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Phys 728, Spring 2003
Homework Problem Set #4

4.1. Construct an array *f*(*u,v*) of 1024 x 1024 pixels
representing a circular aperture of 10 m diameter, operating at 3.6 GHz,
with each pixel corresponding to 1 *l*. How many pixels in diameter
will the aperture be? Obtain the primary beam *F*(*l,m*)
by taking its Fourier Transform using IDL or other package of your choice.
Print an image of the normalized power pattern |*F*(*l,m*)*F**(*l,m*)|,
shifted appropriately. Also plot the 1-d power profile through the
center of the power pattern, labeling the horizontal axis in arcminutes.
4.2. Construct the aperture below by starting with a 100 pixel
diameter circle, cutting out a circular hole of 20 pixel diameter and a
cross of width 6 pixels, and obtain the primary beams *F*(*l,m*)
for both the blocked and unblocked apertures. Show that the ratio
of peak of the power patterns of the blocked to unblocked aperature (i.e.
|*F*(0*,*0)*F**(0*,*0)|_{blocked }/ |*F*(0*,*0)*F**(0*,*0)|_{unblocked})
is the same as the efficiency, given by expression *h*_{bl}
= (1- area blocked / total area)^{2}.