24 .2 462 .2 1755 2 3460 2 53401 .2 7080! 2 87 70 167' 102n0
-37' 3.30 7 151) .7 1.38 3 472 .3 3770 .3 3475 .3 5350 .3 7100 3 8780so68' 10300-36:3 12 6 367 6 1.54 .4 482 4 1785 4 3495 4 5 370 4 T7120 .4 88e0 0 69' 3040035 314 5 175 .5 L.72 .5 492 .5 1805 5 3530 I5 390.o.5 71 30 .5 882070'0304804 31 .83 4 193 .6 503 .6 :820 .6 3530 .65430, .6 iis50 .6 88140'7 o7
.3I 3 .0 .7. 2 8 15 837 0 4 Tg!. 6060 73* 072033327 13 1 26 9 53. 8701 . 3' 85 5 460! 20 88,4o
-30' 332 *14 2.24 -r 2.92 9--*IWY 16' lS5 1 II36~ U636 5480-46- 7220 56- 880;75*1087029* 336 -.9-235 .9 32F 13 554 .1 1900 .1 3620 .1 5500 1 .1 72401 .1 :8900 76' 1093086'342 .6 246 a 3.63 2 566 .2 1915 .2 3640 .2 55 101 2 7250 .2 8920'? ! 3000 1Oo-27'3 48 7 262 .7 396 .3 577 .3 3930 .3 3660 .3 55301 .3 7270 .3 :1940 176' 11060-26:35s 6 276 .6 4.38 4 587 .4 1945 .4 3680 .4 55 50 4 7290 .4 :9 50179: 111,80-25 366 15 2.92 .5 484 .5 599 .5 3960 .5 3700 .5 5570 .5 7330 .5 897010 .O 380-24' 378 4 308 4 534 6 630 .6 1975 .6 3720 .6 5 590~ .6 7320 .6 890 :I :112 2023* 394 3 3.27 3 5.90 .7 623 .7 3990 .7 3740 .7 5600;1 .7 73401 .7 89:00'2 1260-22* 414 2 347 2 646 6 633 .8 2005 .8 3760 .8 560 8761 .89313 33
'21441 .3 368 .1 7.10 9 642 .9 2020 .9 3775 .9 5 401 .9 7370~ 9 930 30 84' 1135043392 ._* 9 7~ 653 97 2045- 37'590 37- 566014~7. 7390 57r 9040 85' 113809 415 .9 6.55 .1 664 .1 2060 .1 3810 .1 5680! .1 7410 .1 9060 61428 444 8 935 2 676 .2 2075 .2 3830 .2 57001 .2 7420 2 9070873407 473 .7 10.2 3 687 .3 2090 .3 3850' .3 571 0 1 .3 7440 .,909088I37.6 504 6 ItA .4 698 4 2105 .4 3870 .4 57 301 4 7460 .4 9100 8'395 540 ý5 12.1 .5 730 .5 2130 5 31390 .5 5 7015 7480 .5 9320 '30
4568 4 131 .6 720 .6 2145 .6 3910 6 57701 .6 7490 6 91 30.3 620 .3 143 .7 732 .7 2160 .7 3930 .7 5790 .7 7510 J7 9140!2 665 .2 15.5 8 743 8 2180 .8 39!0 .6 5810 8 7530 .8 9160'
.1 736 .316. .9 754 9 23925 .2. 3965 .9 5820 1 .9 7540 .9 91702'77 - so a, 763 18' 220 2I 3980 38' 5:40 148' 7560 W 91801.9 83 1T3- .1 776 .1 2225 '1 4000 .1 58601 .1 7580 .1 9200
a 9 00 .821,0 2 786 .2 2245 .2 4020 .2 5:880 2 7590 .2 92307 972 .7 22.7 .3 800 3 2260 .3 4040 5~ 590 .3 7610 3 9230
.5 1.14 .5 26.2 .5 823 .5 2290 .5 4080 5 5930j .5 7640 5 92504124 4 28.2 6 835 .0 2330 .6 4300 .6 5 950 .6 7660 .6 9270
3 135 3 302 .7 848 .7 2330 .7 4320 .7 5970 7 7680 .7 92802 t46 .2 3 2.4 'a 59 .8 2345 .6 4140 S 5990 8 7690 .8 93001
1 59 1 346 9 81. 230.9 4160 .9 'COO. .9 ?'FI0 .9 93101-11' 174 *I 37 To 1 I9? * 8219 27529 48 39- 020I~7T 9's 93201-.9 ISO t-.9 395 .1 695 .31 2390 , 1 4200 1 6040! .3 7750 .1 93 401
8 203 I 42.1 .2 907 2 2405 .2 4220 .2 6060! .2 7760 2 93507 225 I.7 44.7 .3 923 .3 2425 .3 4240 .3 6080 i .3 7780 .3 9360,.6 246 I6 47.6 4 935 4 2440 A 4260 4 60901 4 7800 4 9370~5 268 'S 50.6 .5 949 5 245S .5 4280 .5 63301 5 78320 5993 3234 3 57.2 .7 975 7 2475 76 4320 76 60 ,7 380 7 940004 3294 4 5382 .6 962 6 24705.6 4300 .6 6330 6 8530 6 941002 3ý55 .2 605 .8 989 8 2505 8 4340 8 6160 8 7870 8 943501
1 -1.L 1.0 1-,.J.42I1.9L 00 L....9. 2520.JL S 43501.ilk .9...II 610 -...9 DA 70019 944011
13
A is the altitude, 6 the declination, 0 the latitude, and ii the time of the day in hourangles. The Nautical Almanac, The Air Almanac, and the American Ephenmeris andNautical Almanac issued by the Nautical Almanac Office of the United States NavalObservatory, Washington, D. C., are yearly publications containing tile celestial coordi-nates of the sun and the moon and other useful astronomical data.
A very useful summary of solar-radiation observatioons for the major meteoro-logical observation stations in the United States has been published by Atlas and Charles.'8
The vertical, atmospheric transmittance for various horizontal, visible ranges and otherdata are presented.
2. Twilight Radiation. The radiation scattered by the atmosphere when the sunis just below the horizon is called twilight radiation. The twilight period separates theinterval between daytime and nighttime conditions of illumination. There are threeperiods into which the twilight interval is subdivided according to the general levels ofilluminance. These are called the civil, nautical, and astronomical twilight periods. Thecivil twilight period is defined as the time interval between the instant when the appar-ent altitude of the upper solar limb is at 00 (astronomical horizon) and when the centerof the solar disk is at -6*. Under the average, civil twilight conditions, there is enoughilluminance to perform normal daytime activities. The nautical twilight period prevailswhen the apparent solar altitude is between 00 (upper limb) and ~12" (center of solardisk). When the solar depression is between 90 and 120. the illuminance is reduced con-siderably arid, consequently, the horizontal, visible range is reduced to less than 400meters. The brighter planets and stars begin to be visible in the sky from sea level. Theastronomical twilight period extends during the interval when the apparent solar alti-tude is between 0' and -180. When the solar depression is between 12 and 18 degreesbelow the horizon, there is insignificant illuminance for visual purposes but just toomuch scattered solar radiant incidance for proper astronomical observations. The actu-al conditions of ground-level illuminanec during the twlight period will generally de-pend on the optical state of the atmosphere. According to another scheme, the twilightperiod is subdivided into three periods of civil, nautical, and astronomical twilight whenthe solar depression is between 0' - 60, 60 - 120, and 120 - 380, respectively. Theduration of twilight at any place depends upon the apparent angular velocity of the sunand, hence, on the geographical latitude of the location and the time of the year. Tablesof sunrise, sunset, and twilight are published in the literature.' 9
18R. A. Atlas and B. N. Charles, Summary of Solar Radiation Observations, The Boeing Company,Aerospace Division, Seattle, Wash., Document D2-90577-112 (1964), A) 889157.
"1gSupplement to the American Ephemeris for 1946, U. S. Government Printing Office, Washington,D.C.
14
D)uring the transition between day anrd night through tile twilight period, theilluminance at the earth's surface varies by a factor of almost a billion from about1.15 x I04 footcandles in the daytime to about 5 x t0-5 footeandles at night as shownin Fig. 4 for a "clear" atmosphere. Since the variation of iluminance at the earth's sur-face during the twilight period is very rapid, the absolute quantitative measurements arccomparatively much harder to make. The twilight spectra are hi'ghly variable in spectralcomposition and relative strengths of spectral lines with time as the shadow of tihe earthvaries with time thus changing both the excited and attenuating layers of the lower at-mosphere. However, twilight phenomena have attracted worldwide attention throughthe ages. A number of workers have recently published extensive literature on thestudies of twilight phenomena. 2°'25
The twilight spectra are dominated by emissions from ionized molecular nitro-gen (band heads at 3914 A and 4278 A), sodium D lines (at 5896 A and 5890 A), andatomic oxygen lines (at 5.577 A, 6300 A, and 6364 A) in the visible spectrum and thehelium emission (at 10830 A) and molecular oxygen 02 (bands at 1.27 and 1.58 microm-eters) emissions in the infared region. Since the 1.27-micrometer radiation is reabsorbedby the atmospheric oxygen in the lower atmosphere, this band is observed only in high-altitude twilight spectra. Figure 5 shows some low-resolution twilight spectra recordedby Rozenberg,2 6 and Fig. 6 shows a high-resolution twilight spectrum by Chamberlair. 27:
Theseý spectra are characteristically different from the daylight or nightglow spectra inthat certain features arc found in twilight spectra which are either absent or much differ-ent in the nightglow or solar spectra. Most of the twilight emissions are caused by theresonance scattering or fluorescence while the atmosphere is directly irradiated by thesolar radiation. (The processes of excitation whereby atmospheric atoms or moleculesabsorb solar radiation which is subsequently released or re-emitted as atmospheric radia-tion will be discussed later.)
2 0j. W. Chamberlain, Ihysics of the Aurora and Airglow, Academic Press, New York (1961).
21j. A. Ratcliffe, Physics of the Uppcr Atmosphere, Academic Pre•S, New York (1960).
22B. NI. McCormac and A. Omholt, editors, Atmospheric Emissions, Van Nostrand Reinhold
Company, New York (1969).2 3 B. M. McCormac, editor, The Radiating Atmosphere, Springer-Verlag New York, Inc., New York
(1971).
24(;. V. Rozenherg, Twilight, Plenum Presq, New York (1966).
2 5M. F. Ingham, "The Spectrum of the Airglow," Scientific American 226, 78 (1972).26(;. V. Rozenherg, Loc. cit.
27j. W. Chamberlain, Loc. cit.
15
LaiCa C
j" LOI44f 0
I--u E.a.J -n
c* a
p'.d-szM I 3viv
D ODt 9
10 LLO 9
IN DOES !
- 2(n .<
X
CD
CD
-,
~~~31 HIM*O •il.l•33NVIOVUt
I -", "a
3. Nighttime Radiation. When the sun is more than 18 degrees below the celes-tial horizon, the earth's surface and the lower atmosphere do not receive any directsolar radiation. Yet, even on a moonless night, there is a faint amount of diffuse radia-tion reaching the earth's surface. The nighttime radiation is composed of the followingcomponents:
(a) The integrated stellar radiation originating from the distant stars.
(b) The zodiacal radiation which is solar radiation scattered by theinterplanetary dust.
(c) The nightglow (or night airglow) originating in the upper terrestrialatmosphere due to the intei-action of the solar radiation on gaseousatoms and molecules. The excitation energy is later released as thenightglow radiation.
(d) The integrated nebular radiation from the distant gaseous nebulae.
(e) The auroral emissions which are often visible at high latitudes.
(f) The lunar radiation which is the solar radiation reflected by themoon.
All radiation originating either in the extra-terrestrial space or in the upperterrestrial atmosphere is scattered and attenuated by the lower atmosphere beforereaching sea level. Knowedge of the characteristics of nighttime radiation is importantto the atmospheric physicist or acronomer who is interested in the optical, physical,and chemical processes in the atmosphere. The spectra of the nighttime radiation pro-vide essential clues to the nature of these processes at different heights in the terrestrialatmosphere as well as in the extra-terrestrial space.
a. Nightglow. A number of authoritative and exhaustive treatises2 s's3 and
2 8j. W. Chamberlain, Physics of the Aurora and Airglow, Academic Press, New York (1961).
29J. A. Ratcliffe, Physics of the Upper Atmosphere, Academic Press, New York (1960).
N. M. McCormac and A. Omholt, editors. Atmospheric Emission,, Van Nostrand Reinhold
CAompany, New York (1969).
31 i. N.lMcCormae, editor, The Radiatling A.timosphere, Springer-Verlag Nw York In,., New
York (1971).32 (;. V. Rozq'n1wrg, Twilight, Plenum Pre-s, New York (1966).
., 18
excellent review articles 3 3 "4 have been published recently on various measurementsand theories of the excitation processes which may be responsible for various compo-nents of nighttime radiation. Tile problem of exactly how various nightglow emissionsare produced and exactly at what height in the atmosphere is still not completely re-solved. There are multiple excitation and de-excitation processes which are responsiblefor atmospheric emissions under different dynamic conditions of the terrestrial atmo-sphere. The complexity of the nightglow emissions is due to the variability of the con-centration and composition of atmospheric constituents (atoms, molecules, and ions)as well as the energy of the extra-terrestrial photons or other particles which interactwith atmospheric particles at various heights above sea level in the presence of a varia-ble electromagnetic field.
The major processes of excitation whereby energy may be absorbed byan atmospheric atom or molecule and later released as nightglow radiation are brieflydescribed here:
(1) Resonance scattering-the process in which an atom absorbs inci-dent, radiant energy and later emits radiation of the same wavelength.
(2) Fluorescence-the process in which an atom absorbs radiation ofone wavelength and emits radiation of a longer wavelength.
(3) Chemical association-the process by which atoms and moleculescombine and undergo chemical change resulting in the release of radiative energy.
331%. F. Ingham, "The Spectrum of the Airglow,"Scientific American 226, 78 (1972).
34 F. E. Roach, "The Light of the Night Sky: Astronomical, Intcrplanetary and Geophysical,"Space Science Reviews 3, 512 (196W).
"5F. E. Roach, "The Nightglow ," Advances in Electronics 18, 1(1963).
36 V. 1. Kraisovsky and N. N. Shefov,"'Airglow "Space Science Reviews 4, 176 (1965).
"37S. M. Silverman, "Night Airglow l'hcionieology," Space Science Reviews II, .341 (1970).
38J. F. N oxon, "Day Airglow," Space Science Reviews 8. 92 (1968).
391).,%. .lhnten, "Spectroscopic Studies of the Twilight Airglow," Space Science Reviews 6.493 (1967).
40)A. L. Hroadioot and K. R. Ki-ndall, "T'h Airglow Spwctrum, 3100-10,000 A," Jour. Geophy.
lies., Spare Phy.s. 73, 426 (19681).41V. i. Krassovosky, N. N. Shefov, and V. I. Yarin. "Atlas of the Airgiow Spectnrm 3000-12,1O A,-
Planetnar Space Srt 9, 883 (11962).
19
(4) Ionic reaction-the process in which ionized gaseous molecules re-combine with available electrons resulting in dissociative recombinations with con-sequent release of radiation.
(5) Photo-dissociation (or radiative dissociation)- the process in whicha molecule may absorb radiation resulting in one or more atoms in an excited statewith subsequent de-activation and re-emission of radiation.
(6) Particle collision-the process in which an energetic particle collideswith atmospheric atoms or molecules resulting itt a change of internal energy ofthe participants and subsequent release of radiation.
(7) Transfer of excitation-the process in which excitation energy maybe transferred to another atom or molecule leaving the latter in an excited statewith subsequent emission of radiation.
Figure 7 shows a high-resolution airglow spectrum from 310 nm to1000 nm, recorded by lroadfoot and Kendall at the Kitt Peak Observatory, Arizona, atan altitude of 2080 meters.42 The prominent features of this spectrum are the oxygen 301 5577 A, 01 6300-6364 A, Sodium Na 1 5893 A (unresolved doublet 5890-5896 A),and the hydroxyl OH emissions spread almost all over the entire spectrum but quitedominant beyond the visual cutoff at about 7200 A. The other important features arethe atmospheric oxygen molecular bands (Herzberg) from about 3140 A to 4840 A andthe contamination due to mercury lines Hg 4358 A and 5461 A from artificial lights onthe ground-a common problem in the United States even in "remote" locations. Thereis an absorption band system, starting at 7619 A, due to the atmospheric oxygen 02.Figure 8 shows some low-resolution, total night-sky radiant sterance (radiance) spectradue to the entire hemispheric radiation recorded by Vatsia, Stich, and Dunlap at groundlevel for various lunar phases. 4 3 These spectra cover the spectral range from 450 nm to1950 nm. Curve 1 corresponds to the total, moonless-night-sky radiation consisting ofthe nightglow (airglow), the zodiacal radiation, the integrated stellar radiation, and thenebular radiation. Curves 2, 3, and 4 are duc to the radiation represented in curve Iplus contributions from the solar radiation as reflected by the moon for various phases.In addition to the prominent emission features of 01 5577. 6300-64 A, Na 1 5893, andOil emissions between 7200-19500 A, there are characteristic absorption bands due tothe constituents of the lower atmosphere, chiefly atmospheric molectular oxygen, water
42A. L, Broadfoot and K. R. Kendall, "The Airglow Spectrum, 3100-10,000 A,,"Jour. Geophy.Res.. Space Ph ys. 73, 426 (1968).
43M. L. Vatsia, U. K. Stich, and D. i)unlap, "Night Sky Radiant Sterance from 450 nm to 2000 nm,""1. Opt. Soc. Am. 59, 483 (1969): also Technical Report ECOM-7022, Night Vision Laboratory,Vinionics Technical Xrea, Fort tlelvoir, Virginia (1972).
