Matrices provide a practical and elegant tool for describing the transformation properties of beam splitters and waveguide couplers acting on single-mode optical fields. Using a systematic approach, we show how the application of various physical constraints determines the form of the matrix for both classical fields and quantum number states. The goal is to provide a clear explanation of the conditions under which various matrix forms are appropriate to represent four-port couplers and beam splitters. Examples of calculations using the matrices are provided.
The theory behind compressive sampling pre-supposes that a given sequence of observations may be exactly represented by a linear combination of a small number of vectors. In practice, however, even small deviations from an exact signal model can result in dramatic increases in estimation error; this is the so-called basis mismatch" problem. This work provides one possible solution to this problem in the form of an iterative, biconvex search algorithm. The approach uses standard ℓ1-minimization to find the signal model coefficients followed by a maximum likelihood estimate of the signal model. The process is repeated until a convergence criteria is met. The algorithm is illustrated on harmonic signals of varying sparsity and outperforms the current state-of-the-art.
KEYWORDS: Diffusion, Sensors, Image fusion, Data acquisition, Physics, Data fusion, Principal component analysis, Image registration, Signal processing, Analytical research
This work considers the problem of combining high dimensional data acquired from multiple sensors for the
purpose of detection and classification. The sampled data are viewed as a geometric object living in a highdimensional
space. Through an appropriate, distance preserving projection, those data are reduced to a lowdimensional
space. In this reduced space it is shown that different physics of the sampled phenomena reside on
different portions of the resulting "manifold" allowing for classification. Moreover, we show that data acquired
from multiple sources collected from the same underlying physical phenomenon can be readily combined in the
low-dimensional space i.e. fused. The process is demonstrated on maritime imagery collected from a visible-band
camera.
We use a nonlinear dimensionality reduction technique to improve anomaly detection in a hyperspectral imaging
application. A nonlinear transformation, diffusion map, is used to map pixels from the high-dimensional spectral
space to a (possibly) lower-dimensional manifold. The transformation is designed to retain a measure of distance
between the selected pixels. This lower-dimensional manifold represents the background of the scene with high
probability and selecting a subset of points reduces the computational overhead associated with diffusion map.
The remaining pixels are mapped to the manifold by means of a Nystr¨om extension. A distance measure is
computed for each new pixel and those that do not reside near the background manifold, as determined by
a threshold, are identified as anomalous. We compare our results with the RX and subspace RX methods of
anomaly detection.
KEYWORDS: Nonlinear filtering, Signal detection, Signal processing, Receivers, Statistical analysis, Electronic filtering, Linear filtering, Sensors, Complex systems, Analytical research
Higher-order spectral analysis is one approach to detecting deviations from normality in a received signal. In
particular the auto-bispectral density function or "bispectrum" has been used in a number of detection applications.
Both Type-I and Type-II errors associated with bispectral detection schemes are well understood if the
processing is performed on the received signal directly or if the signal is pre-processed by a linear, time invariant
filter. However, there does not currently exist an analytical expression for the bispectrum of a non-Gaussian
signal pre-processed by a nonlinear filter. In this work we derive such an expression and compare the performance
of bispectral-based detection schemes using both linear and nonlinear receivers. Comparisons are presented in
terms of both Type-I and Type-II detection errors using Receiver Operating Characteristic curves. It is shown
that using a nonlinear receiver can offer some advantages over a linear receiver. Additionally, the nonlinear
receiver is optimized using genetic programming (differential evolution) to choose the filter coefficients.
KEYWORDS: Free space optics, Analog electronics, Transmitters, Modulators, Receivers, Photodetectors, Signal to noise ratio, Atmospheric optics, Radio optics, Modulation
Free-space optical (FSO) links typically carry digital data over short to moderate distances (100m - 50 km). From a
military perspective, FSO links have the advantages of low probability of interception, inherent anti-jam capability and a
reasonable degree of covertness. In certain applications it is desirable to minimize size, weight and power of the
transmitter and this pushes the designer to eliminate power-hungry digitizers and to transmit raw analog, instead of
digital, information. However, the transmission of analog signals presents significant technical challenges due to strong
fluctuations in received optical power resulting from atmospheric turbulence. In this case the standard RF link properties
of gain, noise factor, and linearity must be described entirely in statistical terms. In this paper we present preliminary
experimental results from a short (500m), single-tone, 5 MHz analog FSO link and compare the data to theoretical
predictions. Theory suggests, and our preliminary experimental results confirm, that the statistical properties of all the
RF performance metrics of a FSO analog link are determined entirely by the statistical properties of the received optical
power. We show that the distribution of values of RF link parameters can be obtained directly from the distribution of
received optical power, without the need for modeling the received power with a continuous function.
