A1731 check the maps

Intro:

• map around coma with dimensions 8.25 by 8.25 degrees. The map is gridded to .05 degree (3 arcminutes). One map was made driving in ra and stepping in dec. A second map was made driving in dec and stepping in ra. These two maps were then basket woven together.
• a 430 beam map taken on 3C433. It spans 2 degrees by 2 degrees. It  is gridded to .05 degrees( 3 arcminutes). Two beam maps were made. Both were driven in azimuth and stepped in za.

Processing:

• Read in the data map fits file. It is 168 by 167 pixels with 3 amin spacing. Subtract the map minimum value and then take the square root.  We want to work in voltage rather than power (for the uv processing).
• Read in the two beam maps made and average them. The averaged beam map is 40 by 40 pixels with 3 amin spacing. Subtract the minimum value and then take the square root of the map.
• Zero extend the beam map to 168 by 167 pixels to match the dimensions of the data map. Before doing the extension, 2d hanning smooth the beam map so there are no sidelobes created by the zero extension.
• fft the data map and then compute the magnitude. Shift the map to center it.
• fft the zero extended beam map and compute the magnitude. Shift the map to center it.
• average the two beam maps that were made.
• Compute the uv spacing in lambdas for the uv maps:
• The grid spacing is 3 amin. The highest angular frequency that can be measured is 2*3 amin = .0017 radians.
• The highest spatial frequency is 1/Maxangular freq= 1/.0017=573 lambdas
• In meters the max spatial frequency=573*.7=401 meters.
• These value were determined by the grid spacing*2 (6') and not the beam width (11') so the higher spatial frequencies should not have power from the sky. The largest dimension of the illumination is about 240 meters.
• Create a normalized data map  by dividing the uv datamap by the uv beam map. The data map was convolved with the beam on the sky. To remove this you divide by 1/transform(beammap).
• Break the normalized uv data map into 100 bins of spatial frequencies (min to max) and then average.

The plots:

• This an image of the power. The color table has a linear stretch.
• The axis are in pixels. Each pixel is 3 Amin.

• The top image is the voltage beam map. The stretch is a log scale. The line plot at the bottom of the image is a horizontal cut through the center of the map. It is a db scale. The first sidelobe null is at 13.4 amin. This is the convolution of 11 amin beam with the 6 amin smoothing function used for gridding.
• The bottom image is the uv amplitudes of the beam map. The stretch is a log scale. The bright circles (low amplitude) are inverse transforms of the nulls in the beammap.
• The first beammap null is at 13.4'  (.0039 radians).  Using UVDistance=Lambda/angularSeparation gives 179 meters for the location of the first null in the uv plane.
• The 2nd ring in the uv plane is probably the edge of the beam (average about 225 Meters).
• The outermost ring may correspond to the ground screen edge.
• The half circles at the top, bottom of the map occur in the direction we stepped (za) and not in the driven direction azimuth. They may have something to do with this.
• The asymmetry in the uv plane is from the elliptical beam. The azimuth illumination is larger than the za illumination (240 by 210 meters).

• The top image is the uv map of the data image (first image). The stretch is a log scale.
• The cross  at u=0 and v=0 comes from strip to strip variation. Maps were made driving in ra stepping in dec and then driving in dec and stepping in ra. These two maps were then basket woven together. The cross is the strip to strip gain variations that the basket weaving did on remove.
• The cross outside of the 175meter radius is about 30 db below the peak.
• The bottom image is the uv data divided by the uv beammap. The null rings in the uv beammap that are close to zero give larger rings in this map.

• Page 1 top  beam map (voltages):  with offsets for plotting. The vertical scale is a log scale.
• Page 1 bottom uv map of beam: the vertical scale in in db's.
• Page 2 top Cuts through uv data map: where u=0 (green) and v=0 (black).  You can see the fall off in the amplitude from 0 to 200 meters caused by the convolution with the beam.
• Page 2 bottom cuts through  uv datamap/ uvBeamMap: This has the same strips thru u=0 and v=0. Division by the uvbeammap has flattened the amplitudes in the 0 to 200 meter range. The values outside of 200 meters are blownup because the beam map had small values out there. The distances corresponding to the nulls in the uvBeamMap are blownup.
• Page 3 top integrated amplitudes: The uv data map and uv beammap were binned to 100 distances  and then integrated. The black plot is the uv data, the red line is the uv beam map. The limits of 30 to 300 were set to compare with the values found at drao.
• Page 3 bottom  integrated amplitudes uvdata/uvBeammap: This plot integrates the uvdata/uvbeam map. The values at 240 and 270 (lambdas) correspond to the first null in the beammap at 175 meters. The two peaks are the different az, za dimensions  of the illumination pattern.

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