This paper presents a new technique of localization of Optical Vortex center (Vortex Point), which is based on Artificial
Neural Network. The network accepts as inputs intensities of pixels in a square sub-area of fixed size and produces two
output signals correlated to X and Y coordinates of vortex point. A feed-forward neural network with one hidden,
non-linear layer was used. The learning criterion was Mean Squared Error and the net was trained with
Levenberg-Marquardt algorithm implemented in MATLAB with distorted and noisy images of simulated Optical Vortex
Interferometer. The authors provide the results of localization for two sizes of sub-area and two types of simulated
interference patterns. The first type of interferogram contain lattice of optical vortices obtained by interference of three
plane waves and the second type of interferogram with fringe bifurcations created by interference of lattice of optical
vortex with additional, fourth plane wave. The results of simulations suggest possible employment of the proposed
method in an experimental setup due to the localization error median being around 0.4 pixel for "three waves" case and
0.9 pixel for "four waves".
Optical vortex interferometer (OVI) is a useful tool to generate a regular lattice of optical vortices. The lattice is
generated by the interference of the three plane waves. As was shown in earlier papers such a vortex lattice can be
practically used in metrology. Application of optical vortex interferometer in metrology depends on the precision of the
vortex points localization. In this paper we present a novel localization method, which uses the phase shifting technique
applied to the additional fourth wave. Phase shift of the fourth wave doesn't change intensity in vortex points and
increases intensity gradient in their vicinity. The applicability of this method was verified in the experiment.
In an interferometer based on optical vortices there are generated regular net of phase singularities. There are
two kinds of optical vortex named positive and negative. The sign of the vortex is often named a topological charge of
the optical vortex because its existence is related to the characteristic of the geometric wavefront. The ability to
determine the sign of the optical vortices in the experimental measurements may be used to reconstruct the wavefront. In
this paper authors present the experimental method to determine the sign of the optical vortices.
In this paper the new method of parallel glass plat test is presented. In the method an Optical Vortex Interferometer (OVI) is used. The OVI generate the regular net of optical vortices by interference of three plane waves. One wave is deformed after crossing measured parallel glass plate. The deformation of the wave-front is measurable because the deformation of vortex net structure arises from the wave-front deformation. The record of the vortex points' positions before and after parallel glass plate insertion in the optical arrangement is essential. Shown in this paper the analysis vortex points positions change gives high precision information about real shape of the parallel glass plate.
A regular net of optical vortices generated by three plane waves interference allows for a new kind of interferometer -
Optical Vortex Interferometer. The precision of that kind of interferometer depends on a localization accuracy and phase
reconstruction. One problem is the unique phase reconstruction. Interference of three waves can generate two identical
interferograms with opposite topological charge of vortices, so information from three waves interferogram is not
enough to the unique phase reconstruction. First method of topological charge determination requires one interferogram
of two waves analyzed in an experiment and knowledge about a direction of laser beams. Second method is based on
analysing interferogram with the fourth wave added.
In the paper we present the prototype of a straightness measuring device that uses a frequency stabilized Zeeman He-Ne laser. The He-Ne laser line is split by Zeeman effect into two circularly polarized laser beams. The frequency of the radiations differ of 1,2 MHz. The surface stabilized ferroelectric liquid crystal cell is used to stabilize the laser frequency. As the result of the laser frequency stabilization the power of both radiation is equal. The circular polarizations of two laser beams are converted into two linear polarizations perpendicular to each other. The two laser beams pass close to the measured axis. Along the axis the analyzing probe is moved. The analyzing probe changes the ratio of the power of the horizontal to the vertical polarization. This ratio is analyzed by the receiver composed of the ferroelectric liquid crystal switcher, the polarizer and the detector. The straightness of 2 m long optical bench was measured with this techniques. The resolution of 0,1 μm and the accuracy of 0.5 μm were obtained. The accuracy of presented technique is not so good as in the methods using laser interferometer but is comparable with methods using PSD, quadrant detectors or CCD at the same time offering bigger resolution.
The regular net of optical vortices can be generated by three plane wave interference. Such regular vortices are used in a new kind of interferometry—optical vortex interferometry. In this work, the experimental method for topological charge determination of optical vortices in a regular net is presented. This allows for unique phase reconstruction in optical vortex interferometry and solves what is known in interferometry as the phase unwrapping problem.