Intensity fluctuations in laser links between the ground and a satellite

Laser-beam-intensity fluctuations between an uplink (ground to satellite) and a downlink (satellite to ground) are described. The dependence of the beam radius on log-intensity variance in the uplink and the dependence of receiving-aperture diameter on the log-intensity variance in the downlink using a known theory were calculated. Statistical analysis of the experimental data on the laser links was performed, and high correlation coefficients of 0.94 between the normalized intensity variances of the uplink and those of the stellar scintillation were obtained. The beam-pointing error in the satelliteborne laser transmitter chiefly caused fluctuations in the downlink.     

Atmospheric inner-scale effects on normalized irradiance variance

We have investigated five types of atmospheric optical-turbulence inner scales for their effects on normalized laser irradiance variance in the Rytov and early saturation regimes: (1) zero inner scale, (2) Gaussian inner scale, (3) Hill's viscous-convective enhancement inner scale, (4) Frehlich's parameterization of the viscous-convective enhancement, and (5) turbulence spectrum truncation because of the discrete grid representation. Wave-optics computer simulations yielded normalized irradiance variances within 2% of the results from numerical integrations of the Rytov-Tatarskii predictions. In the Rytov regime a Gaussian inner scale reduces the normalized irradiance variance compared with the zero-innerscale case, and the viscous-convective inner scale first raises, then lowers the irradiance variance as the inner-scale size increases. In the saturation regime all inner-scale models increase the intensity variance for a spherical wave.     

Time-resolved measurements of statistics for a Nd:YAG laser

Time-resolved measurements of the fluctuating intensity of a multimode frequency-doubled Nd:YAG laser have been performed. For various operating conditions the enhancement factors in nonlinear optical processes that use a fluctuating instead of a single-mode laser have been determined up to the sixth order. In the case of reduced flash-lamp excitation and a switched-off laser amplifier, the intensity fluctuations agree with the normalized Gaussian model for the fluctuations of the fundamental frequency, whereas strong deviations are found under usual operating conditions. The frequencydoubled light has in the latter case enhancement factors not so far from values of Gaussian statistics.     

Low-frequency intensity noise in semiconductor lasers

The low-frequency intensity noise at 25 MHz of a Fabry-Perot semiconductor laser is measured as a function of injection current. All the measurements are taken at room temperature and the laser is operated with a commercial current source (the conditions under which laser diodes are often used). At the highest injection current of twice threshold, the intensity noise is 5.5 dB above the shot-noise limit. When the longitudinal side mode suppression of the laser is 20 dB or larger, the intensity noise is modeled adequately by an expression derived from the single-mode, small-signal, linearized, semiclassical rate equations. All the parameters used in the theory are derived or referenced.     

Effects of reference laser intensity noise in a Fourier transform spectrometer

Many noise sources deteriorate the performance of a Fourier-transform spectrometer. When such an instrument utilizes a reference source such as an HeNe laser to sample the measurement data, it is desirable to determine how the intensity fluctuations of the reference source will affect the final spectrum. This text shows how the intensity noise of the reference laser is transformed at the output of the interferometer, how it translates into a sampling jitter by a simple linear relation under a small bandwidth approximation, and how it is manifested in the final spectrum as a noise floor. Analytical and simulation results show that for an instrument designed for optical communication applications, the intensity noise of the reference laser may be one of the dominant noise source limiting the overall performance of the instrument.     

Trivariate characteristics of intensity fluctuations for heavily saturated optical systems

Trivariate cumulants of intensity fluctuations have been computed starting from a trivariate intensity probability distribution function, which rests on the assumption that the variation of intensity has a maximum entropy distribution with the constraint that the total intensity is constant. The assumption holds for optical systems such as a thin, long, mirrorless gas laser amplifier where under heavy gain saturation the total output approaches a constant intensity, although intensity of any mode fluctuates rapidly over the average intensity. The relations between trivariate cumulants and central moments that were needed for the computation of trivariate cumulants were derived. The results of the computation show that the cumulants have characteristic values that depend on the number of interacting modes in the system. The cumulant values approach zero when the number of modes is infinite, as expected. The results will be useful for comparison with the experimental triavariate statistics of heavily saturated optical systems such as the output from a thin, long, bidirectional gas laser amplifier.     

Bound on range precision for shot-noise limited ladar systems

The precision of ladar range measurements is limited by noise. The fundamental source of noise in a laser signal is the random time between photon arrivals. This phenomenon, called shot noise, is modeled as a Poisson random process. Other noise sources in the system are also modeled as Poisson processes. Under the Poisson-noise assumption, the Cramer-Rao lower bound (CRLB) on range measurements is derived. This bound on the variance of any unbiased range estimate is greater than the CRLB derived by assuming Gaussian noise of equal variance. Finally, it is shown that, for a ladar capable of dividing a fixed amount of energy into multiple laser pulses, the range precision is maximized when all energy is transmitted in a single pulse.     

