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We report on the development of a point diffraction interferometer in visible light with surface figure measurement accuracy of λ/50 PV. The system enables simultaneously testing of the radius of curvature with the accuracy δR/R =5×10-4.

Zernike circle polynomials are in widespread use in the commercial software of interferometer. However, they are not appropriate for noncircular pupils, such as annular, hexagonal, elliptical, and rectangular pupils. The traditional wavefront fitting or analysis in interferometric software are all for circular pupils, although working with the corresponding noncircular masks. For wavefront fitting with complex pupils, the necessity of applying orthogonal Zernike polynomials is demonstrated. Besides, the conventional method of removing misalignment error is illustrated to be adequate for the complex pupil.

Previous two-wavelength calculation algorithm technique must be implemented on the basis of the single-wavelength phase data. Here, we propose a new approach that combines ideas of moire’fringe theory and phase shifting interferometry. The patterns of two wavelengths are multiplied directly and filtered out the low frequency component to obtain the fringe pattern of equivalent wavelength. Then the phase of equivalent wavelength can be extracted by the conventional phase-step algorithm. Also, the algorithm can avoid the phase-step miscalibration introduced by traditional two wavelength phase shifting method.

Wavefront aberration function is modified and expressed by combination of Bi-Zernike polynomials in rotationally symmetric optical systems. The field and pupil parameters of wavefront aberration function are separated and described respectively by orthonormal Zernike polynomials.