Determination of phase mode components in terms of local wave-front slopes: an analytical approach.

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.