Stochastic models of stable frequency and time sources and theirrelationship

Different stochastic models of a stable frequency and time sources showing white phase noise, white frequency noise, and random walk of frequency noise are considered. A continuous time model of phase fluctuations is associated with the power law model of relative frequency fluctuations. The ARIMA (0,2,2) and the Kalman models of the sampled phase derivations are derived from the continuous model. Equations relating the characteristic parameters of these three representations of the source behavior are given. The Allan variance of relative frequency fluctuations is expressed as a function of the characteristic parameters. The approximation inherent to the simplified Kalman model is discussed, and the limit of validity of this model is stated     

Blood-flow measurements with a small number of scattering events

Results of simulations of the diffraction of a laser beam by a small blood vessel imbedded in scattering tissue are presented. The form of the spectra of biospeckle intensity fluctuations is analyzed. The Doppler shift of intensity fluctuations of scattered light is investigated as a function of the laser beam radius, the radius of the blood vessel, the depth of the vessel in the tissue, and the scattering characteristics of flowing blood. A formula that serves as the basis for a method of absolute measurements of blood-flow velocity is derived.     

Wide-band suppression of laser intensity noise

A simple and efficient laser intensity stabilization system was constructed based on an electro-optical modulator (EOM) and a photodetector. It is capable of reducing the laser intensity fluctuations to the shot noise limit within the range of Fourier frequencies from a few tens of hertz to a few megahertz. The achieved bandwidth of the laser control system is limited by the light handling capacity of the photodetector and spurious resonances of the EOM. We discuss the general approach to the design of the laser intensity stabilization system and its noise properties.     

平顶多高斯光束通过球差透镜的聚焦特性

利用广义惠更斯-菲涅耳衍射积分公式,研究了平顶多高斯光束通过球差透镜的聚焦特性。推导出轴上光强分布的表达式,并对轴上光强进行大量的数值计算及分析。研究结果表明,当平顶多高斯光束的阶数N一定时,透镜的球差将在很大程度上影响光束的聚焦特性;当透镜的球差一定时,N值的改变将影响轴上最佳聚焦点的位置;当无球差时,轴上最佳聚焦点并不在几何焦点处,轴上最佳聚焦点位置随着N值增加向几何焦点靠近,例如当阶数N由0增大为1时,则归一化最佳聚焦点由0.91增大到0.98。     

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.     

Atmospheric optical communication with a Gaussian Schell beam

We consider a wireless optical communication link in which the laser source is a Gaussian Schell beam. The effects of atmospheric turbulence strength and degree of source spatial coherence on aperture averaging and average bit error rate are examined. To accomplish this, we have derived analytic expressions for the spatial covariance of irradiance fluctuations and log-intensity variance for a Gaussian beam of any degree of coherence in the weak fluctuation regime. When spatial coherence of the transmitted source beam is reduced, intensity fluctuations (scintillations) decrease, leading to a significant reduction in the bit error rate of the optical communication link. We have also identified an enhanced aperture-averaging effect that occurs in tightly focused coherent Gaussian beams and in collimated and slightly divergent partially coherent beams. The expressions derived provide a useful design tool for selecting the optimal transmitter beam size, receiver aperture size, beam spatial coherence, transmitter focusing, etc., for the anticipated atmospheric channel conditions.     

Analysis of transient-grating signals for reacting-flow applications

Single-shot transient-grating measurements for thermometry in pressurized reacting flows are examined in the context of rapid digital signal processing. Simple approaches are discussed for temperature determination and rejection of unwanted signals in real-time measurement applications. Examples of temperature data in pressurized postflame gases are presented in the form of probability-density functions (PDFs). Three contributions to the PDF half-widths are discussed. Analysis of phase-matching requirements indicates that beam steering as a result of density fluctuations affects the signal amplitude but not the grating period. Therefore, such stochastic beam deviations have little effect on the derived temperatures. Mode noise on the cw probe beam as well as linear light scattering are found to be insignificant in the frequency range of the observed transient-grating acoustic signature. Use of a single-mode laser for the pump beams is shown to enhance the signal intensity.     

Measurement of Atmospheric Turbulence Induced Intensity Fluctuations in a Laser Beam

We report measurements of the statistical properties of the intensity fluctuations in a He/Ne laser beam which had propagated 1·125 km through the earth's atmosphere. The beam size was such that the beam propagated as a spherical wave, and atmospheric conditions such that most measurements were made in the ‘saturation’ region (β₀ ～ 1-4). We found (1) that the variance of the intensity was considerably larger than that previously reported for plane wave propagation, and (2) that the probability distribution of the intensity and the derived moments were close to the K-distribution and its moments. The origin and significance of the K-distribution in atmospheric propagation is considered. Photon counting techniques were used for all measurements.     

