Primary Beam Calibration
Last Update: JeffMangum - 02 Mar 2006
Specification (From the ALMA Calibration Specifications and Requirements)
- Must determine the antenna power pattern response of each ALMA antenna to a measurable and repeatable precision of better than 1% (nu =< 400 GHz) and 2% (nu > 400 GHz) of the boresight power response at all points within the -10 dB contour of the beam pattern, for each polarization. This means that at the -10 dB point the precision of that measurement is 10%/20%, respectively.
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JeffMangum - 05 Dec 2005
Contents
Issues Derived from Other ALMA Documents
Pointing Precision Required to Measure Beam HP to 1% at 350 GHz
Gaussian function (normalized) in voltage:
y = exp[-(x2/(2*sigma2))]
At the half-power point:
y = sqrt(0.50) = 0.7071
y+1% error = sqrt(0.50 + (0.50)(0.01)) = sqrt(0.505) = 0.7106
If the voltage pattern at 350 GHz is a Gaussian with amplitude 0.7071 at ±9", then the point at which an amplitude of 0.7106 occurs can be found as follows:
y1 = sqrt(0.50)
y2 = sqrt(0.505)
x1 = 9.0
x2 = ?
Using the equation for a Gaussian (above):
x22 = x12*[ln(y2)/ln(y1)] = (92)*[ln(sqrt(0.505))/ln(sqrt(0.50))] = 81*(0.9856447)
x2 = 9*(0.992796) = 8.935167 arcsec
9.0 - 8.935167 = 0.0648 arcsec
This pointing precision is about 10% of the offset pointing specification. It is also comparable to some of the "unimprovable" contributions to the offset pointing performance.
It appears to me that asking for 1% at the half-power point is unattainable.
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JeffMangum - 02 Mar 2006
The following is a now-outdated discussion of this spec.
As I mentioned in the text which has been included in the Cal Plan, I don't think
6% PB accuracy at the half power point is sufficient -- maybe 6% at the 10% PB level
is OK. Anyway, I think we have plenty of sensitivity to determine the PB much more
accurately than that.
The above conversion between PB error and VP error is not correct:
- At the 0.10 PB level, the VP is 0.316.
- An error of +0.06 in PB, or 0.16 PB, gives us VP = 0.40 (error of 0.084)
- An error of -0.06 in PB, or 0.04 PB, gives us VP = 0.20 (error of 0.116)
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MarkHoldaway - 13 Oct 2004
Mark: You might want to ping
AlWootten about this, because, if I understand you correctly, the Calibration Specs and Reqs are wrong...
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JeffMangum - 15 Oct 2004