# How close is a 2D Gaussian to an Airy disk?

by omoplata
Tags: airy, disk, gaussian
 P: 315 0) If by "how large" you mean the angular diameter of the Airy disk, looking at the wikipedia article, the intensity of the Airy disk $I(\theta)$ is related to the radius of the aperture $a$ ( in this case the radius of the satellite dish? ), using the same notation as the wikipedia article. ( I'm using the term Airy "disk" and not "function" here, because it seems different from an Airy function ) 1) If detector (LBNF) has full sensitivity to an angle larger than the angle of the dish edge, I think we can take ignore the angular sensitivity distribution of the detector, because then the aperture is going to be the whole dish ( if the background behind the dish emits little radio signals of the relevent frequency) . If the sensitivity of the detector falls off with increasing angle from the central axis with such a rapid rate that it drops off before it reaches the dish edge, then I guess we have to take that in to account. 2) This is certainly an issue. 3) We were detecting a geocentric satellite. So it did not move in relation to our position. 4) So I guess considering 1) and 2), it is possible that our plot can NOT be the cross section of an Airy disk. When I told the professor in charge of the experiment that I fitted a Gaussian, he said "Why did you fit a Gaussian? It's supposed to be an Airy disk." The reason why did not fit one yet is because the fitting software I am using right now does not have Bessel functions ( the wikipedia Airy disk equation is given in terms of Bessel functions ). I'm going to find another fitting software which has Bessel functions and fit it. So this observation might be premature, but I can't see any secondary peaks. The other two members in our group have the same problem. How to find a fitting software that can fit an Airy disk. But we think we found one ( IDL ), and we are going to try it out. This link lists the functions in the NASA IDL Astronomy User's Library for IDL (which is very widely used in the Astronomy community) , and even they seem to be fitting Point Spread Functions with Gaussians and not Airy disks ( functions FIND and GETPSF ).