Research on real time detection of departure angle for the laser beam through atmospheric channels

The precision of departure angle detection for the laser beam can be improved by optimizing algorithms by which the high precision and stability of the laser beam pointing and tracking would be obtained, namely, improving the performance and accommodation of the free space optical communications. Atmospheric turbulence-induced optical intensity scintillations have a strong impact on the location precision of the laser spot through the atmospheric channels. Consequently, new requests come into view for the optimization of the algorithms. In the paper, the advantages and disadvantages of the traditional centroid method are analyzed. In terms of variations of laser spot, combined with the requests for real-time detection of departure angle, we proposed a new detection method. The edge of the laser spot on the detection sensor was redefined, and then the redefined spot was used to calculate the departure angle of the laser beam. The results of the simulations and experiments show that the precision of departure angle detection has been improved by more than 16%, which could reduce the effect of detection errors on the tracking procedure.     

Fading statistics for intersatellite optical communication

The narrow beam widths associated with intersatellite optical communication links make such links susceptible to signal fading because of pointing jitter. Such fading can be aggravated by stationary offsets in pointing. We calculated the fade rates for the case of two spaceborne telescopes having Gaussian beam profiles, a pointing offset, and pointing jitter that can be described by Gaussian statistics. An integral solution is derived for the general case of a nonsymmetrical system, with and without pointing bias, and closed-form solutions are presented for the case of a symmetrical system (identical platforms and optics). These results show that, for a system with 3-dB margin, the rms pointing jitter must be held to less than 7% of the full beam width to keep the fade rate below once per year.     

Statistical distribution of the optical intensity obtained using a Gaussian Schell model for space-to-ground link laser communications

Abstract

Based on the characteristics of the laser device and the inevitable error of the processing technique, a laser beam emitted from a communication terminal can be represented by the Gaussian Schell model (GSM). In space-to-ground link laser communications, the optical intensity is affected by the source coherence parameter and the zenith angle. With full consideration of these two parameters, the statistical distribution model of the optical intensity with a GSM laser in both downlink and uplink is derived. The simulation results indicate that increasing the source coherence parameter has an effect on the statistical distribution of the optical intensity; this effect is highly similar to the effect of a larger zenith angle. The optical intensity invariably degrades with increasing source coherence parameter or zenith angle. The results of this work can promote the improvement of the redundancy design of a laser communication receiver system.     

Error sources and their impact on the performance of dual-wedge beam steering systems

This paper presents analytical and numerical results that elucidate the impact of error sources on the performance of dual-wedge beam steering systems. Different types of error sources are considered. Specifically, we investigate optical distortions in the pattern scanned out by a single ray through a pair of rotatable wedge elements with slightly different parameters. Case examples are given to reveal the difference between the distorted patterns and the patterns produced by a pair of perfectly equal wedge elements. Furthermore, nonparaxial ray tracing is performed to investigate the impact of assembly errors on the accuracy of steering a laser beam to a remote target. We found that a misalignment in a bearing axis of rotation with respect to the system optical axis will result in a change of beam deflection off-axis that gives rise to a severe decrease of pointing accuracy to a level well below the level that a tilted wedge prism may attain.     

Scintillation characteristics of cosh-Gaussian beams

By using the generalized beam formulation, the scintillation index is derived and evaluated for cosh-Gaussian beams in a turbulent atmosphere. Comparisons are made to cos-Gaussian and Gaussian beam scintillations. The variations of scintillations against propagation length at different values of displacement and focusing parameters are examined. The dependence of scintillations on source size at different propagation lengths is also investigated. Two-dimensional scintillation index distributions covering the entire transverse receiver planes are given. From the graphic illustrations, it is found that in comparison to pure Gaussian beams cosh-Gaussian beams have lower on-axis scintillations at smaller source sizes and longer propagation distances. The focusing effect appears to impose more reduction on the cosh-Gaussian beam scintillations than those of the Gaussian beam. The distribution of the off-axis scintillation index values of the Gaussian beams appears to be uniform over the transverse receiver plane, whereas that of the cosh-Gaussian beam is arranged according to the position of the slanted axis.     

Propagation properties of partially coherent dark hollow beam in inhomogeneous atmospheric turbulence

Abstract

Propagation properties of a partially coherent dark hollow beam (PC-DHB) in inhomogeneous atmospheric turbulence are studied in detail. Analytical formulae for the root-mean-square (rms) spatial width, rms angular width, M²-factor of PC-DHB in inhomogeneous turbulence are derived based on the extended Huygens–Fresnel integral. It is found that PC-DHB spreads in inhomogeneous turbulence more rapidly than the free space, and the saturation propagation distances (SPDs) of relative spatial and angular spreadings for uplink slant paths with zenith angles of 45° or less are about 5 and 0.6 km, respectively. M²-factor of PC-DHB in turbulence depends on beam order, waist width, inner scale of the turbulence and the SPD of the normalized M²-factor for the propagation with zenith angles of 45° or less is about 30 km. Our results are useful for the free space optical communications and the beam propagation in the slant path.     

