Backscatter from atmospheric aerosols and molecular nitrogen and oxygen causes “clutter” noise in direct detection ladar applications operating within the atmosphere. The backscatter clutter is more pronounced in multiple pulse, high PRF ladars where pulse-averaging is used to increase operating range. As more and more pulses are added to the wavetrain the backscatter increases. We analyze the imaging of a transmitted Gaussian laser-mode multi-pulse wave-train scatteried off of aerosols and molecules at the focal plane including angular-slew rate resulting from optical tracking, angular lead-angle, and bistatic-optics spatial separation. The defocused backscatter images, from those pulses closest to the receiver, are analyzed using a simple geometrical optics approximation. Methods for estimating the aerosol number density versus altitude and the volume backscatter coefficient of the aerosols are also discussed.
Atmospheric turbulence produces intensity modulation or "scintillation" effects on both on the outward laser-mode path and on the return backscattered radiation path. These both degrade laser radar (ladar) target acquisition, ranging, imaging, and feature estimation. However, the finite sized objects create scintillation averaging on the outgoing path and the finite sized telescope apertures produce scintillation averaging on the return path. We expand on previous papers going to moderate to strong turbulence cases by starting from a 20kft altitude platform and propagating at 0° elevation (with respect to the local vertical) for 100km range to a 1 m diameter diffuse sphere. The outward scintillation and inward scintillation effects, as measured at the focal plane detector array of the receiving aperture, will be compared. To eliminate hard-body surface speckle effects in order to study scintillation, Goodman's M-parameter is set to 106 in the analytical equations and the non-coherent imaging algorithm is employed in Monte Carlo realizations. The analytical equations of the signal-to-noise ratio (SNRp), or mean squared signal over a variance, for a given focal plane array pixel window of interest will be summarized and compared to Monte Carlo realizations of a 1m diffuse sphere.
Atmospheric turbulence produces intensity modulation or "scintillation" effects, on both on the outward path and on the
return path, that degrade laser radar (ladar) target acquisition, ranging, and imaging. Quantitative previous
measurements of ladar scintillation have used tiny flat mirrors and corner-cube retro-reflectors as their objects. In
actuality, the real finite sized objects create scintillation averaging on the outgoing path and the finite sized telescope
apertures produce scintillation averaging on the return path. We will quantify these effects and compare them to the tiny
mirror and corner-cube retro-reflector quantitative data from the literature. Methods for modeling the outward path and
the inward path scintillation effects and the target produced laser-speckle over arbitrary focal plane array detector areas
will be discussed. The analysis of the ladar receiver-operating-characteristic (ROC) and signal-to-noise ratio (SNRp) or
mean squared over a variance will also be discussed.
A methodology for laser radar / ladar imaging through atmospheric turbulence is studied for target feature extraction,
acquisition, tracking, identification, etc. The procedure follows sequentially by (1) laser-mode propagation through the
outward atmospheric path, which is modeled by using multiple turbulence phase-screens; (2) the propagated laser mode
illuminates a target which is modeled using multiple facets; and (3) simultaneously, or near simultaneously, the return
path turbulence effects are modeled by a reverse order Cn
2(h), Lo, and lo set of phase-screens assuming a plane-wave.
This return path amplitude & phase screen is then used to create a pupil plus atmospheric effects impulse-response
which is used to (4) accurately construct the image of a diffuse target on the detector focal plane array using
conventional Fourier optics. Agreement of both the outward and the return path phase-screen matrices with their
respective analytical turbulence parameters, which are independently computed, is shown. The Fourier optics
construction process of the target's image is reviewed, and typical diffuse target images of facet model objects are
presented illustrating scintillation and speckle effects. The images may then be used in algorithm development for a
specific system performance determination.
