Object identification in deep space is a surveillance mission crucial to our national defense. Satellite health/status monitoring is another important space surveillance task with both military and civilian applications. Deep space satellites provide challenging targets for ground-based optical sensors due to the extreme range imposed by geo-stationary and geo-synchronous orbits. The Air Force Research Laboratory, in partnership with Trex Enterprises and our other contractor partners, will build a new ground-based sensor to address these deficiencies. The Geo Light Imaging National Testbed (GLINT) is based on an active imaging concept known as Fourier telescopy. In this technique, the target satellite is illuminated by two or more laser sources. The corresponding fields interfere at the satellite to form interference fringes. These fringes may be made to move across the target by the introduction of a frequency shift between the laser beams. The resulting time-varying laser backscatter contains information about a Fourier component of the target reflectivity and may be collected with a large solar heliostat array. This large unphased receiver provides sufficient signal-to-noise ratio for each Fourier component using relatively low power laser sources. A third laser source allows the application of phase closure in the image reconstruction software. Phase closure removes virtually all low frequency phase distortion and guarantees that the phases of all fringes are relatively fixed. Therefore, the Fourier phase associated with each component can be recovered accurately. This paper briefly reviews the history of Fourier telescopy, the proposed design of the GLINT system, and the future of this research area.

Fourier Telescopy is an imaging method that can form images of very dim objects with angular resolution of a few nanoradians, attained by means of a synthetic aperture that overcomes the effects of intervening aberrations using mathematical algorithms akin to that of long-baseline radio astronomy. The algorithm makes use of phase closure and advanced wavefront reconstruction techniques from adaptive optics and Knox-Thompson image reconstruction. The imaging technique is active and so can be used even with faint objects. The imaging technique is active and encodes the information in the temporal instead of spatial domain, allowing imaging of faint objects with extremely large, low- cost receivers. An implementation for deep space imaging is shown; it uses large-area solar collectors for the receiver, yielding a low-cost, high-performance design. Simulated images are shown for a potential realization of the system.

Fourier telescopy is an imaging technique in which the Fourier spectrum of an object is built up by sweeping fringe patterns of varying spatial frequency and orientation over the object. The modulated scattered radiation that results is collected by an nonimaging detector. We have performed a laboratory demonstration of Fourier telescopy in order to confirm the validity of the fundamental measurement concept and the image reconstruction method. We show experimentally obtained images and compare them to simulated images. On- going experiments will characterize the consequences of less-than-ideal measurement conditions, such as fringe- spacing errors and less-than-unity fringe modulation. Our ultimate application is the imaging of geosynchronous satellites.

In many electro-optics applications, including some active imaging concepts, it is necessary to measure the amplitude and/or phase of the beat between pairs of optical beams. Here we show that in the presence of Poisson shot noise, under certain conditions the variance of the error in measuring these quantities depends on the characteristics of the beating beams. Specifically, with multiple beats present, if one beat signal has a frequency which is twice the frequency of another beat, then the variance of the estimate of phase of the lower frequency beat will depend on the phase of the higher frequency beat. Also, if the sample rate is such that there are exactly three samples per cycle of any of the beats then the variance of the phase estimate for that beat will depend on the phase being measured. Neither of these effects is present for independent additive detection noise. The effects should be considered when designing an optical system.

Fourier Telescopy is an active laser-based imaging technique based on an aperture synthesis similar to long baseline interferometry. The FT method will potentially allow high- resolution images of objects in Geosynchronous (GEO) orbit. A full-scale system to implement the FT method is being built by TREX Enterprises as part of the Air Force Research Laboratory's Geo Light Imaging National Testbed (GLINT) program. An end-to-end computer simulation has been developed to determine the effects of atmospheric turbulence and beam jitter on the quality of the reconstructed image. We discuss the functions of the simulation code, and present sample results for image quality of the GEO object model. Simulations confirm that the GLINT system is relatively insensitive to atmospheric effects, as long as the seeing is at least moderately good and consistent with current data taken in souther New Mexico.

The properties of the images of remote objects obtained by a method the Fourier-telescope are investigated depending on size of the receiving aperture. The essential role is played consideration of a object surface micro roughness. Is shown, that at the super-large receiving apertures intercepting all reflected energy, the image does not contain speckles and does not depend on a contour of a surface. At the apertures intercepting a part of a reflected energy, the image is fluctuated on luminosity also depends from macro- and micro roughness of a surface. The fluctuation of a image brightness (contrast) depending on sizes of the receiving aperture are investigated. The conclusions about optimum sizes of the receiving aperture are done.

