Effect of speckle on lidar pulse-pair ratio statistics

The ratio of temporally adjacent lidar pulse returns is commonly used in differential absorption lidar (DIAL) to reduce correlated noise. These pulses typically are generated at different wavelengths with the assumption that the dominant noise is common to both. This is not the case when the mean number of laser speckle integrated per pulse by the lidar receiver is small (namely, less than 10 speckles at each wavelength). In this case a large increase in the standard deviation of the ratio data results. We demonstrate this effect both theoretically and experimentally. The theoretical value for the expected standard deviation of the pulse-pair ratio data compares well with the measured values that used a dual CO(2) laser-based lidar with a hard target. Pulse averaging statistics of the pulse-pair data obey the expected varsigma(1)/ radicalN reduction in the standard deviation, varsigma(N), for N-pulse averages. We consider the ratio before average, average before ratio, and log of the ratio before average methods for noise reduction in the lidar equation. The implications of our results are discussed in the context of dual-laser versus single-laser lidar configurations.     

Statistical model for fading return signals in coherent lidars

A statistical model for the return signal in a coherent lidar is derived from the fundamental principles of atmospheric scattering and turbulent propagation. The model results in a three-parameter probability distribution for the coherent signal-to-noise ratio in the presence of atmospheric turbulence and affected by target speckle. We consider the effects of amplitude and phase fluctuations, in addition to local oscillator shot noise, for both passive receivers and those employing active modal compensation of wavefront phase distortion. We obtain exact expressions for statistical moments for lidar fading and evaluate the impact of various parameters, including the ratio of receiver aperture diameter to the wavefront coherence diameter, the speckle effective area, and the number of modes compensated.     

Improved speckle statistics in coherent differential absorption lidar with in-fiber wavelength multiplexing

Remote detection of gaseous pollutants and other atmospheric constituents can be achieved with differential absorption lidar (DIAL) methods. The technique relies on the transmission of two or more laser wavelengths and exploits absorption features in the target gas by measuring the ratio of their detected powers to determine gas concentration. A common mode of operation is when the transmitter and receiver are collocated, and the absorption is measured over a return trip by a randomly scattering topographic target. Hence, in coherent DIAL, speckle fluctuation leads to a large uncertainty in the detected powers unless the signal is averaged over multiple correlation times, i.e., over many independent speckles. We examine a continuous-wave coherent DIAL system in which the laser wavelengths are transmitted and received by the same single-mode optical fibers. This ensures that the two wavelengths share a common spatial mode, which, for certain transmitter and target parameters, enables highly correlated speckle fluctuations to be readily achieved in practice. For a DIAL system, this gives the potential for improved accuracy in a given observation time. A theoretical analysis quantifies this benefit as a function of the degree of correlation between the two time series (which depends on wavelength separation and target depth). The results are compared with both a numerical simulation and a laboratory-based experiment.     

Probability Density Functions of Speckle Intensity Produced by Weak Diffusers

By using the discrete cell model for the rough surface of objects, a general expression is derived which gives the probability density function of speckle intensity produced by weak diffusers having an arbitrary phase distribution and an arbitrary cell number, N, of contributions for the formation of speckles. In some special cases, it gives the probability density functions which have been previously derived and are well known in the statistics of speckles. In the case of the small number N = 2, an analytical solution of the probability density function is obtained from that general expression. Some features on the probability density functions of speckles are discussed for the case of small roughness and small number N.     

Wave optics simulation of atmospheric turbulence and reflective speckle effects in CO2 lidar

Laser speckle can influence lidar measurements from a diffuse hard target. Atmospheric optical turbulence will also affect the lidar return signal. We present a numerical simulation that models the propagation of a lidar beam and accounts for both reflective speckle and atmospheric turbulence effects. Our simulation is based on implementing a Huygens-Fresnel approximation to laser propagation. A series of phase screens, with the appropriate atmospheric statistical characteristics, are used to simulate the effect of atmospheric turbulence. A single random phase screen is used to simulate scattering of the entire beam from a rough surface. We compare the output of our numerical model with separate CO(2) lidar measurements of atmospheric turbulence and reflective speckle. We also compare the output of our model with separate analytical predictions for atmospheric turbulence and reflective speckle. Good agreement was found between the model and the experimental data. Good agreement was also found with analytical predictions. Finally, we present results of a simulation of the combined effects on a finite-aperture lidar system that are qualitatively consistent with previous experimental observations of increasing rms noise with increasing turbulence level.     

