Polynomial fit of interferograms

Polynomial fit of interferograms is analyzed quantitatively. The errors from polynomial fit, such as fit error, digitization error, roundoff error, and finite sampling error, are explained. The advantage of using orthonormal polynomials are presented. The best reference wave front and the relative reference wave front are defined, and their characteristics are compared. The possibility of using nonorthonormal polynomials for analysis of noncircular aperture interferograms is discussed. A simulation using Zernike polynomials for an annular aperture interferogram is shown. Finally a method of obtaining the surface figure error information from several smaller subaperture interferograms is introduced, and a simulation of testing a large flat is shown.