Optical modeling of finite element surface displacements using commercial software

Transformation of the results of the finite-element analysis of optical-surface displacements for use in optical-analysis packages

“…High accuracy of the approximation is achieved by using AZEP: The deviations were Δ 1.84 nm and σ 0.61 nm, which are two orders of magnitude lower than the allowed value for telescopes for remote probing of the earth. 4 …”

“…This method is preferable in accuracy to the method that uses the Zernike polynomials, except when sharp local distortions of the OS shape are present-for example, when there are local or fine-structure deformations. 4 In the first studies carried out in the area considered here, it was ignored that the points of the OS when deformation occurs are misaligned not only along the optical axis, but also perpendicular to it. It was pointed out in Refs.…”

“…Therefore, when a transition is made to optical analysis, the positions of the nodes of the undeformed FEL are first projected in the direction of the optical axis onto the exact OS. 4 Various authors have considered the possibilities of approximating the displacements of an OS both in the direction of the normal to the undeformed surface and in the direction of the optical axis. 5,7 The former approach has the advantage that the displacements along the normal are ordinarily used to describe the variation of the geometry of the OS when files of interferograms are formed.…”

“…However, the latter approach makes it possible to obtain a more accurate approximation. 4 This article discusses questions of increasing the accuracy by using Zernike polynomials to approximate the displacements of the points of an OS in the direction of the optical axis obtained by the FE method, associated with discriminating displacements of the surface as a rigid whole.…”

Mathematical construction and perturbation analysis of Zernike discrete orthogonal points

“…The surface aberrations or wavefronts of an optical system are recorded with a uniform sampling array like a CCD and then recovered with certain algorithms, such as phase shifting algorithms [3,4] in modern digital phase shifting interferometers. In optomechanical analysis, predicting optical performance under the actual operational environment of an optical system often requires importing finite element computed surface displacements into the optical model such as the Zernike description of surface undulation [5,6]. The finite element meshing for optics is carried out with certain types of grid partitioning.…”