The phase carries details of the depth information about an optical wave field and is very important in many applications, such as optical field reconstruction and 3D display. However, optical waves oscillate too fast for detectors to record the intensity and phase directly and simultaneously. The phase retrieval technology or algorithm has been the focus of enormous research recently. Among the valuable algorithms transport-of-intensity equation (TIE) and angular-spectrum- iteration (ASI) are widely used in various fields such as electron microscopy and x-ray imaging. Unfortunately, the former one is originally derived for a coherent illumination and can not be directly applied to the phase retrieval of partially coherent light field when not been uniformly lit. While the ASI deducted from wave propagating with wave vector has itself shortcomings due to iterative uncertainty and slow convergence. In this paper, a novel hybrid phase retrieval algorithm extended TIE for partially coherent light illuminations is investigated in both case of uniformly and non-uniformly lit. This algorithm consists of multi-plane ASI to utilize the physical constraints between the object domain and the spectral domain, and the relationship between the intensity and phase among the wave propagation. The phase at the center image plane is calculated from three intensity images. Then this result is treated as the initial value of the multi-plane ASI. Finally, the phase information at the object plane is acquired according the reversibility of the optical path. This hybrid algorithm expands the application of tradition TIE while improving the convergence rate of ASI method.
The goal of phase retrieval is to recover the phase information from intensity distribution which is an important topic in optics and image processing. The algorithm based on the transport of intensity equation only need to measure the spatial intensity of the center plane and adjacent light field plane, and reconstruct the phase object by solving second order differential equations. The algorithm is derived in the coherent light field. And the partially coherent light field is described more complex. The field at any point in the space experiences statistical fluctuations over time. Therefore, traditional TIE algorithms cannot be applied in calculating the phase of partially coherent light field. In this thesis, the phase retrieval algorithm is proposed for partially coherent light field. First, the description and propagation equation of partially coherent light field is established. Then, the phase is retrieved by TIE Fourier transform. Experimental results with simulated uniform and non-uniform illumination demonstrate the effectiveness of the proposed method in phase retrieval for partially coherent light field.