By illuminating an object with a laser and collecting far- field speckle intensity patterns, at a regularly spaced sequence of wavelengths, one obtains the squared magnitude of the 3D Fourier transform of the object. Performing 3D phase retrieval to reconstruct a 3D image (consisting of complex-valued voxels) is relatively difficult unless one has a tight support constraint. An alternative is to perform averaging of the autocovariance of the far-field speckle intensities, over an ensemble of speckle realizations, to estimate the square magnitude of the Fourier transform of the underlying (incoherent) reflectivity of the object, by the correlography method. This also gives us an incoherent- image-autocorrelation estimate, from which we can derive an initial support constraint. Since the image, being incoherent, is real-valued and nonnegative, performing phase retrieval on this data is easier and more robust. Unfortunately the resolution for correlography is only moderate since the SNR is low at the higher spatial frequencies. However, one can then use a thresholded version of that reconstructed incoherent image as a tight support constraint for performing phase retrieval on the original speckle intensity patterns to reconstruct a fine-resolution, coherent image. The fact that the objects are opaque plays an important role in the robustness of this approach. We will show successful reconstruction results from real data collected in the laboratory as part of the PROCLAIM (Phase Retrieval with an Opacity Constraint for LAser IMaging) effort.

Coherent light of one color will form laser speckle upon reflection from a rough object. This laser speckle provides information about the shape of an object. Further information can be obtained if two colors are used, and if the colors are sufficiently close in wavelength that the interference is also measurable. The two speckle patterns and the interference can be shown to provide the minimum information sufficient to form a band-limited image of the object using a root-matching technique described herein. This root-matching technique is performed in the far-field or object plane. This technique is relatively slow and sensitive to noise, and so is supplemented with a technique that minimizes error in the pupil plane. A hybrid technique that combines the two approaches is shown to reproduce images effectively with reasonable computation time.

A technique has been developed and tested in the laboratory where speckled images are reconstructed from pupil-plane speckle data. The wavefront is estimated using a technique similar to optical heterodyne. The method requires pupil- plane data to be mixed with a plane wave whose polarization is orthogonal to the speckle polarization. A polarimeter is then used as part of the detection scheme. If the polarimeter is capable of simultaneous detection of four or more channels, a key advantage to the technique becomes its speed. Fast detection overcomes some of the problems of Doppler shifts seen in the heterodyne detection scheme. This eliminates the need for high frame rate cameras. A simple theoretical basis for the technique is presented along with a description of the experiment and the results from that experiment. Practical applications for this technique are briefly explored.

Shear beam imaging is a coherent reflective imaging technique which inherently contains signal dependent speckle noise, and removal of the speckle using a minimal number of frames is the major concern of this paper. In the past, several methods have been used to eliminate this noise. The complexity of the algorithms ranged from a simple nonlinear median filter to complex linear and nonlinear models. Here, fast morphological and wavelet filters are proposed and are shown to remove speckle better than the previous methods. The morphological filters are non-linear in nature and computationally efficient, thus making them quite attractive. This paper describes the morphological and wavelet techniques used and demonstrates the superior performance of these filters as compared to the previously used ones.

Sampled irradiance measurement in the image plane of a coherently illuminated object are used to estimate the 2D object brightness profile in a shear beam imaging configuration. A field correlation function is used in a minimum variance irradiance estimation algorithm to optimally estimate the objects 2D brightness from a collection of sampled irradiance measurements on a grid of points in the image plane. The efficacy of the reconstruction method is demonstrated by reconstructing simulated coherently illuminated images of a symmetric extended object, an asymmetric extended object and also a spatially distended point source object. A theoretical error metric is determined and shown to compare favorably with simulated results over a range of object sizes.

The problem of interpolating an image from a downsampled version is investigated. In particular, prior knowledge of the statistics of the data and measurement noise, as well as the method of sampling, are shown to lead to an optimal interpolator. The availability of SPOT satellite image data sampled at two resolutions, one twice that of the other, provides a basis for the study. Firstly a direct inverse filter is derived from the satellite data. Secondly, interpolators based on models for the auto-covariance of the higher resolution data are derived and an equivalence for these and the direct type is shown. Thirdly a comparison of the spectra of the interpolators reveals that both the inverse and statistical interpolators give significant boost to frequencies below the nominal bandlimit and that their response is significant at frequencies above but adjacent to the nominal bandlimit. Finally, numerical studies indicate that when the prior knowledge is accurate there is less residual mean square error associated with the direct and statistical interpolators, compared to a sinc-based interpolator.