Effect of atmospheric radiance errors in radiometric sea-surface skin temperature measurements

Errors in measurements of sea-surface skin temperature (SSST) caused by inappropriate measurements of sky radiance are discussed; both model simulations and in situ data obtained in the Atlantic Ocean are used. These errors are typically caused by incorrect radiometer view geometry (pointing), temporal mismatches between the sea surface and atmospheric views, and the effect of wind on the sea surface. For clear-sky, overcast, or high-humidity atmospheric conditions, SSST is relatively insensitive (<0.1 K) to sky-pointing errors of ?10 degrees and to temporal mismatches between the sea and sky views. In mixed-cloud conditions, SSST errors greater than ?0.25 K are possible as a result either of poor radiometer pointing or of a temporal mismatch between the sea and sky views. Sea-surface emissivity also changes with sea view pointing angle. Sea view pointing errors should remain below 5 degrees for SSST errors of <0.1 K. We conclude that the clear-sky requirement of satellite infrared SSST observations means that sky-pointing errors are small when one is obtaining in situ SSST validation data at zenith angles of <40 degrees . At zenith angles greater than this, large errors are possible in high-wind-speed conditions. We recommend that high-resolution inclinometer measurements always be used, together with regular alternating sea and sky views, and that the temporal mismatch between sea and sky views be as small as possible. These results have important implications for the development of operational autonomous instruments for determining SSST for the long-term validation of satellite SSST.     

Evaluation of coherence interference in optical wireless communication through multiscattering channels

Optical wireless communication has been the subject of much research in recent years because of the increasing interest in laser satellite-ground links and urban optical wireless communication. The major sources of performance degradation have been identified as the spatial, angular, and temporal spread of the propagating beam when the propagation channel is multiscattering, resulting in reduced power reception and intersignal interference, as well as turbulence-induced scintillations and noise due to receiver circuitry and background illumination. However, coherence effects due to multipath interference caused by a scattering propagation channel do not appear to have been treated in detail in the scientific literature. We attempt a theoretical analysis of coherence interference in optical wireless communication through scattering channels and try to quantify the resultant performance degradation for different media. We conclude that coherence interference is discernible in optical wireless communication through scattering channels and is highly dependent on the microscopic nature of the propagation medium.     

Propagation characteristics of partially coherent anomalous elliptical hollow Gaussian beam propagating through atmospheric turbulence along a slant path

Based on the extended Huygens–Fresnel principal and the Wigner distribution function, the root mean square (rms) angular width and propagation factor (M²-factor) of partially coherent anomalous elliptical hollow Gaussian (PCAEHG) beam propagating through atmospheric turbulence along a slant path are studied in detail. Analytical formulae of the rms angular width and M²-factor of PCAEHG beam are derived. Our results show that the rms angular width increases with increasing of wavelength and zenith angle and with decreasing of transverse coherence length, beam waist sizes and inner scale. The M²-factor increases with increasing of zenith angle and with decreasing of wavelength, transverse coherence length, beam waist sizes and inner scale. The saturation propagation distances (SPDs) increase as zenith angle increases. The numerical calculations also indicate that the SPDs of rms angular width and M²-factor for uplink slant paths with zenith angle of π/12 are about 0.2 and 20 km, respectively.     

Performance of a laser microsatellite network with an optical preamplifier

Laser satellite communication (LSC) uses free space as a propagation medium for various applications, such as intersatellite communication or satellite networking. An LSC system includes a laser transmitter and an optical receiver. For communication to occur, the line of sight of the transmitter and the receiver must be aligned. However, mechanical vibration and electronic noise in the control system reduce alignment between the transmitter laser beam and the receiver field of view (FOV), which results in pointing errors. The outcome of pointing errors is fading of the received signal, which leads to impaired link performance. An LSC system is considered in which the optical preamplifier is incorporated into the receiver, and a bit error probability (BEP) model is derived that takes into account the statistics of the pointing error as well as the optical amplifier and communication system parameters. The model and the numerical calculation results indicate that random pointing errors of sigma(chi)2G > 0.05 penalize communication performance dramatically for all combinations of optical amplifier gains and noise figures that were calculated.     

