Transport model for the propagation of partially coherent, partially polarized, polarization-gradient vector beams.

Recently we predicted and experimentally validated a new physical mechanism for altering the propagation path of a monochromatic beam [Opt. Express30, 38907 (2022)OPEXFF1094-408710.1364/OE.467678]. Specifically, we showed that by properly tailoring the spatial distribution of the linear state of polarization transverse to the direction of propagation, the beam followed a curved trajectory in free space. Here we extend the model to the partially coherent and partially polarized polychromatic case by redefining the beam amplitude, phase, and polarization angle as appropriate statistical quantities. In particular, the definition of polarization angle represents a fundamentally new quantity in modeling beam propagation and is shown to be consistent with recent works on energy and momentum flow. In the new model, the beam curvature matches that of our previous work in the fully coherent case but is predicted to vanish for an unpolarized, spatially incoherent beam. Simulated beam trajectories are shown for varying levels of initial partial coherence and for different polarization profiles. A new class of non-diffracting beams is also suggested by way of example.

Vector beam bending via a polarization gradient.

We propose, analyze and demonstrate experimentally an entirely new optical effect in which the centroid of a coherent optical beam can be designed to propagate along a curved trajectory in free space by tailoring the spatial distribution of linear polarization across the transverse beam profile. Specifically, a non-zero spatial gradient of second order or higher in the linear state of polarization is shown to cause the beam centroid to "accelerate" in the direction transverse to the direction of propagation. The effect is confirmed experimentally using spatial light modulation to create the distribution in linear polarization and then measuring the transverse location of the beam profile at varying propagation distances. The observed displacement of the beam centroid is shown to closely match the theory out to 34m propagation distance.

Learned linear models for detecting watercraft in a maritime environment.

This work provides a new, to the best of our knowledge, approach to constructing linear models for object detection in a scene. Specifically, we use representative training data in order to estimate the parameters describing a generalized wavelet model for the express purpose of detecting the presence of maritime targets in a scene. The parameter estimates are taken as those that maximize the probability of detecting the targets for a fixed probability of false alarm. The approach is then demonstrated on a database of short-wave infrared imagery containing various watercraft. Results are then compared to some of the more standard wavelet bases used in detection applications.

Transport-based model for turbulence-corrupted imagery.

A new model for turbulence-corrupted imagery is proposed based on the theory of optimal mass transport. By describing the relationship between photon density and the phase of the traveling wave, and combining it with a least action principle, the model suggests a new class of methods for approximately recovering the solution of the photon density flow created by a turbulent atmosphere. Both coherent and incoherent imagery are used to validate and compare the model to other methods typically used to describe this type of data. Given its superior performance in describing experimental data, the new model suggests new algorithms for a variety of atmospheric imaging and wave propagation applications.

Distribution of splice loss in single mode optical fiber.

This work investigates a probabilistic model for splice loss in single mode optical fibers. We derive the probability density function for loss values as a function of lateral and angular misalignment. We then use observed data to estimate these model parameters; both Bayesian and maximum likelihood estimation procedures are described. These estimates can then be used to provide an indication of the relative importance of various loss mechanisms. Alternatively, if one is given values for maximum lateral and angular misalignment, our results allow for predictions of expected distribution of loss values. An overall goal of this paper is to demonstrate that, beyond the mean and variance of splice loss, there is significant information in the shape of the distribution of values. A second goal is to understand the trade-off between the number of splice loss measurements and the confidence in estimates of parameters in the splice loss model.

Experimental infrared point-source detection using an iterative generalized likelihood ratio test algorithm.

This work documents the performance of a recently proposed generalized likelihood ratio test (GLRT) algorithm in detecting thermal point-source targets against a sky background. A calibrated source is placed above the horizon at various ranges and then imaged using a mid-wave infrared camera. The proposed algorithm combines a so-called "shrinkage" estimator of the background covariance matrix and an iterative maximum likelihood estimator of the point-source parameters to produce the GLRT statistic. It is clearly shown that the proposed approach results in better detection performance than either standard energy detection or previous implementations of the GLRT detector.

Bayesian approach to decompression sickness model parameter estimation.

