refractive index of air and precision length...

$: Refractive Index of Air and Precision Length Measurementshumboldtcanada.com/presentations_air/jennifer.pdf · © Government of Canada, 2011 Refractive Index of Air and Precision Length$
© Government of Canada, 2011

Refractive Index of Air and Precision Length Measurements

Jennifer E. Decker

Science, Technology & Innovation DivisionForeign Affairs & International Trade Canada13 May 2011 Vancouver


Introduction

• Historical overview of International System of Units (SI) definition of the metre

• Interferometric length measurement / calibration

• Impact of refractive index of air on accurate length measurement– What is the magnitude of the correction?– How is the correction applied?– Recent Developments


Brief History of the metre

1872 prototype Kilogramme des Archives and Mètre des Archives (c.1799)

1875 Convention of the Metre signed

1887 Michelson proposed using optical interferometers for length measurement; received 1907 Nobel Prize for physics

1892 Michelson interferometer at BIPM (Michelson & Benoît) measured the metre in terms of red line of cadmium; confirmed in 1906 by Benoît, Fabry & Perot

1960 Definition of the metre in terms of wavelength in vacuum of specific radiation from krypton 86

1975 CGPM recommended value for speed of light in vacuum based on wavelength and frequency of laser radiation

1983 Definition of the metre as length of path travelled by light in vacuum during a specific fraction of a second


SI Definition of the metre (m)

• Consultative Committee for Length (CCL) formed in 1952– Provides recommendations for practical realization of the metre

(Mise en Pratique)– Provides wavelengths, frequencies and associated uncertainties of

recommended laser radiations, spectral lamps

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.

http://www.bipm.org/en/si/base_units/


Definition Gauge Block Length

• “. . . the perpendicular distance between point of the measuring face and the plane surface of an auxiliary plate of the same material and surface texture upon which the other measuring face has been wrung …includes the effect of one face wringing.” ISO 3650(E)

• lengths of gauge blocks directly compared with internationally-recommended wavelength standards

• traceability established via comparison measurements


Accuracy (Uncertainty)

c

10-14 Time Frequency standards

10-12 Laser frequency stabilized on molecular transition (Mise en Pratique)

10-9 Polarization-stabilized lasers (distance measuring)

10-8 Equation for Air Refractive Index of Air

10-6 Gauge Block length• 25 mm ± 20 nm• 1 m ± 70 nm

10-6 Frequency of a free-running laser

m/s458792299c

air n


Optical Interferometry

• Main influences:– air temperature, pressure and

humidity on the wavelength of light refractive index, n

– gauge block temperature deviation from 20ºC

– optical phase change on reflection of light from surface

– wringing– design parameters of the optical

instrument (obliquity correction)

lengthGauge Block

Optical Flat


Refractive Index


Twyman-Green Interferometer

Schödel PTB-Mitteilungen 120 (2010), Heft 1


Method of Exact Fractions

• ‘Fringe fraction’ fi observed with wavelength i for several laser sources, each in turn

• Length evaluation by finding the best match for integer interference orders to satisfy:

l fi ii ( )

2


Wavelength Measured/nm fraction543 0.2612 0.7633 0.5

LengthRed Orange Green /mm

31592.5 32676.6 36828.8 9.999 0331593.5 32677.6 36830.0 9.999 3531594.5 32678.7 36831.2 9.999 6731595.6 32679.7 36832.4 10.000 0031596.6 32680.8 36833.6 10.000 3131597.6 32681.8 36834.8 10.000 6431598.6 32682.9 36835.9 10.000 96

Interference Orders

1st Step: Measure fractions from the interference patterns

2nd Step: Evaluategauge length based on Fractions and “known”Nominal length.

Example of a 10 mm gauge block:

Method of Exact Fractions

Decker et al., Applied Optics 42 (2003) 5670-5678


Edlén Equation - Brief History

• 1966: Edlén published empirical equation for n of standard dry air and corrections for water vapour, based on experimental data (Barrell and Sears 1939, Hilsenrath 1955)

• 1988: Birch and Downs revise water vapour constants - higher accuracy

• 1994: Updated by Birch and Downs (1993, 1994) – accommodates the SI units (Pascal vs. Torr) – replaced IPTS-1948 temperature scale with ITS-90– corrects for increased levels of CO2 in laboratory air (62 ppm) – includes improved experimental data on density of air and the

refractivity of water vapour

1 ppm 1 part per million = 1x10-6


An Empirical Equation

21218N m/9.38/15518m/130/233398337.8091101 n

Ct/0.00366101

Pa/C/009876.05953.010160.93214

Pa/118

ptpnn x

tp

Bönsch & Potulski, Metrologia 35 (1998) 133-139

1021 10m/0384.08020.3Pa/ fnn tptpf

0004.05327.0111 N xnn x


Empirical Equations

Bönsch & Potulski, 1998, “Measurement of the refractive index of air and comparison with modified Edlén’s formulae,” Metrologia, 35, 133-139

Ciddor P. E., 1996, “Refractive index of air: new equations for the visible and near infrared,” Appl. Opt., 35, 1566-1573.

