Abstract

An analytical formulation that relates the modal expansion coefficients of a given wave front to its local transverse phase derivatives is proposed. The modal coefficients are calculated as a weighted integral over the wave-front slopes. The weighting functions for each mode are the components of a two-dimensional vector whose divergence equals the corresponding mode function. This approach is useful for analytical phase reconstruction from the input data provided by shearing interferometers or Hartmann–Shack wave-front sensors. Numerical results for a simulated experiment in terms of a set of Zernike polynomials are given.

© 1995 Optical Society of America

Analytical representation of the phase and its mode components reconstructed according to the wave-front slopes

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