The Study Of New Phase Retrieval Algorithms Based On Several Planes

It is a research emphasis in adaptive optics to obtain the optical phase information, but in practice the optical sensors can only obtain the intensity information of optical field directly, so it has become one of the main ideas to recover the phase distribution by optical intensity. Recently, the iterative algorithm for phase recovery has proven to be an effective method, so it is widely applied in active optical systems. But there are also some defects, for example, it is sensitive to initial values and easy to fall into local minimum. This article introduces fractional Fourier transform, Wigner distribution transform into the traditional iterative algorithm, and to some extent, improves the effect the phase recovery. Meanwhile, we try to introduce the wavelet transform into the phase retrieval area to achieve a preliminary result.There are mainly three parts in this thesis: theoretical analysis, numerical simulation, and experimental verification.The first part mainly analyzes basic principles of fractional Fourier transform, Wigner transform, wavelet transform, the intrinsic link between them and the approach to introduce them into phase retrieval algorithm, which includes an optical model designed to achieve fractional Fourier transform as well as its theoretical derivation, and the fractional Fourier transform is applied in the light field transmission process to improve the retrieval algorithm; This part has also introduced the basic principles of Wigner distribution, devised a numerical calculation method of Wigner distribution of the one-dimensional light field which is optimized during the iteration. A wavelet function is constructed based on Fresnel diffraction theory, and using 4f system we design a phase retrieval algorithm based on wavelet decomposition and reconstruction process to extract phase-distribution features of light field. The sampling parameter selection in the optical simulation has also been studied for the following numerical simulation.The numerical simulation section in the thesis proposes basic operations to improve phase retrieval algorithms, the effects of which are simulated at the same time, and results of the FRFT(fractional Fourier transform) phase retrieval algorithm show that the improved algorithm can effectively restore Zernike phase distributions with PV values about 1λ, and the retrieval accuracy RMSE(Root-Mean-Square Error) is about 0.1λ. The algorithm based on Wigner transform can effectively remove the extraneous light-field information to improve the accuracy and pertinence of phase recovery, and when the variance of outside noise is 0.5λ, the phase retrieval accuracy RMSE reaches 0.2λ.The phase retrieval algorithm based on wavelet transform can effectively extract the optical field phase characteristics and achieve a phase distribution in line with its general characteristics.In the experimental verification section, a primary optical experimental platform is devised to authenticate improved phase retrieval algorithms based on fractional Fourier transform and wavelet transform. Experimental results show that the two algorithms can recover the input-beam wavefront effectively, and achieve the desired effects basically.This article introduces three new optical transform methods, fractional Fourier transform, Wigner transform, and wavelet transform into the traditional wavefront reconstruction and has improved the convergence accuracy, noise immunity and other deficiencies of the traditional GS(Gerchberg-Saxton) algorithm. The study lays a foundation for the development of new wavefront reconstruction algorithms which are widely used in the active optical system, and is very important to develop ways to detect wavefront under the weak-beacon conditions and optimize the existing wavefront sensing means.