Phase Retrieval Based On Weak Beacon Light With No Wavefront Sensor

Obtaining the wavefront information of the beam, is an important part of adaptiveoptics. Phase retrieval based on Gesrchberg-Saxton (GS) algorithm was first proposedin the1970s, which established the core theory of phase retrieval. Subsequently,researchers proposed a variety of effective modified GS algorithm, to improve theaccuracy or convergence speed of GS algorithm. In1982, Gonsalves first describedphase diversity phase retrieval(PDPR) using the intensity of the focal plane and adefocus plane in his paper, intended for extended target phase retrieval. It was used forpoint target, soon. Algorithms for two kinds of target were respectively established.Compared to other wavefront sensing methods, phase retrieval can make full use ofenergy, and has a simple structure, is more suitable for weak beacon wavefront sensing.This paper mainly accomplished the following work, focusing the application of phaseretrieval.Based on the research on the current wavefront sensing methods, their limitationsare analysed for weak beacon light wavefront detection, the development of wavefrontsensing using phase retrieval is discussed.Work on the algorithm of phase retrieval based on the scllar field transmissiontheory. Based on the idea of GS algorithm and PDPR, we used GS iteration algorithm inphase retrieval using the intensity of the focus plane and a defocus plane, and realizedphase retrieval initially. To solve the problem that GS algorithm is easy to fall into localextremum and may not lead to an effective result, an improved GS algorithm isproposed, which adds a third plane in the iteration, the steps of phased retrieval usingthree planes are given. Phase retrieval based on conjugate gradient method is studied. Amathematical optimization algorithm-conjugate gradient is introduced for wavefrontreconstruction.The corresponding target function is selected, and the steps of thisalgorithm is given.Phase retrieval based on GS iteration algorithm, improved GS algorithm, andconjugate gradient algorithm is simulated. The calculation results show that, theimproved GS algorithm can achieve higher precision, comparied with GS algorithm, theRMS error of retrieved phase can be up to one percent wavelength. Using this method,wavefront with a large dynamic range of distortion can be well retrieved. This approachdiffers from PDPR that we calculate the defocus plane intensity based on angularspectrum diffraction. Besides, the intensity of the pupil is not necessary to be measured.Simulation results of conjugate gradient method show that, the wavefront can beretrieved well using only the intensity of the focal plane and a defocus plane. Theprecision can be further improved when another defocus plane is concluded. To verify the simulation results, an experimental testbed is built based on pointsource emitting coherent light. Phase of the pupil is fixed, and intensity of severaldefocus planes is measured. GS algorithm and circulatory GS algorithm are used toprocess the measured results.The calculated results are consistent with the simulation asexpected.The optical field of pupil is not so well retrieved using GS algorithm, and canbe well retrieved using improved GS algorithm and three images.Research in this paper has a certain significance in weak beacon wavefront sensing,telescope aberration detection, optical surface detection and other fields that related tohigh-precision or high-space-frequency phase retrieval.