selfcal_mar21

selfcal_mar21 - Astronomy 423 at UNM Radio Astronomy...

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Unformatted text preview: Astronomy 423 at UNM Radio Astronomy Self-calibration Greg Taylor University of New Mexico Spring 2011 G. Taylor, Astr 423 at UNM 2 Outline •   Why self-calibrate? •   How to self-calibrate •   What to watch out for •   Limitations of self-calibration •   Practical examples of self-calibration 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 Self-calibration 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 –   N-1 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 self-calibration work?...
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selfcal_mar21 - Astronomy 423 at UNM Radio Astronomy...

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