20
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21
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vapor, and carbon dioxide at about 0.72, 0.76, 0.78, 0.84, 0.94, 1.13, 1.38, and 1.85micrometers (compare Fig. 3). The individual, sharp features of the atmospheric air-glow emissions are quite prominent until the solar-radiation contribution from the larg-er illuminated lunar fraction becomes overwhelming. The lunar contribution to the in-tegral, nighttime radiation decreases rapidly beyond the visible-radiation, cutoff wave-length and becomes almost insignificant beyond 1.35 um for all phases of the moon. Inthe visible spectral range, however, the lunar-radiation increases the ground-level radiantincidance by a factor of up to 700 for the full moon.
The excitation processes for the prominent atmospheric emissions con-stituting the nightglow are discussed here. Further details may be found in the litera-ture.44 5' Figure 9 shows an atomic oxygen 01 energy-level diagram indicating variousquantum mechanical energy states and the observed emission lines. The green 01 5577 Aemission line represents a transition from the ISO state to the 'D2 state, and the red lines01 6300 A and 01 6364 A result from the transitions between the 'D2 state and the 3P2
44J. W. Chambedain, Physics ofthe Auror and Airglow, Academic Press, New York (1961).
45j. A. Ratcliffe, Physics of the Upper Atmosphere, Academic Press, New York (1960).46B. M. Mccormac and A. Omholt, editors, Atmospheric Emissions, Van Nostrand Reinhold Com-
pany, New York (1969).4 7 B. M. McCormsc, editor, The Radiating Atmosphere, Springer-Vedag New York Inc., New York
(1971).
48G. V. Rosenberg, Twilight, Plenum Press, New York (1966).
49M. F. Ingham, "The Spectrum of the Airglow, "Scientific American 226, 78 (1972).50 F. E. Roach, "The Light of the Night Sky: Astronomical, Interplanetary and Geophysical,"
Space Science Reviews 3, 512 (1964).5 1 F. E. Roach, "The Nightglow," Advances in Electronics 18, 1 (1963).5 2 V. I. Krasaovsky and N. N. Shefov, "Airglow,"Space Science Reviews 4, 176 (1965).
53S. M. Silverman, "Night Airgow Phenomenology,"Space Science Reviews II, 341 (1970).54J. F. Noxon, "Day Airglow," Space Science Reviews 8, 92 (1968).5 5D. M. Hunten, "Spectroscopic Studies of the Twilight Airgiow," Space Science Reviews 6, 493
(1967).5 6 A. L. Broadfoot and K. R. Kendall, "The Airglow Spectrum, 3100-10,000 .t,"Jour. Geophy.
Res., Space Phys. 73, 426 (1960).57 V. I. Krausovosky, N. N. Shefov, and V. I. Yarin, "Atlas of the Airgiow Spectrum 3000.12400 A,"
Planetary Space S.i 9, 883 (1962).
23
eV3S'0°
12.73 3 3s D12.54 3 D
3d u10.99 , ,1 3 m.... . i_ d D3p3p10.74 5
1S446 A 7774 A I 3p P9.52 3sJI
35 0S9.14 3s5 So
SI II' L I a
So I I "-- -- 10.74 sec
I
,:I I I I,-1.9 2se ~i10 sec 2p4D2
I 2 se - I'
0 1 • ,, !2p 3 P2,1 ,0q 30 sec- 1 (i=J~l
-- • 1300 sec-I (J=2)
"Fig. 9. Atomic oxygen (O1) energy levels.
24
.........................
and 3 P, states, respectively. Some of the proposed' excitation mechanisms for 01 emis-
sions follow:
30 0 + 0 (IS) + 0.95 eV (10)
0+ +e O+ O('D)+ 4.99 eV (II)
*20 (ID) + 3.03 eV (12)
*O + 0 (IS)+ 2.78 eV (13)
0* (ID) + 0 (IS) + 0.82 eV (14)
NO+ + e- - N + 0 (ID) + 0.80 eV. (15)
The excitation process represented by equation (10) is the Chapmanproces, a chemical association process, while those represented by equations (11)through (15) are ionic dissociative recombinations. The Chapman process is consideredto be the predominant process for the 5577 A emission at about 100-km altitude whilethe 01 6300/6364 A doublet is emitted in the F layer at about 300-km altitude as aconsequence of the ionic recombination processes.
The Meinel vibration rotation bands of hydroxyl radical OH are thoughtto be due to the chemical recombination process suggested by Bates and Nicolet:
03 + H * OH* + 02 (+3.34 eV). (16)
Krassovsky and Shefov suggest the alternate process for Of emissions:
02 + H -$-OH-* + 0. (17)
The sodium Na D lines at night arc believed to be a result of the processes:
NaO + 0-* Na( 2 P) 4.0 2 (18)and
Na 11 + 0 - Nao2 P) + Off. (19)
Krassovsky and Shefov have proposed the excitation process for the emismion of thegreen continuum due to the reaction:
NO + •0 NO2 4hli. (20)
25
I f
Table VI contains the main nightglow emissions, the emitter level energystate, the altitude of occurrence, the photon exitance in rayleighs* and equivalent pho-ton sterance in Wattg/cm2 -sr, and the excitation process for each.
4
The rayleigh is a unit of airglow emission rate named after the fourth Lord Rayleigh (R. J. Strutt).One rayleigh corresponds to the emission rate of 106 photons per second per cm2 (column) from avolume source of radiation (see Chamberlain, Physics of the Aurora and Airglow, Appendix !!, Aca-demic Press, New York, 1961). The photon-integrated emission E measured in rayleighs is defined:
ER I R = 106 photons s'1 cm"2 (column). (21)
The photon sterance (earlier called radiance or intensity) Lp of the volume source of radiation emit.tingat the rate of one rayleigh will be:
Lp = (106/4ff) photons s" cm"2 ,.. (22)
For monochromatic radiation of wavelength X, the photon sterance in the equivalent energy unitswill be:
Lp(X)) (1061411') (he/W.) 8" cem"2 grel (23)
It 6.6256 x 10"34 W 12 (Planck constant),
c 2.9979 x 10's A s" (Speed of light).
The substitution of the values of the Planck constant h and the speed of light c in equation (23) gives
Lp(N) = (1.5806 x 10"0) / (A)W cm"2 sr t (24)
where X(A) is wavelength expressed in angstroms.
For a volume source with emission rate of R/A (rayleighs per angstrom), the corresponding photonsterance (radiance) will be given by
LX = (R/A) (1.5806 x 10" 0)/X(A) W cm"2 sr"t A'. (25)
In general, the photon emission in rayleighs can be expressed in the equivalent energy units using therelation:
I R - O6 (hc/ X) s' cm"2 , (26)
or I Rh-. 1.9863 x 10' /(A) W Cm"2 (27)
where )X(A) is the wavelength in angitroms.
26
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CDC .C'84- ICL
*C CDI~
aa
o" Zz 8c
Laa
FEEN
r N- -~ nc-L C- z
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is Ii c
27
b. Moonlight. The luminou, incidance (illuminance) cm the earth due tothe solar radiation reflected by the moon goes through variations determined by thealtitude and phasu of the moon. The relative, integral, luminous sterance (luminance),,f the r,,on as a function of lunar phase angle has been experimentally measured byRussel55 and Rougier.s 9 Tables Vila and VIlb and Fig. 10 show the relative, luminous3terance of the moon as a function of the phase angle. The phase angle is the angle sub.tended by the sun and the earth as observed frorn the moon. The phase angle is nega-tive for the waxing moon and positive for the waning moon. The phase. angle v can becomputed from the Nautical Almanac from the longitudes of the stun and the moon.The phase angle is 1800 minus the absolute difference between the longif ides of thesun and the moon at a particular time. The fraction of the moon illuminated and seenfrom the earth is also listed in the Nautical Almanac. The fraction of area of the lunardisk that is illuminated is equal to the illuminated fraction of the diameter perpendicu-lar to the line of cusps. The fraction of the moon illuminated as a function of the phaseangle 4p is given by the relation:
F = (I + cc-- ý)/2. (28)
The luminous incidance (illuminance) of the moon has been reported by Brown.'0 Thefull moon at the zenith produces a luminous incidance (illuminance) of abuut 3.4 x 10"2footcandles on a horizontal plane at sea level under clear atmospheric conditions. Fora zenith angle z and a lunar phase angle p, the horizontal, sea level, lunar luminous inci-dance (illuminance) will be given by the relation:
E = L() go (TIm , (29)
where E is luminous incidance on a sea level horizontal plane, L(p) is the lunar lumin-ance phase function (from Fig. 10), Eo is the sea level horizontal luminous incidancewhen the full moon is at the zenith, T, is the vertical atmospheric transmittance for aunit optical mass (Tt = 0.796), and in is the atmospheric optical air mass. The air massm equals secant z where z is the lunar zenith angle. This is a good approximation untilz approaches over 80 degrees. Accurately computed values of the optical air mass forvarious values or the altitude angle are given in Table II.
5811. N. Russel,Astrophysicul Jour. 43, 103 (1916).
59(;. Rougser, Ann. Obs. Strasbourg 2. 205 (1933).
6h). R. E. Brown, Natural Illumination Charts, Report No. 374-1. Department of the Navy, ltunrau
of Ship, WLsbington, D. C. (1952).
28
- -,, *=
Table Vlla. The Relative Radiant Sterance of the Moon as aFunction of Phase Angle Based Upon Russel's Measurements
BEFORE FULL MOON AFTER FULL MOONPHASE-ANGLE STERANCE MAGNITUDE STERANCE MAGNITUDE
00 100 0.00 100 0-1010 81.7 0.22 81.7 0.22
20 66.7 0.44 64.3 0.4830 54.0 0.67 50.6 0.74
40 43.6 0.90 38.7 1.03
50 35.3 1.13 29.9 1.31
60 28.3 1.37 23.3 1.58
70 21.9 1.65 18.0 1.8680 16.1 1.98 13.6 2.17
90 11.5 2.35 10.0 2.50
100 7.73 2.78 7.18 2.88
110 5.15 3.22 4.92 3.27120 3.10 3.77 3.19 3.74
130 1.75 4.39 1.90 4.30140 0.88 5.14 1.02 4.98
150 0.37 6.09 0.44 5.89
II
Table Vllb. The Relative Radiant Sterance of the Moon as aFunction of Phase Angle Based Upon Rougier'8 Measurements
BEFORE FULL MOON AFTER FULL MOONPHASE-ANGLE
STERANCE MAGNITUDE STERANCE MAGNITUDE
0 100 0.00 100 0.00
10 78.7 0.26 75.9 0.30
20 60.3 0.55 58.6 0.58
30 46.6 5.83 45.3 0.86
40 35.6 1.12 35.0 1.14
50 27.5 1.40 27.3 1.41
60 21.1 1.69 21.1 1.69
70 16.1 1.98 15.6 2.02
80 12.0 2.30 11.1 2.39
90 8.24 2.71 7.80 2.77
100 5.60 3.15 5.81 3.09
110 3.77 3.56 4.0, 3.48
120 2.49 4.01 2.61 3.96
130 1.51 4.55 1.58 4.50
140 0.93 5.08
150 0.46 5.84
30)
- 0
rw-40 go c
MIU Sf-In SYn
31
The geocentric coordinates of the moon can be calculated for any geo-graphical location for any time with the following relations:
cos z = siln A = sin 6 sin 0 + Cos 6 cos 0 cos h (2)
sin Z = (cos 8 sill h)/sin z (30)
where z, A, Z, 6, and h are V :,enith distance, altitude, azimuth, declination, and hourangle of the moon, respectively, and 0 is the geographical latitude of the location. Tocompute the apparent altitude of the moon from the surface of the earth, one has toapply a parallax correction. The parallax is the difference of altitude or zenith distanceof a celestial body as seen from the surface and the center of the earth respectively.The parallax angle equals the angle subtended by the earth's radius at the center of tiecelestial body. The apparent altitude A' is given by:61
A' = A -p (31)
sin p = sin y cos A (31a)
where p is the parallax angle and i is the equatorial horizontal parallax (II.P.) of themoon (tabulated at hourly intervals in the Nautical Almanac). There is no parallax inazimuth, of course.
The spectral radiant incidance (irradiance) due to the radiation from themoon as well as the low-level radiation from nightglow, and zodiacal and integrated stel-lar radiation varies considerably as the proportion of moonlight is added to the low-level,nighttime radiation. Figure II shows nighttime radiation spectra for various altitudes ofthe moon during the same night recorded by Vatsia, Stich, and Dunlap at Lake Montau-ban, Canada.' 2 The relative heights of the airglow spectral emissions over the generallevel of the continuum vary as the contribution due to the lunar radiation increases.The spectral line profiles arc determined by the resolution of the spectroradiometer.
61William Chauvenet, Ai Manual of Spherical and Practical Astronomy. Volume I, p. 103, 5th edition,
D[over Publications. Inc.. New York (1960).62 1. l.. Vataim, U. K. Stich, and 1). Dunlap, "Night Sky Radiant Sterance from 450 nm to 2000 nm,"
1. Opt. Soc. Am. 59, 483 (1969): also Technical Report EC()M.7022, Night Vision Laboratory,V'isionics Technical Area, Fort llelvoir, Virginia (1972).
32
10-9 DATE TIME MOON MOON CLOUD TEMP. R.H.% HORIZ.EI.D.T.) ALT. FRAC COVER (0 CJ ILLUM.
I ILLUM. ILix)* T OCT. 13, 68 2000 -11.80 - 0.06 5.0 S0 1.916xlO-34 OCT. 13. 68 2035 -930 - 0.06 5.0 80 2.lOxlO-3
SOCT. 13, S1 2300 5.80 0.65 0.00 2.0 93 3.124x10-3E 2 OCT. 14, 68 0030 19.00 0.56 0.25 1.0 95 7.556x10-3
210-10. OCT. 14, 68 0330 48.40 0.56 0.87 -0.5 96 1.334x10-2
.6.
"Z 44C-4I
E 21
C.) i-124- A4j
m 2,
10-13 I !,
300 400 511 6110 B( 900U 1000 1 200 1* 140 15 16 1700 1600 1900 200
WAVELENGTH Inm)
Fig. 11. Night sky radiant sterance spectra for various altitudes of the moon as mea-sured by Vatsia, Stich and Dunlap.
33
1
II. ATNIOSPIIERIC TRANSMISSION
4. The Terrestrial Atmosphere. There arv a large number of publications whichcoiitain extensive treatises on various features of the terrestrial atmosphere. 63 I OIdythose properties of the atmosphere which influence the propagation of electromagneticradiation in the wavelength range from 0.2 micrometer to 15.0 micrometers will be re-viewed here. The composition of the permanent atmospheric constituents varies withheight above sea level as shown in Figs. 12 and 13. For all practical purposes, the pro.portions of the four permanent gases- nitrogen, oxygen, argon, and carbon dioxide(which constitute 99.997% of the dry atmosphere up to 90 kilometers)-are generallyconsidered to be constant up to a height of 90 kilometers. However, the concentrationof carbon dioxide does vary slightly and the water vapor content of the atmosphere canvary up to 4%, but it is generally between 0.1 and 1.0%. Table Vill lists the major,permanent constituents of the atmosphere. The principal, man-made atmospheric pol.
lutants which can have a significant influence on the atmospheric transmission are theoxygen compounds (CO, CO, 03), nitrogen compounds (NO, NO2 , N II3), halogens,hydrocarbons, aldehydes, and aerosols. The concentration of the mati-made pollutants
is highly variable. Ozone (03) is an important constituent of the atmosphere, but it isdistributed nonuniformly beteen 10 and 40 kilometers above the earth's surface witha sharp peak between 20 and 30 kilometers.
A temperature-altitude profile in the atmosphere is caused by the physicalinteractions between the solar radiation and the atmospheric constituents and the earth'ssurface. The temperature-altitude profile is a variable with latitude and season. Meanannual temperature-altitude profiles based upon large measurements averaged over
6 3K. Ys. Kondrstyev, Radiation in the Atmosphere, Academic Press, New York (1969).
"64 S. L. Valley, Hlandbook of Geophysics and Space Environments, NlcGraw-Ilill, New York (1965).
(5R. NI. Goody, Atmospheric Radiation, Oxford University Press, London (1964).
66U. S. Standard Atmosphere, 1962, and U. S. Standard Atmosphere Supplements, 1966, U. S. Gov-ernment Printing Office, Washington, D. C. 20402.
67 H. Riehl, Introduction to the Atmosphere, MeG raw-Hill Book Company, New York (1965).
MS. K. Mitra, The Upper Atmosphere, The Asiatic Society, Calcutta (1952).
6911. S. W. Massey and R. L. F. Boyd, The Upper Atmosphere, Philosophical Library, New York (1958).
70 R. W. Fairbridge, The Encyclopedia of Atmospherie Sciences and Astrogeology, Reinhold Publishing
Corporation, New York (1967).7 1 &landbook of Geophysics, Revised Edition, The MacMillan Company. Aew York (1961).
34
CD
do
C4 E
ca-
Pl.
CD w
35 .
¶ C14* J
E4FM-
CDLui
z 3E
NN .4
dipL
C CCCCd. MGM C 0, PLI, C ii,
U, C4~'~C~g N N~
IC.16
Table V III. Composition of the Atmosphere (Dry)Up to About 90 km
PER CENT PER CENT REDUCED THICKNESSCONSTITUENTBY VOLUME BY WEIGHT (atm-cm, STP)
NITROGEN IN2) 78.086 75.b27 6.2434 x 105
OXYGEN (02) 20.949 23,143 1.5750 x 105
ARGON IA) 0.93 1.282 7.436 x 103
CARBON DIOXIDE IC02) 0.03 4.56 x 10-2 2.40 x 102
NEON (Ne) 1.8 x 10"3 1.25 x 10-3 1.44 x 101
HELIUM (He) 5.24 x 10-4 7.24 x 10. 4.19
METHANE 0CH 4) 1.4 x 104 7.25 X 10 1.12
KRYPTON jKr] 1.14 x 10-4 3.30 x 10-4 9.11 x 10-1
NITROUS OXIDE (N20) 5 x 10-5 7.6 x 10-5 4.0 x 10-1
XENON (Xe) 8.6 x 10-6 3.90 x 10-5 6.9 x 10-2
HYDROGEN (H2) 5 x 10-5 3.48 x 10-6 4.0 x 10-1
WATER VAPOR 0.1-1 1AVERAGE) 0.1_-_1__03_-_104
ONE atm-cm, STP, IS AN AMOUNT OF GAS EQUIVALENT TO A COLUMN 1 cm
II HEIGHT AT 760 mm PRESSURE AND 0° C.
