The alignment of the tapered illumination with the antenna's primary dish will not be perfect, and for ALMA has been specified as having an rms error of 0.1 dish radii at all frequencies, and the resulting image errors are therefore independent of frequency. If uncorrected, simulations indicate the effects of this illumination offset will dominate both pointing and surface errors for ALMA's wide field imaging at frequencies up to about 500 GHz.
The main effect of a shift in the tapered illumination on the dish is a phase gradient across the far field voltage pattern, which is given by the Fourier transform of the illumination (neglecting surface errors). A secondary effect will be a distortion in both the voltage pattern's amplitude and phase, caused by the asymmetric illumination pattern on the dish. The phase gradient in the voltage pattern is identical in effect to an error in the baseline. However, the geometry of the baseline and the geometry of the voltage pattern phase gradient are different and will have different time dependences. The phase gradient can be effectively treated by changing the (u,v) coordinates of each visibility to reflect the weighted antenna center accounting for the dish illumination offset. About 85% of the deviation of the offset far field voltage pattern can be corrected by removing the phase gradient; the residual deviation is due to the asymmetric illumination, and is dominated by a bipolar pattern. This indicates that the majority of the effect of the offset illumination can be removed by adjusting the (u,v) coordinates prior to imaging.
The calibration parameters required to perform the (u,v) correction (ie, the phase gradient in the voltage pattern) should be constant with time for each antenna/feed. Thermal noise and atmospheric phase errors will not hamper the measurement of the phase gradient parameters at low frequencies, but will be of concern in determining these parameters at high frequencies. However, both types of error should average down if the calibration observations are performed correctly.
Detailed numerical imaging simulations indicate that after correction of the (u,v) coordinates, the image quality is restored to the level expected when illuminations offsets are not present. In fact, often the image quality of the corrected images was better than when illuminations offsets are not present. This paradoxical result may be explained by the fact that feed leg and subreflector blockage were also included in the simulations. Without the illumination offsets, all antennas' voltage patterns are affected in the same way by the feed legs, resulting in low level asymmetric side lobes that are not reflected in the symmetric beam model. However, the affects of the random asymmetric illuminations of the different antennas tends to smooth out these low level side lobes, making the problem less systematic and less damaging.
View a pdf version of ALMA Memo 402.
Download a postscript version of ALMA Memo 402.
Last modified: 2001-12-13
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