KEYWORDS: Frequency modulation, Fermium, Video, Modulation, Free space optics, Signal to noise ratio, Receivers, Analog electronics, Sensors, Modulators
The Naval Research Laboratory (NRL) in collaboration with the Defence Science and Technology Organisation (DSTO)
of Australia has performed long distance experiments with analog modulated free space optical communication links
across the Chesapeake Bay. Results will be presented on estimating the probability density functions of the RF
parameters of gain, noise factor, and linearity after propagating an RF modulated, 1550nm laser beam over a 32km
distance (folded round-trip across Chesapeake Bay). In addition, results from the transmission of video using analog FM
modulation of a 1550nm laser beam over the link will be presented.
Numerical simulations are used to improve in-band disruption of a phase-locked loop (PLL). Disruptive inputs
are generated by integrating a system of nonlinear ordinary differential equations (ODEs) for a given set of
parameters. Each integration yields a set of time series, of which one is used to modulate a carrier input to the
PLL. The modulation is disruptive if the PLL is unable to accurately reproduce the modulation waveform. We
view the problem as one of optimization and employ an evolutionary algorithm to search the parameter space of
the excitation ODE for those inputs that increase the phase error of the PLL subject to restrictions on excitation
amplitude or power. Restricting amplitude (frequency deviation) yields a modulation that approximates a
square wave. Constraining modulation power leads to a chaotic excitation that requires less power to disrupt
loop operation than either the sinusoid or square wave modulations.
A system for interrogating fiber optic Bragg grating arrays at kiloHertz sampling rates with sub-microstrain resolution was presented recently. The system makes use of a tunable fiber Fabry-Perot filter for demultiplexing and a path-imbalanced Mach-Zehnder interferometer for wavelength conversion. The operationally-passive demodulation technique for the interferometer makes use of probing the 3x3 coupler at the interferometer output for its coupling parameters to execute the technique. In this work, we discuss the effects of how errors in determining these parameters translate into
measurement error and harmonic distortion. We compare measured effects in the laboratory with predictive models to give error
sensitivity metrics. We also consider two modes of sampling errors for such frequency-modulated systems and propose a generalized sampling criterion for minimizing harmonic distortion and measurement error.
Previous studies introduced, examined, and tested a variety of registration-free transforms, specifically the diagonal, whitening/dewhitening, and target CV (Covariance) transforms. These transforms temporally evolve spectral object signatures under varying conditions using imagery of regions of similar objects and content distribution from data sets collected at two different times. The transformed object signature is then inserted into the matched filter to search for targets. Spatial registration of two areas and/or finding two suitable candidate regions for the transforms is often problematic. This study examines and finds that the average correlation coefficient between the corrected histograms of the multi-spectral image cube collected at two times can assess the similarity of the areas and predict object detection performance. This metric is applied in four distinctive situations and tested on three independently collected data sets. In one data set, the correlation between histograms was taken from an airborne long wave infrared sensor that imaged objects in Florida and tested on registered images modified by systematically eliminating opposed ends of the image set. The other data set examined images of objects in Yellowstone National Park from a visible/near IR multi-spectral sensor. This comparison was also applied to images collected using oblique angles (depression angle of 10°) of objects placed at Webster Field in Maryland. Candidate heterogeneous image areas were compared to each other using the average correlation coefficient and inserted into statistical transforms. In addition the correlations were computed between corrected histograms based on the normalized difference vegetation index (NDVI). Similarly, the analysis is applied to data collected at oblique angles (10° depression angle). The net signal to clutter ratio depends on the average correlation coefficient and has low p-values (p<0.05). All statistical transforms (diagonal, whitening/dewhitening, target CV) performed comparably using the various backgrounds and scenarios. Objects that are spectrally distinct from the backgrounds followed the average correlation coefficient more closely than objects whose spectral signatures contained background components. This study is the first to examine the similarity of the corrected histograms and does not exclude other approaches for comparing areas.