Birch K. P. and Downs M. J., 1994, “Correction to the Updated Edlén Equation for the Refractive Index of Air,” Metrologia, 31, 315-316.

Edlén B., 1966, “The Refractive Index of Air,” Metrologia, 2, 72-80.

Decker et al., NRC Document No. 42753 (2000)


Wavelength of light compensation

• Vacuum wavelengths are adjusted for refractive index of air, n vac = n air

• Correction for refractive index of air = (n-1)L n 1.000 27

~300L nm for L [mm] (about 300 nm on 1 mm)

Nominal ValueChange for which

n=+1x10-6

Temperature 20.0°C -1.0°CPressure 101.3 kPa +0.4 kPa

(760 Torr) (+3 Torr)Relative Humidity 40% -100%

Estler Applied Optics 24 (1985) 808


NRC Gauge Block Interferometer Pressure Measurement

101000

101100

101200

101300

101400

101500

101600

101700

101800

8:09 9:38 11:08 12:37 14:06 15:36

Time of Day

Pre

ssur

e /P

a

Rate of change = 200 Pa in 30 minutes 50 nm for L=100 mm

Wavelength of light compensation


Principal Constituent Gases

N2 O2 Ar CO2 0.781 0.209 0.009 0.0004

Molar Concentrations

Other gases such as He, CH4, etc. make up the remaining air composition.

Pendrill Metrologia 25 (1988) 87-93


Variation in Lab Air Composition

• CO2 largest single source of variation & significant contaminant

• Operators are not at rest up to 5 times higher respiration rate!

• Operator near the instrument

• CO2 paired with O2 results in additional change in composition

Birch and Downs “The Precise Determination of the Refractive Index of Air,” National Physical Laboratory (NPL) Report MOM90 (1988) Teddington, UK

~5 nm on 100 mm


PTB Kösters Interferometer

• Kösters design allows real time evaluation of the refractive index of air in the proximity of the gauge block by direct comparison with vacuum.

• Frequency-stabilized laser sources.

• High-accuracy thermometry equipment: thermocouples paired with Pt-25 and precision bridge.

• Cooled CCD camera.


Correction via Refractometer

• Refractive index of air is the largest single correction to length measurements by interferometry (3x10-4 L)

• Measure fringe fractions –determine the difference in number of interference orders mn between air and vacuum

• More accurate than estimation by empirical formulas (Edlén equations).

Cellv

v 21 Lm Cell

vair 2Lnm

vair mmmn

CfL

mL

n

nn

n

21

211

v

Cell

v

Cell


Phase Stepping Interferometry

• Popular technique for interference fringe analysis – flatness-measuring interferometers– optical component evaluation

• Displacement of fringes when the optical path length is changed– Sample interferogram at each of 5 phase steps– Change in grey-scale is related to the change in optical path length and the

wavelength of light• Fringe fraction measurand for:

– Gauge block length– Refractive index of air


Length-Dependent Influences

Influence Type dy/dxi ui Refractive index of air

Window optics correction 3 nm B L/ 3x10-9

LFringe fraction 0.007 fringe B L/2 2x10

-9L

Vacuum cell length, 250 nm B (n-1)L/ 7x10-11

LVacuum wavelength 10

-10 B (n-1)L/ negl.

Influence Type dy/dxi ui Refractive index of air

Edlen Equation 1x10-8 B L 1x10-8

L

Air Temperature 4 mK B -9.5x10-7L 3x10-9

L

Air Pressure 6 Pa B 2.7x10-9L 1.6x10-8

L

Relative Humidity 2% B -8.5x10-9L 1.3x10-8

L

Vacuum Wavelength 10-8

B -1.2x10-5L negl.

