sensitivity -in radio astronomyruta/ras15/poonam-sensitivity.pdf · poonam chandra measures of...

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Sensitivity-In Radio Astronomy

Poonam ChandraNCRA-TIFR

1Wednesday, September 16, 2015

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References

Synthesis Imaging in Radio Astronomy II - Ed: Taylor, Carilli, Perley

Low Frequency Radio Astronomy - Ed: Changalur, Gupta, Dwarakanath

Interferometry and Synthesis in Radio Astronomy, Thompson, Moran, Swenson


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What is Sensitivity

What is the weakest source one can detect in an image?

Sensitivity affects Scientific outcome drastically.


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Measures of antenna performance

From Planck’s Law and its Rayleigh Jean’s approximation in the low frequency regime: Power P=kBTΔν

Power entering antenna feed is amplified by g2

Power from source PA=g2kBTAΔνPower from system noise Psys=g2kBTsysΔν

Tsys: system temperature- contribution from receiver noise, feed losses, spill over, atmospheric emission, Galactic background


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Antenna performance contd.

System temperatures Tsys for GMRT antennas

150 MHz: 615 K

235 MHz: 237 K

325 MHz: 106 K

610 MHz: 102 K

1280 MHz: 73 K


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Antenna Performance

Collecting area = geometric area A x Aperture efficiency ηa

E.g., GMRT antennas (A=45m), ηa ~60% - 40% from lowest frequency 150 MHz to highest frequency 1450 MHz

Received power delivered by antenna in a frequency band Δν, PA = ½g2 ηa ASΔν = g2 kBKSΔν

K=(ηa A)/(2kB): Gain or measure of antenna performance: in degree Kelvin of antennas temperature per Jy of flux density:


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Antenna Performance Contd.

Antenna gains for GMRT:150 MHz: 0.33 K Jy-1 Antenna-1

235 MHz: 0.33 K Jy-1 Antenna-1





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Antenna Performance

System Equivalent Flux Density (SEFD): Tsys in terms of SEFD

SEFD=Tsys/KSEFD takes into account the efficiency, collecting area of the antenna and system noiseSEFD: Useful measure of the system performance

SEFD measured by going on and off source of a known flux density


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Antenna Performance Contd.

SEFD for GMRT:150 MHz: 1864 Jy235 MHz: 718 Jy325 MHz: 331 Jy610 MHz: 319 Jy1280 MHz: 332 Jy


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SEFD for VLA Antennas


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SKA1-Low and Mid sensitivities

Wednesday, September 16, 2015

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Sensitivity of an Interferometer

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si- voltage from the source and ni voltage from noise. Voltage from antenna i is si+ni.Power from antenna i is <Pi> = ai<(si+ni)2> = ai[<si>2+<ni>2]

Since PA=g2kBTAΔν, Psys=g2kBTsysΔν

<Pi> = g2kB(TAi+Tsysi)Δν= g2kB(KiST+Tsysi)ΔνST is the total flux density seen by the antenna


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Sensitivity of a 2-element Interferometer

Power after the cross multiplication in the correlator, antenna i and j<Pij> = √(aiaj)/ηs<(si+ni)(sj+nj)> = √(aiaj)/ηs<sisj> = gigj/ηs √ KiKj kBΔνSc

(Since P=g2 kBKSΔν)Sc is the correlated flux density.


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σ2(Pij)=(aiaj)/ηs2<[(si+ni)(sj+nj)2]> - (gi2gj2)/ηs2 KiKj

kB2Sc2Δν2

Since <x1x2x3x4>=<x1x2><x3x4>+<x1x3><x2x4>+<x1x4><x2x3>

σ2(Pij) = (aiaj)/ηs2 [2<(si+ni)(sj+nj)>2 + <(si+ni)2> <(sj+nj)2>] - (gi2gj2)/ηs2 KiKj kB2Sc2Δν2

= 2 (gi2gj2)/ηs2 KiKj (kBScΔν)2 + (gi2gj2)/ηs2 (kBΔν)2 + (KiST+Tsysi) (KjST+Tsysj) - (gi2gj2)/ηs2 KiKj kB2Sc2Δν2