Stress intensity factor solutions for estimation of fatigue lives of laser welds in lap-shear specimens

Fatigue behavior of laser welds in lap-shear specimens of high strength low alloy (HSLA) steel is investigated based on experimental observations and two fatigue life estimation models. Fatigue experiments of laser welded lap-shear specimens are first reviewed. Analytical stress intensity factor solutions for laser welded lap-shear specimens based on the beam bending theory are derived and compared with the analytical solutions for two semi-infinite solids with connection. Finite element analyses of laser welded lap-shear specimens with different weld widths were also conducted to obtain the stress intensity factor solutions. Approximate closed-form stress intensity factor solutions based on the results of the finite element analyses in combination with the analytical solutions based on the beam bending theory and Westergaard stress function for a full range of the normalized weld widths are developed for future engineering applications. Next, finite element analyses for laser welded lap-shear specimens with three weld widths were conducted to obtain the local stress intensity factor solutions for kinked cracks as functions of the kink length. The computational results indicate that the kinked cracks are under dominant mode I loading conditions and the normalized local stress intensity factor solutions can be used in combination with the global stress intensity factor solutions to estimate fatigue lives of laser welds with the weld width as small as the sheet thickness. The global stress intensity factor solutions and the local stress intensity factor solutions for vanishing and finite kinked cracks are then adopted in a fatigue crack growth model to estimate the fatigue lives of the laser welds. Also, a structural stress model based on the beam bending theory is adopted to estimate the fatigue lives of the welds. The fatigue life estimations based on the kinked fatigue crack growth model agree well with the experimental results whereas the fatigue life estimations based on the structural stress model agree with the experimental results under larger load ranges but are higher than the experimental results under smaller load ranges.     

Frequency-noise sensitivity and amplitude-noise immunity of discriminators based on fringe-side Fabry-Perot cavities

Optical frequency discriminators using fringe-side Fabry-Perot cavities are analyzed studying their sensitivity to laser frequency fluctuations, with particular attention to their amplitude-noise immunity. The frequency responses both to frequency and to amplitude noise were evaluated using transient analysis. Comparisons between different schemes-based on transmission, reflection, or a proper combination of both these signals, and using intensity noise compensation-were carried out, pointing out similarities and differences in their operational properties and performance.     

Optimization of the R-SQUID noise thermometer

The Josephson junction can be used to convert voltage into frequency and thus it can be used to convert voltage fluctuations generated by Johnson noise in a resistor into frequency fluctuations. As a consequence, the temperature of the resistor can be defined by measuring the variance of the frequency fluctuations. Unfortunately, the absolute determination of temperature by this approach is disturbed by several undesirable effects: a rolloff introduced by the bandwidth of the postdetection filter, additional noise caused by rf amplifiers, and a mixed noise effect caused by the nonlinearity of the Josephson junction together with rf noise in the tank circuit. Furthermore, the variance is a statistical quantity and therefore the limited number of frequency counts produces inaccuracy in a temperature measurement. In this work the total inaccuracy of the noise thermometer is analyzed and the optimal choice of the parameters is derived. A practical way to find the optimal conditions for the Josephson junction noise thermometer is discussed. The inspection shows that under the optimal conditions the total error is dependent only on the temperature under determination, the equivalent noise temperature of the preamplifier, the bias frequency of the SQUID, and the total time used for the measurement.     

Propagation of coherently combined truncated laser beam arrays with beam distortions in non-Kolmogorov turbulence

The propagation properties of coherently combined truncated laser beam arrays with beam distortions through non-Kolmogorov turbulence are studied in detail both analytically and numerically. The analytical expressions for the average intensity and the beam width of coherently combined truncated laser beam arrays with beam distortions propagating through turbulence are derived based on the combination of statistical optics methods and the extended Huygens-Fresnel principle. The effect of beam distortions, such as amplitude modulation and phase fluctuation, is studied by numerical examples. The numerical results reveal that phase fluctuations have significant influence on the spreading of coherently combined truncated laser beam arrays in non-Kolmogorov turbulence, and the effects of the phase fluctuations can be negligible as long as the phase fluctuations are controlled under a certain level, i.e., a>0.05 for the situation considered in the paper. Furthermore, large phase fluctuations can convert the beam distribution rapidly to a Gaussian form, vary the spreading, weaken the optimum truncation effects, and suppress the dependence of spreading on the parameters of the non-Kolmogorov turbulence.     

Monitoring the statistics of turbulence: Fried parameter estimation from the wavefront sensor measurements

Near-the-ground laser communication systems must operate in the presence of strong atmospheric turbulence. The effects of atmospheric turbulence on the laser beam that are relevant to optical communications are a broadening of the laser footprint, random jitter of the laser beam, and high spatial frequency intensity fluctuations referred to as scintillation. The overall goal of our program is to improve the performance and extend the range of optical communications systems by exploring the use of adaptive optics and channel coding. Knowledge of the turbulence conditions and the ability to describe its properties are the key aspects to make these improvements effective. The developed multiphase approach is directed to statistically describe atmospheric turbulence based on results derived from experimentally collected data. Statistics of Fried parameter r(0) is derived from 6 TB of data collected over 50 days, and under various day and night atmospheric conditions. Significant fluctuations of r(0) are found with the values ranging from 2 mm and up to 15 cm, corresponding to the significant structure function Cn2 fluctuations from 7.4×10(-14) to 8.1×10(-16).