Statistical characteristics of optical vortices have been analyzed in the paper. As was shown such vortices appear in the radiation wavefront if the initial phase is set as a mathematical raw formed by Zernike polynomials or by a phase screen simulating atmospheric turbulence with a spectrum of the index of refraction fluctuations prescribed by a von Karman formula. In both examples considered here the statistical properties of the vortex distribution satisfy the requirements of the Central limit theorem, and acceptable correspondence is also observed between parameters of beams formed by polynomials and by a phase screen.
In the present article the influence is considered of phase screen characteristics on the statistical properties of dislocations developed in a beam passed this screen. Analysis was performed with application of numerical experiment methods, and in the developed model the screen represented a thin layer of turbulent atmosphere. Special attention was devoted to assessment of the turbulence inner scale impact on distribution of vortices. We have also shown that this distribution meets the requirements of the central limit theorem.
The objective of current investigation is development of the method intended to extract useful information from a beam in the wavefront of which optical vortices are present. Developed numerical model corresponds approximately to an optical communication system operating in a turbulent atmosphere under conditions of strong distortions of radiation. Specific feature of this system is that information is also transferred by an optical vortex.
Properties of vortex radiation are discussed in the article using the data obtained by the authors and information found in references. Possible applications of such radiation are considered. Special attention is devoted to the methods of vortex registration. Precision of two registration algorithms is compared and particularities of their practical realization are analyzed.
The algorithm of an optical vortex coordinates and topological charge detection is considered. In the algorithm a vortex is localized as a point of an interference fringe branching. With application of the algorithm interference patterns obtained in laboratory and numerical experiments are analyzed and characteristics of vortices revealed in corresponding examples are presented.
In this paper the results of simulation are presented of multichannel radiation propagation in a turbulent atmosphere and under conditions of thermal blooming, and correction for nonlinear thermal distortion on the base of the beam phase control is considered. The results demonstrate dependence of correction effectiveness on number of channels and on precision of a reference beam phase reconstruction. Addition increase of effectiveness is possible with adjustment of amplification in the channels of the optical system, i.e., with the use of amplitude-phase control of radiation.
In this paper the results of simulation are presented of multichannel radiation propagation under conditions of thermal blooming, and correction for nonlinear thermal distortion on the base of the beam phase control is considered. The results demonstrate dependence of correction effectiveness on number of channels and on precision of a reference beam phase reconstruction. Addition increase of effectiveness is possible with adjustment of amplification in the channels of the optical system, i.e., with the use of amplitude-phase control of radiation..
In this paper the results of simulation are presented of multichannel radiation propagation in the atmosphere, and correction for turbulent distortion on the base of the beam phase control is considered. The results demonstrate dependence of correction effectiveness on number of channels and on precision of a reference beam phase reconstruction. Additionally increase of effectiveness is possible with adjustment of amplification in the channels of the optical system, i.e., with the use of amplitude-phase control of radiation.
The results of numeric simulation are presented in the paper of multichannel laser radiation propagation under conditions of free diffraction and in a turbulent atmosphere. It was shown that in free space a multichannel system allows one to obtain higher concentration (20-50%) of radiation energy on the object comparing with a Gaussian beam. Intensity of atmospheric distortion decreases with increase of the number of channels. Adaptive correction for turbulent distortions results in two-times increase of energy concentration for systems with 9 and 81 channels. For systems with greater number of channels (201 channels) the results of correction do not depend on turbulence intensity.
In the paper the results of simulation are presented of multichannel laser radiation propagation under conditions of free diffraction. Influence of distortions developed in channels on effectiveness of energy transfer is also considered. It was shown that with increase of channel number the influence of random tilts and piston-type aberration decreased.
In the present paper efficiency of adaptive correction is analyzed in the turbulent atmosphere and under the conditions of thermal blooming. A numerical model of a typical adaptive optics system was developed to carry out the investigations. As it is known, phase conjugation and multidither, i.e., the algorithms commonly employed to correct for thermal and turbulent distortions of laser beams are unstable in nonlinear medium. We demonstrated that stability of phase control is possible to increase introducing the modifications of the algorithms. Also we demonstrated that phase compensation does not insure complete correction for thermal or turbulent aberrations induced by an atmospheric layer. To correct for aberrations under these conditions it is possible to employ amplitude-phase control over the beam, for example, to use the wavefront reversal algorithm. Realization of the algorithm is possible in a two-mirror adaptive system in which the control over beam phase is performed in two planes at the access to the medium. In numerical experiments it was shown that the two-mirror system insures the absolute compensation for a thin turbulent layer placed at arbitrary distance from the aperture of a laser source and high effectiveness of compensation for distributed lens comparing with phase-only algorithms.
A numerical model of a typical adaptive optics system is described in the report. The developed computer application corresponding to the model includes all the main elements of a real system, namely, computer codes simulating radiation propagation in a turbulent atmosphere with thermal blooming and codes simulating the elements of adaptive optics system (a model of a Shack-Hartmann wavefront sensor, two algorithms of dislocation localization, and a model of adaptive mirror with continuous surface). In the report we include solutions to the some of adaptive optics problems obtained with the model: realization of amplitude-phase control in two-mirror adaptive system, the method to improve the stability of correction for thermal blooming, evaluation of a Shack-Hartmann sensor performance, and some others. These results demonstrate that the set of the developed models is a powerful tool for simulations in the field of adaptive optics.