The optoelectronic gain of a linear mode avalanche photo-diode (APD) results from the cascade of electron and hole
impact ionizations that take place in the high-field intrinsic multiplication layer of the APD. Due to the uncertainty
associated with the stochastic nature of the APD's gain, the shot noise present in the resulting photo-generated electrical
signal is accentuated and degrades the detection of single photon initiated avalanche signals. Recent advances in linearmode
InGaAs APD detectors have been demonstrated that have reduced excess noise, along with the high gain necessary
for detecting single photons. In these devices the avalanche buildup is characterized with a temporally varying noise. At
low incident photon / photo-electron levels, the stochastic nature of the impulse response function of these APDs offers
the potential of increased probability that the output exceeds a threshold level resulting in a "detection" and, hence, a
better receiver-operating-characteristic (ROC). In this paper we examine the ROC (Pdetection vs PFalseAlarm) statistics of
these single photon APDs as a function of the quasi-deterministic mean gain and standard deviation for an rms ROIC
(readout integrated circuit) noise level of 25e-. Single photo-electron and multiple photo-electron detection statistics are
also examined for predicting a ROC. Measured linear-mode APD data are also presented.
Several multiple-hypothesis range-rate algorithms are investigated to determine initial target acquisition capabilities of a
direct detection ladar operating under low photo-electron return conditions. During initial acquisition of an object, the
location of the object is not known, therefore the ladar returns cannot be simply summed in order to improve detection
statistics. Analogous to classical radar multiple hypothesis algorithm approaches a "shift and sum," a "shift and
accumulate," and a "numerically shift and histogram" algorithm are investigated. The probability density function for
the maximum of the multiple-hypothesis range-rate algorithm matrix output is developed so that a threshold crossing
probability can be determined and a "detection" declared (receiver-operating-characteristic). This is expressed as a
function of false alarm rate which is a function of the number of ladar returns processed in the acquisition process and
the length of the acquisition window.
A facet model of a helicopter containing 35,000 facets is used to compare coherent ladar waveform performance in
precision and in resolution. The helicopter represents a convenient man made object for these tests. Several coherent
ladar waveforms have been compared previously applying "range-resolved Doppler and intensity" (RRDI) or "inverse
synthetic aperture ladar" (ISAR) algorithms in order to numerically construct an image of the target in slant-range and
Doppler frequency spread. The targets are generally at large distances and are much smaller than the diffraction limited
laser spot size or the diffraction limited detector's field-of-view. In this study we emphasize the "tangent-FM"
waveform and review its performance relative to other waveforms. Note that thousands of facet models of interest are
available on the internet and are usually low cost or even free. We also utilized a new "analytic signal" construction,
recently published, for a small improvement in the final image quality.
A dust or aerosol cloud represents a convenient target to examine the capabilities of range-resolved Doppler and
intensity (RRDI) or inverse synthetic aperture ladar (ISAR) imaging coherent laser radar, known as coherent "lidar" for
optically thin targets. The poly-phase P4 ladar waveform and its RRDI images are described and compared with
previous pulse-burst, linear-FM chirp pulse-compression, pseudo-random phase modulation waveforms, and several
other waveforms which have not been utilized to date. A "dust cloud" has very many independently moving point
scatterers with velocities that are approximately Gaussian randomly distributed in x,y,z with standard deviations of about
10% of the mean wind + aerosol velocity. This is contrary to a hard-target where the point scatterers are rigidly attached
and moving together. The dust cloud produced speckle effects for the various ladar waveforms are compared. In
addition, a reference set of four corner-cube retro-reflectors within the dust cloud further illustrates the differences in the
various waveform capabilities and resolution.
Coherent ladar imaging of satellite retro-reflector arrays is analyzed to determine some of the potential capabilities of
coherent ladar systems for long range imaging. The satellites are at mega-meters of slant range and are basically
angularly unresolved assuming a nominal one meter telescope used at a laser wavelength of 1.064 μm corresponding to a
281,625 GHz center-frequency. A coherent ladar may have a selectable waveform ranging from single nanosecond
pulses through tone-pulses, but the imaging waveform considered here is the linear-FM chirp pulse-compression ladar
waveform, which consists of a series of frequency chirps over a long period of time. The linear-FM chirp return is pulse
compressed digitally using several possible approaches. Image reconstruction follows basic ISAR algorithms in forming
a "range-resolved Doppler and intensity" (RRDI) image. A retro-reflector ring on the SEASAT satellite is used to
illustrate the ladar's capability, although we spin the satellite faster than the true rotation rate to demonstrate waveform
resolution. Several other useful algorithms as (multi-chirp) range-time-intensity (RTI matrix) range-bin summation
and segmented-spectrum frequency-bin summation are also discussed. A covariance matrix calculation is applied to
the RTI matrix and also to the segmented-spectrum matrix for the extraction of additional target information.