37
I .... i-
periods of several decades have been adopted for various latitudes and reported in theliterature.72 Figure 14 shows the temperature altitude profile up to 100 kilometersfor the U. S. Standard Model Atmosphere, 1962.
The terrestrial atmosphere is subdivided into five shells-troposphere, strato-sphere, mesosphere, thermosphere, and ionosphere. The lowest shell of the atmospherein which temperature decreases with altitude at an approximate rate of 6.5* C/kin or
3.6* F/kft is called the tropophere (named from the Greek word "tropos" meaningturn). This is the mixing layer of the atmosphere. The atmosphere is mainly heated byconvective heat transfer fron the ground. At the tropopause, there is no further de-crease in the temperature with increasing altitude. The altitude of the tropopause variesfrom 6 to 18 kilometers. High wind speeds and the highest cirrus clouds dominate atthe tropopause. The second shell is called the stratosphere because there is stratification,or layering, without rapid mixing. There is an increase in temperature with increase inaltitude until there is no further increase at the stratopause. The absorption of the solarultraviolet radiation by ozone produces higher temperatures in the upper strata of thestratosphere. The third shell is called the mesosphere (the middle sphere) where thetemperature decreases with increasing altitude. The lapse rate is approximately half ofthe troposphere, namely 30 C/km. The mesopause has the minimumn temperature in theterrestrial atmosphere which is about -90w C. The fourth atmospheric shell, called thethermosphere, is characterized by an increase in temperature with an increase in altitude.The outermost shell called the ionosphere contains a sufficiently large density of elec-trons and ionized atomic oxygen and nitrogen. The ionosphere plays a major role in thepropagation of radio waves and in the production of airglow and auroral emissions. Theoutermost region of the ionosphere wherein molecular escape from the earth is signifi-cant is called time exosphere. The height of the exosphere is thought to be about 1000kilometers.
For the purpose of transmission of electromagnetic radiation through the at-mosphere, it is a fortunate coincidence of nature that a major part of the ultravioletradiation is absorbed by ozone in the stratosphere and that the major constituents ofthe atmosphere, the molecules of nitrogen and oxygen, are transparent to the visibleand most of the near infrared radiation. Near the earth's surface, the principal absorbersfor the infrared radiation arc water vapor (1120) and carbon dioxide (C0 2). Water vaporis highly variable in concentration in the atmosphere because the humidity of air fluctu-ates widely with geographical location, season, and time. Mlost of the water vapor is con-fined to the troposphere.
72U. S. Standard Atmosphore, 1962, and U. S. Standard Atmosphere Supplements, 1906, U. S. Gov-
ernment Printing Office, Washington, D. C. 20402.
38
I I .0010.001 90 THEROSPHERE 300
7O .0i0.01 - -OPAUSE1~
250-
.10
0 r.4 MESOSPHERE 2
.60- . .. .
E
.5,om* ~1.0 STRATOPAUSE -
91. NLU
cal10%10 0I STRATOSPHERE
100. 50-10 I
.10 - TROPOPAUSE
TROPOSPHERE180 __ _ _ _ _ _ _ _ _ _ _ _ _ _
1000 (-10 0"C 200 220 240 260 (06C1280
TEMPERATURE (IkJFig. 14. Temperature-altitude profile to 100 km for U. S. 8tandard atmosphere, 1962(Valley).
39Yp
5. Atmospheric Attenuation and Emission. The interactions between electro-magnetic radiation and matter may be classified either as attenuation (extinction) oremission of radiation by matter. If there is a net increase in the radiant flux along thedirection of propagation, we have emission; if there is a decrease in the radiant flux,we have attenuation. Attenuation of electromagnetic radiation by matter is caused byatsorption or scattering or both. Scattering is due to diffraction, reflection, refraction,or a combination of these effects. For a general and more extensive treatment, thereader should consult extensive literature on this subject." 74 75
The fundamental law of attenuation is known as the Lambert, Beer, orBouger law. It states that for monochromatic radiation the attenuation process islinearly proportional to the intensity of radiation and the amount of attenuating mat-ter provided that the physical state (i.e. pressure, temperature, composition) of thematter remains constant. There are some cases in which Lambert's law does not apply;the photon density required for nonlinear effects is extremely high, such as in high-power lasers. If the inter-molecular distances and forces are fixed, then Lambert's lawapplies.
If the spectral intensity IX of a monochromatic parallel beam of radiation ischanged by an amount dIlX due to attenuation by matter after traversing a length dx ofthe optical medium along the direction of propagation, then
dIX IX dx. (32)
Similarly, for the emission process, the change in intensity of the emitted radiationcorresponding to a source function J, is given by
dIX=+c JX dx. (33)
The constant of proportionality a-X is called the attenuation (extinction) coefficient(per unit length). If the attenuation coefficie-it ds' is expressed per unit mass, equation(32) will be written as
dWX ý - •P (x) !x dx, (34)
73 K. Ya. Kondratycv, Radiation in the Atmosphere, Academic Pres, New York (1969).7 4 R. M. Goody, Atmospheric Radiation, Oxford Univenrity Prew, Lcndon (1964).7 5 D. Anding, Band-Model Methods for Computing A tmospheric Moledular Absorption, Report No.
7142-21-T, Willow Run Laboratories, The Univtermity of Michigan, Ann Arbor, Michigan (1967).
40
I iS
where p(x) is the density of the medium at the point of consideration. From equation(32), we note that the product (a dx) is dimensionless. This is known as thc (differen.tial) optical path or optical thickness,
dr), = a x dx. (35)
For a general interaction between radiation and matter involving both attenuation andemission, from equations (32), (33), and (35), one obtains the change in intensity,
-dIx I, dr, - J), drX,, (86)
and thus
-(dlX/dr)= I, -J). (37)
Equation (37) is the general equation of transfer; the left.hand side being a differentialalong the direction of propagation. This equation is used to solve radiative, heat-transferproblems.
If we integrate equations (82) and (34) for a homogeneous, non-radiatingmedium from x o to x .- X, the transmitted intensity IX, is given byk [/X
IxI 0 oxexp - dx (38)
or
IX loxexp JLf iJit p~UAd (39)
where Iox is the incident intensity at x = o.The transmittance T and absorptance A of the medium are defined by the
relations:
TX =IX/Io,, (40)
A I - Tx. (41)
In the real atmosphere, the attenuation coefficient may vary from point topoint along an arbitrary slant optical path. However, in a stable atmosphere tinder
41
specified representative conditions, one can define average atmospheric parameters anid,hence, the average attenuation coefficient at varioiiE layers above the point of observa-tion. Variou~satmospheric models have beeni proposed with increasing accuracy as bet-ter observational data are obtained .7 6
71 '' The total atmospheric transmittance T),for j layers of a particular model atmosphere cani be computed from equations (38) and(39):
Tx exP -Z Oe~ Ax~i (42)
For a homogeneous optitAl path of length R having an ettenuation coefficient formonochromatic radiation of wavelength X, the atmospherie :.;ansmittance is given by
T.X= exp[-t) R. (429.)
In general, the attenuation coefficient &Axis tlie sum of aii absorption coefficient k), and
a scattering coefficient a),
k?,= + aX(43)
T'he terrestrial atmosphere is composed of gasenus rnolecul..s and aerosols.The total atmospheric attenuation coefficient a), is the sum of absorption and scatter-ing coefficients for molecules and aerosols-, thus
aX = kn,+ nX+kX+ aW(4
where the subscripts m and a indicate molecule and aerosol respectively. Each of thesecoefficients is w tivele.-gth dependent.
The optical transmittance per unit distance of a medium T ii sometimes Ocx-pressed in terms of the optical density or opacity of the medium using the relations:
7 6 U. S. Standard .4tn.uaphere, 1962, and U. S. Standard A trnosphere Supplements, ! 960, 1. 8 Gov-ernment Printing Offire, Washington, 1). C. 20402.
~L Elterman. Vertical A't ten ua tion Model with Eight Surface Meteorological iRanges 2 to 13 Kilom-exers, AFCHL.70-0200), Environ. Res. Paimir No. 318, 11. S9. Aii Force Canmbridge item~hrch LAborm-tories, liedfofd, Mlamachuse~tts (1970).
78R. A. NVcqatchty, R. A'. Fenn, J. E. A. Selby. F. W. Volt, and J. S. Garing, Opticaf lPropernies ofthe Atmosphero (Revised), AFC[IL-71-0279, Environ. Iles. Paper No. 354, Air F~orce CambridgeResearch Laboratories, Bied ford, Nlassacliuset ts (197 1).
42
Density, D = log, 0 (T)" , (45)
Opacity, 0 -'j' , (46)
or D = log, 0 0, (47)
0 = 10I) (48)
thus T = 10^. (49)
The attenuation coefficient t may he written in terms of the optical density D. Re-membering that the atmospheric trawismittance for a unit optical path length fromeuation (42a) is given by
T -= (50)
an~d a comparison of equations (49) and (50) gives
a 1) : 10 D, (52)
or a =2.30258•51 x 1). (53)
The attenuatiUn coefficient a ean also •i, expressed in terms of decibels (db)
using the relation: ;
1IOlog,0 1 1()/I (1 .b (54) Ior 10 ogwo 0 = 10 . (52)
Thtrefore. 10 I) = d. (56)
thus I) = 0l. db. (57)
('omparismi (if equlations (13) aind (,';'+) gives
C(.2.105115 (1l.
43
or attenuation loss in
dh/kin 4.3367936ot(km-1). (58a)
A comparison of equations (49) and (57) gives the relationt between transmittance Tand the signal loss in db per unit distance:
T = 10-O'Idb (59)
6. Outdoor, Horizontal, Long-Path Atmospheric Transmittance. Dut to the un-steadiness of the real atmospheric optical environment, it is rather difficult to make suc-cessful and reliable measurements o" atmospheric spectral transmittance. In a relativelyclear and stable atmospheric optical environment, the atmospheric turbulence may intro-
duce small-scale variations in atmospheric transmittance. However, over long, outdoor,horizontal, optical paths involving haze, fog, and large concentration- of smoke and dustaerosols, large-scale fluctuations in atmospheric transmittance are added due to spaceand time variations in the optical thickness of the medium caused by rapid movementsof haze, fog, or dust banks in the optical path. In order to make reliable atmosphericoptical measurements, the following parameters should be measured at as many locationsas practical along the optical path:
(a) Atmospheric spectral transmittance.
(b) Geometry of the optical path with respect to the surface terrain and themrroundings.
(c) Ambient air temperature at a number of altitudes below, at, and above
the optical path.
(d) Atmospheric pressure at a number of relevant locations.
(e) Relative humidity at a number of altitudes.
'f) Number and size distributions of atmospheric aerosols at a number of
relevant points.
(g) Concentration of any abnormal atmospheric constituents in the opticalpath such as smoke, dust, exhaust fumes, and chemical effluent,.
(h) Measurement of refracii~e indices of all types of aerosols encounteredin the optical path.
44
(i) Chemical analysis of any abnormal gases in the optical path.
Due to the enormity of this task, it 6s no wonder that just a few teams ofworkers have been successful in making atmospheric transmittance measurementsthroughout the world. There is still an acute shortage'of measurement data on the spec.tral transmission through heavy haze, fog, dust, and smoke environment. A set of spec-
troradiometers with large input apertures and optimized cooled sensitive detectors tomeasure the entire spectrum simultaneously (such as Fourier sptctroradiometers) wouldbe an ideal instrument .ystem for atmospheric transmittance measurements.
A summary of the major, outdoor, horizontal, long-path atmospheric spectraltransmittance measurements is presented in Table IX. Gebbie et al. made their measure-ments about 30 meters above the sea surface on the east coast of Scotland over opticalpath lengths of 2 and 4 kilometers.7' Rock salt and lithium fluoride prisms were usedin the spectrograph. The detector was a vacuum thermocouple. Most of their measure-ments were made under clear and stable atmospheric environments.
From 1952 to 1955, the French lnsttute of Optics grr up lead by Arnulfmade atmospheric transmission measurements near the sea at SL. Inglevert and near theParis airport through haze and fog. Unfortunately, their haze spectra still remain unpub-lished in 1972, but they did publish their fog-transmission spectra.80 They used rangesof 50, 100, 200,600, and 1200 meters to measure transmission of quite-dense opticalpaths involving haze and various types of fogs. They measured fog droplet size and num-ber spectra and calculated spectral transmittance using Mic theory calculations. Theaerosol spectra measurements and spectral transmittance measurements both had a num-ber of stated errors mainly due to the method of collection of aerosols and inhomogen-city of fog layers.
The spectral transmission measurements by the Naval Research Laboratorygroup of Taylor and Yates were made at three sea level ranges of 0.3, 5.5, and 16.25
* kilometers under good visibility and stable atmospheric environmental conditions.8"Yates and Taylor also madc atmospheric transmission measurements at an altitude ofabout 3 kilometers above sea level through a horizontal optical path length of 27.7 km
7911. A. Gebbir, W. R. Ilarding, C. Iiilsum, A. Pryce, and V. Ruh4.rts, "Atmospheric Transmission inthe I to 14 Micron Region,"Proc. Roy. Soc. A 206, 87 (1951).
80A. Arnuilf, J. Bricard, E. Cure, and C. Veret, "Transmission by Haze and Fog in the Spectral Region0.35 to 10 Microns,"J. Opt. Soc. .4mer. 47, 491 (1957).
8 1j. 1l. Taylor and Il. W. Yates, "Atmospheric Transmissionin the Infrared," J. Opt. Soc. Amer. 47,223 (1957).
45
Table IX. Major Hlorizontal Long-Path Atmospheric Transmittance Measurements
WAVELENGTH OPTICAL PATH OPTICAL REFERENCEENVIRONMENT
1 TO 14 pm 2.07, 4.09 km CLEAR, STABLE1I1511
• HAZE, FOG, ARNULF at al. (b)0.35 TO 10 pm 50 TO 1200 m "VARIABLE (11571
TAYLOR i YATES (')0 10.3, 5.5,16.25 km CLEARLIGHT HAZE 1157)
!.0.5 TO 15 pm (d)T _27.7 km *, ., ,, YATES I TAYLORE 1
STREET[()
0.56 TO 10.7 pm 25 km CLEAR, LIGHT HAZE 1165)
FILI'POV al l,.0.59 TO 12 pm 1.3, 2.6 km HAZE
0.63 pm LASER3.5 pm LASER 2.6 km HAZE, RAIN, SNOW CHU t HOGS
10.6 pm LASER 11131
(a) It. A. Gebbie, W. R. Harding, C. Hilsim. A. Price. and V. Roberts, "Atmospheric Tranmismion in the I to 14Micron Region," Proc. Roy. Society A2C6, 87 (1951)."(b) A. Arnuif, J. Bricard, E. Cure, and C. Veret, "Tranmisisaon by Haze and Fog in the Spectral Region 0.35 to
10 Microns."J. Opt. Soc. Amt. 47, 491 (1957).(e) J. H. Taylor and H. W. Yates, "Atmospheric Transmison in the Infrared,"J. Opt. Soc. Amer. 47, 223(1957).(d) H. W. Yatesand J. H. Taylor, Infrored Transmission .1iae Atmosphere, NRL Report W453. U. S. Naval Re.
search Laboratory, Washington. D. C. (1960).(e) J. L. Streete, "Infrared Measurements of Atmospheric Tranmission at Sea Level." ). OpL Soc. Amer. 7, 1S45
(1958).
(f) V. L. Filippoy, L. M. Artem'yeva and S. 0. Minumyants. "Spectral Attenuation of Infrared Radiation in WinterHaze," uvuttiya, Aczdemy of Science, U.S.S.R., Atmospheric and Ocean•c Physics (English Trunsition) 5,521(1969).
(g) V. L. Filippov and S. 0. Mirumyants, "The Spectral Transparency of the Atmoqsheric Boundary Layer toInfrared Radiation," Izvekiya, Academy of Science, U.S.S.R., Atmospheric and Oceanic Physics (Engfiah Trans-Action) 5, 742(19%9).
(h) T. S. Chu and D. C. Hlog& "Effect, of Precipitation on Propagation at 0.63, 3.5, and 10.6 Microns" The 8@11System Technical Journ, 722 (1968)
46
between two mountain peaks-Mauna Loa and Mauna Kea in Hawaii.8s The transmis-sion spectra covering the spectral range 0.5 to 15 pm were recorded through a varietyof amounts of precipitable water vapor 0.11 to 38 cm in the optical path.
Streete made the atmospheric transmission measurements through a 25-kin-long optical path about 10 meters above the Atlantic Ocean water surface at Cape Ken.rnedy, Florida.' 3 He used an NaCI prism spectroradiometer with a thermocouple de-tector to study transmission of radiation in the 0.56 io 10.7 Am range from six carbonarc searchlights, each with a 150-cm-diameter aperture. His measurements covered aprecipitable water vapor range from 21.5 cm to 43.3 cm in the 25-km optical path.
