Phase Retrieval Based On SLM Tunable-Lens And Transport Of Intensity Equation

Optical waves can be described by intensity and phase.However,optical waves oscillate too fast for detectors to measure anything but time-averaged intensities.This is unfortunate since the phase can reveal important information about the object.Therefore,it is necessary to apply the known intensity information to retrieve the phase information,which is called phase retrieval.Currently,the technology has been used in many fields,such as X ray diffraction imaging,optical phase microscopy,optical measurement and adaptive optics.The transport of intensity equation is one of the typical phase recovery methods,it describes the quantitative relationship between the axial light intensity variation and the phase,so the phase information can be obtained directly and quantitatively by solving the partial differential equation.Therefore,the TIE gains many unique advantages such as non-interferometry,non-iterative,does not requires the complicated optic system and stringent experimental environment.The solution of TIE requires a set of intensity images at longitudinal planes to realize the numerical finite difference for estimating the axial intensity differential,which is usually realized by translating the camera or object manually or mechanically,however,slowing down the process of capture intensity images,introducing the error caused by mechanical movement,losing a great advantage over the iterative phase retrieval method.In this paper,we introduce the spatial light modulator in the calculation of phase recovery based on its characteristics of light field modulation,and propose new phase retrieval algorithms to solve the above problemsThe main works and innovations are summarized as following:(1)Phase retrieval based on transport of intensity equation and LCOS tunable-lens.A quadratic phase pattern is displayed on the LCOS to provide a lens effect for realizing different defocus distance by varying the focal length of the lens.The Fresnel lens phase pattern is encoded on the LCOS to realize the function of tunable-lens instead of the Fourier lens in the traditional single lens optical propagation system.By varying the focal length of the loaded Fresnel lens phase pattern,distinct intensity images of different defocus distance can be collected without moving the acquisition device,and the phase is solved using the transport of intensity equation.The experimental system is set up,and the experimental results show that the algorithm can obtain the quantitative phase result rapidly and efficiently.(2)Phase retrieval using transport of intensity equation based on SLM tunable-lens and 4f system.A SLM is located in the Fourier domain of the 4f system and the lens phase pattern is loaded on the SLM,diifferent light intensity images at different defocus distances can be recorded in the same imaging plane by varying the focal length of the phase pattern,realized a precisely programmable defocus light intensity acquisition system with fast speed and non-mechanical movement,the Fourier method is used to solve the TIE rapidly.The phase retrieval methods based on the transport of intensity equation in coherent light field and partially coherent light field are discussed respectively.Real experiments are given under two different light source conditions,and the validity of the algorithm is verified.