Analysis of Michelson interference images

This page represents a portion of an ongoing project aimed at mapping the surface of a diamond wafer using the interference pattern that the diamond wafer creates when it is placed in the beam path of a Michelson interferometer. In his work on this project, Matthew Demas created a parallel Simulated Annealing algorithm designed to analyze the interference patterns and he tested it out on a simulated surface and its interferogram. The next step is to create simulated surfaces that more and more closely resemble the surface of a real diamond wafer and use the algorithm to analyze their interferograms so that we have an idea of how the algorithm will react to a real diamond wafer.

Creating a Surface Generator
Matlab was used to create a program that would generate simulated surfaces and their interferograms to be analyzed using the algorithm. As was true for the test surface used in Reference [1], Legendre polynomials of two variables were chosen as a basis set with which to describe the surfaces. The surfaces are described by the weighted sum of the matrix elements $$a_{i,j}P_{i}(x)P_{j}(y)$$ [1]. These elements take the products of the Legendre polynomials of x and of y in all possible combinations of respective i's and j's and assign to each product its own coefficient, namely $$a_{i,j}$$. This is what the surface generator is designed to do. The first set of surfaces was kept somewhat similar to the original test surface. Their interferograms were kept at fifty pixels by fifty pixels, but the coefficients were randomly generated and Legendre polynomials up to the 2nd degree were incorporated. These changes make the surface more closely resemble the surface of a real diamond wafer, but also make the surface a little more difficult for the algorithm to analyze.