The Russian work performed over a period of several months during 1967-68and reported by Filippov et al. contains atmospheric transmittance spectra from 0.59pm to 12 p•m recorded at the Zvenigorod Scientific Station of the Institute of Atmo-spheric Physics, Moscow." as The measurements were conducted on a 1300-m hori.zontal, optical path under typical Moscow winter and summer environments involvingclear, haze, haze mixed with snow, and dense haze conditions corresponding to meteoro-logical visible ranges of 1.5 km to 20 km. The precipitable water-vapor content of theoptical path ranged from 0.047 cm to 3.5 cm.
The measurements made at the Bell System Laboratory, Holmdel, New Jer-sey, and reported by Chu and Hogg were made with very narrow band coherent radia-tion sources; namely, an He-Ne laser operating at 0.63 pim, an He-Xe laser operating at3.5 pm, and a CO laser operating at 10.6 Am.s6 The optical path, 2.6 km in length,passed over a terrain containing grassy and plant nursery land partially planted andplowed with a few asphalt and dirt roadways. Atmospheric transmittance through haze,light fog, rain, and snow was studied at the three wavelengths. Chu and Hogg concluded
8 2 H. W. Yates and J. I1. Taylor, Infrared Transmission of the Atmosphere, NRIL Report 5453, U. S.Naval Research Laboratory, Wauhington, D. C. (1960),
8J. L. Streete, "Infrared NMeasuremcnts of Atmospheric Transmission at Sea Level," J. Opt. Soc. Amer.7,1545 (1958),
84V. L. Filippov, L. N1. Artem'yeva, and S. 0. Mirumyants, -Spectral Attenuation of Infrared Radia-tion in Winter Haze," Izvestiya, Academy of Scien-e, U.S.S.R., Atmospheric and Oceanic Physics(English Translation) 5, 521 (1969),
85 V. L. Filippov and S. 0, Mirumyants, "The Spectral Transparency of the Atmospheric BoundaryLayer to Infrared Radiation," Izvestiya, Academy of Science, US.SR., Atmospheric and OceanicPhysics (English Translation) 5. 742 (1969).
86T. S. Chu and D. C. Hogg, "Effects of Precipitation on Propagation at 0.63, 3:5, and 10.6 Microns,"The Bell SyAtem Tech. Jour. 722 (1968).
47
that the attenuation due to haze (called light fog by them) was up to one order of mag-nitude less at 10.6 #m compared to that at 0.63 pm; attenuation due to fog at 10.6 Amexceeded 40 dh per km (Transmittance, T = 10"4 per kin). The attenuation in rain at0.63 Am is less than 20 db per km (Transmission, T = 1("2 per kin). For Ihe sake ofconvenience of tile rvader and for comparison, some of the major worldwide atmospher-ic transmittance measurements are presented here.
Figure 15 shows a sea-level spectrum of solar radiant incidance (irradiance)with spectra of the "infrared active" atmospheric gases recorded individually in thelaboratory. The intensities of the spectral lines for individual gases are approximatelyrelative to the concentration of each gas in the vertical atmospheric path. This figureis based on the work performed at Ohio State University .8 Carbon monoxide (CO)has only a fairly weak absorption band at about 4.8 pm. Methane (C H4 ) has two ab-sorption bands at 3.2 pm and 7.8 pm. Nitrous Oxide (N2 0) has two strong absorptionbands at 4.7 pm and 7.8 pm; the latter almost coincides with tile absorption band ofmethane. Ozone (03) has a strong absorption band at 9.6 pm and another at 14 pM.Carbon dioxide (CO2) has three very strong absorption bands centered at 2.7, 4.3, and15 pm. IIDO, the rare isotopic form of water, which has an abundance of 1/3355 in1120 , has a very conspicuous absorption band at 3.67 pm and another at 7.13 pmn;whereas, the important absorption bands of water vapor (112 0) are centered at 1. 14,1.38, 1.88, 2.7, 3.2, and 6.3 pm.
Figure 16 presents an atmospheric transmission spectrum based upon tilemeasurements of Gebbie et al.58 The precipitable water vapor in the path was 1.7 erm.The average transmittance in the 3.4 pm band is about 0.90 compared to about 0.75in the 8.12 Am band.
Figures I 7a through v present atmospheric transmission spectra through fogat various stages of evolution and stability. These spectra are based upon the work ofArnulf et al.89 To our knowledge, this is the only outdoor work ever reported in theworldwide literatire for the spectral transmittance of fog. There were a number ofsources of probable error and inaccuracy in this work as stated by tihte authors. Theneed for more work with improved itistru mentation in order to obtain better accuracyand reliability is obvious,
87.1 N. I toward, "The' 'nmsmissimo of the Atmosphere in the Ifrared," Prm,. IRE. t7, 1451 (1959).
1101. A. (;ebble, W. It. Ilhrdinig, C. Ililsurn, A. Pr cv, and V. Roberts, "Atnospherie Transmission inthc I to 14 Nlicron Iteic, ,"Pro'. Roy. Sor..4 206, 87 (1951).
119A. Arolf, ,. Ilricard, E. . Cure, awld G. Vcre-l, '"Irrns issiun loy Ilaxze aed Fog iii the, Speictral IRegiot
0.35 to I0 Microms," J, opt. So, ,I m'r. ,17, .491 (1957).
.18
1 Co
I0
0 . i * * * *,, ' '
01 N2 0
.J I __ i I I •
00S~03
40 . * * * * * , , A i I , S
HO
0.
I SO • • ILA
SPECTRUM
00oo3000 2000 p OO2o o0o o 700 ,5000 WAVE NUMBER (cm-1 _
1 2 3 4 5 6 7 6 9 10 11 12 13 14 15
WAVELENGTH Ipml
Fig. 15. Spectral transmittance of atmosplwrie gases (laboratory measurements) andthe solar radiait incidatce spetrum ( Valley).
49
I • ... . ... . . . . .... .... : _ . ..._ _ . . . . . . .. . . •.. .• . .. ._ , ., , •. . .-. , . ... - . ..... .. .... .. • l
IA
- F.
30NVilIWSNVOI OIH3HdSONiV tz50
55
HI
I . I I.., I
30103
18 NOV 5410-25
2518 NOV 54e
20 isNOV 1-20
- 103 MM 18 NOVH 54
~15 -01
wiVISIBLE RANGE (in) \ \\
10 1 .. 0.i-~ 097 JAN 55 22
7 JAN 55
5 7 JAN 55 \26-10-5
7 JAN 55 .850m.
CD~ C *IP -C4 P- .
WAVELENGTH [micrometers)Fig. 17a. Atmospheric transmittance spectra for selective fogs as; measured by Arnuifet at.
5'
IIDATE 18 NOV 1953TEMP 7.30 CRH 0.99WIND W 1-2 ms-1
TIME l
2 1. 1034 " 0.000%,o 14i 10-12
11; 160m
21045 HRS J -. I0_1010 I- 105q1. \ -U:101
.•, -r-
l 722HMRS Ikk10- 8 a
4. 1122MRS~ij7N\La 6 . 1o5o HRS 288 m "0 ".11 " 0... \g \ \\
"3 " HRS _, _ 0
t•mUU.,E,-N. "... ' I36. 1146 MRS Go m
2 VISIBLE RANGE [m) NO "17. It534 HRS 1900m
7. rg. =o1, ., , , , •- . ÷. . . o
WAVELENGTH (micrometers)
Fig. I 7h. Atmospheric transmittance spectra for evolving fogs as measured by Arnulfet al.
52
3 TEMP__R DATE TIME __________111 3 MAR 53
(2) 3 MAR 53 6
70
(4) 6.90, 0.99, 11 DEC 53, 0930 HAS 4. e. Jo
(5) 1.40, 0.99, 17 NOV 53, 0316 HAS .--
20
'F 8I 0.40, 0.96, 7 DEC 53, 1100 HAS
15 0-15K130 Ml~I
( 91 19 MAR 53
1121 0.00, 1.00, 23 NOV 53. 1009 HRS : ;(13l) 0.00, 10.9, 25 NOV 53, 1801 HR 1
14 22..NOV..53,.1019.. 10
131 22NOV53
25 10-25
VISIBLE RANGE [m)
20 DATE 85m. ,, '. 10_20
4 MAR 53 4e 97. - ,. -
16 DEC 54 9t 7
1 DEC501 m
10-DEC54 -54 d..o-U 101
20 MAR 53 0..rio"- "%. ý-"
C..4"1000Lm...... m . 100 ", •,
WAVELENGTH (micrometers)
Fig. 17d. Atmospheric tranrnsmttaricc spectra for stable' fogs, 'lype. 2, as• measured by
Arnuif et al,
54
-: 2 DATE 21 JAN 53 0.01
VISIBLE RANGE IS1 km1103 HRS OPTICAL MEASUREMENT
-.. 1120 HRS OPTICAL MEASUREMENT---- 1130 HRS OPTICAL MEASUREMENT
A •m. 1113 HRS PHYSICAL MEASUREMENT1.5 0.03
. VISIBLE RANGE 0Sli~(T 0.551im) -
0.5 0.32
.. 1.0
10
WAVELENGTH Imlcrometersl
Fig. I 7e Atmomupheri. translmittan ce, s1,(tra for hu.;.t am uwasurhe dI by Arnulf et uat
.:" 1*I
Figures 18 mnd 19 present atmospheric transmittance spectra based upon thework of Taylor and Yates who used optical ranges of 0.3, 5.5, 16.2, and 27.7 km withthe precipitable water vapor vontent of 0. 11, 1 37, 5.2, and 20 cm resperctively. Theirwork has the best accuracy, reliability, and spectral resolution (VAN = 300), but mostof this study wos limited to clear and stahle atmospheric conditions.'° "
Figure 20 contains atmospheric transmittance spectra recorded on a 25-kmoptical path by Streete for various amounts of precipitable water vapor ranging from21.5 cm to 43.3 cm."2 In this study, the optical path was over the Atlantic Ocean atvarying heights above the water suriace with occasional sprays of mist tossed up intothe optical path by ocean waves. Streete used Fowle's spectroscopic method to com-pute the amount of precipitable water instead of using valies of temperature and rela-tive humidity at a number of points along the optical path.9" The IIDO absorptiol'band at 3.67 Am in the Yates and Taylor data was used to determinu the relation be-tween transmittance and precipitabho water vapor. This method assumes that the at-mospheric optical environments under which the two measurements of Taylor-Yatesand Streete were conducted were identical. This procedure may have intruducied aconsiderable inaccuracy in the detcrmination of the prccipitable water vapor contentof the optical path. McCoy has also analyzed this problem and has come to the sameconclusion.9
4
Figures 21 and 22 present ten atmospheric transmittance spectra recorded byFilippov and Mirumyants for various amounts of precipitable water vapor raliging from0.105 cm to 3.5 cm on 1.3 km or 2.6 km long optical paths ncn' \ !u w.9 5 Figure 23shows the spectral variation of attenuation coefficients in the 0.69 rm to 12 Am range
_90J. I!. Taylor and II. W. Yat..,, "Atmospheric Transmission in the Infrared,"J. Opt. Soc. Amer. 47.
223 (1957).
H. W. Yates and J. It. Taylor. Infrared Transmission of the .4tmosphere, NRL Report 5453, U. S.Naval Research Laboratory, Washington, 1), C. (1960).
92J. L. Streete, "Infrared Measurement, of Atmospheric Tranmission at Sea Level,"J. Opt. Soc. limer.
7,1545 (1958).9 3 F. E. Fowle, "The Spectroscopic Determination of Aqueous Vapor," The Astrophyvical Journal, 35,
149 (1912), also "The Determination of Aqueous Vapor above Mount Wilson," The Astrophy. Jour.t 371, 367 (1913).
94J. II. McCoy, Atmospheric Absorption of Carbon )itvxide Laser Radiation Near Ten llicrons, Tech.nical Report 2476-2, T'hie Ohio State University, Columbus, Ohio (1968).
9 5 V. L. Filippov and S. 0. NMi umyants, "The Spectral Transparency of the Atmospheric BoundaryLayer to Infrared Radiation," lzvestiyg, Academy of Science, lIS..S.f,, ,ttnmsphrrie and OcennicPhysics (English iranslation) 5, 742 (1969).
56
Iv I11F1F
as -q ~ c
Cd D
CdD
Cd c-a C~d -to 0ca -
ca MI CD a
C4 ca
6 - C
Cd'Ln Ln c
_D CDI-C
30VIWNa
57,
p.--
CC
C:;U
UC.
cm
C2" A U *
Br
C;
a an ii.NV~
an
RIP~
C"4
CIC4 C4 Cca D 4D 0o0 =D coC2C
I-.0 uco cl
LaiZ
Ica 3C4' t
o0 w 0CD~
C2P
-D
to C4 ca 0 OD W C)~
C ca CD to CD D ca CDo
33NViIIWiSNVdi1
59
iI
OIL CPI ATMOS- RELA-OPTICAL PATH CIPIT PHERIC TEMP OC TIVDCURVE DATE, TIME LENGTH (kmi WATER TRANS- HUMID-WATERITY
w ,c. MITTANCE (%j
A 17 MAY, 1968 1100 1.3 0.105 0.68 -21.0 75
B 13 APRIL, 1968 1000 1.3 0.27 0.72 -2.1 46
C 14 APRIL, 1968 1500 1.3 0.53 0.75 +4.6 66D 24 APRIL, 1968 0800 1.3 1.05 0.79 +9.5 86
E 9 APRIL, 1968 1700 1.3 0.78 0.74 +14 50
- ---
: .0.
. •0.5B
0.50.
0.9 1.5 2.1 2.7 3.3 3.9 4.5 5.1 5.7 6 9 12
WAVELENGTH Ipm)Fig. 21. Atmospheric transmit tan , sp(trla for v'arioal •s lnamountsl ol lJreip)it•lhh, waf arvapor: (A) 0. 105 cm. (11) 0.27 urm. (C) 0.53M cru. (1D) 1.05 cm. aLId (E) 0.711 vm.recorde• by Iilippov 'i al.
60
PTE ATMOS- RELA-OPTICAL PATH CIPIT- PERIC TIVE
CURVE DATE. TIME LENGTH Ikmi ABLE TRANS- TEMP C HUMID-WATER MTAC Tw,cm MITTANCE irv
A 11 AUG., 1968 2000 1.3 1.55 0.65 '15.2 90
B 8 OCT., 1967 1345 2.6 2.05 0.92 .10,7 81
C 10 AUG., 1966 1830 2.6 2.47 0.92 t20 54.5
0 11 AUG., 196B 1600 2.6 3.0 0.85 '15.7 86
E 13 AUG., 1968 2030 2.6 3.5 0.90 '15.4 96
1.0 '•, r " " -
. ~0,
1,(.,,,, ,.• ,,.• -r v.-r-i-r-1r- r-T-r. ii; - r - t- - -'-"rt-I. . . . ..r ---r ,
AM....I~ g/ N Ž A i. ...i1. 0 1-_ -. -* r .T -_ I , . _T
S0.5UiyT rc.3. 4D 10 ~ -' r-- i Tt i T r 1*, i -- r--
t* 0.5 0
ac 0 1 1. i -.
0.0 1.5 21 2 r T3.3 3 r9 4,5 5.1 5.7 6 9 12 15
WAVELENGTH (pm)
•; I~~~~ig. 22. Atmrn•phirh. transmittarn:, •pi'ctra roir vilriljiis• lniimuint l• p)lrccipitabhe wuher,, ~~~vaipor, (A) I,, 55nm, (11) 2.05 cmi (( ,) 2,47 c.m, (I)) 3.0 nim, &uid (F) :,,5 cm11, riicorlde~dIy V'ilip p o v eT a l.
0.9 1 .31
by Fi i o et ia"li.
I.--
I5 km C RHO. DATE AND TIME REMARKS
"212 1.97 -30.0 90 0053 23 JAN 1961. 1740 HRS HAZE AND WIDELY SPACED SNOW157 3.1 -14.5 39 0 297 25 DEC 1967. 1600 MRS SAME233 2.6 -30.0 82 0.047 24 JAN 1161, 1200 RiS DENSE HAZE20o 2.70 -22.0 2 0.100 21 1.. D HIS SAMEIN 7.ý -1150 85 0.144 20 1750 HIS HAZE277 3.75 -3.0 I5 0.278 29 1930 HIS SAME117 14.9 -21.0 33 0.100 20 1300 HIS SAME271 74. -7.0 05 0.330 29 1020 HIS SAME221 2.7 -30.0 12 0,047 24 1210 HIS DENSE HAZE245 4.75 -17.5 14 0,144 25 1550 HMS HAZE AND WIDELY SPACED SNOW206 2,5 -22.0 32 0.100 21 - 1610 HS DENSE HAZE200 4.5 -11.4 79 0122 25 1145 HMS HAZE265 5.55 -50 30 0,330 2 - 1110 HMS SAME250 3.9 -23.0 14 0.090 21 JAN 1968. 1010 HAS HAZE AND WIDELY SPACED SNOW243 9.37 -17,5 10 0.132 25 1400 HMS HAZE272 31 -7-0 5 0330 29 1400 HIS SAME190 7.I -11.0 35 0,144 20 -o 1820 HMS SAME260 I 92 -300 90 0 053 23 - 1515 HMS HAZE AND WIDELY SPACED SNOW
2.0AA B
Z
Z 262
1.0- 5.•• • •157 p228 ,.
233 i- 245
2 55
____5 .~ N 250*1 198 -~243
277 272
0.4 1.0 5 10 0.4 1.0 5 10 20
WAVELENGTH Imicrometers)Fig. 23. Spectral attenuation coefficients for winter haze in the 0.59 to 5.0 /m and0.59 to 12.0 Am regions reported by Filippov et al,
62
for winter haze measurements made by Filippov et al.* They have ilot published atmo-spheric transmittance for thick haze or light fog conditions.
