Multi-frame iterative blind deconvolution algorithms for image enhancement have been widely used for over ten years. Originally developed for enhancing astronomical images from large ground based telescopes, the algorithms were adapted for ground based satellite observations. Most algorithms involve some type of multi-frame iterative Bayesian optimization assuming either Poisson or Gaussian statistics. Many algorithms use an iterative conjugate gradient search technique, however it has been our experience that an algorithm based on Gaussian statistics, combined with projection onto convex sets adaptation leads to a simple algorithm that quickly converges to a result. Recently our thrust has been to transition these algorithms to the airborne imaging problem. We present a number of examples. First, results from observation of low earth orbit satellites with uncompensated data taken at the focal plane of a large telescope. Finally we move to the problem of air-to-ground imaging. Such scene based imaging scenarios require an algorithm that can operate in the presence of anisoplanatic effects. For this case we have developed an algorithm that calculates a position varying point-spread function.

Considerable tactical utility is anticipated for systems that coherently illuminate remote target scenes to form detailed images over long, turbulent optical paths through wide FOV optical components. Typical viewing conditions greatly exceed the isoplanatic angle, and isoplanatic patch sizes approach the area of individual pixels on the imaging array. Although adaptive optical systems have met limited success in the restoration of anisoplanatically formed images, such hardware is unsuitable for tactical applications, and requires multiple point-source imagery to adapt the optical system to the turbulence. Our previous work demonstrated a fast, information-theoretic postprocessing algorithm that seeks to jointly maximize the likelihood of the image given a remote scene, as well as an estimate for Fried's seeing parameter to describe current atmospheric conditions. That research employed a short-exposure OTF to model the anisoplanatic system response for a series of motion-compensated images. Although results from the algorithm were encouraging, it was understood that the short-exposure OTF provided an optimistic model for the overall anisoplanatic blur function caused by turbulence. A more accurate OTF accounts for not only the global shift of each image collected in the ensemble, but also for the blur induced by random and uncorrelated shifts of each of the many isoplanatic patches collected at the imaging device. This research complements the blind deconvolution algorithm by deriving an anisoplanatic OTF (AOTF) that better models the blur function of a motion-compensated ensemble of images. Results are presented that compare the recovered images obtained using both the short-exposure OTF as well as the AOTF.

Image restoration algorithms compensate for blur induced attenuation of frequency components that correspond to fine scale image features. However, for Fourier spatial frequency components with low signal to noise ratio, noise amplification outweighs the benefit of compensation and regularization methods are required. This paper investigates a generalization of the Wiener filter approach developed as a maximum a priori estimator based on statistical expectations of the object power spectrum. The estimate is also required to agree with physical properties of the system, specifically object positivity and Poisson noise statistics. These additional requirements preclude a closed form expression. Instead, the solution is determined by an iterative approach. Incorporation of the additional constraints results in significant improvement in the mean square error and in visual interpretability. Equally important, it is shown that the performance has weak sensitivity to the weight of the prior over a large range of SNR values, blur strengths, and object morphology, greatly facilitating practical use in an operational environment.

It is well known that positivity constraints improve the performance of image reconstruction procedures such as deconvolution. However, their impact on the recovered image is more difficult to characterize than linear constraints such as support. For the problem of deconvolution in the presence of additive Gaussian noise, we derive an approximation to the bias and variance of the maximum likelihood estimator and compare the improvement in mean-square error due to positivity with the gain derived from support constraints. Then we propose a generalized Bayes estimator and demonstrate that it has lower mean-square error in most cases than the maximum likelihood estimator. The degree to which it outperforms maximum likelihood is especially dramatic when SNR is low or blurring is strong.

This research develops a Model-based Spectral Image Deconvolution (MBSID) algorithm based on statistical estimation to spectrally deconvolve images collected from a spectral imaging sensor. The development of the algorithm requires only two key elements, 1) the statistics of the light arrival and 2) an in-depth knowledge of the spectral imaging sensor. With these two elements, the MBSID algorithm can, through image post-processing, dramatically increase the spectral resolution of the images as well as give insight into the performance of the imaging sensor itself. While MBSID algorithms can be developed for any spectral imaging system, for this research an algorithm is developed for ASIS (AEOS Spectral Imaging Sensor), a new spectral imaging sensor installed with the 3.6m Advanced Electro-Optical System (AEOS) telescope at the Maui Space Surveillance Complex (MSSC). The primary purpose of ASIS is to take spatial and spectral images of space objects. The stringent requirements associated with imaging these objects, especially the low-light levels and object motion, required a sensor design with less spectral resolution than required for image analysis. However, by applying MBSID to the collected data, the sensor will be capable of achieving a much higher spectral resolution, allowing for better spectral analysis of the space object.

