OPTICAL PHASE RECONSTRUCTION FROM THE WAVE-FRONT SLOPES

摘要

Phase of laser beam propagated in medium can be exposed to nonlinear effects and distorted essentially. The phase compensation utilizing a single deformable mirror in the presence of strong scintillation has its performance limited not by the varying illumination levels across the pupil but by the presence of phase singularities that accompany the intensity nulls. An analytical expression connecting the optical beam phase with the values of its partial derivatives is proposed to solve a problem of the phase reconstruction from the measurements of wavefront slopes by Hartman sensor, shearing interferometer, and from the interference measurements of Knox-Thompson. This relationship is a consequence of the statement of a task to reconstruct the phase from the wavefront slopes as a boundary problem of mathematical physics and allows an analytical presentation of the coefficients of the phase expansion on a prescribed system of functions to be written. The derived analytical representations for the phase and its mode components are used for numerical reconstruction of the singular phase characteristic of the optical speckle fields. The reconstructed phase consists of the regularized approximation which makes it possible to detect the position and orientation of the wavefront dislocations and the singular part obtained from the measured wavefront slopes with allowance for the vortex properties of the phase gradient.