Finally, the comparative studies of the effects of haze, rain, and snow on thepropagation of laser radiation at 0.63, 3.5, and 10.6 lm as reported by Chu and Hloggare presented in Figs. 24, 25, and 26.97 Figure 24 shows that in e6olving haze and lightfog, with changing number and size of aerosols, the transmittance of 10.6 Pm radiationis much better than that of 3.5 pm and 0.63 pm radiation. In the earlier stage of hazedevelopment, the transmission, per kilometer, of 0.63 and 3.5 pm radiation was about0.03 whereas that of 10.6 pm was 0.63. Later (n, when the haze became thick and thetransmittance of the 0.63 pm radiation fell down by two orders of magnitude, therewas no appreciable change in the transmittance of the 10.6 pm and 3.5 Am radiation.Here, the conclusion is that small changes in the aerosol size can drastically affect wave-length dependence of transmission. Figure 25 shlows the variation in transmittance with"variable rainfall in the optical path. Here, the spectral transmittance is reversed with re-spect to that in haze or light fog. For rain, the transmission is the highest for 0.63 ,m,is lower for 3.5 pm, and is the lowest for the 10.6 prm radiation. Figure 26 shows the"variation of atmospheric transmittance with variable amounts of light snow in the opti-cal path for the three laser wavelengths. The attenuation of 10.6jpm radiation appearsto be larger than that of the other two wavelengths which appear to be equallyattenuated.
Based upon outdoor, long-path, atmospheric spectral attenuation measure-ments, Knestrick, Cosden, and Curcio have computed atmospheric scattering coeffi.cients in 10 narrow wavelength bands between 0.4 micrometer and 2.3 micrometers.9,The wavelength hands were chosen so as to avoid atmospheric molecular absorptionand were isolated by interference filters. Curcio, Drummeter, and Knestrick have madehigh-resolution (AX = 0.2A) spectral absorption measurements from 5400 A to 8520 Aover a sea level, 16.25-km-long, horizontal, optical path over water."
9 6 V. L. Filippov, L. NM. Artem'yeva, and S. 0. Mirumyants, "Spectral Attenuation of Infrared Radia-tion in Winter [late," lzvestiya, Academy of Science, U.S.S.R., Atmospheric and Oceanic Physics.(Enqlish Tranlation) 5, 521 (1969).
97T. S. Chu and I). C. Hogg, "Effects of Precipitation on Propagation at 0.63, 3.5, and 10.6 Microns,"The Bell System Tech. Jour. 712 (1968).
98G. L. Knestrick, T. If. Copdri, ant J. A. Curcio, "Atmospheric Scattering Coefficients in the Visibleand Infrared Regions,"J. Opt. Soec. Am. 52, 1010 (1962).
-9)j. A. Curcio, L. F. irumnmeter, and G. L, Knestrick, "An Atlas of the Absorption Spectrum of theLower Atmosphere from 540) A to 8521) A," App. Opt. 3, 1401 (1964).
63
CD
i 4
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cacm 91)
di Cl
Snpge CA -CD-
10 Co
* O)C2 G2GE2 s
C4 In
S139133
a6
0cIIJ
C.3
2Z-2 0G 0-
a-" -20 \ X
- .6 5 0.63m N, I. -30 35.& \/~ •i-- 3,DSpm _,______.__
S...... ~10.6 ;Am \. i
.-40~F
j 125
.100-
- 75OC 50-z 25
11:00 11:30 NOON 12:30
E.S.T. IHRSJ
Fig. 25. Transmittance of 0.63 prm, 3.5 Mm, and 10.6 pm laser radiation through variable lrain in 2.6 km optical path as measured by Chu and Hogg.
65
41"' .m
,,4 • -. W
IO,
OPPm
-,t£ -
-- 3":,,,*--4_ -
J Ci
LaiG-. a
(nn I
64.~ *~ iaC Q
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66
*II~sW .- w . ~ ~ . -w !ot -, ' ..... .. " ' . I 1_ -, ' " ' ' V- w .- -" . 'J L:L .n" w-t_• -'" " - -- -- - .............
Attenuation of visible and infrared laser radiation by clouds was studied bySanders and Selby using five continuous-wave lasers operating P t wavelengths of 0.63,1.15, 3.39/jm, (Helium-Neon), 10.6 Am (CO 2 - N2 - Ne), and 337 Am (CN radical).,'0The meteorological optical ranges (visibiities) varied from 40 meters to 200 meters dur-ing the measurement period. They concluded that during these conditions there wereno significant differences in cloud attenuation at 0.65, 1.15, and 3.39 AM; however,the attenuation at 10.6 um averaged about half that at 0.63 Am when cloud densitywas not too high. The scattering loss at 337 um in clouds is small in comparison withmolecular absorption by water vapor.
Precipitable Water Vaport The precipitable water vapor in the optical path isthe amount of water that would be obtained if all the water vapor contained in a cylin-der of unit area cross section extending along the entire optical path is precipitated. Theheight of this column of precipitable water vapor w, measured in centimeters, can be ob.tained by the following relations:
w28 x 104w (pr cm H20) [ T ] p L, (60)
or w (pr cm H20) [ 2.88x 10"2 (Rll)p L, (61)T
since Rt = p/ps, (62)
or w (pr cm 12 0) = p(T) (RH)'I, (62a)
where r is the air temperature in the optical path, expressed in degrees Kelvin, Ril isthe fractional relative humidity, 1) and p, are respectively the partial and saturated pres-sures of water vapor at the temperature of measurement, in torr (mm I1g), p(T) is thewater vapor density at the ambient temperature T, and 1, is the optical path length ex-pressed in meters. The saturated water vapor pressure and density are given in tablespublished in several handbooks (such its I)- 106 and E- I. CRC Handbook, 1966).101Froma: equation (60), one, shouhld iote that the amount ot water vapor in the opticalpath is a function of the lemperature and the partial pressure of the water vapor. Itshould lie emphasized that the atmospheric transmittance is not a unique funitimi of
")0 It. Sanders and J. E. A, Selby, Compamtie, Merasure'te nits of the A ttenhuution of V'isible and Infra.
red Iaser Radiation in Cloud, Report I)MP 3151, IM EIIctroitim Linited, IhIyyes, Mlidlhwex,England (19068).
IM1iHandbook of (hemistry and Physies, 'rhe Chemical Rubber Co., Chlvelund, Ohio (1966); alsoSmithsonian Meteorologcal Thbles, 11) It. J. LiAt, Smithsonian Institution, Wadtington, 1). C. (1908).
f67
A.~ A.P~lMU,,i~.4*. I ~ -4,AAA , fl4SPM~4dS~I4,. .
precipitable water vapor in the optical path, but it is dependent upon the partial pres-sure of the water vapor, the total pressure, and the temperature of the medium.
7. Laboratory Studies of the Attenuation of Radiation by Atmospheric Gases.Since outdoor studies of atmospheric transmission cannot he conducted under con.trolled atmospheric environments, the alternate approach to study the properties ofgaseous attenuation is to measure optical properties of individual atmospheric games inthe laboratory under controlled conditions. Multiple-path crIls are used to study opti-cal properties of gases. These cells are designed to study the spectral absorption of radi-ation by individual gases at various partial pressures, temperatures, and total pressures.A synthetic atmosphere is created by introducing a known amount of absorbing gas in-to the evacuated cell along with an infrared transparent gas such as nitrogen to createthe desired total pressure in the cell. The variations in partial pressure of the absorberand the total pressure in the cell enable the simulation of atmospheric optical environ-ments corresponding to those existing at various altitudes in planetary atmospheres.
The most notable laboratory studies of attenuation by atmospheric gaseshave been reported by Howard, Burch, and Williams;°02 and Burch et al,,o03 Gryvnakand Shaw,'°4 Shaw,10 s and Rensch'|' of Ohio State University; Palmer of Johns Hop.kins University-' 0 7 Tidwell, Plyler, and Benedict of the National Bureau of Standards;106Burch and Gryvnak, of the Aeronutronic Division, Philco-Ford Corporation;, 0 1 andZuev of Tomask University.11n
IOftj. N. Howard, [). E. Burch, and I). Williams, "Near-infrared Transmission Through Synthetic Atmo.
spheres,"J. Opt, Sac. Am. 46, 186, 237, 248, 334, 452 (1956).10 3 D. E. Burch, E, B. Singleton, W. L, France, and D. Williams, "Infrared Absorption by Minor Atmo-
spheric Constituents," Final Report, C-AFI 9(604).2633 (1960); also Sci. Reports I (1960) and Sel.Report 2 (1961) Ohio State University, Columbus, Ohio; AFCRL Rept..62.698 (1962); AppliedOptics, I, 359, 473, 587, 759 (1962), 2, 585 (1963) and 3, 55 (1964).
1041). A. (;ryvnak and J. II. Shaw, Sci. Rept. 2, AFI9(604)6141, The Ohio State Univ. (1961),10 5j1. I. Shaw, Report No. AF19(122)-65, The Ohio State Univerfity (1954).
1061). B. Rensch, Extinction and Blackacatter of Visible and lnfmred Loser Padiation by A tmospheric
Aerosols, Report 2467-3, The Ohio State University (1969).
10711. Palmer, J. Opt. Soc. Am. 47, 367, 1024, 1028, 1054 (1957); 49, 1139 (1959); 50, 1232 (1960).
108E. 1). Tidwell, E. K. Plyler, and W. S. Benedict, J. Opt. Soc. Anm. 50, 1243 (1960).1091). E. Bureh and 1). A. Gryvnak, Aeronutronic, Philco-Ford Reports U-2955, U.2995, U-3127,
U-3200, U-3201, U-3202, U-3204, U.3857, U.3930, U-3972, U4076, 1J4132 (1964.67).
1 IOv. E. Zuev, Atmospheric Tmnsparency in the Visible and the. Infrared Engiish Trnslation, lraelProgram for Scientific Translationt, Jerusalem (1970), also Propagation of Visitle and InfraredRadiation in the Atmosphere, Sovietakoye Radio Press, Moscow (1970).
68
ISMcClatchey of the Optical Physics Laboratory, AFCRL, is presently compil-
S~ing the latest fundamental spectr~oscopic data oil the spectral lines of all molecules re-
sponsible for atmospheric absorption. The spectral line data are to include frequency,line intensity, half width, and energies of the quantun' mechanical energy states in-volved in the radiation transfer process. The gases involved in this study are CO 2 , 1120,
03, N2 0, CO, Cl!4 , 02, N2 , and 11NO 3 . A report on this work is expected to be com-pleted by the end of 1972.111
Recently, Perry, Layman, and Ealy have conducted a study of the "atmo-spheric window" transmittance through artificial fog.' 12 They have measured the rela-tive transmittance in the "visible," 3-5 pm, and 8-12 pm spectral bands through a 45.72m (150 ft) optical path. The fog chamber is reported to have the capability to producehomogeneous fog with variable density but with a constant relative size distribution offog droplets. Figure 27 shows the relative size distribution of fog particles used in thisstudy. Figure 28 presents the relative transmittance for their "visible,"' 3-5 pm, and8-12 Am spectral band radiation-detection-systems through artificial fog of varying op-tical density or transmittance. From Fig. 28, it is clear that the relative spectral bandtransmittance through fog increases with wavelength in the three atmospheric windowsunder consideration. However, the transmittance for the 3-5 pm and 8-12jpm spectralband system falls to 0.02 and 0.2, respectively, when the optical density of fog reachesa value of 2 (visible transmission of 0.01). Further, the relative transmittance of the8-12 pm spectral band detection system falls below a rather low value of 0.02 whenthe optical density of fog reaches 2.7 (visible transmittance of 0.002). The real outdoorfogs have optical densities varying from 1.7 to 30 which correspond to visible ranges of1 km to 50 meters, respectively (see Fig. 17). The 8-12 pm spectral band system has areasonable transmittance advantage over the visible and the 3-5 pm band systems espe-cially in the optical density range of 1.7 to 2.7 (visible range 1000 - 630 m) where thetransmittance of the 3-5 pm system falls below 0.02.
8. Fundamental Principles of Gaseous Absorption. The spectral transmission ofradiation by the atmospheric constituents is rather complex owing to the multiplicity
of physical processes involved in the interaction of radiation and matter. A completetreatment of the theory of atmospheric gaseous absorption is presented in a number of
11 IR. A. McClatchey, private communication.
!12J. E. Perry, S. F. Layman, and W. R. Ealy, Comparison of the Transmission Through Fog of the 3-5and 8-14 pm Spectral Regions as a Function of the Visible Transmission, Research and DevelopmentTechnical Report ECOM-7013, U. S. Army Electronics Command, Fort Monmouth, New Jersey(1971).
69
r Iru.Iu
0.16-•
Z 0.12
IC0-
=: 0.06
ca
0.04
0tL . L .I L l L I I I L5 10 15 20 25 30 35 40 45 50
FOG DROPLET DIAMETER IpmJ
FI ig . 2 7 . Ile la .i,,e A iz e d is t rilb t io n o f fo g p a r ti le s ( in t hl c fo g c h a m b e r a s r e p o r te d Ib yPerry and l,ayman.
70)
p
e EmI----- 4 -I--a-.-
- -00 C
44 ~ a )I1iAn eq
aca u"IC 4 i =c -
I-- _ 3
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33NViIIISNVdiI 3AIIV13H
recent publications and references listed therein.'13 114 Only the basic principles arcpresented here.
a. The Shape and Width of a Spectral Line. The molecular spectral lineshave a number of analytical shapes or contours and half-widths which are determinedby the following processes:
(1) Natural broadening.
(2) Pressure or collision broadening due to interaction among molecules.
(3) Doppler broadening due to relative motion of molecules.
The natural width of a spectral line is set by Heisenbcrg's UncertaintyPrinciple which states that if the lifetime of a molecule in an excited state is At, thenthe uncertainty in its energy AE will be given by
AE - h/27r(At) (62)
where h is Planck's constant. This excitation ncrgy is releasecd as a photon of frequencyinterval Av' (liz) given by
AE = h Ap'. (63)
In terms of wave-numbers, , in cm",
AE = htc Av, (64)
where v = v'/c . (65)
A comparison of equations (62) and (64) gives
AVN___ (66)
27T c (At)
In the infrared, the vibrational energy region states havew a lifetlinc of the order of 0.1s'cond. Substitution of this valihe for (At) and 3 x 1010 e'm/sre for v g•e's Ihe na!uralwidth of a speciral line AN
I 13K. Ya. Kondralyi'v, Randitlim iti thu..lno.•ehr'. .AWiigle,hAv i lrde .- Nvuw York (1969t).
I It. \. (N. dy. ,1 tmy ,.A r ttspherir. HIdilti. ( )t ford I'niv,.it v i 'r,..% . I . dom i (I ((6 t).
72
APN - 5 x 10"11 cm- (67)
which is trivial as compared to wave numbers associated with infrared radiation in atmo-spheric phenomena (25000 - 666 in 0.4- 15 pm region), and the broadening caused bythe Doppler effect and collision broadening.
The theory of collision or pressure broadening was given by Lorentz;according to this theory, the shape of a gaseous absorption line is given by the reldtion: 115
_ S a1 .k -= + (O L (68)
where all = a11 [~Žl (69)
where kv is the frcquency-dcpeiident absorption coefficient, S is the strength of thespectral line (intensity). E" is the vibration-rotational energ of the ground state. I) andT are the effective pressure and tcnperaturc of the absorbing gas, VO is the frequency atthe center of the spectral line, a1 is the half-width of the spectral lime, and n is a con-stant, different for each gaseous specimen (ri = I for linear molecules and n = 1.5 forassymetric and linear top molecules). The subscript o in equations (69) and (70) refersto the quantities at standard conditions of temperature and pressure.
The D)oppler effect profile caused by :Ic ,ompoiiciit of velocity of mole-cules along the direelion of emission of radiation is give lby
kv = k exp (- y2 ) . (71)
wher kQ (72)
(v- vO)=n -"" (73i)
-] "'D. Andin d. l indel-IftMI 1I'f~iod., Sr cviiiirli'ig .1I niosp/ieric .Ilofi,lhwiar .,1 bsorplinim'illri No.
1.42-21 -r. \illow lVii I ,aNriLori ie's. 'li'h I tive.rsitiv ot lriiigaii..\n11 Arbor. Michiigan (1 9)•7.).
73
and aD = 3.58 x 107 o 74)
Here all is the Doppler half-width and M is the molecular weight of the absorber.
The Doppler width of the 5577 A line of atomic oxygen at 3000 K is3.3 x 10.2 cm', while the typical Lorentz (or collision) widths at the standard tempera-ture and pressure (S.T.P., are of the order of 8 x 10"2 cm". Doppler and Lorentz linewidths are comparable at higher altitudes. For the lower atmosphere where the pres-sure is high, the Lorentz profile is the most predominant. in the upper atmosphere,the effect of collision broadening decreases and Doppler broadening is more important.Figure 29 shows the relative shapes of the Doppler and Lorentz spectral lines of thesame strength.
In the real atmosphere, the absorption lines obtained with a spectrome-ter are caused by the simultaneous absorption of all absorbers. Thus, the resultingspectra have blended shapes modified by the slit function of the spectrometer. TheBeer-Laambert-Bouger law may not hold for such spectral regions,
A number of modified furinM of Lorentz and some totally new spectral-line profiles have been proposed by a number of investigators.116 One should note thatthe half-width of a pressure-broadened or Lorentz line varies linealy with the totalpressure and approximately inversely as the square root of the absolute temperatureand that the intensity or strength of a spectral line is a function of temperature.
b. The Rigorous Method for Computing Gaseous Spectral Absorptance.The spectral absorptance A. rather than spectral transmittance T,, is genc ally computedsince the absorption curves "grow" in depth and widlh as the amount of the absorber isincreased. The average absorptance A. over a bandwidth IV is given by Lambert's law:
-l '2 r N X
AP=~ lc) [- /kx)p(x) dxJ (IV (75))
where N corresponds to th,, number of different absorption lines c(intribtuting to absorp-
lion in the interval P, to P2 (assuming that there is no appreciable variation in absorp-
lion coefficient with wavelength iii this interval). The rigoroius mnethod for the compu-
tation of absorption is direct integration usinig ,quation (75), For this method, oli( has
116R. .Goody, A tmrsph,,ri" Radiation, O xford U Tniversity Prvss, lohndh (I )164).
