review of concepts in lecture1
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Review of concepts in Lecture1. By Tom Wilson. Lecture 2 page 1. 1972: T MIXER = 3000 K (SSB)L MIXER = 2(3 dB loss) T LNA = 20 KG LNA = 10 3 (30 dB gain) So T RX = 3000 K + 40 K + (1/500)T 2. 2005: T MIXER = 50 K (SSB)L MIXER = 1.2for n =100 GHz T LNA = 5 KG LNA = 10 3 - PowerPoint PPT PresentationTRANSCRIPT
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Review of conceptsReview of conceptsinin
Lecture1Lecture1
By Tom Wilson
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Lecture 2 page 1Lecture 2 page 1
1972: TMIXER = 3000 K (SSB) LMIXER = 2 (3 dB loss)
TLNA = 20 K GLNA = 103 (30 dB gain)
So TRX = 3000 K + 40 K + (1/500)T2
T T L TL
GTR X M IX E R M IX E R L N A
M IX E R
L N A
2 . . .
2005: TMIXER = 50 K (SSB) LMIXER = 1.2 for =100 GHz
TLNA = 5 K GLNA = 103
So TRX = 50 K + 1.2*5 K + (1.2/(1000))
In addition to the receiver, the atmosphere will add perhaps 20 K extra. In cm wavelength range, less improvement in noise temperatures with time, but most receivers are HEMTs, and we now can build MULTI-BEAM SYSTEMS
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Lecture2 page 2Lecture2 page 2
RECEIVERS
Fundamental Relation:
TimeTime 1 sec1 sec 1 hour1 hour 16 hours16 hours 64 hours64 hours
TT
R M SSY S
T
TR M S
SY S
1
0 0 1 6.
0 0 0 4.
0 0 0 2.
• For broadband measurements, try to keep TSYS small, but also good to have large (bolometers)
• For very narrow spectral lines, coherent receivers have as small as you want. for example one can have = 10-9 0
•Note that from Doppler relation, V= c/
•At 100 GHz, 1 km s-1=333 kHz
Factor of500 improvement
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Lecture2 page 3Lecture2 page 3
• Coherent receivers preserve phase, but TRX > h/k ( at 115 GHz, h/k = 5.5 K ) from the uncertainty principle Et=h
• TSYS includes noise from Rx, atmosphere and source
• In coherent systems, noise from first stage is most important
•Mixer is a non-linear device with signal (s) and local oscillator (l) input:
sinltsinstcos(lt+st) + cos(st-lt……………
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t t
F.T.
F.T.
R A t B t d t( ) ( ) ( ) ( )2
(Must be careful with limits in integral of periodic functions)
Lecture 2, page 3bArrows here show sampling at twice the frequency
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Lecture 2: Antennas and Lecture 2: Antennas and CalibrationsCalibrations
Single dishes in simple termsSingle dishes in simple terms
CalibrationsCalibrations
ExamplesExamples
Single dishes in more formal termsSingle dishes in more formal terms
Lecture 2 page
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Simple Diffraction Simple Diffraction First Null First Sidelobe
Diameter, D
Wavelength,
Can use example of waves passing through an aperture
Lecture 2 page 5
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Rectangular ApertureRectangular Aperture
SilverMIT RadiationLabSeries
Lecture 2, page 6
sin
Du
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Lecture2 page 7Lecture2 page 7
FILLED APERTURES: Simple Approach
From diffraction = k / D=200k (mm)/D(m), where k is about 1, but can have larger values, but then need a more complex antenna theory
Reciprocity: Parameters of transmitting antennas same as those for receiving antennas
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Usually “Filled apertures” means “paraboloids”
The ALMA 12 meter millimeter/sub-mm prototype radio telescopesin Socorro New Mexico
Lecture2 page 8Lecture2 page 8
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2
2
)(3520
8
2
1
meterD
KTSor
k
DwhereST
dTkdSAdWPower
A
A
AA
Ae
BA
M B
T
T
S: Flux density
TA: This is assuming that the atmosphere of earth has little effect
