Research And Modeling Of Free-space Transmission Characteristics Of Free-form Large Deviation Wavefront

A wavefront is the locus of points characterized by identical phase.Within the framework of geometric optics,the wavefront propagates along its normal.Its geometrical shape and boundary will be continuously changed if the wavefront is not ideal plane or spherical plane.The relationships between geometric deformation and propagation distance of freeform wavefronts that are highly deviated or aberrated from reference wavefront,is a basic and key research content in the field of optical design and testing.During the past ten years,the research on the propagation of highly aberrated wavefronts has become increasingly significant in the field of interferometry,wavefront sensing and vision applications.In this dissertation,in-depth research about the propagation of highly aberrated wavefronts in free space and its modeling is carried out.From analytical and numerical aspects,different kinds of existing research results of wavefront propagation modeling within the framework of geometric optics are summarized.Their characteristics and limitations are analyzed.With the use of Zernike circular orthogonal polynomials and XY polynomials,an analytical wavefront-propagation model based on first-order Taylor approximation is proposed and implemented to treat the propagation of the aberrated wavefront from a highly irregular human eye.This propagation model can be applied in most vision applications to treat the propagation of ocular wavefronts since they satisfy the first-order Taylor approximations and their boundaries are still approximately circular after propagation.With respect to the issues that there still exist wavefronts whose slopes dissatisfy the first-order Taylor approximations and boundaries propagate to be non-circular,the wavefront-propagation-model based on numerical method is proposed.Firstly,ray vectors composed of slope and position data of the original wavefront is derived from the original wavefront functions.Secondly,the ray transmission matrix normalized by the radius of original wavefront is proposed and applied to treat the propagation of the ray vectors.After that,a non-iterative method is proposed to derive numerically orthogonal Zernike gradient polynomials from gradients of Zernike circular polynomials.The numerically orthogonal Zernike gradient polynomials are then used to characterize the discrete slope data obtained by ray transfer matrix.Finally,the freeform wavefront is inversed according to the relationship between the slopes and sagittas.This method can be applied not only to treat the propagation of highly aberrated wavefront from real eyes in vision applications,but also to realize the retrace error correction in the testing of freeform optical components.In this way,the proposed method has significant application values and prospects in the field of ophthalmic optics and freeform optics.