74
I,
C4
Lhi
CDC
I-'
cz0
ca a
gc
ga 41:
?PC
to know the absorption coefficient k(x, v) at each frequency and at each point alongthe optical path. This method requires exact knowledge of the characteristics of eachspectral line, namely its position (center), line shape, half-width, and intensity, as wellas the concentration of each absorber. The rigorous method should produce very accu-rate absorption spectra if all the parameters are well known and all the corrections dueto the variations of temperature, pressure. and concentrations are completely taken in-to account. This does require a great deal of computation effort and patience. A coin-plete data bank cm spectral lines is still in preparation in 1972.117
For the transmission of laser radiation, one does require high-resolution.spectral-transmission data to make accurate computations.
c. Band Models for Computing Spectral Absorptance. Lambert's law ofabsorption is obeyed for monochromatic radiation within one-fifth of its line widthwhich varies from 2 x 10"2 cm` for a gas at S.T.P. to about 2 x 10-4 cm" for Dopplerbroadening. This presents a formidable challenge for experimental and computational
task. The present conventional spectrometers do not have the required resolution. Onemay have to use Fourier Spectrometers to obtain high-resolution spectra to study thereal spectral line shapes, width, and intensity variations with absorber concentrations.For the sake of practical compromise, the spectral lines are averaged into spectral bands.A spectral band is assumed to contain an array of spectral lines of a certain shape, inten-sity, and half-width and spacing distributed according to some statistical pattern. In thereal spectra, this is not so. This is a major source of discrepancy between real and com-puted spectra. A number of statistical models have been proposed for calculating ab-sorption due to molecules of various gases as the patterns of the arrangement or repeti-tion of molecular spectral lines are different for various types of molecules. The mainfeatures of the band models are discussed in detail in the literature." 8 1191 20
The Elsasser, or regular, model assumes that a band is made up of an in-finite array of spectral lines of equal intensity, half-width, and spacing. This model isapplicable to hands of linear molecules. Lorentzian line shape is used. Absorption forvarious values of optical thickness (a function of absorber amount., line intensity, andspacing) can be computed for various values of the line-discreteness parameter.
S171t. A. MeClatchey, private communication.
118K. Ya. Knndratyev, Radiation in the Atnosphere, Acadentic Press, New York (1969).
I1 9 1t. ,1. (;Oo(lv, . tonospherie Radiation, Ox ford I niversity Press. L,onlon (1964).
1201). Anditig, BaIl-llodi'l a uthods for Conpualing I Imospherie Molecular .. bsorption. Reiport No.
7142-21 JT, Willow ur IH ahUralories, The University of Mlichigan, Ann Arbo'. Michigan (1967).
76
The statistical, random, or Mayer-Goody, model assumes that the posi-tions and line intensities are random and are given by a probability function. Thismodel has been used for water vapor using the Lorentz profile. Telles, Mayer, andGoody developed this model.
The random Elsasser, Plass, or Kaplan model assumes a random super-position of Elsasser bands of different intensities, half-widths, and spacing intervals.This model predicts absorption intermediate between the regular Elsasser and randomGoody models.
The quasi-random model of Wyatt, Stull, and Plass assumes that the
spectral lines are randomly distributed into small-frequency intervals.'2 1 122 The trans.mission over larger frequency intervals is calculated by averaging the results from thesmaller intervals. The spectral lines are grouped into intensity subgroups which simu-late actual intensity distribution. The contribution from the wings of the spectral lineswhose centers are outside a given spectral interval is included. This method has beenapplied to water vapor and carbon dioxide molecules. Transmittance tables for variousamounts of absorber are available in the literature.' 23
Recently Zachor and Gibson anl Pierluissi have proposed generalizationsof the Mayer-Goody statistical model, Zachor has used his model to calculate absorptionby carbon dioxide.' 2 4 Gibson and Pierluissi have proposed a " five-parameter" modeland have applied it to the infrared transmittance of water vapor and carblon dioxide.125
Various workers have prepared computer programs for the computationof molecular absorption by 112(), (O2 , N2 (0, 03 , and (:114 using various hand models indifferent spectral regions,.12' 127
121 p. j. Wytt, V. I. Skill, and (. N. Plase, "'Ihe Infrared raunsmittanee of Water Vapor," AppI. Opt.
3, 229 (1964).
I 22V. It. Stuill, P. J. Wyatt, and G. N. Nass, "Tl' Infrared Transrnitlance of Carbon l)ioxide," Appl.
* Opt. 3, 243(1964).S123S. L. Valley, Hlandbook of Geophysicas wd Spare', Environments, •.;raw-Ilill, New York (1965),
I 2 4 A. S. Zachor, J. uantl. Specrros. Radiat. 71hiasfer 8, 771, 1341 ( 19(41).
12 G(;. A. Gibson al.I ,1 , II. Pier1 ui* , "Acrurate I"monuLla for (;ustcous 'l'ratns itt inliiian h, ill the Infrared,"
AppL. Opt. 10, 150)9 (1971).
1261). Aidieig. IPtd-.1idetl Methods Jor C(ionptting AI tis ophlriv' .lhehcular .,ixorptionu. HIport NP.
, 142.2.-IA Willow Russn I,aboratoriei, The, 1iniverhitv of Micligaii, A,,nt Arbor, Nichigauc (IT.(e7).
12711. NI. ;ol hilkski ,y a wd N. iL. N iskalenko, "Sp ei,.ral Tran tntission FI i iitio ni4s in tIl " I Y 11 11c 1 ( ( 2
IB041ds, I14dl. (hi.) rtn. Sc. USSR • ltinos, anti (tevn. 'hvs. I., 194 (I Will).
A i7
d. Empirical Methods for Calculating Spectral Transmittance. Mc('atcheyet al. have prepared a set of empirical transmittance functions and a computer programto calculate horizonlal or slant-path transmittance from ground level to an altitude of100 km for a set of ten model atmospheres."'2 The spectral region covered is from0.25 micrometer to 25 micrometers with a resolution of 20 cm-'. There are two hazemodels corresponding to visible ranges of 23 and 5 kilometers. Figures 30 and 31 pre-sent atmospheric transmittance functions per kilometer horizontal optical path lengthfor five atmospheric models containing haze with 23 and 5 km horizontal visibilityranges.
Golubitskiy, Moskalenko, and Mirurmyants have developed an empiricalmethod for computing atmospheric spectral transmittance using the general form ofLambert's law: 129-134
= exp I - P, w' 1) I'• I (76)
where w is the absorbing mass, P, is the effective pressure (for water vapor,
Pe = p + B P, 20 , where H is self-broadening coefficient), my, np and Py are wavcelength.lepende nt parameters determined from experimental duta. They have describedthe method for computing the constants and have prepared extensive tables of constantsfor the computation of spectral transmittance in the infrared region. This method is
1211. A NicClatchey, It. W. Fenn, J. E. A. Selby, F. W, Volz, and J. S. Garing, Optical Properties ofthe Atmosphere (Revised), AIFCRL.71-0279, Environ. Res. Paper No. 354, Air Force CambridgeIt,•earch Laboratories, Bedford, Nlasaclusettw (1971).
129B. N. G olubitskiy, anI N. L. Nloskalhnko. "Spectral Transmiisionl FuncLionis in the I Is )and (A2BaIns(," Bull. (zr.) Ara. Se. USSI1/l{ Atmios. and Oeyin. Phys, 4, 194 (1961).
I * M~Gl. (;olubitskiv and N. I,. !loskuhvnko, "Mtasurvniernt and Calculatiori of Spiectral Trnaimiissioti
in the N2 0) Bands in the Near Infrared IRegion," Bull. (lzv.) .ra. Se. U(SR ,Itnuos. and O('•n. Phys.4. 204 (19641).
1IN. L. Moskalh'nko, "Spectral Trans nissioi Founctions io Solint 1124 )-Vapor, DI), and (II4 Iands,"
/lull. (lv.) .ea. Sr. IUSSR.I 'lmos, and Ovean. Ph vs. 4, 445 (19611).
132N. I,. Noskalenko, "Th Sliectral TI r zimion hi the Ilaids of "a Icr Vaplmr 1)3. N2 (), aid N2
At inospheric {'.onipoiimnls," t1/l. (Izv.) ,I yr. Se. I /iSSR A I tnos. and Ocean. IAvhs. 5. 6(-8 (1969).
"I1 N. I ,N , .. M sk lelnkco l S. •I, !diruolyaimL , "( *h tliiMIthoi t ls IIf S -Ivrei .\lbsorptiuue ' hfinfrarvil
Radliation by AtinosphFric G ,ases," hull. (UI,.) , Va. Se. I SSR/.,|tnros. & O'ean, Physvs., . 615 (197)).
1:4V. L,, Filippo% and S. 0 Mirtimeiants, "I conlyaraitiio 'tli.I- of]ENI)e rimnentul aoid ( eil,'uhitud Ifra-rvt I" 'ratiFliar,,ry ivp,4,tra o H; roun I,• L 'Il lhorir.ontal AI\t nau phicric Pa I I ii" Bull. (tl r.) Ilea. S%.I !5fl, .timos. wand (),.'an. Phyvs. 6, 076 (1970)).
781
0+0
__ C
EM
a. III;! Mmc
O Ll) L&J
'C,
0-6cm0c
ab-
33N~iiWSNV0
490
........
c*+ 40 )
~mm
CL In co
C U.2
CDC
CDC
C C 4
~~ 3ONVIIIWSNVHI.
reported to provide, in s)me cases, better accuracy thun the quasi-random, Wyatt-Stdl-Plum band model if the spectral resolution > 5-20 vin", An accuracy of 5 to 7% inTcomplite'd values of siwxtra! transmittance is obtained. I'urthlrmore, a corr*ction forthe tenmperature effect is includcd.
At present, to our knowledge, there are no satisfactory atmosphericmodels to compute spectral transmittance covering the spectral range from 0.5 mierom-eter to 15.0 micrometers for low-visibility, atmospheric environments characterized bythick haze, fog, dust, and smoke where the horizontal, visible range is rcduced from 4kilometers to 20 meters or so.
9. Scattering of Radiation by the Atmosphere. The attenuation of rudiation byscattering is caused by the spatial inhomogeneities in the refractive index of the mediumof propagation. In the terrestrial atmosphere, the maina scatterers are the aerosols (wa.ter droplets, dust, or smoke particles) and air-density fluctuations. The scattering dueto the fluctuutions in air density is caused by molecules of the atmospheric gases (mo-lecular scattering). If the wavelength of incident radiation is considerably smaller thanthe size of the scattering particles, the interaction is called Rayleigh scattering. Thescattering of ultraviolet and visible radiation by molecules and ultrahigh frequencyradio waves by cloud particles is Rayleigh scattering. When the wavelength of radiationis comparable to the dimensions of the scattering particles, the interaction is culled Mie"scattering. There are a number of excellent treatises on the theory of electromagneticscattering, "*"'ts The main features and terminology of the Rayleigh and Mie scatter-ing phenomena are outlined, and the procedures to compute scattering and attenuationcoefficients in each case are described in the fullowing paragraphs.
a. Rayleigh Scattering, The Rayleigh scattering coefficient oR (0) in a di-rection 0 with respect to the direction of incidence is given by: 139 140
1I1, C. Van de It iilst, Light Scattering by Small Pnrnicles, John Wiley, New York (1957).
i36ýh, Kcrker, editor, Ellectronmagnetic Scattering, The Mucmillan C)e., New York (1963), and TheScattering of Light and Other ElectronwgaMetir Radiation, Acadehmic Press, New York (19649),
I37. )eiruiidn, I lertrorngnetic Scattering (in Spherical Polydispersionm, 1,isevier, New York
(19169).1:8lR, Pe.|dtorf, "Angular Mie Scaltering,".J. Opt. Sac. ' tAi,, 52, 402 (1962).
"' OiK. Ya. Kondrutyev, Radiation in the,/l ttiosphere, Acade'mic Press, New ) ork (1969).
"14 0 It. 'endorl', lablo'.s of the RIefractitve' Index for Standard /lir nnd the Rlayleigh Scatterintg Coeffi.
eient for the Spectral Region between 0.2 and 20.0 Imt and Their AIpplication to/lmniosaphericOptien, A F( C-.'I' N. 55-206, p. 26, Air Forc- ( undiridgi! Isevarch ILanruralorit-s, Bedford, Massa--011ht is ts (1955).
Vt() ' (tn,2 2 (1 + COS, 6) 7() 2 N \~4(7
where nm is the refractive index, N is the number of scatterers per unit volume, and( X~ isthe wavelength of the incident radiation. Thle factor (I + cos2 0) is called the "Rayleighscattering function." It has maxi mum values for 0 0 and 0 =1800 (forward and backscattering) and minimum values for 0 = 900 and 0 =270". Equation (77) also showsthat the volume scattering coefficient is inversely proportional to the fourth power ofthe wavelength of the incident radiation. The integral of equation (77) over the scat-tering angle 0 gives the Rayleigh volume scattering coefficient all
0W301 - 1i~~~j ("3
This relation is strictly accurate only for transparent nonconductors. If there are ainyabsorbing conductors in the Scattering medium, the complex refractive index is givenby m =:n, - inj where n, is the real refractive index (same am m for a non-absorbingmedium) and n2 is thle absorbing intdcx. Ini the case of small absorbing particles, thleabsorption coefficient is not given by thve Rayleigh formula. Following Shifril, 141 11he
attenuation coefficient due to the absorption and scattering by a single particle is givenby
3~61ri, n3 V(m2 + 2)2 X (9
where a) is thev attenuation ceifficient and V is the voluv (incf the particle. Equal inn(79) Shows that the attenuation coefficient for an absorbing particle is inversely propor-tionul to the wavelength of the( incident radiation.
b. Nlie Scattering. Several treatises mntieroned earlier give a dletailvd Lit(-coiiiit of thie mathematical treatmieiit of the Nlic hltory whiech describes the tittemiua-tion of radiant tflux L~y aerosols whose size is comparable to thle wavelength of the invi-dent radiation. Particles of a Si'~e greate((r thtan 0.03I micromieter radius must be I reatedaccording to the exact-idiffractinn theory given by Nliv.
MIii' solved till! caisv ot it lilOliot I n iriat ii 1)1 ime wave Vi' cide oiltni a h on o.gene. 111, iso no pic mphere of rudli I s r su r round ed bi a tra nsprenrit hiomogetwu ae nsaid iso.tropic nmediurn. The incidenit wave induces foirced oscillat io'ns Of tree and bound chargvs
~'K. S, Shi rriii, Sewalur'n'ng tif Light in a Ii~rbid Weditini, C(istI'lirdat, NIItcow (1911), or NSTIechnical 'I'm iil titici , NASA '11 li- 77, Nut ioiiil Ae' now t iuiit wid Spav A dinstat i~miiii WaUNi.
112
in synchronism with the applied field resulting in a secondary electric and magneticfield-one outside and the other inside the sphere. The intensity of the scattered radia-tion at a large distance from the scattering aerosol particle at a scattering angle 0 is giveutby
S1=10 l ,(mx,x0) + t2 (m,x,O) l (80)
where w. = the refractive index of the particle
x = 21rr/),, dimensionless size parameter
r = radius of the spherical particle
0 = angle between the incident and the scattered radiationdirection (0 = 0 for the forward direction)
10 =: the intensity of the incident radiation.,
The intensity functions t, and t2 are proportional to the components of the electricfield perpendicular and parallel to the scattering plane. The Intensity functions arcgiven by the squares of amplitude functions S1 (0) and S2 (0) where
2 + I.%S 1 (0) (tll ( Tit; + 1.11 711),n(n+
S2 (0) (1)n) +L,, Tit,, t 71
where Sl( -7 I1 (com 0)
i (10 I (cos 0),
'rhe terms P2 are associated Legemlre Polynyitninals anid T,, and T1" are l'ouictioi)Im uf the,scattering angle 0. Figure :12 Hhowm the variatiou Ef r ao d T llr f or I t 1)1 6. ' The! co.efficients all and h.l i ein qation (t11) tire lHi('ceti-Ilcsmcl fillutliollm which c'lul heu wrillell
in terms of spherical Ilessel functiollt, and Lill atl b1 , are flllilonn Elf X nil in hbut areindepenident of Ithe satlterinig angle.
113
I
I1I
206 20
15 n 15 5
10 10 4
3 35-
-15-30 60 90
Fig. 32. wn and rn functon, of scattering angle for n = 1 to 6 used in NIlE theory (afterVan de Ilulst).
84
The scattering efficiency KS is defined as the ratio of the scattered fluxto the incident flux per unit cross-sectional area of the scattering particle. The efficien-cy factors ar. given by the expressions:
K, - (2n+ 1)lan1 2 + IbnP), (82)
K = - = (2n+ 1) Re(a. + bn), (83)n=1
Ka = K- Ks, (84)
where the subscripts a and s refer to absorption and scattering, respectively, and K isthe attenuation efficiency of the scattering particle.
If a unit volume of scatterers contains N particles of the same relative
size parameter x = 2w r/X, then the volume scattering coefficient is given by the relation
oaN K5 , (85)K.