In this paper, we will present the optimum interpolation functions minimizing various measures of approximation error simultaneously. For an ordinary interpolatory approximation using sample values of a band-limited signal and a FIR filterbank system having analysis filters H_m((omega) ) (m equals 0,1,...,M - 1), we outline necessary formulation for the time-limited interpolation functions (psi) _m(t) realizing the optimum approximation in each limited block separately. Further, under some assumptions, we will present analytic or piece-wise analytic interpolation functions (phi) _m(t) minimizing various measures of approximation error defined at discrete time samples t_n equals n (n equals 0,+/- 1,+/- 2,...). In this discussion, (phi) _m(n) are equal to (psi) _m(n) (n equals 0,+/- 1,+/- 2,...). Since (phi) _m(t) are time-limited, (phi) _m(n) vanish outside of the finite set of n. Hence, one can use FIR filters if one wants to realize discrete synthesis filters which impulse responses are (phi) _m(n).

Using the estimate-maximize technique for maximum-likelihood estimation, a multiframe generalization of the Richardson- Lucy algorithm is derived which encompasses additive Poisson noise sources in addition to source dependant photon noise. This enables the estimation algorithm to properly treat situations in which the signal is similar in strength to noise sources such as background radiation and ark current. Simulations are used to investigate the level of restoration performance that may be expected at various noise source strengths.

Phase-Diverse Speckle (PDS) is a short-exposure data- collection and processing technique that blends phase- diversity and speckle-imaging concepts. PDS has been successfully used for solar astronomy to achieve near diffraction-limited resolution in ground-based imaging of solar granulation. Variants of PDS that involve narrow-band, spectroscopic, and polarimetric data provide more information observations. We present results from processing data collected with the 76-cm Richard B. Dunn Solar Telescope (DST) on Sacramento Peak, NM. Three-channel data sets consisting of a pair of phase-diverse images of the solar continuum and a narrow-band image were collected over spans of 15 - 20 minutes. Point-spread functions that are estimated from the PDS data are used in a multi-frame deconvolution algorithm to correct the narrow-band imagery. The data were processed into a number of time series. A rare, short-lived continuum bright point with a peak intensity at a factor of 2.1 above the mean intensity in the continuum was observed in one such sequence. The field of view spans multiple isoplanatic patches, and strategies for processing these large fields were developed. We will discuss these methods along with other techniques that were explored for accelerating the processing. Finally, we show the first PDS reconstruction of adaptive-optics (AO) compensated solar granulation taken at the DST. As expected, we find that these data are less aberrated and, thus, the use of AO in future experiments is planned.

Reconstructed scene intensity distribution obtained from deconvolution using three different iterative reconstruction methods: phase diversity, deconvolution, and iterative blind deconvolution approaches are presented. For images degraded with as much as a quarter wavelength of aberration and a signal to noise ratio of 10, we show that the correlation between the `truth' scene and the reconstructed scene is 0.9761 for deconvolution, 0.9680 for phase diversity, and 0.9169 for iterative blind deconvolution. The correlation coefficient becomes even higher as the signal to noise ratio and the aberration strength decrease. In spite of the sometimes severe edge effect, we show that these algorithms as adapted by our group yield relatively decent reconstructed objects as determined visually and by peak correlation coefficient comparison. The success of these adapted algorithms on extended scenes makes them potentially useful in imaging with degraded optical systems.

The Air Force Research Laboratory is in the process of demonstrating an advanced space surveillance capability with a heterodyne laser radar (ladar) system to be used, among other applications, for range-resolved imaging of orbiting satellites. A small-scale version of this system, the Heterodyne Imaging Laser Testbed (HILT), is used for obtaining pulsed reflection returns from targets that are located on the ground at a distance of approximately 1 km. Presented in this paper are a description of HILT and the preliminary results: image reconstructions of the ground targets using reflective tomographic techniques.

The Air Force Research Laboratory, Directed Energy Directorate, is in the process of demonstrating an advanced space surveillance capability with a heterodyne laser radar system to be used for range-resolved imaging of orbiting satellites. This system, called HI-CLASS (High Performance CO₂ Ladar Surveillance Sensor), uses a CO₂ laser in a modelocked configuration to generate approximately 10 microsecond(s) bursts of approximately 1 ns pulses repeated at a 30 Hz rate. When reflected from an orbiting satellite, these pulses contain information about the range-resolved reflectivities and the Doppler spectrum of the target. For earth-stabilized satellites, cross-range motion is insufficient to produce Doppler-resolved images from the range-resolved data for the HI-CLASS system parameters. However, an image reconstruction method called reflection tomography can be used to reconstruct satellite images by using a tomographic reconstruction approach. An important issue in tomographic image reconstruction is correct registration of the individual projections. For accurate image reconstruction, all projections must be aligned to the target center of rotation. Due to typical system alignment uncertainties, atmospheric fluctuations, and random satellite displacements, range cannot be measured accurately enough to determine the satellite center of rotation. Therefore, this information must be inferred from the projection data itself. Here, we present an algorithm that uses a phase-retrieval approach to determine the required center of rotation from the projection data. We demonstrate the effectiveness of this algorithm using computer-simulated data. We also discuss the future application of this algorithm to actual ladar data.