偏距对改进X-Y双轴式光电跟踪系统跟踪性能的影响

天顶跟踪盲区是地平式光电跟踪系统的固有缺陷。X-Y双轴式光电跟踪系统（规则X-Y双轴式）可以解决过顶跟踪问题,但跟踪范围极为有限,把视轴沿X轴方向平移偏距D,形成一种改进的X-Y双轴式光电跟踪系统,即偏X-Y双轴式光电跟踪系统。偏X-Y双轴式光电跟踪系统可以解决过顶跟踪问题,其跟踪范围与规则X-Y双轴式光电跟踪系统相比有很大提高。由D引入的跟踪误差可以忽略或修正,但具有更大的地平面跟踪盲区。     

Moment-matching method for extraction of asymmetric beam jitters and bore sight errors in simulations and experiments with actively illuminated satellites of small physical cross section

Optical returns from remote resident space-based objects such as satellites suffer from pointing and tracking errors. In a previously reported paper [Appl. Opt.46, 5608 (2007)APOPAI0003-693510.1364/AO.46.005608], we developed a moment-matching technique that used the statistics of time series of these optical returns to extract information about bore sight and symmetric beam jitter errors (symmetric here implies that the standard deviations of the jitter measured along two orthogonal axes, perpendicular to the line of sight, are equal). In this paper, we extend that method to cover the case of asymmetric beam jitter and bore sight. The asymmetric beam jitter may be due to the combination of symmetric atmospheric turbulence beam jitter and optical beam train jitter. In addition, if a tracking control system is operating, even the residual atmospheric tracking jitter could be asymmetric because the power spectrum is different for the slewing direction compared to the cross-track direction. Analysis of the problem has produced a set of nonlinear equations that can be reduced to a single but much higher-order nonlinear equation in terms of one of the jitter variances. After solving for that jitter, all the equations can be solved to extract all jitter and bore sight errors. The method has been verified by using simulations and then tested on experimental data. In order to develop this method, we derived analytical expressions for the probability density function and the moments of the received total intensity. The results reported here are valid for satellites of small physical cross section, or else those with retroreflectors that dominate the signal return. The results are, in general, applicable to the theory of noncircular Gaussian speckle with a coherent background.     

Chromatic Refraction with Global Ozone Monitoring by Occultation of Stars. II. Statistical Properties of Scintillations

The statistical properties of stellar scintillations are discussed with special attention to correcting the atmospheric transmittance data for scintillations in measurements made with the Global Ozone Monitoring by Occultation of Stars (GOMOS) instrument. Both anisotropic and isotropic turbulent inhomogeneities are taken into account. Calculated rms scintillation reaches several percent for altitudes of 30-35 km, an amplitude comparable with the expected absorbing features. Estimates of cross-correlation functions show that the GOMOS correction procedure can be applied efficiently for scintillations caused by anisotropic inhomogeneities, in contrast to the isotropic case. Some recommendations are given for conditions of observations with which to make better corrections of scintillations.     

Tracking in a ground-to-satellite optical link: effects due to lead-ahead and aperture mismatch, including temporal tracking response

Establishing a link between a ground station and a geosynchronous orbiting satellite can be aided greatly with the use of a beacon on the satellite. A tracker, or even an adaptive optics system, can use the beacon during communication or tracking activities to correct beam pointing for atmospheric turbulence and mount jitter effects. However, the pointing lead-ahead required to illuminate the moving object and an aperture mismatch between the tracking and the pointing apertures can limit the effectiveness of the correction, as the sensed tilt will not be the same as the tilt required for optimal transmission to the satellite. We have developed an analytical model that addresses the combined impact of these tracking issues in a ground-to-satellite optical link. We present these results for different tracker/pointer configurations. By setting the low-pass cutoff frequency of the tracking servo properly, the tracking errors can be minimized. The analysis considers geosynchronous Earth orbit satellites as well as low Earth orbit satellites.     

Laser beam propagation in atmospheric turbulence

The optical effects of atmospheric turbulence on the propagation of low power laser beams are reviewed in this paper. The optical effects are produced by the temperature fluctuations which result in fluctuations of the refractive index of air. The commonly-used models of index-of-refraction fluctuations are presented. Laser beams experience fluctuations of beam size, beam position, and intensity distribution within the beam due to refractive turbulence. Some of the observed effects are qualitatively explained by treating the turbulent atmosphere as a collection of moving gaseous lenses of various sizes. Analytical results and experimental verifications of the variance, covariance and probability distribution of intensity fluctuations in weak turbulence are presented. For stronger turbulence, a saturation of the optical scintillations is observed. The saturation of scintillations involves a progressive break-up of the beam into multiple patches; the beam loses some of its lateral coherence. Heterodyne systems operating in a turbulent atmosphere experience a loss of heterodyne signal due to the destruction of coherence.     