For a polydisperse system of scatterers with a size distribution n(r), the scattering co-efficient is given by the integral
r2
a = 7 f/ KS n(r) r2 dr (86)
or, alt,!rnately, in terms of the size parameter x,Go
a82 J x2 n(x) K.(x) dx. (86a)0
Similarly, the attenuation coefficient a can be computed by using the appropriate valueof attenuation efficiency K in cquation (86),
r2
of Ir K n(r) r2 dr. (6i
has found.that -kiniospheric avrosols hawe 'wein studied by a nurnber of workers. Junge
has found thiat the size distribution of natural "contincntal" aerosols is given by therelation
I85-
N(r) = (c/2.3) r4( ) (86c)
where c is a constant and v varies between 2.5 and 4.0.142
Figure 33 shows the wavelength dependence of the attenuation and scat-tering coefficients for variou, aerosol models based upon Diermendjian's haze and cloudmodels.'" Figure 34 shows a similar set of attenuation coefficients computed byRensch.'" In Figure 33, the M, L, and 1I curves represent three hiaze models, and C1 ,C2 , and C3 are cloud models. Figure 34 contains attenuation coefficients for four at-mospheric models characterized by clear and light haze to light fog. For atmosphericmodels with low visibility, the attenuation coefficient is comparatively a very slowlyvarying (almost constant) function of wavelength in the visible and near infrared region,and it has a minimum value between 10 and 12 ptm in the far infrared region. On theother hand, for atmospheric models which correspond to comparatively better visibility,there is a rapid decrease in attenuation with increase in wavelength; and there awe sharpmaxima of attenuation coefficients near 2.7 /m and 6.3 pm which correspond to thecenters of the strong water vapor absorption bands. If one compares these calculatedspectra with the measured haze and fog spectra given in Figs. 17a to e and Fig. 23,based upon the work of Arnuilf et al. and Filippov et al., one notices that in the mea-sured spectra there are no auch peaks shown at 2.7 pm and 6.3 pm. This ie due to thedeliberate exclusion of the water vapor absorption bands by the experimenters.
The normalized intensity or phase function P(,,m,0), introduced by"Chan4.asekhar,'14 is defined as
P(,m,O) V/2 [ P1 (0)+ P2 (0)M =l ,() (O) (87)x2 K5(x)
The phase function represents the ratio of the radiant energy scattered per unit solidangle in a given direction to the average radiant energy scattered per unit solid angle inall directions.
14 2 C. E. Junge, Air Ch- nistry and Radioactivity, p. 118, Academnic Press, New York and London(1963).
143D. Deirmendjian, Electromaneptic cattering on Spherical Polydispersiona, Hulmvier, New York
(1969).
1441). B. Rensch, Extinction and ,jackscatter of Visible and Infrared Laser Radiation by At mosphericAerosols. Repost 2467-3, The Ohio State University (1969).
145S. Chandrasekhar, Radative Transfer, larendon Press, (Witord (1950), also Dover Publications,New York (1960).
86
aa
C. O
CD
--
1004 1
WAVELENGTH jm
Fig. 33. Spectral attenuation and scattering cotfficients for various haze (1, NM. 11) andI cloud (C, ,C 2 , CO) models (adapted from lDeirmendjian).
I 87
mc
U7 -
~LaiAn II I II IC.F
C4 m CD cm ini~i a a n
09 C.3
i N3131JO33NoiivflN3iiV
IIU)oo
W- CJFa
ac~
floss~~.~ I--1 LA;A
- i'd
(Iw1 8811J33ovn~i
For a polydi;perse system of scatterers with size distribution n(x), thephase function is given by
00S_ 4w, 7
3( -0 n(x) ti(o) dx (88)
where u is the scattering coefficient and k = 2w/, is the propagation constant. 46 IThe normalized phase function for backscattering (0 = 180") is given by
r2p ( ,, ,1 0 o _ 4 w fP(-m-18 -) =4-J I S(?,m, 180") 12 n(r) dr (88.)
ri
where S(X,m,180o) is the backseatter amplitude function for a single particle. An exactcalculation of S(180*) is made by the Mie method; but, for particles for which the sizeparameter is large, the computaticis become rather lengthy. Some approximate meth-ods have been used to determine this function. Rensch and Long have calculated valuesof attenuation and backscattering coefficients for various theoretical models of haze,fog, and rain aerosols for the wavelength range from 0.34 pm to 10.6 pAm.1 47
The backscattered radiant energy in watts QR (X,180*) is given by theequation
QR (",l80o) = E? A l, w T, T2 [P(,,180*)/4w] a (89
where E), is the radiant incidance (irradiance) (W-cm"2) on the scattering volume havingan area A (cm 2) perpendicular to the optical path of length L (cm) of the scatteringvolume, T, is the atmospheric transmittance between the radiator and the scatteringvolume, T2 is the transmittance between the scattering volume and the detector, Wo isthe solid angle subtended by the optical system of the receiver (sr), a is the atmosphericvolume scattering coefficient (cm'), and P( 1808) is the backscattcring phase function.Diermendjian has tabulated values of the normatizcd phase function for various modelsof haze and cloud acroso•s of various compositions.' 48
1461). I)cirmendjian, Electrornagnetic Srattering nn Spherical Poaydispersions, EIser, N,,% York
(1969).
147D. B. Rensch, Extinction and Ilwks•alter of Visible and Infrared Laser Radiation by A tmiospheric
Aerosols, Report 2467-3, The thibi State Uniivrsity (1969).1481). Deirmendjian, Loc. cil.
89
The atmospheric aerosols have a real refractive index if they are com-pletely transparent. However, the natural aerosols have a complex refractive index(they have some absorption). The behavior of the variation ot attenuation efficiencyis a very sensitive function of the size parameter and the absorption index of aerosols.Figure 35 shows the variation of the attenuation effitiency K as a function of the sizeparameter x for various values of refractive indices. For a large value of the size param-eter x, the attenuatio, efficiency factor K approaches the value 2. Small changes inthe absorption index have quite large effects on the attenation efficiency of the parti-de. Deirmendjian has tabulated values of complex refractive indices for the commonconstituents of atmospheric aerosols such as water droplets (at various temperatures),ice, silicate, limonite, and iron.149 The Mie theory has been extended to nonsphericalparticles also.tso
The natural dust aerosols contain mostly clay rmiinerals of aluminum sili-cates, silica, metallic oxides, and calcium carbonate. The. dust particles range in diame-ter from 0.1 to 100 pm, but the most probable sizes are between 0.1 pm to 1.0 pm.The dust particles have quite significant absorption in the infrared region particularlyaround 9.6 micrometers.' There are, of coursc, innumerable other types of aerosolsin the atmosphere. These aerosols can be organic, inorganic, or biological; and theirsources of origin include the sea, forest fires, volcanic eruptions, industrial emissions,meteoric dust, and debris from thermonuclear explosions in the atmospheric or spaceenvironment. Mie scattering ly atmospheric aerosols mubt account for their complexrefractive index and nonspherikl shape.
e. Atmospheric Turbulence. Atmospheric turbulence causes further scat-tering of electromagnetic radiation in addition to that caused by the atmospheric gase-ous molecules and ucerosols. This scattering is caused by the large-scale (compared tomolecular dimensio,:.) inhomogeneities in the refractive index of the medium of prop-gation in the optical path. The effect of turbulence on the degradation of imagery hasbeen studied by Smith, Saunders, and Vatsia during the daytime for horizontal, ground-level, outdoor conditions. 5 2 Figure 36 shows the degradation of photographic resolu-tion as a function of horizontal range for various values of exposure time. There is a
149D. Deirmendjian, Fiectromagnetie Scattering on Spherical Polydispersions, Elsevier, New York(1969).
I5ON. Kerker, editor, Eleetromagnetic Scattering, The Macmillan Co., New York (1963), and The
Scattering of Light and Other Electromagnetic Radiation, Ac'ademic Pres, New York (1969).151 I). F. Flaigan and II. P. DIeLong, "Stw,,tral Alsorption (haracteristitu of the Major (Compon,.nts
ofDust louds,"AppI. Opt. 10, 51(1971).15 2 A. G. Smith, NI. J. Sounder. and M. 1L. VAtia, "Soee, Effects of i'urlruleence on Mhotographic
Resolution,"J. Opt. Soc. Amer. ,17, 755 (1957).
90
.................
a as
c;c
ai
apIi-,.c
44 4
I * .i - 44 ('*4
C~
SaJ
Ingo U w 9 4c
v AMM I NOIVONGu
910
C4#
See
cm
m co
CDD
Sw.
1Cm
inmCD C*4.j.
.C .
CDu ~1 NIf1S~
II
great deal of interest in the measurement of the intensity of turbulence and its temporaland spatial variatiois for various types of terrain and surfaces under various atmosphericoptical environments.t s3""s' The variation of image degradation as a function of the in-tensity of turbulence needs to be further investigated in order to determine the quanti-tative effects of atmospheric turbulence on the performance of electro-optical devicesunder various types of atmospheric optical environments.
d. Multiple Scattenng. Numerous investigators have developed a numberof computational methods which have been used with limited success for multiple-scattering calculations. Some of these methods compute both intensity and polariza-tion of scattered radiation.
The Monte Carlo method, first used by Collins and Wells for the studyof atmospheric scattering,' 5' has been used most prolifically by Plass and Kattawar." 0
This method is versatile and provides a tractable approach to a number of problems in-eluding anisotropy and inhomogeneities in the density and refractive index in the hori-zontal or vertical directions in the atmosphere. Blattner, Collins, and Wells have ex-tended the applications of the Monte Carlo method to calculations in spherical-shell
153R. S. Lawrence and J. W. Strohbehn, "A Survey of Clear-Air Propagation Effects Relevant toOptical Communications," Proc. 'EEE, 58, 1523 (1970).
154R. G. Buser, "Interferometric Determination of the Distance Dependence of the Phase StructureFunction for Near-Ground Horizontal Propagation at 6328 A,"Jour. Opt. Soc. Am. 61, 488(1971).
15R. G. Buser and G. K. Born, "Determination of Atmospherically Induced Phase Fluctuations byLong-Distance Interferometry at 6328 A," Jour. Opt. Soc. Am. 60, 1079 (1970).
1 54p, M. Livingston, P. II. Delft, and E. C. Alcarsz, Light Propagation through a Turbulent Atmo-sphere: Measurement of the Optical Filter Function, BRL Memo, Report 2018, Ballistic ResearchLaboratory, Aberdeen Proving Ground, Md. 21005 (1969), and J.O.S.A. 60, 925 (1970).
1 57 E. C. Alcaraz and P. M. Livingston, Measurement of the Beam Wander Phenomenon in a Turbulent-Medium, BRL Technical Report, Ballistic Rerearch Laboratory, Aberdeen Proving Ground, Md.21005 (1970).
158M. L. Wesely and E. C. Alcaraz, Diurnal Cycles of the Refractive Index Structure Functio' Coeffi.cient, Ballistic Research Laboratory, Aberdeen Proving Ground, Md. 21005 (1972).
159D. G. Collins and M. B. Wells, Monte Carlo Codesfor the Study of Light Transport in the Armas-phere, Vol. I and HI, Radiation Research Associates, Inc., Fort Worth, Texas (1965).
16 0G. N. Pils and G. W. Kattawar, "Monte Carlo Calculations of Light Scattering from Clouds,"Appl. Opt. 7, 415 (1968).
93
atmospheric problems.161 The main disadvantage of this method is that to achieve ahigh accuracy the computational time becomes very large.
Dave has recently used the Gauss-Seidel iteration scheme for the solu-tion of the equation of radiative transfer to calculate multiple scattering for Rayleighand Mie atmospheres with good accuracy. 2 163 This method involves the expansionof the phase function into a series of Legendre polynomials. It has been applied sue.ceasfully to study plane-parallel, horizontally homogeneous atmospheres. The latestform of this method reported by Dave and Gazdag is the "modified Fourier transform"method for multiple-scattering calculations." 6
Hansen has used the "doubling method" to compute multiple scattering
of polarized light reflected by terrestrial water clouds at 1.2, 2.25, 3.1, and 3.4 microm-
eters. 16 166 His study shows that polarization characteristics are more sensitive thanthe intensity characteristics to aerosol size, shape, and number distributions. Other in-vestigators who have contributed substantially to the study of atmospheric scattering V
include Chandrasekhar,"s' Sekera, Coldson et al.," Mullikan, Querfeld," 9 Twomey,
161W. G. Blattner, D. C. Collins, and N1. B. Wells, Monte Cado Calculations in Spherical Shell Atmo-
spheres, R RA-T7104, Radiation Research Associates, Fort Worth, Texas (197 1).
1620. V. Dave, "Coefficients of the Legendre and Fourier Series for the Scattering Functions of Spheri-
cal Particles," Appl. Opt. 9, 1888 (1970).
163j. V. Dave, "Intensity and Polarization of the Radiation Emerging from a Plane-Parallel AtmosphereContaining Monodisperse Aerosols," Appl. Opt. 9, 2673 (1970).
164J. V. Dave and J. Gazdag, "A Modified Fourier Transform Method for Multiple Scattering Calcula-
tions in a Plane Parallel Mie Atmosphere," Appl. Opt. 9, 1457 (1970).
165j. E. flansen, "Niultiple Scattering of Polarized Light in Planetary Atmospheres. Part I. The
Doubling Method,"J. Atmos. Sci. 28, 120 (1971), and "Part II. Sunlight Reflected by TerrestrialWater Uouds,"J. Almos. Sci. 28, 1400 (1971).
166W. C. Blittner, D. G. Collins, and NM. B. Wells, Loc. cit.
1679. Chandrasekhar, Radiative Tranrdjr, (,arendon Press, Oxford (1950), also l)over Publications,
New York (1960).
168K. L. Coulson, J. V. Dave, and Z. Seliera, Tables Related to Radiation Emerging from a PlanetaryAtmosphere with Rayleigh Scattering, TUniversity of California Press, Berkeley and Los Angeles,'California (1960).
169C. W. Querfeld, Multiple Scattering in a Synthetic Foggy Atmosphere, Ph.D. Dissertation, Clarkson
College of Technology (1969) University Microfilms 70-20,0004, Anp Arbor, Michigan (1970).
94
Jacobowitz, and Howell. Rullrich and de Bary. Herman, Browning, and Curran"O wholist all the relevant references, present a good introduction to the problems associatedwith this important and most complicated experimental and theoretical problem in at-mospheric physics.
Thee is a need for more observational data on the variation of aerosolswith height and the variations in their size distribution and index of refraction. Volz hasrecently published infrared absorption properties of atmospheric aerosol substances. '"Solution of the problem of multiple scattering is far from satisfactory at the presenttime.
10. Tables of Attenuation Coefficients. Some investigators have calculated at-tenuation parameters, based upon various models of atmospheric optical environments,over a wide range of wavelengths from ultraviolet to far infrared. McClatchey et al.have computed values of attenuation coefficients at 12 laser wavelengths, namely0.3371, 0.4880, 0.5145, 0.6328, 0.6943, 0.86, 1.06, 1.536, 3.392, 10.591, 27.9, and337 micrometers, for 10 model atmospheres for altitudes ranging from 0 to 100 kilom-eters above sea level.172 Elterman has computed attenuation parameters at 20 wave-lengths from 0.27 micrometer to 2.17 micrometers for 8 surface meteorological rangesfor altitudes from 0 to 50 kilometers. 1 3 Deirmendjian has calculated attenuation co.efficients for two haze models and three cloud models.174 One should remember thatall the calculations mentioned above are based upon well-chosen, representative, atmo-spheric optical environmental parameters. In real, outdoor, atmospheric environments,there can be wide variations in atmoopheric optical conditions. Tables X through XIIIcontain attenuation coefficients in the spectral range of 0.4 to 14 pm for calculatinghorizontal, ground-level atmospheric transmittance for various types of haze and fogconditions as specified by the visual range (at 0.55 pim). Similar data for other visible
17 0 B. M. Herman, S. R. Browning, and R. J. Curran, "The Effect of Atmospheric Aerosols on Scat-tered Surdight,"J. Atmos. Sci. 28, 419 (1971).
17 1 F. E. Volz, "Infrared Absorption by Atmospheric Aerosol Substances,"J. Geophys. Res. 77,1017(1972), and "Infrared Refractive Index of Atmospheric Aerosol Substances, "Appl. Opt. II, 755(1972).
17 2 R. A. McClatchey, R. W. Fenn, J. E. A. Selby, F. W. Volz, and J. S. Garing, Optical Properties of
the Atmosphere (Revised), AFCRL-7140279, Environ. Res. Paper No. 354, Air Force CambridgeResearch Laboratories, Bedford, Massachusetts (197 1).
173 L. Elterman, Vertical Attenuation Model with Eight Surface Meteorological IRuge, s 2 to 13 Kilom-
eters, AFCRL.70-0200, Environ. Res. Paper No. 318. U. S. Air Force Cambridge IRtogearch Labors.tories, Bedford, Massachusetts (1970).
174 D. Deirmendjiun, Electromagnetic Scattering on Spherical Polydisperuions, Elsevier, New York (1969).
95
Tabie X. Attenuation Coefficients for Haze for Various Values ofHorizontal Visible Ranges (AdApted from Elterman)
VISIBILITY(A VISIBILITY 2 km 6 km 10 km 23 km
SATTEN.I COEFF.--
/TRANSM.k/Nm- a T a T a T a T
0.40 2.66 0.07 0.904 0.405 0.553 0.5)5 0.243 0.78
0.45 2.34 0.10 0.788 0.455 0.478 0.620 0.206 0.82
0.50 2.13 0.12 0.713 0.490 0.429 0.651 0.184 0.83
0.55 1.95 0.14 0.652 0.521 0.391 0.676 0.170 0.64
0.60 1.74 0.17 0.578 0.561 0.346 0.707 0.159 0.85
0.65 1.57 0.21 0.523 0.593 0.312 0.732 0.148 0.66
0.70 1.47 0.23 0.488 0.614 0.291 0.747 0.139 0.86
0.80 1.29 0.27 0.427 0.652 0.254 0.776 0.130 0.88
0.90 1.17 0.31 0.386 0.680 0.229 0.795 0.122 0.88
1.06 1.05 0.35 0.345 0.708 0.205 0.815 0.114 0.89
1.26 0.946 0.39 0.312 0.732 0.185 0.831 0.108 0.90
96
Table XI. Spectral Attenuation Cmofficientit forFog for Visibiitits orf 0.100 and 0.755 km
tAdapted from Arnulf ef a/.)