A general model of a typical adaptive optics system is described in the report. The model includes all main elements of a real system: the path of a beam propagating in the atmosphere, wavefront sensor, and adaptive mirror with continuous surface. Solution to the some of adaptive optics problems was obtained with the model. These results were included in the report as illustration ofthe model utility.
There are exists several sources of errors in an adaptive optics system. The main source associated with the violation of the optical reciprocity principle in algorithm of phase conjugation, namely, with substitute of beacon amplitude distribution by distribution of a Gaussian beam generated by a laser. Absolute correction of turbulent aberration is possible only in case of strict maintenance of a reciprocity principle, i.e. in case of phase reversal algorithm application. In paper the possibility is considered to realize phase reversal algorithm in a linear system with the use of phase control of the beam. The system should include two mirrors separated by the vacuum gap of a finite size. Comparison of efficiency of correction on the base of phase conjugation and with the use of two mirror adaptive system were obtained.
KEYWORDS: Mirrors, Segmented mirrors, Telescopes, Algorithm development, Phase shifts, Chemical elements, Reflector telescopes, Reflectors, Large telescopes, Control systems
This paper considers the problem of forming a preset surface of a segmented mirror of a telescope. An iteration algorithm based on analysis of the interference pattern of the radiation reflected from the mirror is used for phasing the mirror segments. At every iteration, the current interferogram is compared with the reference one obtained for the surface of a preset shape. The value of the control goal function, whose minimum is determined in the algorithm, decreases with the decreasing discrepancy between the interferograms. This technique provides for formationof a plane-reflecting surface of the mirror, if the relative displacement of segments does not exceed the half wavelength. It is shown that to extend the range of acceptable displacements, it is necessary to introduce additional sources of radiation of specially chosen wavelengths. In such a case, the dynamic range of the algorithm can be extended up to 30 μm.
The algorithm of a segmented mirror co-phasing is described in the paper. The algorithm is based on the analysis of interference pattern, special criterion is introduced for this purpose. It is shown that initial shift of the segments must be less than half of the wavelength. To increase the dynamic range of the system the second (or even third) wavelength should be used in the algorithm. In this case the dynamic range can be increased up to 30 mkm.
It was shown that there exist two sources of errors in an adaptive optics system. The first source appears due to limitations induced by the elements of the system such as a Shack Hartmann sensor and deformable mirror. The second associated with the violation of the optical reciprocity principle in algorithm of phase conjugation, namely, with substitute of beacon amplitude distribution by distribution of a Gaussian beam generated by a laser. Absolute correction of turbulent aberration is possible only in case of strict maintenance of a principle, i.e. in case of phase reversal. In the paper the possibility is considered to realize phase reveresal in a linear system and only with the use of phase control of the beam. The system should include two mirrors separated by the vacuum gap of a finite size. Estimations were obtained by correction efficiency on the base of phase conjugation and with the use of two mirror adaptive system.
In the paper an analysis was performed on the base of numeric experiment methods of a laser beam propagation in a turbulent atmosphere. Comparison of efficiency was carried out of phase and amplitude-phase adaptive control algorithms. It was noted that only wavefront reversion insures the absolute compensation for turbulent distortions of laser beams. It is also shown that wavefront reversion is possible to realize in two-mirror adaptive optics system. The mirrors should be divided by a gap where a beam propagates under conditions of free diffraction.
Correction for turbulent distortions with an adaptive optics system including Shack-Hartmann sensor is considered in the paper. Efficiency of control was analyzed under conditions of singular points development in a wavefront of a laser beam. It was shown that the presence of dislocations cuases the discrepancy of wavefront detection by the sensor and as a consequence leads to the control instabilities. It was also shown that dislocations appear mainly in the peripheral regions of the beam. Using this feature and optimizing the size of the sensor the stable adaptive control could be achieved in an adaptive optics system.
Correction for turbulent distortions with an adaptive optics system including Shack-Hartmann sensor is considered in the paper. Efficiency of control was analyzed under conditions of singular points development in a wavefront of a laser beam. It was shown that the presence of dislocations causes the discrepancy of wavefront detection by the sensor and as a consequence leads to the control instabilities. It was also shown that dislocations appear mainly in the peripheral regions of the beam. Using this feature and optimizing the size of the sensor the stable adaptive control could be achieved in an adaptive optics system.
It was shown that there exist two sources of errors in an adaptive optics system. The first source appears due to limitations induced by the elements of the system such as a Shack Hartmann sensor and deformable mirror. The second associated with the violation of the optical reciprocity principle in algorithm of phase conjugation, namely, with substitute of beacon amplitude distribution by distribution of a Gaussian beam generated by a laser. Absolute correction of turbulent aberration is possible only in case of strict maintenance of a principle, i.e. in case of phase reversal. In the paper the possibility is considered to realize phase reversal in a linear system and only with the use of phase control of the beam. The system should include two mirrors separated by the vacuum gap of a finite size. Estimations were obtained by correction efficiency on the base of phase conjugation and with the use of two mirror adaptive system.
In the present article the problem of Gaussian beam propagation in the turbulent atmosphere is considered on the base of numeric methods. Singular points (dislocations) development in the wavefront is analyzed. Two algorithms of dislocation detection were proposed. One of them based on the interferogram processing and can be realized in a laboratory experiment. In the second algorithm the whole wavefront is analyzed and dislocations are localized as points where cuts of the surface in 2(pi) begin. The precision of the algorithms is compared and statistics of dislocations on the path of propagation is represented.
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