Phase Diversity Wavefront Detecting Technology Research Based On Taylor Expansion

While the aperature of space telescope becomes larger and larger,the environment such as vibration,gravity and stress discharge has a worse impact on the telescope when it is transferred and sent to space.If the passive support structure couldn'd ensure that the quality of image is up to the mustard,the active optics technology will be introduced in the telescope system to correct the misalignment.Active optics mainly includes three parts: first,detecting the wavefront of the misaligned system;second,solving the misalignments using the detected wavefront;last,correcting the misalignments.Wavefront detecting with high accuracy is the precondition of using active optics to make sure that the quality of image is up to the mustard.Many methods have been proposed to detect the wavefront of the system.These methods can be classified into two types: one depends on detecting the slope of the wavefront and then reconstructs the wavefront using specific algorithm,such as Shack-Hartmann detector,the other depends on detecting images on different planes and then reconstruct the wavefront using corresponding algorithm,such as Phase Retrieval(PR)and Phase Diversity(PD).Because the method based on detecting the slope of the wavefront needs extra structure to be installed in the optical system,this will occupy the space on the telescope.The method depends on detecting images on different planes can use the existing structure on the system,which is quite easily to realize.Meanwhile,because Phase Diversity could be used when the observed object is an expanded target,it appeals to many researchers.Based on the needs of building large aperature space telescope,this paper is carried around the key issues of using Phase Diversity algorithm to detect the space telescope's wavefront,the main research work are summarized as below:1.Study the solving model of traditional Phase Diversity algorithm,and use the first-order Taylor expansion to utilize an iterative linearization of the PSF/OTF at two or more diverse planes when the aberration is very small.By building the relationship between the real images and those reconstructed using linear approximate of PSF/OTF,we deduce the dominant relationship between the aberration and the image,which can decrease the calculated amount of Phase Diversity algorithm with a good astringency.A large amount of numerical simulations verify the accuracy of the modified algorithm.2.Analyze the error model of Phase Diversity algorithm when it is used in active optics on space telescope system,such as defocus error,image noise,image alignment error,etc.We analyze the influence of these errors on the accuray of the algorithm,and for some kinds of errors,methods to eliminate these impacts through modifying the phase diversity algorithm without other auxiliary correction strategies are presented,which can provide important technology support for the usage of phase diversity wavefront detection technology in practical engineering.3.Propose a kind of Phase Diversity algorithm by extending the Zernike polynomial term to the complex field when the light intensity on the pupil plane is not uniform.By regarding the distribution of the light intensity as the imaginary part of the phase,it can be solved together with the phase aberration(the real part of the phase),which can reduce the influence of the light distribution on Phase Diversity algorithm.4.Analyze the influence of tiny vibration on Phase Diversity algorithm,and present a method using the power spectrum to estimate the vibration factor.The use of the vibration factor to execute a reconvolution with the image could increase the accuracy of wavefront reconstruction.5.Use the function of ray trace in ZEMAX to verify the accuracy of the modified Phase Diversity algorithm based on first-order Taylor expansion.By using the point spread function of SNAP telescope acquired from ZEMAX,we reconstruct the wavefront map of SNAP,and compare it with the real wavefront map acquired from ZEMAX.The large amount of monte carlo numerical simulation show that the modified Phase Diversity algorithm has a high accuracy.6.Design viable experiment protocols and build optical test platform to verify the feasibility and correctness of the algorithm based on first-order Taylor expansion.Design inhomogeneous light intensity illumination experiment protocols to verify the feasibility and correctness of the algorithm based on complex Zernike polynomial term.Design tiny vibration experiment protocols using fast steering mirror to verify the feasibility and correctness of the algorithm based on vibration factor to execute a reconvolution with the image.