KEYWORDS: Speckle, LIDAR, Doppler effect, Target detection, Signal processing, Detection and tracking algorithms, Sensors, Direct detection LIDAR, Interference (communication), Electric field sensors
The ability to estimate the mean frequency, peak frequency, and frequency spread of angularly unresolved hard targets is examined using both coherent and direct detection ladar simultaneously. It has been proposed that the direct detection of the return speckle intensity can be used to enhance the coherent detection ladar spectral estimates and signal processing algorithms. The direct detection ladar uses the orthogonally polarized speckle E-field return, with respect the local-oscillator laser, and does not affect the coherent detection sequence. We are concerned in obtaining precise frequency information with only coarse range requirements and, therefore, consider Q-switched laser pulses whose spectral width is much narrower than the target’s spectral bandwidth. We use spinning diffuse cones for examples. The direct detection speckle intensity spectrum is computed and is shown to be corrupted by a strong DC-component and interference between the positive and negative frequencies, which causes additional frequency spread of nearly twice the target spectral width. However, useful target spectral width information can be obtained by direct detection to help in the coherent detection signal processing. Three algorithms are described which are each shown to be within a factor of about 2 times the Cramer-Rao lower bound estimate on mean and peak frequency precision. Surprisingly robust performance of the autocorrelation function first-lag algorithm (“pulse-pair”) is demonstrated for these targets.
Coherent laser radars observing a resolved (larger than the incident laser mode) target vibrating surface can estimate the target's piston-mode displacement motion from the target's Doppler produced frequency spectrum. We review recent work showing that a newly developed joint time-frequency transform algorithm is superior to older joint time-frequency transforms, the common short-time-Fourier transform (spectrogram) algorithm, and other elementary spectral estimation
algorithms for resolving the target's spectra. In this paper we extend these approaches when the ladar is observing an unresolved (smaller than the incident laser mode) piston-mode vibrating object situated on the ground. Because the target is smaller than the laser spot, the surrounding ground produces a narrow-band constant frequency "clutter" signal at the baseband frequency. We show that a recently developed "sech-window" joint time-frequency transform is
superior to other algorithms for separating the frequency modulated target piston motion signal from the narrow-band ground return. The analysis in this case includes a "signal-to-clutter ratio" (SCR) parameter variation as well as a "carrier-to-noise ratio" (CNR), or target signal strength to LO-laser noise strength, parameter variation.
KEYWORDS: Signal to noise ratio, Scintillation, LIDAR, Turbulence, Speckle, Data modeling, Atmospheric scintillation, Atmospheric propagation, Signal detection, Telescopes
The signal-to-noise power ratio parameter of coherent ladar systems operating within the atmosphere and including atmospheric scintillation effects is modeled. Previously published round-trip geometry ladar data of the variance of the normalized-irradiance as a function of the one-way path integral Rytov parameter are utilized to estimate a signal-tonoise power ratio. However, these data were taken in the strong signal case where local-oscillator-laser noise was
negligible. A model is proposed to combine the local-oscillator-laser produced noise, a zero-mean wideband-Gaussian random process corresponding to normal coherent ladar operation, with the scintillation produced by round-trip turbulence based on a calculation of the one-way path-integral Rytov parameter. Close agreement with Shapiro's 1981 analysis is found, provided one modifies the Shapiro formulation to account for scintillation saturation.
