Changes

== Creating a Surface Generator ==

== 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 [[#References|[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 <math>a_{i,j}P_{i}(x)P_{j}(y)</math> [[#References|[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 <math>a_{i,j}</math>. 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.

Matlab was used to create a program that would generate simulated surfaces and their interferograms[[Image:Alisatest2-6-2008.jpg|thumb|An interferogram generated by the surface generator]] to be analyzed using the algorithm. As was true for the test surface used in Reference [[#References|[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 <math>a_{i,j}P_{i}(x)P_{j}(y)</math> [[#References|[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 <math>a_{i,j}</math>. 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.

== ParSA and Runlength ==

== ParSA and Runlength ==