(0 is in units of arc min and the beam and source are gaussian. Wavelength in cm and TA is corrected for absorption in earth’s atmosphere)
Lecture2 page 9Lecture2 page 9
Show that these are equivalent
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Descriptive Parameters to characterize antennas:
: Full width to half power beam size
MB: Main beam solid angle
: Antenna efficiency
: Beam efficiency
Lecture2 page 10Lecture2 page 10
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Lecture2 page 11Lecture2 page 11
Measure B using intense point sources, assume B is a gaussian. Then
MB = 1.133 B2 (Gaussians)
COMPACT SOURCES:
Ag: Geometric area of antenna
Effective area
Aeff = Ae =A Ag A : Antenna efficiency
0 : Observed beam size relation for gaussians
B : Beam
S : Source
02 2 2 B S
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IkT kT
S I dkT
M B
M B
2 2
2
2 2
2
22
2
222
22
Beams
ssMB
sBeamobs
ssobsMB
TT
TT
Call TMB
the ‘Main Beam
Temperature’
Integrating over the beam
Could also integrate over The source
MB
ST
cmM B
2 6 5 02
2.( )0 is in units of
arc min and the beam and source are gaussian. Wavelength in cm)
Rayleigh-JeansFrom Lecture 1:
Lecture2 page12Lecture2 page12
(Problem for you: Given the previous relations between T(Problem for you: Given the previous relations between TMBMB , T , TAA and Sand S , determine a relation for the ratio of , determine a relation for the ratio of AA to to in terms of in terms of antenna diameter, antenna diameter, and and
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Lecture 3 page 7Lecture 3 page 7
APPLICATION OF THESE CONCEPTS
NGC7027 (a PNe) has SS = 5.4 Jy at 1.3 cm. What is the T= 5.4 Jy at 1.3 cm. What is the TMBMB (main beam (main beam
brightness temperature) if the 100-m FWHP beam size is 43”?brightness temperature) if the 100-m FWHP beam size is 43”?
UseUse
Where Where 0 is the telescope beam size in are min.
Suppose the “true” gaussian source size is 10”, what is TB (true brightness temperature). Could use
ST
cm
T
T K
M B
M B
M B
2 6 5
5 4 2 6 5
4 36 0
1 3
6 7
02
2
2
2
.( )
. ..
.
STM B
5 4 2 6 5
1 06 0
1 3
2
2. ..
(Problem: Repeat for the (Problem: Repeat for the
30-m, with beam 30-m, with beam
27’’, wavelength 27’’, wavelength
3.5 mm, flux density3.5 mm, flux density
4.7 Jy)4.7 Jy)
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Lecture 3 page 8Lecture 3 page 8
Or
And get
We know from optical spectroscopy that the electron temperature of NGC7027 is Te = 14000 K. Use equation of radiative transfer:
To get 0 0 0 9.
This is a source which is thermal, so the radiation is free-free or Bremsstrahlung (will discuss in Lecture 3)
2
22
10
1043MBB TT
KTB 124
eTT eB 1
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Lecture 3 page 9Lecture 3 page 9
VenusVenus, at closest approach, has a size of 62”. If we measure an antenna temperature, TA, of 4.2 K with an 8.7’ beam, and a beam efficiency of B = 0.5, what is the surface temperature of Venus?
T K T T so T K
T T
T K
A B M B M B M B
S S M B B S
S
4 2 0 5 8 6
8 68 7
6 26 0
6 26 0
6 6 0
2 2 2
22
2
. . .
..
Jansky used a telescope with a 30° beam at = 14.6 m. The maximum intensity was 1.5 .106 Jy in a beam(this was calibrated in the 1970’s; see Lecture 1). What is the TMB?
1 5 1 0 2 6 53 0 6 0
1 4 6 0
4 1 0
6
2
2
5
. .
T
K T
M B
M B
If B = 0.5, then TA = 2 .105 K >> TRX
At 14.6 meters, the whole sky shines brightly, night and day!!
Jansky did not detect the Sun, WHY?
(see Lecture 1 page 2)
(Repeat for 3 mm(Repeat for 3 mm
with a 27” beam)with a 27” beam)
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Lecture 3 page 10Lecture 3 page 10
SURVEYS: THE SKY HAS 41,252 SQUARE DEGREES
Suppose you survey the whole sky with a 30’ beam at 408 MHz. Need 3 samples per beam. (try to characterize a cosine with fewer points).