Scintillation and beam-wander analysis in an optical ground station-satellite uplink

In an optical communication link between an optical ground station and a geostationary satellite the main problems appear in the uplink and are due to beam wander and to scintillation. Reliable methods for modeling both effects simultaneously are needed to provide an accurate tool with which the robustness of the communication channel can be tested. Numerical tools, especially the split-step method (also referred to as the fast-Fourier-transform beam propagation method), have demonstrated their ability to deal with problems of optical propagation during atmospheric turbulence. However, obtaining statistically significant results with this technique is computationally intensive. We present an analytical-numerical hybrid technique that provides good information on the variance in optical irradiance with an important saving of time and computational resources.     

Propagation of Gaussian-Schell beam in turbulent atmosphere of three-layer altitude model

We propose a method that is used to derive the moment radius of intensity distribution in a turbulent atmosphere. From this study, we have found that the second moment radius is affected only by the first-order expansion coefficient of the wave structure function. If our attention is directed to a higher moment radius, a higher order approximation of the expansion needs to be used. As an example, the propagation of a Gaussian-Schell beam in a slant path has been studied based on the turbulent atmosphere of a three-layer model. The variation of some beam properties, such as the relative waist width, angular spread, and kurtosis parameter with the initial waist width, wavelength, and zenith angle, has been analyzed and discussed in detail. The study shows that there is little difference between the three-layer model and the Kolmogorov model in studying uplink propagation, and the difference is large for downlink propagation. The intensity profile of the Gaussian beam in turbulence does not keep a Gaussian shape unless the beam spreading due to turbulence is very large or very small.     

Beam width and transmitter power adaptive to tracking system performance for free-space optical communication

The basic free-space optical communication system includes at least two satellites. To communicate between them, the transmitter satellite must track the beacon of the receiver satellite and point the information optical beam in its direction. Optical tracking and pointing systems for free space suffer during tracking from high-amplitude vibration because of background radiation from interstellar objects such as the Sun, Moon, Earth, and stars in the tracking field of view or the mechanical impact from satellite internal and external sources. The vibrations of beam pointing increase the bit error rate and jam communication between the two satellites. One way to overcome this problem is to increase the satellite receiver beacon power. However, this solution requires increased power consumption and weight, both of which are disadvantageous in satellite development. Considering these facts, we derive a mathematical model of a communication system that adapts optimally the transmitter beam width and the transmitted power to the tracking system performance. Based on this model, we investigate the performance of a communication system with discrete element optical phased array transmitter telescope gain. An example for a practical communication system between a Low Earth Orbit Satellite and a Geostationary Earth Orbit Satellite is presented. From the results of this research it can be seen that a four-element adaptive transmitter telescope is sufficient to compensate for vibration amplitude doubling. The benefits of the proposed model are less required transmitter power and improved communication system performance.     

Effects of cosine error in irradiance measurements from field ocean color radiometers

The cosine error of in situ seven-channel radiometers designed to measure the in-air downward irradiance for ocean color applications was investigated in the 412-683 nm spectral range with a sample of three instruments. The interchannel variability of cosine errors showed values generally lower than +/-3% below 50 degrees incidence angle with extreme values of approximately 4-20% (absolute) at 50-80 degrees for the channels at 412 and 443 nm. The intrachannel variability, estimated from the standard deviation of the cosine errors of different sensors for each center wavelength, displayed values generally lower than 2% for incidence angles up to 50 degrees and occasionally increasing up to 6% at 80 degrees. Simulations of total downward irradiance measurements, accounting for average angular responses of the investigated radiometers, were made with an accurate radiative transfer code. The estimated errors showed a significant dependence on wavelength, sun zenith, and aerosol optical thickness. For a clear sky maritime atmosphere, these errors displayed values spectrally varying and generally within +/-3%, with extreme values of approximately 4-10% (absolute) at 40-80 degrees sun zenith for the channels at 412 and 443 nm. Schemes for minimizing the cosine errors have also been proposed and discussed.     

Polarization-splitting common-path interferometer based on a zero-twist liquid crystal display

We present a compact optical polarization-splitting common-path interferometer based on a zero-twist liquid crystal display (LCD). The LCD is encoded with a diffraction grating pattern and illuminated with a polarization state with both horizontal and vertical components. The polarization component perpendicular to the director axis of the liquid crystal molecules is not affected by the LCD and forms the reference beam. However, the polarization component parallel to the director axis is diffracted at an angle determined by the period of the grating. By imposing an analyzer polarizer, these two beams create an interferogram that can either display retardance patterns encoded onto the LCD or analyze external birefringent optical elements. The programmability of the system allows new ways of increasing the utility of the interferograms. Experimental results are provided, including the visualization of optical vortices with different and opposite topological charges.