Optical Wavefront Reconstruction: Theory and Numerical Methods

• Published in: SIAM review Vol. 44; no. 2; pp. 169 - 224
• Main Authors: D. Russell Luke, Burke, James V., Richard G. Lyon
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.06.2002
• Subjects: Algorithms; Applied classical electromagnetism; Applied sciences; Approximation; Calculus of variations and optimal control; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; electron and ion optics; Exact sciences and technology; Fourier transformations; Fundamental areas of phenomenology (including applications); Geometric planes; Geometry; Hubble Space Telescope; Imaging; Least squares; Mathematical analysis; Mathematical functions; Mathematical programming; Mathematics; Operational research and scientific management; Operational research. Management science; Optical lenses; Optics; Physics; Sciences and techniques of general use; Space telescopes; Survey and Review; Wave diffraction; Radiations; Helmholtz equations; Thin lens; Non convex programming; Kirchhoff condition; Theory; Boundary conditions; Geometrical optics; Numerical method; Rayleigh Sommerfeld diffraction; Algorithms; Diffraction; Wave front; Dirichlet problem; Least square fit; Phase reconstruction
• ISSN: 0036-1445; 1095-7200; 1095-7200
• DOI: 10.1137/s003614450139075

Optical wavefront reconstruction algorithms played a central role in the effort to identify gross manufacturing errors in NASA's Hubble Space Telescope (HST). NASA's success with reconstruction algorithms on the HST has led to an effort to develop software that can aid and in some cases replace complicated, expensive, and error-prone hardware. Among the many applications is HST's replacement, the Next Generation Space Telescope (NGST). This work details the theory of optical wavefront reconstruction, reviews some numerical methods for this problem, and presents a novel numerical technique that we call extended least squares. We compare the performance of these numerical methods for potential inclusion in prototype NGST optical wavefront reconstruction software. We begin with a tutorial on Rayleigh-Sommerfeld diffraction theory.