Theory of singular-phase reconstruction for an optical speckle field in the turbulent atmosphere

Analytical expressions are derived and computational algorithms are constructed for retrieving optical-field phase distribution under strong scintillation. The input data for the phase reconstruction are the wave-front slopes registered by a Hartmann sensor or shearing interferometer. The theory is based on representing the slope-vector field as the sum of its potential and solenoid components; it introduces the concept of phase-source and phase-vortex density and uses strict integral expressions relating these quantities to the wave-front slopes. To overcome the difficulties arising from the singular character of phase distribution, use is made of regularization of the wave-front slopes. The slopes can be measured with an ideal point wave-front sensor. It is shown that the slopes measured at the output of a nonideal sensor can be treated as regularized values of these slopes. Numerical simulation of phase unwrapping from the reference values of the wave-front slopes has shown that the algorithm designed for visualization of local phase singularities and those for phase reconstruction are very helpful in eliminating the measurement noise.