KEYWORDS: Speckle, Signal processing, Doppler effect, LIDAR, Modulation, Curium, Frequency modulation, Fermium, Time-frequency analysis, Monte Carlo methods
We examine the signal processing of both linear and sinusoidal frequency modulation (FM) coherent ladar returns from resolved and unresolved targets, which are spread in Doppler. The Doppler spread may be due to target spin, tumbling, or vibration as well as to the applied linear or sinusoidal-FM on the transmitted E-field. Monte Carlo realizations of the target surface random phasor reflector elements interact with the incident Efield producing laser speckle, and the speckled returns are analyzed in this study. The speckle signals are processed (1) using several spectrum (periodogram based) estimators, (2) the conventional “spectrogram” approach, and (3) ten joint time-frequency transforms (JTFT). We show that the Born-Jordan JTFT is superior to the other spectral estimators tested here in suppressing local oscillator laser noise and accurately estimating the target's spectrum for signal processing under speckle target return conditions pertaining to coherent laser radar. A new algorithm which sums particular pixels of the JTFT image is introduced and is shown to be much more robust in low CNR conditions than the JTFT maxima or JTFT centroid processing when utilizing the applied linear or sinusoidal-FM modulation waveform.
KEYWORDS: Doppler effect, Speckle, Mode locking, LIDAR, Digital filtering, Monte Carlo methods, Signal to noise ratio, Optical character recognition, Pulsed laser operation, Reflectivity
Mode-locked solid-state coherent laser radars operating continuously and at short wavelengths are capable of forming range-resolved Doppler and intensity images of distant spinning objects. The continuous mode-locked repetitive pulse operation allows demonstrated long laser coherence- lengths to achieve efficient heterodyne detection. The continuous repetitive pulsed operation also allows one to probe an object for arbitrarily long observation times resulting in precise center-of-mass-Doppler estimation and micro-Doppler vibration and spin measurements, as well as the temporal integration of the received signals to increase effective signal strength. We investigate this ladar waveform for imaging spinning cylinders at large distances, so that there is on the order of two detected photons approximately every 1,000 micro-pulses and applying simple estimators to the Doppler center-of-mass and Doppler-width for automatic target recognition purposes. A simple preliminary model for 'reflective' cylinders is also presented.
KEYWORDS: Filtering (signal processing), Monte Carlo methods, Linear filtering, LIDAR, Sensors, Pulsed laser operation, Photons, Electronics, Signal processing, Picosecond phenomena
The number of photons returning form a target in a given time interval is well described by a negative-binomial distributed random variable. A photomultipler tube (PMT) photon-counting detector is optimal for direct detection, and the number of detected-photon 'electron pulses' produced is also negative-binomially distributed per time bin, with a reduced mean due to the device quantum efficiency. These time distributed electron pulses are amplified and filtered by the preamplifier electronics prior to digitization and signal processing. The voltage output pulse per individual photo-electron event is known as the 'impulse-response- function' of the detector and preamplifier. In this study we employ a typical analog preamplifier filter response, modeled as a Butterworth lowpass filter of order two, which filters a 200 ps wideband PMT input voltage pulse. The random summation of these lowpass voltage impulse-responses, as created by the negative-binomial photon arrival times and random photo-electron creation, is the classical electronic 'shot-noise' random process. We derive numerically the voltage probability density function of this negative- binomial/impulse-response driven shot-noise random process following the stochastic process literature. We also show a technique to include PMT variations in gain, known as the 'pulse height distribution,' and to incorporate Gaussian baseline-noise voltage. Agreement with AMOR experiments is shown to be excellent. In addition, a Monte Carlo realization is presented, using the same impulse-response temporal shape, which also gives excellent agreement with AMOR data and with the analytical/numerical calculations.
