Reflector errors: ruze curves.
mar 2009
The error in the reflectors will cause the gain to
decrease as the wavelength decreases. The ruze formula tells how much
this is:
- Gain=Gain0 * exp(-(4*pi*delta/lambda)^2)
- Gain0 is the gain for a perfect reflector (or long wavelength).
- Delta is the rms surface error (which should be random)
- Lambda is the wavelength in the same units as delta.
The measured telescope gain from jul08 thru feb09
was used to compute the ruze curves.
The plot shows the gain
vs frequency with the ruze curves over plotted (.ps) (.pdf):
- 3409 gain measurements were used (lband thru xband).
- For each frequency, the median gain value for za=[5 to 14]
degrees was plotted (purple *).
- Gain0 was taken to be 10.75 Jy. This value was picked because it
went thru the highest lband point.
- 2762 m^2 is 1 kelvin.
- A 225 spherical aperture has 39760 m^2 or 14.4 K/Jy.
- This assumes a uniform flux across the area. The edge taper
will decrease this:
- 12K/Jy/14.4K/Jy = .83 aperture efficiency
- 10.75 K/Jy/14.4 = .75 aperture efficiency.
- The dashed color lines are the gain vs frequency from the ruze
equation using various surface errors:
- black: rms= 1.5 mm
- red: rms=2.0 mm
- green: rms=2.5 mm
- blue: rms=3.0 mm
- The 2.5 mm comes closest to the data. Some of the errors in the
data are:
- cbh (6-8 Ghz) under illuminates the tertiary (so the gain is
low).
- The cals could be a bit off.
- For higher frequencies, some of the sources with 15" extent or
more are no longer point sources.
processing: ~phil/talks/ausac09/surfErr.pro
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