Singular wavefront reconstruction with the tilts measured by Shack-Hartmann sensor

Abstract

In the present report the possibility of singular points detections using a Shack-Hartmann sensor is described and the precision of the developed detection algorithm is estimated. Also the algorithms of a singular wave front reconstruction are analyzed. Two algorithms are considered and their properties compared. One of them was developed by D. Fried, its description was found in literature. The second algorithm was developed by authors of the report. The both algorithms were introduced into the software of the sensor and insured satisfactory quality of singular phase reconstruction. The precision of algorithms compared in numerical investigations as well in real laboratory experiments.

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.…”

“…After inserting the spiral phase plate 5 and when switching off the adaptive mirror, the wavefront in near field in Figure 22b acquires the spiral form with λ-break (PV=0.63 μ) so the far-field intensity has a doughnut form (see Figure 23b). Note that the wavefront corrector software in the computer 13 is based on the singular reconstruction technique [157][158][159]; the conventional least-squares approach fails here. The vortex in far field is the LG 0 1 mode distorted by presence of other modes mainly because of the phase surface imperfection of the reference beam.…”

Adaptive Optics Progress

“…After inserting the spiral phase plate 5 and when switching off the adaptive mirror, the wavefront in near field in Figure 22b acquires the spiral form with λ-break (PV=0.63 µ) so the far-field intensity has a doughnut form (see Figure 23b). Note that the wavefront corrector software in the computer 13 is based on the singular reconstruction technique [157][158][159]; the conventional least-squares approach fails here. The vortex in far field is the LG 0 1 mode distorted by presence of other modes mainly because of the phase surface imperfection of the reference beam.…”