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Unformatted text preview: Astronomy 423 at UNM Radio Astronomy Selfcalibration Greg Taylor University of New Mexico Spring 2011 G. Taylor, Astr 423 at UNM 2 Outline • Why selfcalibrate? • How to selfcalibrate • What to watch out for • Limitations of selfcalibration • Practical examples of selfcalibration in action • Demo of calibration in AIPS This lecture is complementary to Chapter 10 of ASP 180 and is based on a lecture by Tim Cornwell G. Taylor, Astr 423 at UNM 3 Selfcalibration of a VLA snapshot • Original Image • Final image Initial image G. Taylor, Astr 423 at UNM 4 • Fundamental calibration equation V ij ( t ) = g i ( t ) g j * ( t ) V true ( t ) + ε ij ( t ) V ij ( t ) Visibility measured between antennas i and j g i ( t ) Complex gain of antenna i V true ( t ) True visibility ε ij ( t ) Additive noise Calibration equation G. Taylor, Astr 423 at UNM 5 • Calibration equation becomes V ij ( t ) = g i ( t ) g j * ( t ) S + ε ij ( t ) S Strength of point source Calibration using a point source • Solve for antenna gains via least squares algorithm • Works well  lots of redundancy – N1 baselines contribute to gain estimate for any given antenna G. Taylor, Astr 423 at UNM 6 • The complex gains usually have been derived by means of observation of a calibration source before/after the target source • Initial gain calibration is insufficient – Gains were derived at a different time • Troposphere and ionosphere are variable • Electronics may be variable – Gains were derived for a different direction • Troposphere and ionosphere are not uniform • Observation might have been scheduled poorly for the existing conditions Why is a priori calibration insufficient? G. Taylor, Astr 423 at UNM 7 What is the Troposphere doing? • Neutral atmosphere contains water vapor • Index of refraction differs from “dry” air • Variety of moving spatial structures G. Taylor, Astr 423 at UNM 8 • Don’t need point source  can use model V ij ( t ) = g i ( t ) g j * ( t ) V ij model + ε ij ( t ) V ij model Model visibility Calibration using a model of a complex source • Redundancy means that errors in the model average down • Can smooth or interpolate gains if desired G. Taylor, Astr 423 at UNM 9 • Made a fake point source by dividing by model visibilities X ij ( t ) = g i ( t ) g j * ( t ) + ε ' ij ( t ) X ij ( t ) = V ij ( t ) V ij model ε ' ij ( t ) Modified noise term Relationship to point source calibration G. Taylor, Astr 423 at UNM 10 Why does selfcalibration work?...
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 Fall '11
 GregTaylor
 Astronomy, Amplifier, Das Model, The Source, Taylor University

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