calibration_mar7

calibration_mar7 - Astronomy 423 at UNM Radio Astronomy...

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Unformatted text preview: Astronomy 423 at UNM Radio Astronomy Calibration and Editing Greg Taylor University of New Mexico Spring 2011 G. Taylor, Astr 423 at UNM 2 Outline Why calibrate and edit? How to calibrate What to Edit Practical Calibration Planning Calibration Evaluation A Dictionary of Calibration Components More on editing and RFI Summary This lecture is complementary to Chapter 5 of ASP 180 and is based on a lecture by George Moellenbrock G. Taylor, Astr 423 at UNM 3 Why Calibration and Editing? Synthesis radio telescopes, though well-designed, are not perfect (e.g., surface accuracy, receiver noise, polarization purity, stability, etc.) Need to accommodate engineering (e.g., frequency conversion, digital electronics, etc.) Hardware or control software occasionally fails or behaves unpredictably Scheduling/observation errors sometimes occur (e.g., wrong source positions) Atmospheric conditions not ideal (not limited to bad weather) RFI Determining instrumental properties (calibration) is as important as determining radio source properties G. Taylor, Astr 423 at UNM 4 From Idealistic to Realistic Formally, we wish to obtain the visibility function, which we intend to invert to obtain an image of the sky: In practice, we correlate (multiply & average) the electric field (voltage) samples, x i & x j , received at pairs of telescopes ( i,j ) Averaging duration is set by the expected timescales for variation of the correlation result (typically 10s or less for the VLA) Single radio telescopes are devices for collecting the signal x i (t) and providing it to the correlator. V u , v ( ) = I l , m ( ) e i 2 ul + vm ( ) dl dm sky G. Taylor, Astr 423 at UNM 5 What signal is really collected? The net signal delivered by antenna i, x i (t), is a combination of the desired signal, s i (t,l,m), corrupted by a factor J i (t,l,m) and integrated over the sky , and noise, n i (t) : J i (t,l,m) is the product of a host of effects which we must calibrate In some cases, effects implicit in the J i (t,l,m) term corrupt the signal irreversibly and the resulting data must be edited J i (t,l,m) is a complex number J i (t,l,m) is antenna-based Usually, |n i |>> |s i | x i ( t ) = J i ( t , l , m ) s i ( t , l , m ) dldm sky + n i ( t ) = s i ( t ) + n i ( t ) G. Taylor, Astr 423 at UNM 6 The Measurement Equation We can now write down the calibration situation in a general way - the Measurement Equation: and consider how to solve it! r V ij obs = t J i t J j * ( ) r I l , m ( ) sky e i 2 u ij l + v ij m ( ) dldm G. Taylor, Astr 423 at UNM 7 r V ij obs = t J i t J j * ( ) r I l , m ( ) sky e i 2 u ij l + v ij m ( ) dldm = t J i vis t J j vis * ( ) t J i sky t J j sky * ( ) r I l , m ( ) sky e i 2 u ij l + v ij...
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This note was uploaded on 12/13/2011 for the course ASTRO 423 taught by Professor Gregtaylor during the Fall '11 term at New Mexico.

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calibration_mar7 - Astronomy 423 at UNM Radio Astronomy...

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