= kB2Δν2 (gi2gj2)/ηs2 x (KiKjSc2+KiKjST2+KiSTTsysi

+KjSTTsysj+TsysiTsysj)


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For square bandpass of width Δν, and correlator accumulation time τacc, the number of independent samples will be 2Δντacc (Nyquist sampling)

Thus to write noise level in Jy, divide by square root of total independent samples, i.e. √(2 Δντacc), and divide by gigj √(KiKj) kBΔν to convert in flux density


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Two limiting cases:Strong source limit: Weak Source limit


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Strong Source limit

Weak Source limit


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For complex correlator, above analysis applies to each channel, with Sc corresponding to the appropriate component of the complex visibility.

Two output channels can be represented in terms of either sine and cosine channels or real and imaginary channels.


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Complex visibility, also in terms of amplitude and phase

Sm=√(SR2+Si2)

Φm=tan-1(Si/SR)


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Sensitivity of a synthesis image

The image sensitivity will be combined sensitivity of all the interferometer combinations integrated over the full time on target.

The noise limit will determine the weakest feature that can be detected in absence of other imaging limitations, such as confusion or dynamic range.


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Consider that each pixel of an image is a linear combination of each measured data point: Im(l,m)=C ∑ TkWkwkVke2πi(ukl+vkm)

Vk- Complex visibility data located at (uk, vk)Tk is the taper functionWk is the density weighting function, natural or uniform weighting

wk weight reflecting SNR of the data point. Imp. for VLBA etc.


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At l=0, m=0 Im(0,0) =2C ∑ TkWkwkSRk

(ΔIm)2- sum of varianceΔIm =2C √(∑Tk 2 Wk 2 wk 2 ΔSk 2)For simplest case, natural weighting, no taper , C such that flux density per beam area ΔIm=ΔS/√L, L=1/2N(N-1)(tint/τacc)


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Sensitivity of a single polarization image formed by N identical antennas

If simultaneous dual polarization observations, then sensitivity of an image of Stokes parameters I, Q, U and V will obey Gaussian statistics i.e.


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Sensitivity of a synthesis


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Sensitivity

The sensitivity and synthesized point spread function (PSF) quality at a specified angular resolution are determined by the total system equivalent flux density (SEFD), the array configuration, the duration of source tracking, the fractional bandwidth being sampled as well as the method of visibility data weighting employed in imaging. These quantities will vary with the central observing frequency.


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Factors degrading Image Sensitivity

Image limitations, confusion and dynamic range

Some effects can give rise to higher noise at the edge than at the center.The sensitivity derived assuming DFT. But usually FFT is used. Associated convolution and gridding in UV plane will lead to higher noise at the edges.

Each antenna has own primary beam gain pattern, causing reduced sensitivity off center


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Also affected by fringe fitting and self calibration

Errors in determining antenna calibration parameters will introduce errors in visibility data

For an unresolved source, self-cal error √(N-1)/(N-3)Natural weighting and no tapering results in highest sensitivity but undesirable many times.


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For the more commonly-used "robust" weighting scheme, intermediate between pure natural and pure uniform weightings, sensitivity a factor of about 1.2 worse

Weather. The sky and ground temperature contributions to the total system temperature increase with decreasing elevation. This effect is very strong at high frequencies.


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Confusion: There are two types of confusion:

(i) Due to confusing sources within the synthesized beam, which affects low resolution observations the most. E.g. D configuration in VLA. Confusion noise should be added in quadrature to the thermal noise in estimating expected sensitivities. (ii) confusion from the sidelobes of uncleaned sources lying outside the image, often from sources in the sidelobes of the primary beam. This primarily affects low frequency observations.


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GMRT parameters


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Time on source


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http://gmrt.ncra.tifr.res.in/~astrosupp/obs_setup/sensitivity.html






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sensitivity -in radio astronomyruta/ras15/poonam-sensitivity.pdf · poonam chandra measures of...

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