Matthew P. Dierking

Optical sparse aperture imaging

The resolution of a conventional diffraction-limited imaging system is proportional to its pupil diameter. A primary goal of sparse aperture imaging is to enhance resolution while minimizing the total light collection area; the latter being desirable, in part, because of the cost of large, monolithic apertures. Performance metrics are defined and used to evaluate several sparse aperture arrays constructed from multiple, identical, circular subapertures. Subaperture piston and/or tilt effects on image quality are also considered. We selected arrays with compact nonredundant autocorrelations first described by Golay. We vary both the number of subapertures and their relative spacings to arrive at an optimized array. We report the results of an experiment in which we synthesized an image from multiple subaperture pupil fields by masking a large lens with a Golay array. For this experiment we imaged a slant edge feature of an ISO12233 resolution target in order to measure the modulation transfer function. We note the contrast reduction inherent in images formed through sparse aperture arrays and demonstrate the use of a Wiener-Helstrom filter to restore contrast in our experimental images. Finally, we describe a method to synthesize images from multiple subaperture focal plane intensity images using a phase retrieval algorithm to obtain estimates of subaperture pupil fields. Experimental results from synthesizing an image of a point object from multiple subaperture images are presented, and weaknesses of the phase retrieval method for this application are discussed.

Holographic aperture ladar

Holographic aperture ladar is a variant of synthetic aperture ladar that seeks to increase cross-range scene resolution by synthesizing a large effective aperture through the motion of a smaller receiver and through the subsequent proper phasing and correlation of the detected signals in postprocessing. Unlike in conventional synthetic aperture ladar, however, holographic aperture ladar makes use of a two-dimensional translating sensor array, not simply a translating point detector. Also unlike in conventional synthetic aperture ladar, holographic aperture images will be formed in the two orthogonal cross-range dimensions parallel and perpendicular to the sensor platforms direction of motion. The central focus is on the development of the stripmap and spotlight holographic aperture transformations. These transformations will allow sequentially collected pupil plane field segments to be coherently stitched together in order to synthesize complex pupil plane fields with larger spatial extent. The challenge in this process is in accounting for the practical fact that both the receiver aperture and the transmitter will be in motion in real-world airborne applications. However, we demonstrate that, owing to the synchronous motion of the transmitter and receiver, resolution enhancements of more than two (stripmap case) or three (spotlight case) times the ratio of the synthetic aperture to the real receiver aperture diameter can be realized. We also demonstrate that in practical applications the holographic aperture ladar image formation process is relatively insensitive to scene depth if a good estimate of nominal scene range is available.

Periodic, pseudonoise waveforms for multifunction coherent ladar

We report the use of periodic, pseudonoise waveforms in a multifunction coherent ladar system. We exploit the Doppler sensitivity of these waveforms, as well as agile processing, to enable diverse ladar functions, including high range resolution imaging, macro-Doppler imaging, synthetic aperture ladar, and range-resolved micro-Doppler imaging. We present analytic expressions and simulations demonstrating the utility of pseudonoise waveforms for each of the ladar modes. We also discuss a laboratory pseudonoise ladar system that was developed to demonstrate range compression and range-resolved micro-Doppler imaging, as well as the phase recovery common to each of the coherent modes.

Improving mid-frequency contrast in sparse aperture optical imaging systems based upon the Golay-9 array

Sparse aperture imaging systems are capable of producing high resolution images while maintaining an overall light collection area that is small compared to a fully filled aperture yielding the same resolution. This is advantageous for applications where size, volume, weight and/or cost are important considerations. However, conventional sparse aperture systems pay the penalty of reduced contrast at midband spatial frequencies. This paper will focus on increasing the midband contrast of sparse aperture imaging systems based on the Golay-9 array. This is one of a family of two-dimensional arrays we have previously examined due to their compact, non-redundant autocorrelations. The modulation transfer function, or normalized autocorrelation, provides a quantitative measure of both the resolution and contrast of an optical imaging system and, along with an average relative midband contrast metric, will be used to compare perturbations to the standard Golay-9 array. Numerical calculations have been performed to investigate the behavior of a Golay-9 array into which autocorrelation redundancy has been introduced and our results have been experimentally verified. In particular we have demonstrated that by proper choice of sub-aperture diameters the average relative midband contrast can be improved by over 55%.

Experimental demonstration of a stripmap holographic aperture ladar system

By synthesizing large effective apertures through the translation of a smaller imaging sensor and the subsequent proper phasing and correlation of detected signals in postprocessing, holographic aperture ladar (HAL) systems seek to increase the resolution of remotely imaged targets. The stripmap HAL process was demonstrated in the laboratory, for the first time to our knowledge. Our results show that the stripmap HAL transformation can precisely account for off-axis transmitter induced phase migrations. This in turn allows multiple pupil plane field segments, sequentially collected across a synthetic aperture, to be coherently mosaiced together. As a direct consequence, we have been able to confirm the capability of the HAL method to potentially provide substantial increases in longitudinal cross-range resolution. The measurement and sampling of complex pupil plane field segments, as well as target related issues arising from short laboratory ranges, have also been addressed.

