Peter N. Crabtree

Polarimetric wavelet phenomenology of space materials

This paper describes new polarimetric wavelet detection principles applied to the backscattering characteristics of space materials in the near infrared. Efficient polarimetric detection techniques are combined with cross-correlation and wavelet analysis for enhanced characterization of space materials. The outcome of this study will support remote characterization of space materials and structures with enhanced discrimination, localization, and high-dynamic range while maintaining uncompromised sensitivity.

Cramer–Rao bounds for intensity interferometry measurements

The question of signal-to-noise ratio (SNR) in intensity interferometry has been revisited in recent years, as researchers have realized that various innovations can offer significant improvements in SNR. These innovations include improved signal processing. Two such innovations, the use of positivity and the use of knowledge of the general shape of the object, have been proposed. This paper investigates the potential gains offered by these two approaches using Cramer-Rao lower bounds (CRLBs). The CRLB on the variance of the positivity-constrained maximum likelihood (ML) estimate is at best 1/4 of the variance of the unconstrained estimator. This is compared to the positivity-constrained ML estimator, which delivers a best-case variance reduction of only (1-1/π)/2=34.1%. The gains offered by prior knowledge depend on the quality of such information, as might be expected from optimal weighting of such data with the measured data. Furthermore, biases are induced by the application of constraints, and these biases can eliminate some or all of the advantage of lower variances, as found when considering the total root-mean-square error. A form of CRLB for variance is presented that properly incorporates prior information.

Infrared photon discrimination of lung cancer cells

The objective of this study is to explore the polarimetric phenomenology of near infrared light interaction with healthy and lung cancer monolayer cells by using efficient polarimetric transmission detection techniques. Preliminary results indicate that enhanced discrimination between normal and different types of lung cancer cell stages can be achieved based on their transmitted intensities and depolarization properties of the cells. Specifically, the sizes of the nuclei of the cancer cells and the nucleus-to-cytoplasmic ratios appear to have potential impact on the detected polarimetric signatures leading to enhanced discrimination of lung cancer cells.

Object detection and characterization by monostatic ladar Bidirectional Reflectance Distribution Function (BRDF) using polarimetric discriminants

The purpose of this study is to explore novel monostatic ladar detection principles utilizing polarimetric Bidirectional Reflectance Distribution Function (BRDF) and single-pixel detection parameters. The depolarization of backscattered elliptical polarized light beams, from extended area space materials, was studied at different sample orientations. Specifically, the depolarization ratio for both linearly and circularly polarized light waves was estimated under quasimonostatic transceiver geometry. The experimental results indicate that space object materials exhibit distinct depolarization signatures, which provide enhanced discrimination capabilities. The outcome of this study would enhance the monostatic-ladar detection and discrimination capabilities.

Polarimetric wavelet fractal remote sensing principles for space materials

A new remote sensing approach based on polarimetric wavelet fractal detection principles is introduced and the Mueller matrix formalism is defined, aimed at enhancing the detection, identification, characterization, and discrimination of unresolved space objects at different aspect angles. The design principles of a multifunctional liquid crystal monostatic polarimetric ladar are introduced and related to operating conditions and system performance metrics. Backscattered polarimetric signal contributions from different space materials were detected using a laboratory ladar testbed, and then analyzed using techniques based on wavelets and fractals. The depolarization, diattenuation, and retardance of the materials were estimated using Mueller matrix decomposition for different aspect angles. The outcome of this study indicates that polarimetric fractal wavelet principles may enhance the capabilities of the ladar to provide characterization and discrimination of unresolved space objects.

Binary phase-only filtering for turbulence compensation in fiber-coupled free-space laser communication systems

Binary wavefront control in the focal plane (i.e., binary phase-only filtering) for partial compensation of atmospheric turbulence in fiber-coupled free-space laser communication systems is investigated. Numerical results from wave-optics simulations show that in an air-to-air scenario, the combination of binary phase-only filtering and centroid tracking provides mean fiber coupling efficiency close to that resulting from ideal least-squares adaptive optics, but without the requirement for direct wavefront sensing. This result suggests a simpler and less computationally demanding turbulence mitigation system that is more readily applied to tactical applications.