The number of photons returning from a target in a given time interval is a negative-binomially distributed random variable. The resulting detected photon 'electron pulses' produced by a photomultiplier tube (PMT) photon-counting detector are also negative-binomially distributed per time bin with a reduced mean. These time distributed electron pulses are amplified and filtered by the receiver electronics, prior to digitization and signal processing. The voltage output pulse per individual photo-electron event is known as the 'impulse-response- function' of the detector and amplifier. The random summation of these voltage impulse-responses, as created by the negative-binomial photon arrival times and photo-electron creation, is the classical electronic 'shot-noise' random process. We derive the voltage probability density function of this 'negative-binomial driven shot-noise' random process following the stochastic process literature. We also show a technique to include PMT variations in gain, known as the 'pulse height distribution,' and also to incorporate Gaussian baseline-noise voltage. Agreement with several experiments is shown to be excellent.
A simple analytical model of a laser radar's subtended irradiance probability-density-function has been developed for both direct detection and coherent detection laser radar. The vacuum speckle irradiance statistics are developed following Goodman's 'M parameter' treatment for direct detection ladar and also by setting the M-parameter equal to one (negative- exponential power statistics) for coherent laser radar. A 'turbulence M parameter' is then computed using the round-trip aperture averaging analyses of Gudimetla and Holmes based on the Rytov-variance parameter computation over an atmospheric path of interest. The 'vacuum M parameter' and the 'turbulence M parameter' are then combined to form an 'effective M parameter.' This effective M parameter is used in an analytically simple gamma distribution probability-density- function for the laser radar's subtended irradiance. We will show excellent agreement with the more analytically complicated two-parameter K-distribution from the literature. We will also indicate how one may include the turbulence scintillation in addition to the fundamental vacuum speckle, with increasing levels of turbulence to determine ladar performance.
Direct-detection laser radars can measure the range and the intensity returns from a target, with or without clutter, for each part of the target resolved in angle by the optical system. Because the ladar's angular resolution is in micro-radians, there are generally at least a few angular pixels 'on target.' In addition, for narrow pulse (approximately 1 ns) ladar systems, there may be ten or so sequential intensity measurements in range per pixel as the laser pulse propagates down the target's surface. The output image is, therefore, potentially a three dimensional 'cube' of intensity measurements and quantized in the range axis by the range-bin size or 'voxel' size. This is known as 'range resolved angle-angle-intensity' ladar. In a previous paper we transformed this 3D-matrix image into the spatial-frequency domain using 3D- Fourier transforms and followed conventional 2D template correlation techniques to perform target recognition and identification. During this previous study, it was noted that the 2D range-bins could be placed in sequence and 2D filtering used on these synthetic images. Results of 3D and 2D-sequence target correlators using the 'joint transform correlator,' 'the inverse filter,' the 'phase-only matched-filter,' the 'binary phase-only filter,' and the classical 'matched filter' are presented here. Far-field test data using conical shaped targets are used to study the 3D and 2D correlators, and the effects of laser speckle are discussed. Recent developments in negative-binomial driven shot- noise effects in range-resolved direct-detection ladar are reviewed as well. These 3D or 2D-sequence template correlators may supplement or refine less computationally intensive algorithms such as total signal; range-extent; x-z, y-z, and x-y plane image centroid estimation; and image moments.
The numerical use of the fast Hankel transform E-field propagator is described in this paper. For azimuthally symmetric E-field applications, this propagator is a useful tool for solving many common problems such as super-Gaussian and unstable resonator laser mode propagation within optical trains and then out to a target. Overlap integrals for coherent ladar may be easily computed. In addition, laser resonators with gain medium may be analyzed for mode structure and output power incorporating go(r), Isat(r), and extinction(r) with radially varying reflectivity and phase optics.
In direct detection ladar systems, the received irradiance statistics and, therefore, the detected photon counting statistics are determined by two parameters: the average collected irradiance value and the M parameter. The M parameter is the number of independent speckle cells, per polarization and per independent laser mode, subtended by the receiving aperture and focused onto a detector. In the 1960's Goodman analytically determined the M parameter for simple ladar geometries such as circular, square, and Gaussian shaped targets and circular and square shaped receiving apertures. This paper examines the numerical evaluation of this M parameter for arbitrarily shaped target source regions, per pixel or per pixel-range-bin, and arbitrarily shaped receiving apertures using the 2D discrete Fourier transform. This evaluation method is capable of treating the cases of high reflectivity target source regions, such as a cylinder's or cone's glint-line, and Gaussian spatial mode illumination which effectively reduce the source area. The analyses apply when round-trip atmospheric scintillation effects are negligible.
