Laser Wave-Front Analyzer Software Improvement.

A software package was written which will analyze annular shaped laser wave-fronts. This involved generating a set of orthogonal polynomials from the Zernike polynomials by using the Gram-Schmidt orthogonalization process. The coefficients of the polynomials are determined by using the orthogonality of the polynomials, instead of using the common least-squares method. The coefficients of the generated polynomials are converted to Zernike coefficients, and both sets of coefficients are presented to the user. By using the first moments of the wave-fronts position in the collection array, the software is able to define the basic parameters of the wave-front. These parameters are center, outside radius, and the obscuration ratio of the wave-front. With these parameters, the soft-ware computes 6, then 11, then 22 coefficients to show the stability of the coefficients. With well-defined circular and annular wave-fronts, the program was consistently able to compute the coefficients with an RMS error of less than 0.050 waves.