Need 36 samples per square degree, or 1.5 .106 samples in all.
Receiver has = 10 MHz. Use = 10 MHz. Use = 10s /point and assume TSKY >> TRX
TT T
TR M SSY S SY S
SK Y
1 01 0
8
4
In all measurement time = 1.5 ..107 sec = ½ year
Now: Try = 5 GHz, = 5 GHz, = 2.4’, TRX = 50 K with integration = 50 K with integration time = 10s
and and = 500 MHz= 500 MHz
T
KKR M S
5 07 1 0 4
Really more since need to switch to reduce atmospheric noise fluctuation, so TTRMSRMS =10 =10-3-3 K. If K. If A = 0.5, on a 100-m telescope, get 1.3 K, TA per Jy, so SSrmsrms = 0.7 = 0.7 . .1010-4-4 Jy. Detect at 4 Jy. Detect at 4 TTRMSRMS =3 =3 ..1010-4-4 Jy = 0.3 mJy. Jy = 0.3 mJy.
But need 2.3But need 2.3 . .101088 samples, or 6.5 samples, or 6.5 ..101055 hours = 74 years. hours = 74 years.
Need Need MULTIBEAMINGMULTIBEAMING
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isintegral overentire power pattern
12b
More details of antennasMore details of antennas
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Lecture2 page 13Lecture2 page 13
Define A as integral over whole Power Pattern, PN:
A NP d d ( , ) s in
00
2
M B NM A INB E A M
P d BM B
A
B: Fraction of power in main beam used for sources which are extended to about size of main beam.
For point sources, use A
A Ae A g
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Example: Why need mm calibration Example: Why need mm calibration
From Lecture 1: The Moon is measured at 3mm wavelength with a 12m telescope. The antenna beamsize is =50”, less than Moon size of 30’. So the source fills the main beam and we know that the temperature of the Moon is 220K. This should be the main beam brightness temperature, TMB = 220 K. The beam efficiency is =80%, so the measured antenna temperature should be TA=0.80*220K=176K. We find it is more since the sidelobes also receive power from the Moon. This is like the situation for CO lines in the This is like the situation for CO lines in the millimeters. We need to take this into account.millimeters. We need to take this into account.
Lecture 2 page 15
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Rectangular ApertureRectangular Aperture
Silver, MIT RadiationLabSeries
Lecture2 page16Lecture2 page16
First Sidelobe(for a 12mantenna at =3 mm,at 75” from axis)
Half width To half power
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Historical Introduction to CalibrationHistorical Introduction to Calibration
In centimeters, atmosphere has little effect, and In centimeters, atmosphere has little effect, and can use flux density transfer from standard can use flux density transfer from standard sources for calibrationsources for calibrationThis is by means of a pulsed calibration, injected This is by means of a pulsed calibration, injected periodically together with the signalperiodically together with the signalThis was to transfer scale from a known source to This was to transfer scale from a known source to the source of interestthe source of interestAtmosphere had little or no influenceAtmosphere had little or no influenceThis is This is notnot so in the millimeter wavelength range so in the millimeter wavelength range Water vapor is the larger problem: this has a scale Water vapor is the larger problem: this has a scale
height of 2 kmheight of 2 km Oxygen has a scale height of 8 kmOxygen has a scale height of 8 km
Lecture2 page17Lecture2 page17
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Lecture2 page 18Lecture2 page 18
T T T T eB B 0
Calibration for MillimetersFROM LECTURE 1:
Equation of radiative transfer and Rayleigh-Jeans approximation gave
on source off source
If use
for “on-source
minus off-source” get
TB: Measured
T: Atmosphere
T0: Astronomical source
T T e T e T T eB A A( ) 1 10
Must correct for thisloss in the atmosphere
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Lecture2 page 19Lecture2 page 19
3 4 5 2 2 5
4 6 0 2 2 5
8 0 6 2 2 5
3
6
2 0
Carbon monoxide, CO, line frequencies
Fine structureLines of neutralCarbon (C I)
GHz is not close to any water lines, butThe opacity is representative
Thisplot for
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Thus the source intensity is reduced. In the millimeters, historically the measurements concentrated on spectral lines, especially carbon monoxideCO. To calibrate the very extended emission from molecular clouds, one used the ‘chopper cal’ method. This made use of measurements of a warm absorber, the atmosphere and then (often) a cold absorber.