This report examines a series of multispectral or hyperspectral image data cubes collected of a given scene at different times. The diagonal, whitening/dewhitening, and target CV (Covariance) transformations use collected image data of spatially overlapping regions from data sets collected at different times to evolve target spectral signatures. The previously studied registration-free transformations are described using a single general equation and form a subset of a larger family of accurate transforms. The diagonal, whitening/dewhitening, and target CV transformations are characterized by a parameter n having n=0,1, 2 respectively. The transformed target signatures, used in matched filter searches, are tested on images taken from two data collects that use different sensors, targets, and backgrounds. Transforms with n between 0 and 2 yield the largest Target to Clutter Ratio (TCR) and remain relatively constant for 0
A fiber optic infrared (IR) spectroscopic system to be used with the cone penetrometer has been developed. This system can be used to perform real time, in-situ site characterization and analysis by identifying and quantifying organic contaminants in soil.
A compact, ruggedized fiber optic IR reflectance probe for remote, in-situ screening of underground waste sites has been developed. Using cabled chalcogenide optical fibers and a FTIR system, remote spectroscopy has been performed over distances of 20 meters. This paper discusses the design and performance of this system.
Infrared fiber optic reflectance spectroscopy is a powerful tool for identifying various organic compounds in soils. Using this technique a mixture of benzene and TCE on sand was measured; peaks due to both compounds are readily evident and correspond to the peaks in the pure liquid. At low concentrations of diesel fuel marine (DFM) on sand the band depths scale linearly with respect to DFM concentration. As the DFM concentration increases, the plot of DFM band depth versus concentration becomes nonlinear.
A novel fiber optic Raman probe for determination of organic vapors is described. The probe utilizes an absorbent resin, C-18, to concentrate the organic vapors in the optical path of the Raman probe. The probe exhibits a fully reversible response to organic vapors such as carbon tetrachloride or benzene.
An array of eight fiber optic vector magnetometers was designed and constructed for use in undersea applications such as harbors, ports, and waterways. We describe the design and performance characteristics of the array including the single-mode fiber optic system and magnetostrictive transducers. Data is presented from both laboratory measurements and from actual undersea operation.
Nonlinear transduction mechanism in electrostrictive and magnetostrictive materials is exploited to demonstrate multiplexed low frequency fiber optic electric and magnetic field sensors. The sensor utilizes a single interferometer and a single unmodulated laser while demonstrating extremely low cross-talk between the electric and magnetic channels. Low frequency electromagnetic signals from remotely located electric and magnetic dipoles are detected with the fiber optic sensor.
Frank Bucholtz, Carl Villarruel, Clay Kirkendall, Dominique Dagenais, J. McVicker, A. Davis, S. Patrick, Kee Koo, Anthony Dandridge, Gunnar Wang, Terje Lund, H. Valo
The 1/r3 dependence of the magnetic field with distance r makes the vector magnetometer an ideal sensor in undersea systems for the localization and tracking of vessels. Since the undersea system typically spans several hundred meters to several kilometers, use of fiber optics for both telemetry and sensing offers inherent advantages of low cable weight, immunity to electromagnetic interference on the signal transmission paths, and high channel capability.
We demonstrate a fiber optic interferometric dc and low frequency voltage sensor based on the electrostrictive effect in lead magnesium niobate (PMN) transducers. The sensor exhibits ultra-low drift and has a noise floor of 35 nV/?Hz at 10 mHz and 20 nV/?Hz at 1 Hz.
Laboratory and field tests have proven that magnetostrictive fiber-optic
interferometric sensors can detect small low-frequency disturbances of the earth magnetic
field [1]. With proper sensor design, the thermal noise limitation [2] does not rise above the
interferometer baseband noise of around 0.3 µrad?Hz.
Considerable progress has been made in the use of fiber optic magnetic sensors in actual field environments, especially for undersea applications. This paper reviews the results of three fiber magnetometer systems: 1) a heading sensor for undersea towed array applications; 2) a remote ac magnetometer designed for land use; and 3) a magnetometer array for undersea magnetic measurements. In each case, relevant design parameters, laboratory test results, and, where applicable, field test results are presented.
We review developments over the past five years in fiber optic magnetometry based on magnetostriction. Recent work has demonstrated
detection of magnetic fields from dc to over 1 MHz with resolution of 10 pT P1Hz at 1 .0 Hz and 0.07 pTpIHz at35 kHz
in laboratory devices. We present the basic device operating principles and discuss factors which limit the resolution of fiber
optic interferometric magnetic sensors. Results are presented for a number of configurations including a ruggedized, compact,
three-axis magnetometer for dc and low-frequency measurements, a single-axis gradiometer, a single-axis heterodyne configuration
for narrowband detection of fields in the frequency range 0.01 Hz to 1 MHz, and a magnetostrictive oscillator which exhibits
period doubling bifurcations and chaos.
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