Sphere-to-sphere diffraction propagation method for a phase-retrieval algorithm in the measurement of optical surfaces

We present an improved phase-retrieval algorithm that is based on the Sziklas and Siegman coordinate transformation (SSCT) and applied to optical surface testing. With the SSCT, a spherical-wave diffraction problem can be transformed into a plane-wave diffraction problem, and the fast Fourier transform can be applied directly in propagation computations. Compared with conventional diffraction propagation methods, the proposed method is simple and relatively fast, and the computation efficiency for the phase-retrieval algorithm can be increased to a certain degree. Analysis and simulation were performed for this method, and simulation results exhibit correct diffraction computation and good phase-retrieval capability. A practical 200 mm diameter, f/5 spherical surface was tested; testing results showed good agreement with that of a ZYGO interferometer, which confirmed the feasibility and accuracy of the proposed method.