We examine both maximum likelihood and Bayesian approaches for estimating probabilistic decompression sickness model parameters. Maximum likelihood estimation treats parameters as fixed values and determines the best estimate through repeated trials, whereas the Bayesian approach treats parameters as random variables and determines the parameter probability distributions. We would ultimately like to know the probability that a parameter lies in a certain range rather than simply make statements about the repeatability of our estimator. Although both represent powerful methods of inference, for models with complex or multi-peaked likelihoods, maximum likelihood parameter estimates can prove more difficult to interpret than the estimates of the parameter distributions provided by the Bayesian approach. For models of decompression sickness, we show that while these two estimation methods are complementary, the credible intervals generated by the Bayesian approach are more naturally suited to quantifying uncertainty in the model parameters.

Analytical expression for pixel-averaged point sources as observed by a focal plane array.

A closed-form expression is derived for pixel-averaged point source signals as observed by an imaging array. Obtaining this solution requires the probability distribution of squared Euclidean distances in two dimensions when the end points are confined to a uniformly spaced square domain. The derivation and associated expression are provided.

Range performance of the DARPA AWARE wide field-of-view visible imager.

In a prior paper, we described a new imaging architecture that addresses the need for wide field-of-view imaging combined with the resolution required to identify targets at long range. Over the last two years substantive improvements have been made to the system, both in terms of the size, weight, and power of the camera as well as to the optics and data management software. The result is an overall improvement in system performance, which we demonstrate via a maritime target identification experiment.

A study of molecular adsorption of a cationic surfactant on complex surfaces with atomic force microscopy.

The study of molecular adsorption on solid surfaces is of broad interest. However, so far the study has been restricted to idealized flat smooth rigid surfaces which are rarely the case in real world applications. Here we describe a study of molecular adsorption on a complex surface of the submicron fibers of a fibrous membrane of regenerated cellulose in aqueous media. We use a cationic surfactant, cetyltrimethylammonium chloride (CTAC), as the adsorbing molecule. We study the equilibrium adsorption of CTAC molecules on the same area of the fibers by sequentially immersing the membrane in pure water, 1 mM and then a 20 mM solution of CTAC. Atomic force microscopy (AFM) is applied to study the adsorption. The force-volume mode is used to record the force-deformation curves of the adsorbed molecules on the fiber surface. We suggest a model to separate the forces due to the adsorbed molecules from the elastic deformation of the fiber. Interestingly, knowledge of the surface geometry is not required in this model provided the surface is made of elastically homogeneous material. Different models are investigated to estimate the amount of the adsorbed molecules based on the obtained force curves. The exponential steric repulsion model fits the force data the best. The amount of the adsorbed surfactant molecules and its dependence on the concentration are found to be reasonable compared to the data previously measured by means of Raman scattering done on a flat surface of silica.

Analytical expression for the average ensquared energy.

We derive an expression for the average area of intersection between a blur spot of radius R and a square pixel, where the center of the blur is uniformly chosen from the pixel interior. Implications of the result are then discussed in the context of a point source detection problem.

Moving off the grid in an experimental, compressively sampled photonic link.

Perhaps the largest obstacle to practical compressive sampling is an inability to accurately, and sparsely describe the data one seeks to recover due to poor choice of signal model parameters. In such cases the recovery process will yield artifacts, or in many cases, fail completely. This work represents the first demonstration of a solution to this so-called "off-grid" problem in an experimental, compressively sampled system. Specifically, we show that an Alternating Convex Search algorithm is able to significantly reduce these data model errors in harmonic signal recovery.

Characterization of the AWARE 10 two-gigapixel wide-field-of-view visible imager.

System requirements for many military electro-optic and IR camera systems reflect the need for both wide-field-of-view situational awareness as well as high-resolution imaging for target identification. In this work we present a new imaging system architecture designed to perform both functions simultaneously and the AWARE 10 camera as an example at visible wavelengths. We first describe the basic system architecture and user interface followed by a laboratory characterization of the system optical performance. We then describe a field experiment in which the camera was used to identify several maritime targets at varying range. The experimental results indicate that users of the system are able to correctly identify ~10 m targets at between 4 and 6 km with 70% accuracy.

Characterization of a compressively sampled photonic link.

The emerging field of compressive sampling has potentially powerful implications for the design of analog-to-digital sampling systems. In particular, the mathematics of compressive sampling suggests that one can recover a signal at a smaller sampling interval than is dictated by the rate at which the samples are digitized. In a recent work the authors presented an all-photonic implementation of such a system and experimentally demonstrated the basic operating principles. This paper offers a more in-depth study of the system, including a more detailed description of the hardware, issues involved in real-time implementation, and how choice of signal model and model fidelity can influence the reconstruction.

