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A novel approach based on the two-channel moir\'e deflectometry has been used to measure both wave-front and transverse component of the Poynting vector of an optical vortex beam. Generated vortex beam by the q-plate, an inhomogeneous liquid crystal cell, has been analyzed with such technique. The measured topological charge of generated beams are in an excellent agreement with theoretical prediction., Comment: 3 pages, 2 figures

An adjustable, high sensitivity, wide dynamic range two channel wave-front sensor based on moire deflectometry has been constructed for measuring distortions of light wave-front transmitted through the atmosphere. In this approach, a slightly divergent laser beam is passed through the turbulent ground level atmosphere and then a beam-splitter divides it into two beams. The beams pass through a pair of moire deflectometers which are installed parallel and close together. From deviations in the moire fringes we calculate the two orthogonal components of angle of arrival at each location across the wave-front. The deviations have been deduced in successive frames which allows evolution of the wave-front shape to be determined. The dynamic range and sensitivity of detection are adjustable by merely changing the separation of the gratings and the angle between the rulings of the gratings in both of channels. The spatial resolution of the method is also adjustable by means of bright, dark, and virtual traces for given moire fringes without paying a toll in the measurement precision.

A wavefront sensor which takes advantage of the moire deflectometry has been constructed for measuring atmosphere induced wavefront distortions. In this sensor a collimated laser beam propagates through turbulent atmosphere, then a beam splitter splits it into two beams and the beams pass through a pair of moire deflectometers. Directions of the grating's rulings are parallel in each moire deflectometer but are perpendicular in the two beams. Using a suitable array of lenses and mirrors two sets of moire patterns are projected on a CCD camera. A suitable spatial filter removes the unwanted frequencies. Recording the successive moire patterns by the CCD camera and feeding them to a computer, allow temporal fluctuations of the laser beam wavefront phase to be measured highly accurately. Displacements of the moire fringes in the recorded patterns correspond to the fluctuations of two orthogonal components of the angle of arrival (AA) across the wavefront. The fluctuations have been deduced in successive frames, and then evolution of the wavefront shape is determined. The implementation of the technique is straightforward and it overcomes some of the technical difficulties of the Schlieren and Shack-Hartmann techniques. The sensitivity of detection is adjustable by merely changing the distance between two gratings in both moire deflectometers and relative grating ruling orientation. This overcomes the deficiency of the Shack-Hartman sensors in that these require expensive retrofitting to change sensitivity. Besides, in the moire deflectometry, the measurement is relatively insensitive to the alignment of the beam into the device. Hence this setup has a very good potential for adaptive optics applications in astronomy. Since tilts are measured in the Shack-Hartmann method at discrete locations, it cannot detect discontinuous steps in the wavefront. By this method discontinuous steps in the wavefront are detectable, because AA fluctuations are measured across the wavefront.

Recently, an adjustable, high-sensitivity, wide dynamic range, two-channel wavefront sensor based on moire deflectometry was proposed by Rasouli et al (2010 Opt. Express 18 23906). In this work we have used this sensor on a telescope for measuring turbulence-induced wavefront distortions. A slightly divergent laser beam passes through turbulent ground level atmosphere and enters the telescope’s aperture. The laser beam is collimated behind the telescope’s focal point by means of a collimator and the beam enters the wavefront sensor. First, from deviations in the moire fringes we calculate the two orthogonal components of the angle of arrival at each location across the wavefront. The deviations have been deduced in successive frames which allows evolution of the wavefront shape and Fried’s seeing parameter r0 to be determined. Mainly, statistical analysis of the reconstructed wavefront distortions are presented. The achieved accuracy in the measurements and comparison between the measurements and the theoretical models are presented. Owing to the use of the sensor on a telescope, and using sub-pixel accuracy for the measurement of the moire fringe displacements, the sensitivity of the measurements is improved by more than one order of magnitude. In this work we have achieved a minimum measurable angle of arrival fluctuations equal to 3.7 × 10−7 rad or 0.07 arc s. Besides, because of the large area of the telescope’s aperture, a high spatial resolution is achieved in detecting the spatial perturbations of the atmospheric turbulence.