Cramer-Rao lower bound and object reconstruction performance evaluation for intensity interferometry

This paper addresses the fundamental performance limits of object reconstruction methods using intensity interferometry measurements. It shows examples of reconstructed objects obtained with the FIIRE (Forward-model Interferometry Image Reconstruction Estimator) code developed by Boeing for AFRL. It considers various issues when calculating the multidimensional Cramér-Rao lower bound (CRLB) when the Fisher information matrix (FIM) is singular. In particular, when comparing FIIRE performance, characterized as the root mean square difference between the estimated and pristine objects with the CRLB, we found that FIIRE performance improved as the singularity became worse, a result not expected. We found that for invertible FIM, FIIRE yielded lower root mean squared error than the square root of the CRLB (by a factor as large as 100). This may be due to various regularization constraints (positivity, support, sharpness, and smoothness) included in FIIRE, rendering it a biased estimator, as opposed to the unbiased CRLB framework used. Using the sieve technique to mitigate false high frequency content inherent in point-by-point object reconstruction methods, we also show further improved FIIRE performance on some generic objects. It is worth noting that since FIIRE is an iterative algorithm searching to arrive at an object estimate consistent with the collected data and various constraints, an initial object estimate is required. In our case, we used a completely random initial object guess consisting of a 2-D array of uniformly distributed random numbers, sometimes multiplied with a 2-D Gaussian function.

Comparison of forward models and phase retrieval for image formation from intensity interferometer data

Many imaging techniques provide measurements proportional to Fourier magnitudes of an object, from which one attempts to form an image. One such technique is intensity interferometry which measures the squared Fourier modulus. Intensity interferometry is a synthetic aperture approach known to obtain high spatial resolution information, and is effectively insensitive to degradations from atmospheric turbulence. These benefits are offset by an intrinsically low signal-to-noise (SNR) ratio. Forward models have been theoretically shown to have best performance for many imaging approaches. On the other hand, phase retrieval is designed to reconstruct an image from Fourier-plane magnitudes and object-plane constraints. So it’s natural to ask, “How well does phase retrieval perform compared to forward models in cases of interest?” Image reconstructions are presented for both techniques in the presence of significant noise. Preliminary conclusions are presented for attainable resolution vs. DC SNR.

An automated ladar polarimetric system for remote characterization of space materials

The calibration, testing, and operational principles of an efficient multifunctional monostatic polarimetric ladar are introduced and related to the system performance metrics. The depolarization, diattenuation, and retardance of the materials were estimated using Mueller matrix (MM) decomposition for different aspect angles. The outcome of this study indicates that polarimetric principles may enhance the capabilities of the ladar to provide adequate characterization and discrimination of unresolved space objects.

Geometric super-resolution via log-polar FFT image registration and variable pixel linear reconstruction

Various image de-aliasing techniques and algorithms have been developed to improve the resolution of pixel-limited imagery acquired by an optical system having an undersampled point spread function. These techniques are sometimes referred to as multi-frame or geometric super-resolution, and are valuable tools because they maximize the imaging utility of current and legacy focal plane array (FPA) technology. This is especially true for infrared FPAs which tend to have larger pixels as compared to visible sensors. Geometric super-resolution relies on knowledge of subpixel frame-toframe motion, which is used to assemble a set of low-resolution frames into one or more high-resolution (HR) frames. Log-polar FFT image registration provides a straightforward and relatively fast approach to estimate global affine motion, including translation, rotation, and uniform scale changes. This technique is also readily extended to provide subpixel translation estimates, and is explored for its potential combination with variable pixel linear reconstruction (VPLR) to apportion a sequence of LR frames onto a HR grid. The VPLR algorithm created for this work is described, and HR image reconstruction is demonstrated using calibrated 1/4 pixel microscan data. The HR image resulting from VPLR is also enhanced using Lucy-Richardson deconvolution to mitigate blurring effects due to the pixel spread function. To address non-stationary scenes, image warping, and variable lighting conditions, optical flow is also investigated for its potential to provide subpixel motion information. Initial results demonstrate that the particular optical flow technique studied is able to estimate shifts down to nearly 1/10th of a pixel, and possibly smaller. Algorithm performance is demonstrated and explored using laboratory data from visible cameras.