Lecture2 page20Lecture2 page20
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)( rxHH TTGV
1
y
yTTT LH
rx
)( rxLL TTGV
rxL
rxH
L
H
TT
TT
V
V
Lecture2 page21Lecture2 page21
y
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AeTFGTTFGVVV atmeffskyHeffskyHcal )(
AeTGVVV Aoffsourcesig ´
eff
A
cal
sigA F
T
V
VT ´
´
eff
effMB B
FT
])1([ rxHeffskyeffsky TTFTFGV
Lecture2 page 22Lecture2 page 22
Beff isthe same as
Tsky=Tatme
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Details: Error Beam Details: Error Beam
Lecture2 page23Lecture2 page23(At 1.3 mm, the power in the error beam is about 20% of that in the main beam)
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30-m Error Beam (Greve et al. 1998 A&A Suppl 133, 271) Lecture2 page24Lecture2 page24
214.2 FB
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The Effect of Feed Legs on the Telescope Beam Pattern
Lecture2 page25Lecture2 page25
Effelsberg 100-mtelescope: a classic case of ‘fat feed legs’’
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Reflections in the TelescopeReflections in the TelescopeLecture2 page27Lecture2 page27
Reflection is at the feed horn
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Instrumental Baseline RipplesInstrumental Baseline Ripples
Lecture2 page28Lecture2 page28
Both spectra are ‘signal minus reference over reference’, at different axial focus settings
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Observing StrategiesObserving Strategies
Position SwitchingPosition Switching
Beam SwitchingBeam Switching
On the Fly MappingOn the Fly Mapping
Frequency SwitchingFrequency Switching
Lecture2 page29Lecture2 page29
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Beam Switch/Position SwitchBeam Switch/Position Switch(Also ‘wobble Switching’)(Also ‘wobble Switching’)
Noise is factor of two larger than in total power spectrum
Lecture2 Lecture2 page30page30
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On-the –Fly MappingOn-the –Fly Mapping
For n on’s, spend more time on off source
Have ‘n’ on’s for each off
Total integration time, t, for each on-source spectrum is the sum of ton & toff
Lecture2 page31Lecture2 page31
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Frequency SwitchingFrequency Switching
more noise in this spectrum, compared to a total power spectrum
Lecture2 page32Lecture2 page32
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Telescope Pointing Telescope Pointing
Must have fairly intense sources with Must have fairly intense sources with known positionsknown positions
These must be small compared to the These must be small compared to the telescope beamtelescope beam
Could be spectral line or continuum Could be spectral line or continuum sources, planets, moons of planets, some sources, planets, moons of planets, some asteroidsasteroids
Lecture2 page33Lecture2 page33
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Full Width to Half Power points: The position of the source is most accurately
found by determining these locations
Could also use a Gaussian fit to the scan, if the signal to noiseRatio is sufficient. This is usually done for continuum measurements.For spectral line pointing, one usually measures at the source peak and 4 points around the peak, usually at the half power points.
Lecture2 page34Lecture2 page34
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Calibration SourcesCalibration Sources
Even though the chopper calibration gives a Even though the chopper calibration gives a value for Tvalue for TAA* or T* or TMBMB, may be additional factors, , may be additional factors, such as mixer sideband ratio, telescope gain vs such as mixer sideband ratio, telescope gain vs elevation effects, pointing errors…elevation effects, pointing errors… With fixed tuned SSB mixers this is less true, but one With fixed tuned SSB mixers this is less true, but one
may still want to have a system check using a may still want to have a system check using a ‘standard’ source. ‘standard’ source.
Not as large a problem with continuum measurementsNot as large a problem with continuum measurements But using measurements of standard sources allows But using measurements of standard sources allows
one to determine an intensity scale that others can one to determine an intensity scale that others can relate their measurements to. relate their measurements to.
Lecture2 Lecture2 page35page35