The effects of round-trip atmospheric turbulence on ladar for unresolved target detection are being investigated using a Monte Carlo code with many phase-screens to simulate atmospheric turbulence effects. These phase-screens are located along the outward path of the laser-mode and the inward path of the backscattered laser speckle pattern. The targets used are variable in size and smaller than the propagated laser-mode transverse dimension, and they are therefore termed 'unresolved'. In this paper previous round- trip turbulence analyses and data are reviewed, and the current Monte Carlo simulation code for unresolved targets is discussed. Simulation results to date are presented indicating that intensity fluctuations are best described by a new two-parameter K-distribution probability density function. This intensity distribution may then be used in deriving a ladar receiver-operating-characteristic for determining the target detection probability including round-trip turbulence.
The linear frequency-modulation chirp pulse compression technique of classical microwave radar is examined in the context of coherent laser radar. A coherent CO2 laser radar may operate near 9.115 micrometers and 33,000 GHz. Because of this short wavelength, a large target Doppler-spread is realizable in a single ladar measurement. In addition, target surface roughness with respect to wavelength causes the target backscatter points to be uniformly distributed over 2(pi) radians in phase resulting in Gaussian/Rayleigh/negative-exponential receiver statistics. Target Doppler spread and speckle as well as target down- range extent affect the linear-FM-chirp pulse compression efficiency thereby degrading the peak compressed-pulse carrier-to-noise. This degradation in carrier-to-noise is quantified using a 'maximum of M Rayleighs' detector model which allows a simple scale factor degradation for other coherent ladar wavelengths, chirp magnitudes, and pulse lengths. The receiver-operating-characteristic of the sum of many Rayleigh distributed random variables is also developed for comparison to the classical sum of many negative- exponential statistics.
KEYWORDS: Signal processing, LIDAR, Digital signal processing, Doppler effect, Image processing, Target acquisition, Data acquisition, Detection and tracking algorithms, Imaging systems, Signal detection
Textron has designed and built a high-powered CO2 laser radar for long range targeting and remote sensing. This is a coherent, multi-wavelength system with a 2D, wide-band image processing capability. The digital processor produces several output products from the transmitter return signals including range, velocity, angle, and 2D range-Doppler images of hard-body targets (LADAR mode). In addition, the processor sorts and reports on data acquired from gaseous targets by wavelength and integrated path absorption (LIDAR mode). The digital processor has been developed from commercial components with a SUN SPARC 20 serving as the operator workstation and display. The digital output products are produced in real time and stored off-line for post-mission analysis and further target enhancements. This LADAR is distinguished from other designs primarily by the waveforms produced by the laser for target interrogation. The digital processing algorithms are designed to extract certain features through operation on each of the two waveforms. The waveforms are a pulse-tone and a pulse-burst designed for target acquisition and track, and 2D imaging respectively. The algorithms are categorized by function as acquisition/track, 2D imaging, integrated absorption for gaseous targets, and post mission enhancements such as tomographic reconstruction for multiple looks at targets from different perspectives. Field tests are now in process and results acquired from Feb.-June '96 will be reported on. The digital imaging system, its architecture, algorithms, simulations, and products will be described.
Mode-locked CO2 lasers have been developed which can produce long coherent pulse trains consisting of many narrow subpulses. This laser waveform may be used to numerically generate range-Doppler images (inverse synthetic aperture radar images) of a target wherein the Doppler spread of a spinning target is used to create a synthetic cross-range target dimension. The narrow micro-pulse temporal width provides good range resolution, and the long coherent pulse train provides good frequency resolution of the (cross-range) target Doppler spread. In this paper we examine the algorithms and imaging capabilities of this waveform as implemented for the FLD and Hi-CLASS laser radar (ladar) systems which are now being installed in the AMOS facility on Mt. Haleakala, Maui and in an aircraft testbed.
