Phase retrieval wavefront measurement model based on the numerical Fourier theory

Phase retrieval (PR) is widely applied in wavefront sensing for adaptive optics, diagnosing the aberrations, and wavefront measurement of optics elements. A single lens is often used in PR models to achieve better transmission of optical radiation thereby avoiding loss of high frequency information. In this paper, the sampling requirement of PR wavefront measurement model based on numerical Fourier optical theory is analyzed clearly. First, combined with the Fresnel diffraction theory, the diffraction field of the wavefront after passing through the lens is established. Next, according to the Nyquist sampling theorem, the sampling requirements for the phase factor of wavefront spatial frequency are deduced. Further, according to the relationship between the pixel size of CCD and the sampling pitch of pupil surface, the constraints and applicable range of PR model based on various diffraction transform are discussed quantitatively. The numerical simulations are carried out to verify the effectiveness of PR model based on the GS algorithm within the analyzed diffraction constraints, which shows that the recovery accuracy of the PR model can reach 0.0025 λ. The established sampling strategy and the constraint theory in this paper would provide a theoretical guidance for full-band wavefront measurement of the PR technology.