Speckle dynamics for intensity-modulated illumination

We analyze the dynamics of laser speckle patterns, designed for sensing with a receiver, based on spatial filtering. The speckle translation arises after free-space propagation of light scattered from nonspecular surfaces of a solid object in motion. The speckle pattern is manipulated by modulating the intensity of the coherent light, illuminating the target. The space-time normalized cross covariance of speckle patterns incident on the spatial sensor is calculated for the field distribution of three Gaussian beams having arbitrary directions and separations when incident on the target. The modulation of the intensity distribution at the target introduce a higher spatial frequency component in the speckle pattern. The theoretical analysis provides the statistical parameters for both the speckles and the higher spatial frequency component. The analysis reveals that the speckles and the higher spatial frequency component do not necessarily translate as a rigid structure. The theoretical findings are supported by measurements.     

Statistics of intensity in adaptive-optics images and their usefulness for detection and photometry of exoplanets

This paper is an introduction to the problem of modeling the probability density function of adaptive-optics speckle. We show that with the modified Rician distribution one cannot describe the statistics of light on axis. A dual solution is proposed: the modified Rician distribution for off-axis speckle and gamma-based distribution for the core of the point spread function. From these two distributions we derive optimal statistical discriminators between real sources and quasi-static speckles. In the second part of the paper the morphological difference between the two probability density functions is used to constrain a one-dimensional, "blind," iterative deconvolution at the position of an exoplanet. Separation of the probability density functions of signal and speckle yields accurate differential photometry in our simulations of the SPHERE planet finder instrument.     

Intrapulse temporal and wavelength shifts of a high-power 2.1-µm Ho:YAG laser and their potential influence on atmospheric lidar measurements

A high-power, flash-lamp-pumped, Q-switched Ho:YAG laser has been developed to produce up to 150 mJ in a 100-ns Q-switched pulse. The Ho laser was initially used in a direct detection lidar-differential absorption lidar (DIAL) system to measure vertical density profiles of aerosols and water vapor in the atmosphere. It was found, however, that the Ho laser operated simultaneously on two closely spaced spectral emission wavelengths (2.090 and 2.097 μm) and that the distribution of energy between the two wavelengths could change significantly on time scales of several seconds to minutes. Such intrapulse temporal and wavelength shifts were found to alter the atmospheric lidar return significantly because one of the laser lines coincided with a water vapor absorption line in the atmosphere. This laser spectral output problem was overcome by the use of intracavity étalons that controlled the laser spectral-temporal characteristics but reduced the laser output energy to approximately 75 mJ/pulse in a 100-ns pulse length. These results are important as they serve to point out the difficulties of developing and using a high-power 2.1- μm Ho laser for atmospheric lidar when high-resolution spectral and temporal characteristics can significantly influence the lidar return and be misinterpreted as resulting from atmospheric signals.     

Femtosecond laser speckles

The concept of femtosecond laser speckles is put forward. The theory of a speckle pattern in light of finite bandwidth is applied to describe femtosecond laser speckles. Basic representations of the contrast and the spectral correlation of femtosecond laser speckles are presented. The relationship between the speckle contrast and the bandwidth of a femtosecond laser is given. Experimental results are given that indicate an obvious difference between the speckle patterns produced by a continuous-wave laser and those produced by a femtosecond laser.     