VISIBILITY 0.1 km 0.755 km
WAVELENGTH [ km"1 T[ km-I a I kM- 1 ) TI km 1
Pal~~
II 01
0.35 42.568 , 10- 4.89 0.0075
0.45 40.608 " 5.04 0.0065
0.55 39.690 " 5.18 0.0056
0.75 39.386 " 7.20 0.00075
1.24 39.386 " 6.06 0.00032
1.70 39.386 7.20 0.00075
3.70 39.386 8.35 0.000236
10.00 20.607 10-9 3.45 0.0317
Table XII. Spectral Attenuation by llaze and Light Fog-,_ _ _ _Visibility ft I!km
(Adapted from Chu and [log)
WAVELENGTH ATTENUATION COEFFICIENT TRANSMITTANCE
-pm) k kn-1J T I km-1
0.63 3.09998 0.04505
3.5 1.5046 0.2221
10.59 0.3544 0.7016
974
A
4
Table XIII. Spectral Attenuation Coefficients for Coastal or Marine Hazewith Horizontal Surface Visibility of 2 Kilometers
(Adapted from Deirmendjian)
WAVELENGTH ATTENUATION COEFF. TRANSMITTANCE
(Jm) ca 1km--1 T (km-l)
0.45 1.956 0.141
0.70 1.954 0.142
1.19 1.634 0.195
2.25 0.785 0.456
3.00 1.099 0.333
3.50 0.963 0.382
3.90 0.436 0.647
5.30 0.208 0.812
6.03 0.351 0.704
0,15 0.116 0.890
10.00 0.083 0.920
11.50 0.180 0.835
13.00 0.222 0.801
14.00 0.232 0.793
__________________________________ _________________________________________________ _____________________________________?
I I I I I i i8
ranges may be generated from the spectral transmittance or attenuation curves of Figs.16 through 26 for the conditions under which tih' measurements preseented in thesefigures were made. Interpolation between measured wavelength points should bu. madewith care. The absorption bands of water vapor iand carbon dioxide should be kept inmind (see Fig. 15).
Computer programs to calculate atmospheric transmittance in the 0.3 pm to15 am spectral region for various model atmospheres for horizontal and slant opticalpaths have been developed by various workers. 75
111. CONTRAST TRANSFER BY THE ATMOSPHERE
The apparent difference botween the radiant sterance (radiance) of an object andits surroundings enables an observer to detect the object in his field of view. The char-acteristic variations in the radiant sterance of the object provide cues for the recognitionor identification of the object. The apparent difference in sterance is a measure of thecontrast between the object and its surroundings. Although the concept of contrast iseasy to grasp, it is rather difficult to agree upon a standard, internationally recognizeddefinition of this term. Furthermore, the measurement of contrast is one of the mostcomplex and difficult problems in the multidisciplinary field of visionics involving vi-son, psychology, atmospheric optics, and electro-optical technology. Some important -contributions on this subject are reported in the literature.176"5
11. Definitions of Contrast. Let us consider an isolated object or target surround.ed by a uniform and fairly extensive background. The contrast between the target and
175R. A. NlcCatchey, R. W. Fenn, j. E. A. Selby, F. W. Volz, and J. S. Garing, Optical Poperties ofthe 4tmospheric(Reaiised), AFCRL-71.0279, Environ. Rca. Paper No. 354, Air Force CambridgeResearch Laboratories, Bedford, Mlassachusetts (1971).
17%•.. E. K. Nliddleton, [Vision Through the Atmosphere, University of Toronto Press (1952).
177S. Q. Duntley, R. W. Johnson, J. I. Gordon, and A. R. Boileau, Airborne Measurements of Optical
Atmoapherie Properties ta Night, AFCRL-70.0137, SIO Ref. 70.7, Scripps Institute of Oreanngra. 4
phy, Visibility Laboratory, University of California, San Diego, Calif. (1970).1781. M. Biberman and S. Nudelman, Editors, Photoelectronic Imaging IDvices, Vol. 1, Plenum Pres,
New York (1971).
17 9 F. E. Nicodemus, Radiometric Nomenclature, bichelson Laboratory, Naval Weaponm Center, ChinaLake, California (1971).
18 0 F. F. Nicodemus, Applied Optics and Optiral Engineering, Volume IV, Editor R. Kingslake, Asa.demic Press, New York (1967).
99
the background may be expressed in a number of ways, for example,
LT(C L - , (LO0)IB
=a -T I.11T' , (91)
=• LT + i- (92)
•.LT+L
and C4= L (92a)
where C is contrast, L represents the radiant steraner (va.riously called radiance, lumin-ance, or brightness), and superscripts T and B indicate target (object) and background,respectively. C, is sometimes called "Weber's fraction" by psychologists. CS is nowcalled "modulation," though earlier it was named "visibility" by Michelson in connec-tion with interferometric fringes. As the relative sterance o! the object (target) becomeslarger or smaller with respect to that of the background, C, varies from -1 to +-, C2varies from +1 to -o, and C3 viaries from 0 to 1; C, and C2 change sign, but C3 and C4do not change sign.
Fur an electro-optical system such as a TV.type monitor display where therearc gain (contrast) and reference radiation level (brightness) controls, the significantquantity in the electro-optical image is the minimum-detectable. luminous-sterance(brightness) difference,
AL = I _- [R I. (93)
For infrared imaging systems, the minimum-detectable radiant sterance (radiance) isgenerally given as the minimum-detectable, sterance temperature difference,
AT = JT - TB 1, (94)L L
where TL is sterance temperature.
12. The Alteration of Contrast by the Atmosphere. The apparent contrast of adistant object is mnodified by two 'actors: (I) the atmospheric attenuation causes a
100
reduction in the amount of radiation propagating from the distant target object to theobserver; and (2) the molecules and aerosols contained in the optical path contributeto the observed radiation by scattering and emission. The net radiation due to thesecond factor produces the so-called "optical path slerance (radiance)."
The apparent contrast of a target object, located at a distance R from the ob-server, according to equation (90), is given by
It = ! (95)' LBR
and the inherent contrast (at distance approaching zero) is given by
LT- LBL 0 0 (96)
0L
The ratio of the apparent contrast to the inherent contrast, called the "atmosphericcontrast transferance," Te (variously called atmospheric contrast transmittance or atmo-aspheric contrast transfer function) is given by
T, -(97)C
o
Let Ti and LP1 denote, respectively, the atmospheric transmittance and radiant sterance(radiance) of the optical path of length R between the obsterver and the target. Thus.the apparent sterance of the target LT and that of the background LI will be given by
11T = LT TR + L(9,,
LD = 1.8• TH + L.P,,,
Combining equations (95), (96). and (97), we get
-_ (LT -L)L(0, l~� _L o) Lt
Substituting the values or LT1 and !1. from equations (9i8) and (99) into equat ion (100)gives
101
S(LT - LB Tn ) LB
(LoT + e L0-Ls)(1,B TR + L0
or
T~ ~ LM'rUTC TR Lo a = " (101)T,, LOB + LP LS
T. Transmitted Background Sterance (Iola)Apparent Background Sterance
Division of the middle terms in equation (101) by TR LO gives
Te T [ LO~B.1 (102)TH LoB j
i.e., To r+ Optical Path Sterance ("
=1 L Transmitted Background Sterance I
If the contrast definitions expressed by equations (91) and (92) are used inequation (97) and the values from equations (98) and (99) are again substituted, theexpresions for T and T. are giveii by
T1! = I TiR T (103)
T = + Optical Path Steranee 1 (103a)2 L Transmitted Target Sterance
al T= [I + R, l + ) (104)
+2 (Optical Path Stc-ratice)
r Tran:wmitted Sterairwc of (104a)Target and hackgroiamd
A comparison of the three defining equations of contrast and the e(orre,-ponding equations for contrast transferance reveals that the divisor in the defining
102
equation of contrast and that in the second term in the corresponding expression forcontrast transferance is the same.
The important conclusion here is that the atmospheric contrast tranisferanceis a function of: (a) the radiant sterance (radiance) of the optical path, (b) the atmo-spheric transmittance, and (c) the inherent radiant sterance of thebackground and/orthe target. The atmospheric contrast transferance is thus dependent upon the complexnature of the optical blate of the optical path. The atmospheric phenomena of scatter-ing, absorption, emission, and turbulence all play important roles in the transfer of con-trast by the atmosphere. Thus, a knowledge of the composition of atmospheric gases,the physical characteristics of atmospheric aerosols, and the ambient radiant incidanceis essential for a complete description of an atmospheric optical environment.
Equations (101) and (102) are the most general expressions for the law ofcontrast transfer by the atmosphere. The value of atmospheric contrast transferancedecreases with increasing values of optical path sterance as expected. The use of gatedviewing techniques at nighttime minimizes the optical path sterance and thus enhancesthe apparent contrast.
The contrast transferance of the atmosphere is a wavelength-dependcnt par-ameter; it increases with increase in wavelength as does atmospheric transmittance,except in atmospheric absorption bands.
13. Optical Measurements for Derivation of Atmospheric Contrast Transferance.Using the Monte Carlo method, Wells et al. have made theoretical computations of at-mospheric contrast transferance (transmittance) for two model atmospheres havingground-level, horizontal, visible ranges of 23 km (clear) and 3 km (hazy)."'I Figure 37based upon Wells' study indicates that for various values of the nadir angle ( 1800 minusthe zenith angle) the contrast transferance can decrease by a large factor if a target isviewed through a long optical path. especially under reduced visibility conditions. Thisstudy indicated the necessity for field measurements. Under an Air Force CambridgeResearch Laboratories' program directed by R. W. Fenn and supported by VisihilityLaboratory, Duntley, .Iohnson, Gordon, and iBoileau have conducted extensive airborneand ground-level measurements of the properties of the atmosphere at night.'82 The,
181 M. B. Wells, 1. C. Collins, and F. A. Hlooper, Contrast Transmission Data for (1ar and Iltax Modal
Atmospheres," Report :,\FCRL-f40660, 1, 11, 111, Radiation Research Associates, Furt %orth,TAa, (1968).
1823. Q. )untl,'y, R. W.Johnsin., J. I. Gordon, and A. I. Iloihrau, Airborne Mtasurements of Optical
Armospherie Properties at Night, AKI(L-70.0137, SI() ltf. 70-7, Scripps Institut.e of (Ocesnogra-phy, Visiuility laboraton, tnievvrsit,, of California, San I)iego, Calif. (19740).
103! ii4%
1. 004000 8000
S100 25 k so
il25km--8
. RECEIVER10" 3km GROUND VISIBIL11 0 NADIR
"10, 3km
NOMAL T NCITDENT. ~0.55 WAVELENGTH LIGHT-
1004
-3km GROUND VISIBILITY
I0•0 1 2 3 4 5 6
ALTITUDE JkM)
Fi.3.Variation of atmospheric contrast transference (transmittance) with observer
Flig.d 37. variousk look (11dir) angles for two model atmospheres (adapted from Wells
et al.)
have made measurements of optical parameters necessary to compute optical path radi-ant sterance (radiance). The airhorne measurements of atmospheric optical parametersincluded: (I) upwelling and downwelling (terrain and sky) radiant sterance (radiance)each over a 21r steradian field of view, (2) directional and total scattering coefficients,(3) upwelling and downwelling radiant incidance (irradiance), (4? number and size dis-tribution of aerosols, and (5) usual meteorological parameters such as dew point andambient air temperature, pressure, relative humidity, altitude, and air speed. Theground-based measurement systems were similar to those used for airborne observations.Special care was taken to make terrain directional reflectance and ground.lcvel radiantincidance and sky radiant sterance measurements. The aerosol counters were operatedon a 24-hour duty cycle at a few times.
"The atmospheric contrast transfcrance (transmittance) was computed usingthe alternate relation
T I+ (Pf/Po)l (105)
"where poB is the directional inherent background reflectance and pp is the "directionalpath reflectance" defined as
P r L/ET , (106)
where LP is the optical path sterance, E is the downwelling incidance, and Tit is theatmospheric transmittance. All the quantities in this work have wavelength, altitude,and directional dependence.
The beam transmittance was computed from scattering measurements of thenephelometer.
The optical path sterance L was computed using the relation
nl,= 14 T!• AR (107)
R I t t
where LP is the Duntley "optical path sterance function" defined 5y the relation
14't at (108)
where Iqt is the "equilibrium steran'e" and oa is the total scattering coefficient at an
altitude level t.
1054 4di
The equilibrium sterance Lq is computed using the relation
Lq =f L [-]dS, (109)47
where L i6 the apparent sterance of the sky or ground in a particular direction, op is thedirectional scattering coefficient, and [ulot I is called the "proportional directionalscattering coefficient" along the scattering direction -..
Thus the calculations are made in the following order: (1) equilibrium ster.ance, (2) Duntley's optical path sterance function, (3) optical path sterance, (4) direc-tional path reflectance, and (5) atmospheric contrast transferance (transmittance).Figure 38 shows the variation of contrast transferance with altitude for two types ofbackgrounds observed in a vertical, downward direction using the detector with an S-20spectral response. The contrast transferance is higher for the background with higherreflectance.
Direct nighttime field measurements of ground-level, horizontal-optical.pathsterance require the use of a sensitive, large-aperture teleradiometer aimed at a largeradiation trap.
Schie has made nighttime measurements of the distance at which the atmo-spheric contrast tranferance is 0.5 using a teleradiometer with S-20 response.' 83 A two.dimensional histogram, expressing the level of luminous incidance and the percentage of
occurrence when a certain distance for which 0.5 of the inherent contrast is obtained,has been presented. This study indicates that the moat probable range of about 300meters for Te = 0.5 occurs for luminous incidance of 10"' lux.
14. The Effect of Contrast on the Performance of Viewing Systems. The per.formance of a viewing device is proportional to the square of the apparent contrast ofan object according to the well-known Rose equation
L C2 aC = Constant (110)
where L is the luminous sterance (luminance) of the scene, C is the apparent contrast ofthe object, and a is the angular size of the object.'64
183J. van Schie, Nocturnal Illumination and Decrewe of Contrast in the Atmosphere, Report Ph. L.
1969-4, Physics Ltboratory TNO, National Defence Research Organization, The Hague, Nether.lands (1969).
184A. Rose, "The Sensitivity Performance of the Human Eye on an Absolute Scale," J. Opt. Soc. Am.
38, 196 (1948).
106
Lij ca J
CD ,
44~
'-
C4)
U)107
From equation (110), it is clear that an accurate determination of the appar.ent contrast or the atmospheric contrast transferance (see equation (97)) is essential forthe determination of the performance of visual or imaging systems which have to beused in the natural outdoor atmospheric optical environments.
A nighttime-contrast-measuring system using a 3-stage image intensifier anda teleradiometric system has been designed by Vatsia and used for nighttime, outdoor,contrast studies.'a8 These studies confirm that there can be quite a considerable degra-dation of apparent contrast by thick haze and fog.
15. Meteorological Visibility of Objects Seen Against the Sky Background. Themeteorological visibility is defined as the farthest distance at which a black object, sub-tending an angle between 0.5* and 7.00 at the observer's eye, can be recognized withunaided eye sgainst the horizon sky (or, in the case of night observation, could be recog-nized if the general illumination were raised to the daylight level). .
The meteorological vinibility, when objectively measured, equals the opticalpath which will have a transmittance of 0.05 for a collimated beam from an incandcs.cent lamp operating at a color temperature of 27000 K when measured with a photopic(luminous) flux meter.
.•S.
If one uses the criterion of detection of the object (rather than recognition),the transmittance of 0.02 is used for the carresponding meteorological, optical range.
The atmospheric-contrast transferance is given by the general expression
c RI - L2 TR (101)CO LB
In the special case, when the background is the horizon sky, the ratio L j is unityfor all values of the optical range. Equation (101), therefore, reduces to the simple form:
TR = TC (Ill)
That is, when objects are seen against the horizon sky, the atmospheric-contrast trans-ferance equals the atmospheric transmittance. Writing the value of T. in terms of the
185j. M. Moulton, (. P. Intano, W. E. Stump, 1). 11. Newman, It. 1). tlipi, and I). I)unlap, ., SearchPerformance Test on Ground Ilased Thernml Imaging and Pudse Gated Intensifier Night VisionSystems, Preiminary Report, Visionicz, Technical An-a, Night Vision Iaaborator, Fort tIelvoir,Virginia (1972).
108
attenuation coefficient a, we get
ex=Tc (112)
where c& is the attenuation coefficient and R is the optical path length. On taking thenatural logarithm, equation (112) takes the form:
-a&R n[TCeI
or
R " n [IN/TCl. (113)
This equation implies that for objects seen against the sky background the optical range,or visibility, equals the natural logarithm of the reciprocal of the atmospheric-contrasttransferance or "threshold contrast" divided by the attenuation coefficient of the me-dium in the optical path. If TC = 0.02, the optical range it variously called the meteoro.logical optical, visual range, or visibility V.02 , and we obtain
1V.02 n • n1/0.021,
V.02 3.912/at. (I 13a)
Similarly, if one uses the value 0.05 for the threshold contrast, or TC, the meteorologi.cal optical range is given by the expression
V.0 6 Qn (1/0.051
or
V.0= 2.9957/a w 3/a. (I 13b)
When the optical medium has no absorbing gases or aerosols, the absorption coefficientis zero, and the attenuation coefficient of the medium is equal to the scattering coeffi.cient a. Therefore, one can replace ca in equation (11.3) by a. Thus, for a transparentmedium the meteorological optiid range, or visibility, is given by the expressions
V.02 = 3.912/u, (I 14a)
109
or
V.Qs a •/ . (1141))
depending upon whether one choow: the value 0.02 or 0.05 for the thrnhuld contrast.
110