Bradley D. Duncan

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.

Wide-Angle Achromatic Prism Beam Steering for Infrared Countermeasure Applications

The design and analysis of achromatic doublet prisms for use in laser beam steering is presented. The geometric relationships describ- ing the maximum steering angle are given, as are discussions of first- and second-order dispersion reduction. Infrared (IR) material alterna- tives and optimum IR material characteristics for wide-angle achromatic prism beam steering are also investigated. Sixteen materials in 120 dif- ferent combinations have been examined to date. For midwave IR appli- cations it is shown that the minimum dispersion currently achievable across the full 2 to 5 mm spectrum is 1.7816 mrad at an average maxi- mum steering angle of 45 deg. This is accomplished using LiF/ZnS dou- blet prisms. Several issues related to the azimuth and elevation angles into which light is steered as a function of prism rotation angles are also presented.

Aberration production using a high-resolution liquid-crystal spatial light modulator.

Phase-only liquid-crystal spatial light modulators provide a powerful means of wavefront control. With high resolution and diffractive (modulo 2pi) operation, they can accurately represent large-dynamic-range phase maps. As a result, they provide an excellent means of producing electrically controllable, dynamic, and repeatable aberrations. However, proper calibration is critical to achieving accurate phase maps. Several calibration methods from previous literature were considered. With simplicity and accuracy in mind, we selected one method for each type of necessary calibration. We augmented one of the selected methods with a new step that improves its accuracy. After calibrating our spatial light modulator with our preferred methods, we evaluated its ability to produce aberrations in the laboratory. We studied Zernike polynomial aberrations using interferometry and Fourier-transform-plane images, and atmospheric aberrations using a Shack-Hartmann wavefront sensor. These measurements show the closest agreement with theoretical expectations that we have seen to date.

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.

High-speed Shack-Hartmann wavefront sensor design with commercial off-the-shelf optics.

Several trade-offs relevant to the design of a two-dimensional high-speed Shack-Hartmann wavefront sensor are presented. Also outlined are some simple preliminary experiments that can be used to establish critical design specifications not already known. These specifications include angular uncertainty, maximum measurable wavefront tilt, and spatial resolution. A generic design procedure is then introduced to enable the adaptation of a limited selection of CCD cameras and lenslet arrays to the desired design specifications by use of commercial off-the-shelf optics. Although initially developed to aid in the design of high-speed (i.e., megahertz-frame-rate) Shack-Hartmann wavefront sensors, our method also works when used for slower CCD cameras. A design example of our procedure is provided.

Simultaneous MHz Rate Flow Visualization and Wavefront Sensing for Aero-Optics

Abstract : Newly developed optical diagnostic techniques are used to examine the temporal evolution of wavefront aberrations imposed upon an optical beam as it passes through a rectangular compressible turbulent jet. A recently developed MHz rate system based on a pulse burst laser and ultra highspeed CCD camera is used for flow visualization. A newly developed two-dimensional MHz rate Shack-Hartman wavefront sensor is used to measure the wavefront distortion. The wavefront sensor consists of a HeNe laser, a micro-lens array and an ultra high-speed camera. The MHz rate flow visualization and wavefront sensing are used simultaneously to investigate the aero-optic effects of an ideally expanded, high Reynolds number, Mach 1.3 rectangular jet. Preliminary results are presented that show the potential of the technique to acquire time-resolved two-dimensional wavefront data with detailed aero-optic effects. A number of improvements to the technique that will be used in future work are also discussed.

Visualization of surface acoustic waves by means of synchronous amplitude-modulated illumination

A simple technique for visualizing two-dimensional traveling surface acoustic wave (SAW) phenomena in real time was developed. The technique requires illumination of a SAW carrying substrate with a collimated, sinusoidally amplitude-modulated laser beam. Though at first the technique may appear to be stroboscopic in nature, it in fact has its foundations in spatiotemporal correlation theory. It is shown that if the modulation frequency of the illumination beam is equal to, or an integer fraction of, the SAW frequency (i.e., if they are temporally correlated) then, after simple spatial filtering, high-visibility stationary fringes can be produced. In fact, it is shown that a maximum fringe visibility of nearly 60% can be achieved. It is believed that this is the highest visibility yet reported for similar SAW visualization techniques.

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.

Wide-angle decentered lens beam steering for infrared countermeasures applications

A beam-steering system consisting of three cemented achro- matic doublets is presented. Intended for use in IR countermeasure ap- plications, our system is designed to operate over the 2- to 5-mm spec- trum with minimum angular dispersion. We show that dispersion can be minimized by using doublet lenses fashioned from AMTIR-1 and germa- nium. Our system is designed to be compact and lightweight, with no internal foci, while allowing steering to 622.5 deg. We also maintain a minimum 2-in. clear aperture for all steering angles, and a nominal di- vergence of 1 mrad. Plane wave and Gaussian beam analyses of our system are presented.

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%.