Denoising infrared maritime imagery using tailored dictionaries via modified K-SVD algorithm.

Recent work has shown that tailored overcomplete dictionaries can provide a better image model than standard basis functions for a variety of image processing tasks. Here we propose a modified K-SVD dictionary learning algorithm designed to maintain the advantages of the original approach but with a focus on improved convergence. We then use the learned model to denoise infrared maritime imagery and compare the performance to the original K-SVD algorithm, several overcomplete "fixed" dictionaries, and a standard wavelet denoising algorithm. Results indicate the superiority of overcomplete representations and show that our tailored approach provides similar peak signal-to-noise ratios as the traditional K-SVD at roughly half the computational cost.

Signal design using nonlinear oscillators and evolutionary algorithms: application to phase-locked loop disruption.

This work describes an approach for efficiently shaping the response characteristics of a fixed dynamical system by forcing with a designed input. We obtain improved inputs by using an evolutionary algorithm to search a space of possible waveforms generated by a set of nonlinear, ordinary differential equations (ODEs). Good solutions are those that result in a desired system response subject to some input efficiency constraint, such as signal power. In particular, we seek to find inputs that best disrupt a phase-locked loop (PLL). Three sets of nonlinear ODEs are investigated and found to have different disruption capabilities against a model PLL. These differences are explored and implications for their use as input signal models are discussed. The PLL was chosen here as an archetypal example but the approach has broad applicability to any input∕output system for which a desired input cannot be obtained analytically.

Beating Nyquist with light: a compressively sampled photonic link.

We report the successful demonstration of a compressively sampled photonic link. The system takes advantage of recent theoretical developments in compressive sampling to enable signal recovery beyond the Nyquist limit of the digitizer. This rather remarkable result requires that (1) the signal being recovered has a sparse (low-dimensional) representation and (2) the digitized samples be incoherent with this representation. We describe an all-photonic system architecture that meets these requirements and then show that 1 GHz harmonic signals can be faithfully reconstructed even when digitizing at 500 MS/s, well below the Nyquist rate.

Modeling and detecting localized nonlinearity in continuum systems with a multistage transform.

A general method is presented for modeling spatially extended systems that may contain a localized source of nonlinearity. It has direct applications to structural health monitoring (SHM) where physical damage may cause such nonlinearity and also communications channels which may exhibit localized nonlinearity due to bad electrical contacts or component nonlinearity. The method uses a multistage nonlinear transform in order to model the system dynamics. We discuss the application to SHM and provide a preliminary test of the method with experimental data from a randomly shaken beam with loose bolts. We discuss the application to telecommunications, provide an experimental observation of symmetric nonlinearity in a "bad" electrical contact, and provide a preliminary test of using this method to remove nonlinear echo (and thereby improve data rate) on a telephone line used for data transmission.

Bayesian estimation of weak material dispersion: theory and experiment.

This work considers the estimation of dispersion in materials via an interferometric technique. At its core, the problem involves extracting the quadratic variation in phase over a range of wavelengths based on measured optical intensity. The estimation problem becomes extremely difficult for weakly dispersive materials where the quadratic nonlinearity is very small relative to the uncertainty inherent in experiment. This work provides a means of estimating dispersion in the face of such uncertainty. Specifically, we use a Markov Chain Monte Carlo implementation of Bayesian analysis to provide both the dispersion estimate and the associated confidence interval. The interplay between various system parameters and the size of the resulting confidence interval is discussed. The approach is then applied to several different experimental samples.

Chaotic signal detection and estimation based on attractor sets: applications to secure communications.

We consider the problem of detection and estimation of chaotic signals in the presence of white Gaussian noise. Traditionally this has been a difficult problem since generalized likelihood ratio tests are difficult to implement due to the chaotic nature of the signals of interest. Based on Poincare's recurrence theorem we derive an algorithm for approximating a chaotic time series with unknown initial conditions. The algorithm approximates signals using elements carefully chosen from a dictionary constructed based on the chaotic signal's attractor. We derive a detection approach based on the signal estimation algorithm and show, with simulated data, that the new approach can outperform other methods for chaotic signal detection. Finally, we describe how the attractor based detection scheme can be used in a secure binary digital communications protocol.