ALMA Memo 402 Illumination Taper Misalignment and Its Calibration

The alignment of the tapered illumination with the antenna's primary dish will not be perfect, and for ALMA has been speci ed 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 e ects of this illumination o set will dominate both pointing and surface errors for ALMA's wide eld imaging at frequencies up to about 500 GHz. The main e ect of a shift in the tapered illumination on the dish is a phase gradient across the far eld voltage pattern, which is given by the Fourier transform of the illumination (neglecting surface errors). A secondary e ect 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 e ect to an error in the baseline. However, the geometry of the baseline and the geometry of the voltage pattern phase gradient are di erent and will have di erent time dependences. The phase gradient can be e ectively treated by changing the (u; v) coordinates of each visibility to re ect the weighted antenna center accounting for the dish illumination o set. About 85% of the deviation of the o set far eld 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 e ect of the o set 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 o sets are not present. In fact, often the image quality of the corrected images was better than when illuminations o sets are not present. This paradoxical result may be explained by the fact that feed leg and subre ector blockage were also included in the simulations. Without the illumination o sets, all antennas' voltage patterns are a ected in the same way by the feed legs, resulting in low level asymmetric side lobes that are not re ected in the symmetric beam model. However, the a ects of the random asymmetric illuminations of the di erent