[asac] [almanews] ALMA Memo 402 Released

[Stacy Oliver]

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ALMA Memo 402

Illumination Taper Misalignment and Its Calibration

M.A. Holdaway(NRAO/Tucson)

12/12/2001

keywords:  aperture illumination, antenna, imaging, mosaicing

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.
	http://www.alma.nrao.edu/memos/html-memos/alma402/memo402.pdf

Download a zipped ps version of ALMA Memo 402.
	http://www.alma.nrao.edu/memos/html-memos/alma402/memo402.zip

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