Solid-block stationary Fourier-transform spectrometer

A solid-block stationary Fourier-transform spectrometer (SBSFTS) is described that is applicable to a wide range of portable, moderate-resolution instrumentation needs that include the detection of temporally variant signatures. The SBSFTS is a low-cost, extremely rugged stationary Fourier-transform spectrometer based on the combination of three standard prism types. The SBSFTS uses a source-doubling, square-and-triangle common-path topology that is mechanically rugged, simple to align, and virtually immune to alignment perturbation. Its alignment stability makes it suitable for use in a variety of hostile operating environments. When coupled to a fiber-optic input, the spectrometer can be constructed in an extremely compact form. Experimental results have demonstrated the design and the performance of the spectrometer.

Demonstrated resolution enhancement capability of a stripmap holographic aperture ladar system

Holographic aperture ladar (HAL) is a variant of synthetic aperture ladar (SAL). The two processes are related in that they both seek to increase cross-range (i.e., the direction of the receiver translation) image resolution through the synthesis of a large effective aperture. This is in turn achieved via the translation of a receiver aperture and the subsequent coherent phasing and correlation of multiple received signals. However, while SAL imaging incorporates a translating point detector, HAL takes advantage of a two-dimensional translating sensor array. For the research presented in this article, a side-looking stripmap HAL geometry was used to sequentially image a set of Ronchi ruling targets. Prior to this, theoretical calculations were performed to determine the baseline, single subaperture resolution of our experimental, laboratory-based system. Theoretical calculations were also performed to determine the ideal modulation transfer function (MTF) and expected cross-range HAL image sharpening ratio corresponding to the geometry of our apparatus. To verify our expectations, we first sequentially captured an oversampled collection of pupil plane field segments for each Ronchi ruling. A HAL processing algorithm incorporating a high-precision speckle field registration process was then employed to phase-correct and reposition the field segments. Relative interframe piston phase errors were also removed prior to final synthetic image formation. By then taking the Fourier transform of the synthetic image intensity and examining the fundamental spatial frequency content, we were able to produce experimental modulation transfer function curves, which we then compared with our theoretical expectations. Our results show that we are able to achieve nearly diffraction-limited results for image sharpening ratios as high as 6.43.

Effects of Spatial Modes on Ladar Vibration Signature Estimation

Ladar-based vibrometry has been shown to be a powerful technique in enabling the plant identification of machines. Rather than sensing the geometric shape of a target laser vibrometers sense motions of the target induced by moving parts within the system. Since the target need not be spatially resolved, vibration can be sensed reliably and provide positive identification at ranges beyond the imaging limits of the aperture. However, as the range of observation increases, the diffraction-limited beam size on the target increases as well, and may encompass multiple vibrational modes on the targets surface. As a result, vibration estimates formed from large laser footprints illuminating multiple modes on a vibrating target will experience a degradation. This degradation is manifest as a spatial low-pass filtering effect: high-order mode shapes, associated with high-frequency vibrations, will be averaged out while low-frequency vibrations will be affected less. A model to predict this phenomenology is proposed for both pulse-pair and cw vibrometry systems. The cw model is compared to results obtained using an off-the-shelf laser vibrometry system.

An end-to-end vechicle classification pipeline using vibrometry data

This paper evaluates and expands upon the existing end-to-end process used for vibrometry target classification and identification. A fundamental challenge in vehicle classification using vibrometry signature data is the determination of robust signal features. The methodology used in this paper involves comparing the performance of features taken from automatic speech recognition, seismology, and structural analysis work. These features provide a means to reduce the dimensionality of the data for the possibility of improved separability. The performances of different groups of features are compared to determine the best feature set for vehicle classification. Standard performance metrics are implemented to provide a method of evaluation. The contribution of this paper is to (1) thoroughly explain the time domain and frequency domain features that have been recently applied to the vehicle classification using laser-vibrometry data domain, (2) build an end-to-end classification pipeline for Aided Target Recognition (ATR) with common and easily accessible tools, and (3) apply feature selection methods to the end-to-end pipeline. The end-to-end process used here provides a structured path for accomplishing vibrometry-based target identification. This paper will compare with two studies in the public domain. The techniques utilized in this paper were utilized to analyze a small in-house database of several different vehicles.

Sparse frequency LFM ladar signals

Through modeling we explored the possibility of utilizing a sparse frequency linear frequency modulation (LFM) signal for laser radar (ladar) applications. We propose a potential transmit and receive experiment utilizing the superposition of two LFM laser sources with a known difference frequency to provide the necessary segmented bandwidth. Finally we analyzed the signal performance of the proposed system showing that the range resolution of the signal can be improved by two to three times while utilizing the same modulator bandwidth as that of a continuous LFM signal.