## 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.

-- JeffMangum - 05 Dec 2005

### 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.

-- 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The following is a now-outdated discussion of this spec.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:

1. At the 0.10 PB level, the VP is 0.316.
2. An error of +0.06 in PB, or 0.16 PB, gives us VP = 0.40 (error of 0.084)
3. An error of -0.06 in PB, or 0.04 PB, gives us VP = 0.20 (error of 0.116)

-- 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...

-- JeffMangum - 15 Oct 2004

Topic revision: r13 - 2006-08-29, JeffMangum
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