Below its critical temperature (668 K), crystals of the binary alloy Cu₃Au consist of antiphase domains with a length scale determined by growth conditions and annealing history. Superstructure Bragg reflections indicate the extent of long-range ordering of the domains. The use of a coherent beam causes these superstructure peaks to have the appearance of speckles, which have a size determined by the size of the beam. The speckles result from a scattering process with no ensemble averaging and thus describe the specific microscopic arrangement of the domains within the illuminated volume of the sample. However, in real experiments only the diffracted beam intensity can be measured while all phase information is lost. This problem is overcome in conventional holography by the construction of a reference wave; however, the special requirements of x- ray optical design have precluded the direct applications of this approach, and so the use of numerical analysis is required. Iterative methods, including the Gerchberg-Saxton algorithm and the hybrid input-output algorithm, have been successfully demonstrated for computer simulations of Cu₃Au and show early promise for reconstruction of domain structure from real measurements. Data obtained at the Advanced Photon Source beamline 33-ID-D at 8.5 keV are presented, and the requirements for successful reconstruction of images from such data are discussed.

In this paper we report experimental results for a new technique for estimating aberrations which extends the strength of an aberration which may be sensed using Hartmann sensor technology by means of an algorithm which processes both a Hartmann sensor image and a conventional image formed with the same aberration. We find that the theory and the experiment match well within the experimental error, and that very strong defocus aberrations can be accurately sensed with this technique.

Optical path difference (OPD) measurements typically are characterized by 2(pi) phase discontinuities, since optical interference can only determine the wavefront modulo the wavelength. Obtaining an estimate of the actual phase profile from OPD measurements necessitates removing the discontinuities, or `unwrapping' the phase. Monochrome phase unwrapping algorithms have been developed over the years in two broad categories--local and global. Local algorithms generally work by starting at some initial point within the OPD map, assigning an arbitrary surface profile value at that point, and working outward from that location, detecting and removing phase jumps pixel-by-pixel. Global algorithms seek simultaneous solutions over the entire map, or on extended regions within it, that minimize overall error according to some criterion.

Quad trees and dyadic trees are hierarchical data structures that are used to represent spatial data or images. With a collection of images, a tree-indexed Markov chain can be generated by letting the transition probabilities from one level to the next level be estimated by the empirical transition probabilities. Depending on the original collection of images various goals may be achieved. One may for instance synthesize new structures from given structures. Another example is the modeling of heterogeneous structures are multi-scales for geological characterization.

In this paper, the Karhunen-Loeve transform has been applied to the image recovery procedure. According to this method, an particular image can be economically represented by a best coordinate system called eigenimages, which are the eigenfunctions of the averaged covariance of a set of training images. Since the images can be approximated by different linear combinations of a relatively few eigenimages, they can be efficiently recovered by storing only a small set of the eigenimages and a small collection of weight coefficients for each image, which is derived by projecting the original image onto each eigenimage. A volume holographic storage based optical processor is used to implement those projections in parallel. Exploiting the large capacity storage and high parallel read-out ability of the associative memory technique, the processor has an inherent mechanism of multichannel correlation. After the set of eigenimages are stored in a photorefractive crystal by using the two-wave mixing, spatially separated beams with different light intensities will be obtained in parallel when input image addresses the processor. The intensity of each beam just represents the projection result between the input image and each eigenimage.

In this paper, a new method for obtaining 3D shape of an object by measuring relative blur between images using wavelet analysis has been described. Most of the previous methods use inverse filtering to determine the measure of defocus. These methods suffer from some fundamental problems like inaccuracies in finding the frequency domain representation, windowing effects, and border effects. Besides these deficiencies, a filter, such as Laplacian of Gaussian, that produces an aggregate estimate of defocus for an unknown texture, can not lead to accurate depth estimates because of the non-stationary nature of images. We propose a new depth from defocus (DFD) method using wavelet analysis that is capable of performing both the local analysis and the windowing technique with variable-sized regions for non- stationary images with complex textural properties. We show that normalized image ratio of wavelet power by Parseval's theorem is closely related to blur parameter and depth. Experimental results have been presented demonstrating that our DFD method is faster in speed and gives more precise shape estimates than previous DFD techniques for both synthetic and real scenes.