Algorithms for the reconstruction of the singular wave front of laser radiation: analysis and improvement of accuracy

The possibility of reconstructing a singular wave front of laser beams by the local tilts of the wave front measured with a Hartmann sensor is considered. The accuracy of the reconstruction algorithm described by Fried is estimated and its modification is proposed, which allows one to improve the reliability of the phase reconstruction. Based on the Fried algorithm and its modification, a combined algorithm is constructed whose advantages are demonstrated in numerical experiments.