Bryan Butler 
October 31, 1997
Keywords: anomalous refraction, atmosphere, pointing errors
In MMA memo 186 (Holdaway 1997), Mark Holdaway pointed out the important contribution of atmospheric anomalous refraction to the pointing error budget for the proposed MMA antennas. He derived expressions for the magnitude of the effect of anomalous refraction on the pointing of antennas of different sizes, and calculated values for proposed MMA antenna sizes for the particular atmospheric characteristics of the Chajnantor site. I think Mark got the story right, in that his conclusion was that the pointing error due to anomalous refraction is smaller in absolute magnitude for larger antennas, but larger as a fraction of beamwidth. However, it is not clear that he got the absolute values of the numbers right in the non-zenith case. He derived a pretty unwieldy equation for the anomalous refraction for this case (his equation 12), which has some very non-physical terms in it, and I am not convinced that this equation is correct. I have derived what I _think_ is the correct formula for the non-zenith case. This formula is much simpler, and is (see below for notation):
I'll present this derivation and some numerical examples in this memo. It turns out that my numbers have a slightly weaker dependence on elevation than Mark's do, e.g., at 20 deg. my numbers are about 10% smaller than his (I derive a smaller rms pointing error due to anomalous refraction). The intent of this memo is _not_ to imply that Mark did something egregious, but merely to present this simpler formula, and the new values obtained from it. Again, he got the basic story right in memo 186.
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