The conventional Zernike polynomial fit of circular aperture interferograms is reviewed and a more quantitative and statistical analysis is added. Some conventional questions such as the required number of polynomials, sampling requirements, and how to determine the optimum references surface are answered. Then, the analysis is applied to the polynomial fit of noncircular aperture interferograms and axicon interferograms. The problems and limitations of using Zernike polynomials are presented. A method of obtaining the surface figure error information from several smaller subaperture interferograms is analyzed. The limitations of the analysis for testing a large flat, a large parabola, or an aspheric surface are presented. The analysis is compared with the local connection method using overlapped wavefront information. Finally, the subaperture interferogram analysis is used to average several interferograms and to analyze lateral shearing interferograms.