3.7x10-9 L

2.4x10-8 L

Decker et al., Metrologia 41 (2004) L11-L17


End Effect vs. Length-Dependent Influences

84

0

20

40

60

80

100

120

0 200 400 600 800 1000

Nominal Gauge Block Length /mm

Expa

nded

(k=2

) Unc

erta

inty

/n

m

Ciddor EquationRefractometer


Atmospheric Bath

• Gauge block length is defined at the standard atmospheric pressure of P0=101325 PaISO 3650

• Artifact length can change LP as a result of a change in pressure

• Gauge block length increases with decreasing pressure P (higher altitude = lower pressure)

Example: 900 mm gauge block measured in Boulder, CO (altitude 1500 m; 83 kPa) is 34 nm longer than when measured in Paris (at sea level, 101 kPa)

LE

P

LKPLP

213

Pressure calculator: http://www.dangermouse.net/gurps/science/pressure.html

Bayer-Helms Über den Einfluss von Luftdruck und Gewichtskraft auf Endmasse PTB-Mitt. 2/73 (1973) 97-8Darnedde Metrologia 29 (1992) 349, Decker Metrologia 40 (2003) 1


GB Length Change Post Travel

• Length change for 900 mm gauge block following travel from Rio de Janeiro

• Total length change during 5 days of settling = 94 nm 78 nm

• Temperature measurements included as demonstration that they are not correlated

Decker Metrologia 38 (2001) 269


Recent Developments

• Improve dispersion components (wavelength dependence) via frequency comb measurements

– Refractivity of constituent gases– Validation of Lorentz-Lorentz

equations for a dilute gas

• Improved correction for humidity

Zhang et al., Appl. Opt. 47 (2008) 3143.Schödel et al., Opt. Lett. 31 (2006) 1979.

Historical International Prototype Metre bar, made of an alloy of platinum and iridium, that was the standard from 1889 to 1960.


Canada-Germany S&T Treaty

• Canada-Germany S&T Cooperation Agreement signed in 1971

• Governed by the German-Canadian Commission for Scientific & Technological Cooperation

– Meets annually to – Reviews progress– Ensures coordination and

identifies priorities for cooperative action


Some History

• Over 500 joint research projects in priority areas: environment, energy, nanotechnology, health, genomics, photonics

• Future: innovation-based business activities and commercialisation through: tech transfer, partnerships, bilateral R&D cooperation

http://www.bmbf.de/pubRD/30_jahre_deutsch-kanadische_wtz_1971-2001_en-fr.pdf


• Visit of German Federal Minister of Education and Research Prof. Annette Schavan (tentative: Oct 2011)

– Public lecture at NRC, 100 Sussex Dr. Auditorium“Reaching the ultra-small and the ultra-fast using intense light”Paul Corkum, Joint Attosecond Science Laboratory,University of Ottawa & National Research Council of Canada

– Announcement & registration: http://www.science.gc.ca/

• Closing Ceremony: Berlin Feb 2012

• Website: www.de-can-fti.com

Events


Refractometers

Hou W., Thalmann R., 1994, “Accurate measurement of the refractive index of air,” Measurement, 13, pp. 307-314.Hirukawa H., Ogita E., “Measurement of the Absolute Air Refractivity,” Proceedings of the 33rd SICE Annual Conference, International Session, Tokyo Metropolitan Institute of Technology, 26-28 July 1994, pp. 931-936.Leibengardt G. I., Naidenov A. S., Fedorin V. L., Shur V. L., 1993, “Investigations of a Two-wave Laser Refractometer,” Translated from Izmeritel’naya Tekhnika, 7, pp. 29-31.Schellekens P., Wilkening G., Reinboth F., Downs M. J., Birch K. P., Spronck, J., 1986, “Measurements of the Refractive Index of Air Using Interference Refractometers,” Metrologia, 22, pp. 279-287; and Rischel C., Ramanujam P. S., 1989, “Refractive Index of Air - Errata,” Metrologia, 26, p. 263.Hilsenrath J., 1955, US Natl. Bur. Stand. Circ., 564.Barrell H., Sears J. E., 1939, Philos. Trans. R. Soc. London, A238, pp. 1-64.


Related Topics

Other Evaluations :Birch K. P., Downs M. J., Ferriss, D. H., 1988, “Optical path length changes induced in cell windows and solid etalons by evacuation,” J. Phys. E: Sci. Instrum., 21, pp. 690-692.

* Birch K. P. Reinboth F., Ward R. E., Wilkening G., 1993, “The Effect of Variations in the Refractive Index of Industrial Air upon the Uncertainty of Precision Length Measurement,” Metrologia, 30, pp. 7-14.

Estler W. T., 1985, “High-accuracy displacement interferometry in air,” Applied Optics, 24, pp. 808-815.

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