Field demonstration of a scanning lidar and detection algorithm for spatially mapping honeybees for biological detection of land mines

A biological detection scheme based on the natural foraging behavior of conditioned honeybees for detecting chemical vapor plumes associated with unexploded ordnance devices utilizes a scanning lidar instrument to provide spatial mapping of honeybee densities. The scanning light detection and ranging (lidar) instrument uses a frequency doubled Nd:YAG microchip laser to send out a series of pulses at a pulse repetition rate of 6.853 kHz. The scattered light is monitored to produce a discrete time series for each range. This discrete time series is then processed using an efficient algorithm that is able to isolate and identify the return signal from a honeybee in a cluttered environment, producing spatially mapped honeybee densities. Two field experiments were performed with the scanning lidar instrument that demonstrate good correlation between the honeybee density maps and the target locations.     

Rotational vibrational-rotational Raman differential absorption lidar for atmospheric ozone measurements: methodology and experiment

A single-laser Raman differential absorption lidar (DIAL) for ozone measurements in clouds is proposed. An injection-locked XeCl excimer laser serves as the radiation source. The ozone molecule number density is calculated from the differential absorption of the anti-Stokes rotational Raman return signals from molecular nitrogen and oxygen as the on-resonance wavelength and the vibrational-rotational Raman backscattering from molecular nitrogen or oxygen as the off-resonance wavelength. Model calculations show that the main advantage of the new rotational vibrational-rotational (RVR) Raman DIAL over conventional Raman DIAL is a 70-85% reduction in the wavelength-dependent effects of cloud-particle scattering on the measured ozone concentration; furthermore the complexity of the apparatus is reduced substantially. We describe a RVR Raman DIAL setup that uses a narrow-band interference-filter polychromator as the lidar receiver. Single-laser ozone measurements in the troposphere and lower stratosphere are presented, and it is shown that on further improvement of the receiver performance, ozone measurements in clouds are attainable with the filter-polychromator approach.     

探测低空大气温度分布的转动拉曼激光雷达

提出了一种新的探测对流层低层大气温度的转动拉曼激光雷达方法,通过测量N2和O2的后向散射的纯转动拉曼谱的强度,计算它们的比值来确定大气温度的垂直分布,并对其性能进行了数值模拟。转动拉曼激光雷达的光源是一个调Q的Nd:YAG激光器,经扩束器后输出能量200mJ;采用双光栅单色仪提取所需要的氮气和氧气的转动拉曼谱;接收机采用光电倍增管和双通道光子计数器,量子效率是10%(48000个脉冲累加)。夜晚它对近地面10.2km高度内的探测信噪比在10:1以上,白天它对近地面3.6km高度内的探测信噪比在10:1以上,计算的温度与模拟用的温度真值阔线相差约0.3K。     

Heterodyne lidar returns in the turbulent atmosphere: performance evaluation of simulated systems

Simulations of beam propagation in three-dimensional random media were used to study the effects of atmospheric refractive turbulence on coherent lidar performance. By use of the two-beam model, the lidar return is expressed in terms of the overlap integral of the transmitter and the virtual (backpropagated) local oscillator beams at the target, reducing the problem to one of computing irradiance along the two propagation paths. This approach provides the tools for analyzing laser radar with general refractive turbulence conditions, beam truncation at the antenna aperture, beam-angle misalignment, and arbitrary transmitter and receiver configurations. Simplifying assumptions used in analytical studies, were tested and treated as benchmarks for determining the accuracy of the simulations. The simulation permitted characterization of the effect on lidar performance of the analytically intractable return variance that results from turbulent fluctuations as well as of the heterodyne optical power and system-antenna efficiency.     

Decorrelation-induced phase errors in phase-shifting speckle interferometry

The purpose of this research is the quantitative investigation of decorrelation-induced phase errors in speckle interferometry. Measurements in speckle interferometry are inherently affected by decorrelation, i.e., by alterations of the speckle fields during measurement. Likewise, the random phases carrying the interferometric information change during decorrelation. Image plane and pupil plane decorrelation are considered for both smooth and speckle reference wave interferometers. Since the decorrelation effect depends on the aperture and the pixel size, the calculations include not only the case of speckles being well resolved by the camera but also the case of unresolved speckles. Different standard deviations of the phase error are obtained from the probability density of the pixel modulation and the phase before and after decorrelation. Most cases (apart from pupil plane decorrelation in speckle reference wave setups) appear to obey exactly the same phase error statistics. In particular, the number of speckles per pixel does not affect the phase error distribution over the whole image. The only important parameters determining the decorrelation-induced phase errors are the amount of decorrelation and the pixel modulation.     

