Study Of Phase Retrieval Hybrid Algorithm For The Measurement Of Aspheric Surface

Along with the development of modern optical technology, aspheric mirrors arewidely used in optical systems, and it’s been a new challenge to the opticalmanufacturing and testing technology. The precision and efficiency of opticalmanufacturing technology are determined by the optical testing technology, while inthe early stage of aspheric mirror polishing, traditional testing methods can not meetthe requirements of large optical mirror in many aspects. Phase retrieval is a wavefront sensing method that uses the intensity distribution to reconstruct the phasedistribution of optical field. Phase retrieval technology for the optical surface testinghas the advantage of simple structure, wide testing range and good resistance tovibration and air disturbance. In this paper, the hybrid algorithm based on theprinciple of phase retrieval technology is been put forward for the large range error,and the testing of aspheric mirror with phase retrieval technology is been analyzedand studied. The main contents of this paper include the following aspects:1. The basic principle of the surface testing with phase retrieval technology isintroduced, and the testing model based on multiple defocus images is established.The process of optical field propagation is described by the diffraction angularspectrum theory in the Fresnel zone, and as for the problem of high frequencyoscillation phenomenon caused by discrete calculation, the zero-padding method isuseful to improve the quality of diffraction images effectively. Analysis of theconvergence of GS algorithm shows that GS algorithm is essentially a kind of errorreduction algorithm, and the MGS algorithm suitable for optical mirror testing is putforward.2. Phase retrieval algorithm for large range error which has been existing alreadyare summarized and analyzed, and the hybrid algorithm based on gradient searchalgorithm and MGS algorithm is put forward. Wave front distribution is described byZernike polynomial algorithm, and the polynomial coefficients which arecorresponding to the low-frequency error is optimized by the gradient searchalgorithm, then the high frequency error is recovered by the MGS algorithm. Theresult of simulation experiment shows that the hybrid algorithm is rapid convergentand accurate.3. The error range of amplitude and frequency are analyzed, and phase retrieval testing experiment of a130mm diameter spherical mirror is conducted, theexperimental study on the phase recovery surface testing is introduced. Theexperiment result is compared with the result of interference testing, and the residualdistribution and PSD show that the result of phase recovery surface testing andinterference testing are basically same. The light source positioning error and focuspositioning error are analyzed quantitatively, and the methods to reduce these errorsare put forward.4. The reflecting light field of aspheric mirror is analyzed, and through thestudy of the caustic region, the effective regions of defocus images are made clear forphase retrieval aspheric testing. In order to reduce the influence of asphericity, phaseretrieval aspheric testing method based on the best fitting spherical is established,which translates the testing of aspheric mirror into the testing of spherical mirror withlarge range error.5. Phase retrieval testing experiment of a140mm diameter parabolic mirror isconducted, and the experiment result is compared with the result of CGH testing, theexperimental result shows that phase retrieval aspheric testing can realize a hightesting accuracy of aspheric mirror in low requirements of experimental environmentand equipment.