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

Adaptive Optics and Optical Vortices

“…However, the amplitudes of differential phasors and phasors, obtained under reduction and reconstruction, contain information about measurement errors of phase differences in the actual experiment. Based on this reason the algorithm in question has been modified [157,158,159]. The modification involves exclusion of the operation of complex vector normalization and allows an increase in algorithm accuracy.…”

“…In Figure 18 we present the wave front surface of optical vortex reconstructed by the Hartmann-Shack sensor [161,164] with software incorporating the code of restoration of singular phase surfaces [157][158][159]. Comparison of experimental data with calculated results shows that the wave front surface is restored by the actual Hartmann Shack wavefront sensor with good quality despite the rather small size of the matrix of wave front tilts (spots in the hartmannogram).…”

“…We can use the bimorph [166] as well as pusher-type [167,168] piezoceramic-based adaptive mirrors as a wavefront corrector. In the experiments a flexible bimorph mirror [166] and the Hartmann-Shack wavefront sensor with a new reconstruction algorithm [157][158][159] are employed. An attempt is made to correct the laser beam carrying the optical vortex (namely, the Laguerre-Gaussian LG 0 1 mode), i.e., to remove its singularity.…”

Detector of Optical Vortices as the Main Element of the System of Data Transfer: Principles of Operation, Numerical Model, and Influence of Noise and Atmospheric Turbulence

“…Amplitude of noise A nA should always be less than unity, so with A nA = 1 we obtain the minimum value of coefficient before cosign function in (18). This coefficient is equal to (1 + 1/3) −1 = 0.75.…”

“…Such a detector can be built on the base of a unit measuring or reconstructing (1) distributions of phase gradients (Shack-Hartmann sensor [6][7][8] or a pyramid wavefront sensor [9][10][11]), (2) interference patterns (with subsequent analysis of it) [12,13], (3) distributions of white light intensity (with analysis of chromatic patterns) [14][15][16], (4) phase distributions obtained out of local tilts measured by a wavefront sensor [17,18].…”