Optical Surface Measurement using Phase Retrieval Hybrid Algorithm based on Diffraction Angular Spectrum Theory

In order to test the high dynamic range error beyond one wavelength after the rough polish process, we design a phase retrieval hybrid algorithm based on diffraction angular spectrum theory. Phase retrieval is a wave front sensing method that uses the intensity distribution to reconstruct the phase distribution of optical field. Phase retrieval is established on the model of diffractive propagation and approach the real intensity distribution gradually. In this paper, we introduce the basic principle and challenges of optical surface measurement using phase retrieval, then discuss the major parts of phase retrieval: diffractive propagation and hybrid algorithm. The angular spectrum theory describes the diffractive propagation in the frequency domain instead of spatial domain, which simplifies the computation greatly. Through the theoretical analysis, the angular spectrum in discrete form is more effective when the high frequency part values less and the diffractive distance isn't far. The phase retrieval hybrid algorithm derives from modified GS algorithm and conjugate gradient method, aiming to solve the problem of phase wrapping caused by the high dynamic range error. In the algorithm, phase distribution is described by Zernike polynomials and the coefficients of Zernike polynomials are optimized by the hybrid algorithm. Simulation results show that the retrieved phase distribution and real phase distribution are quite contiguous for the high dynamic range error beyond lambda.