Effect of aerosol particle microstructure on cw Doppler lidar signal statistics

Analysis of signal statistical characteristics is carried out, and estimation errors of the radial wind velocity are calculated by use of numerical simulation of a cw Doppler lidar return, taking into account the atmospheric aerosol microstructure. It has been found that, at small sounded volume, the large particles contribute significantly to the scattered field. As a result the lidar return probability density function distribution can differ significantly from a Gaussian distribution. Neglect of the aerosol microstructure effect results in considerable underestimation of the error of cw Doppler lidar velocity estimates at small sounded volume.     

Analysis of a Simplified Radar Simulator for Measuring Probability of Detection

This paper describes a simplified radar target simulator that can approximate the output of a pulse radar receiver so that the detection capabilities of amplitude-sensing video target detection devices can be measured. The simplified simulator uses only video frequency components; therefore, its output is not identical to that from a radar. However, an analysis of the simulator output gives the probability density function for signal plus noise and the equation for the probability of detection. A comparison of the probability of detection for the simplified simulator and an actual radar receiver is made and some results are plotted. Therefore, the output of the simplified radar simulator can be used to measure the probability of detection of amplitude-sensing video target detectors because the results can be related to the case of an actual radar receiver. Although the example discussed involves a radar receiver, the analysis is general in its application to all narrow-band AM receivers using envelope detection.     

Aperture dependence of the mixing efficiency, the signal-to-noise ratio, and the speckle number in coherent lidar receivers

With the aid of the van Cittert-Zernike theorem we develop an analytical expression for the ensemble-averaged heterodyne mixing efficiency in coherent lidar receivers that are looking at a diffuse target that is in the receiver's far field. Our extremely simple and straightforward analysis shows that the dependence of the mixing efficiency on the receive aperture size d(R) first follows a parabolic decrease and later approaches a (d(R))(-2) function. As a consequence, the signal-to-noise ratio does not increase proportionally to the aperture area but saturates. For the system model chosen, the heterodyne mixing efficiency exhibits the same functional dependence on the lidar geometry as the reciprocal of the number of speckle cells within the receive aperture.     

Speckle reduction in laser projection systems by diffractive optical elements

In laser projection systems the observer in the far field of the image points on the screen will recognize serious speckle noise. There are many methods to reduce or eliminate speckles in the near field by reducing or eliminating temporal or spatial coherence of the laser. But for the far field it is hardly possible to change the coherence properties of laser sources so that speckles will disappear. We propose a new method for eliminating speckles in the far field by using a diffractive optical element. The intensity modulation depth in the far-field speckle pattern can be reduced to a few percent while good beam quality is preserved.     

Improvement of speckle statistics in double-wavelength superheterodyne interferometry

In this paper we analyze the probability density function of the superheterodyne signal obtained in a two-wavelength interferometer from the beat of a local oscillator laser beam with a speckled return beam from a rough target. Theoretical investigation shows that, by using an increased number of spatially separated detectors, one can improve noticeably the detection probability of the superheterodyne signal. Experimental results obtained with a four-quadrant detector are in good agreement with theory.     

Frequency Spectral Measurements of a Pulsed,TE CO2

Abstract

Experimental measurements of the intra-pulse chirp and temporal coherence from a Joule class TE CO₂ laser incorporating LAWS transmitter design features are presented. Digitized quadrature data (I and Q) from our ground-based coherent Doppler lidar system utilizing return signals off a hard target in the telescope far field are processed using fast Fourier transform and pulse pair techniques to obtain laser pulse frequency spectral components (offset frequency and spectral width) and high-resolution (～ 50 ns/sample) frequency chirp profiles. Less than 300 kHz of frequency chirp is observed in the first 3·5 μs of the laser pulse which contains approximately 90% of the pulse energy. Spectral width of the laser pulse, including both chirp and transform limited components, are measured to be less than 300 kHz full width at half maximum.