Range information from a laser radar can be used to rapidly converge target track files for theater missile defense from an airborne sensor platform. This paper examines the application of laser radar technology to this mission. Eyesafe lasers including carbon dioxide, holmium/thulium, and YAG shifted by optical parametric oscillators or Raman cells are considered. Performance analyses include the effects of wavelength dependent target cross sections, atmospheric attenuation and background radiation, and either direct or heterodyne detection processes on the received signal to noise ratio. Signal processing analyses include the effects of noise statistics, target fading for either direct or heterodyne detection, and the optical wavelength dependent effects of atmospheric turbulence on system false alarm and detection probabilities.
Basing laser radar systems aboard aircraft provides capability for accurate tracking of ground, airborne, and ballistic missile targets from long range. The atmospheric effects of long propagation paths impact the performance of laser radar systems in two important ways -- molecular and aerosol extinction and optical turbulence. This paper provides quantitative assessment of the impact of these effects for laser radar wavelengths beyond 1.4 microns. The treatment of round-trip turbulence on direct detection systems is believed to be the first estimate of this effect. A more complete system analysis is underway and will be described in a forthcoming paper.
The passage of commercial and military aircraft through invisible fresh volcanic ash clouds has caused damage to many airplanes. On December 15, 1989 all four engines of a KLM Boeing 747 were temporarily extinguished in a flight over Alaska resulting in $DOL80 million for repair. Similar aircraft damage to control systems, FLIR/EO windows, wind screens, radomes, aircraft leading edges, and aircraft data systems were reported in Operation Desert Storm during combat flights through high-explosive and naturally occurring desert dusts. The Defense Nuclear Agency is currently developing a compact and rugged lidar under the Aircraft Sensors Program to detect and estimate the mass density of nuclear-explosion produced dust clouds, high-explosive produced dust clouds, and fresh volcanic dust clouds at horizontal distances of up to 40 km from an aircraft. Given this mass density information, the pilot has an option of avoiding or flying through the upcoming cloud.
The detection statistics of avalanche photodiode detectors when used in laser radar systems are examined. In the laser radar systems considered here, a diffuse hard target is illuminated by a transmitted laser beam and the photons subtended by the receiving aperture and focused onto the detector obey negative-binomial statistics. The specific negative-binomial distribution is determined by the coherence length of the laser and the angular subtense of the target. These received photons are converted into photoelectrons and amplified by the avalanche photodiode which is an imperfect device. Dark current, amplifier, and background-produced noise electrons must be exceeded by the avalanche photodiode output electron pulse for a detection to occur. The required mean number of signal photons from a given negative-binomial target as a function of probability of detection and probability of false alarm is calculated. For perfect photon counters, the probability of detection at high discrete false alarm probabilities is also calculated. It is shown that for probabilities of detection of 0.9, three to five times more laser power may be required than for the generally assumed Poisson signal photons case. At probabilities of detection of 0.3, corresponding to multipulse waveforms, the statistics are independent of the target photon distribution.
The layered-sphere volumetric backscatter coefficient is examined for possibly enhancing the estimates of the aerosol component distributions and their physical parameters with examples utilizing a coherent Lidar at 10.6 microns. It is found that at this wavelength alumina particles coated with soot, water, or sulfuric acid may exhibit greatly reduced backscattering due to destructive interference of the reflected waves plus guided wave action in the absorbing layer. Also, the layered-sphere calculations easily reduce to solid-sphere calculations as needed.
This paper shows how these signal probability density functions in power and in voltage propagate down the signal processing electronics chain using data from the Army Missile Optical Range (AMOR) facility. The AMOR targets considered here are 'analytical targets' consisting of rotating diffuse disks and rotating diffuse spheres illuminated by a CO2 laser. It is hoped that the analyses presented will clarify and clearly illustrate the origins of these various signal probability density functions with the added benefit that the signal processing calculations are performed on data from a coherent laser radar system.
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