Hi guys,(adsbygoogle = window.adsbygoogle || []).push({});

My research project involves a paraboloidal telescope with a primary diameter of 25 meters, and a focal length of 10 meters. My goal is to come up with the mathematics and numerics to determine the surface profile error of the primary mirror. We will take a point source of 2mm wavelength light at a height of about 22 meters above the vertex of the paraboloid, shine it on the primary, and measure the reflected image (field amplitude and phase) using several detectors placed in the same vertical plane as the light source. We will construct a system of linear equations to relate the measured field to a piecewise constant function representing the deformations of the telescope primary.

The first step in doing something like this is to figure out the electric field pattern reflected by the primary. I have been treating this as a diffraction problem. Basically, I have been using the Fresnel-Kirchhoff diffraction formula and numerically integrating the formula over the primary. The Fresnel-Kirchhoff diffraction formula comes directly from the Kirchoff integral theorem, and assuming that the point source of light emits spherical waves. The Kirchoff integral theorem comes from the scalar Helmholtz equation.

Here is my question: I would like to have an idea just how accurate the Kirchhoff model of diffraction is, and whether it would be accurate enough to suit my needs. I would like to get the accuracy of my electric field calculations to 1 part in 1000, hopefully 1 part in 10000. But I have no idea just how accurate the Kirchhoff model would be, given the aforementioned parameters for the dimensions of the problem.

While the Kirchhoff model is the best I know how to use, it is an approximation. If it is not good enough, then what exactly is wrong with the Kirchhoff model, and what would be a better model to use? For example, would I need to go beyond scalar diffraction theory, using instead vector diffraction theory? What sources would you guys recommend, if any, to learn it?

Finally, where can I get a source that compares how accurate various diffraction models are? All of the articles I have been looking through present some pretty detailed mathematics without really explaining how much of an accuracy improvement they really offer. Is it possible to find any formulas that estimate the accuracy of Kirchoff, or more advanced diffraction theory? This would truly give me a better understanding of the situation.

Thanks,

-Sam.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Accuracy of Kirchhoff diffraction theory

**Physics Forums | Science Articles, Homework Help, Discussion**