Appropriate modifications of the image-capture process in a modern imaging system can potentially enhance the digital restorability of the collected image data and thus lead to improved final-image quality. Examples of such modification are insertion of a phase mask in the pupil that encodes depth dependent intensity distribution in the wavefront, insertion of a specific defocus phase in one of the two arms of a conventional phase-diverse speckle imaging system, and use of progressively larger sub-pixel tip-tilts in the otherwise identical low-resolution image channels of an array imaging system. In each case, the final reconstructed image has a higher quality than the intermediate raw image(s) recorded by the sensor. This paper discusses the application of Fisher information to characterize the performance of these three model imaging systems that exploit optical preconditioning to improve the digital restorability and thus the quality of the final image.

Achieving high resolution imagery of distant terrestrial objects from ground based sensors presents a unique technical challenge. The entire optical path is fully immersed in a dense and turbulent atmosphere, resulting in a significant loss of scene contrast and resolution. Although there are strong similarities to the problems of high resolution astronomical and space object imaging, there are also some significant differences. This paper describes the long horizontal path seeing environment, two portable long range imaging systems MIST (Miniature Integrated Speckle imaging Telescope) and TFIC (Terrestrial Fusion Imaging Camera) and the associated image processing workflow. MIST was specifically designed to support long range, high resolution imaging research. TFIC is a very portable and compact high resolution field imaging system. The TFIC image processing workflow uses a combination of luminance processing, speckle imaging and image fusion. Representative high resolution urban and marine environment imagery with horizontal path distances up to 128 km (80 miles) is shown.

Analyses show that astronomical occultation methods may be used to determine the silhouettes of satellites at geostationary distances, a result few other techniques can achieve. Specifically, an array of photon-counting detectors is positioned in the path of the target shadow from one star. Reduction of the received star intensity vs. time can yield silhouette resolution of less than a meter. In this paper, we address the critical issues of a) the limited density of useable stars, b) positioning of the detector array into the path of the shadow, and c) undoing the effects of diffraction. A conceptual design for an imaging station is presented.

Fourier telescopy (FT) is an active imaging technique that is a good candidate for high resolution imaging systems that can be used to obtain satellite images out to geosynchronous target ranges. Fourier telescopy uses multiple beams that illuminate the target with a fringe pattern that sweeps across it due to frequency differences between beams. In this way the target spatial frequency components are encoded in the temporal signal that is reflected from the target. The FT receiver can then be composed of a large area "light bucket" collector, since only the integrated temporal signal is necessary to reconstruct the target image. The GEO Light Imaging National Testbed (GLINT) system was previously designed to obtain satellite images at geosynchronous ranges by using this technique. Laboratory experiments by several groups have demonstrated the validity of this technique to produce images from simulated targets. In this paper we expand upon these previous experiments to present results from both a FT laboratory and field experimental setup that simulated realistic photon noise, speckle noise, and atmospheric turbulence that will be encountered in an actual FT imaging system. To obtain the scaling for the FT experiment, we have used the GLINT system design parameters for our experimental setup. We will also discuss the phase closure process used to eliminate the random phase differences between the beams from the target spatial frequency measurements and the basic reconstruction algorithm used to produce the target image. Results will also be given that demonstrate the phase closure variance is reduced by averaging a small number of high SNR measurements together, as compared to averaging a larger number of low SNR measurements. Target reconstruction improvements obtained by "unbiasing" the average of the individual low SNR phase closure measurements will also be discussed.

In this paper we briefly present the theory of Fourier Transform Heterodyne (FTH), describe past verification experiments carried out, and discuss the experiment designed to use this new imaging technology to perform optical correction. FTH uses the scalar projection of a reference laser beam and a test laser beam onto a single element detector. The complex current in the detector yields the coefficient of the scalar projection. By projecting a complete orthonormal basis set of reference beams onto the test beam, the amplitude and phase of the test beam can be measured, allowing the reconstruction of the phasefront of the image. Experiments to determine this technique's applicability to optical correction and optical self-correction are continuing. Applications of this technique beyond optical correction include adaptive optics; interferometry; and active, high background, low signal imaging.

Fourier telescopy (FT) is an active imaging technique that is a candidate for high resolution imaging systems which can be used to obtain satellite images out to geosynchronous target ranges. Fourier telescopy uses multiple beams that illuminate the target with a fringe pattern that sweeps across it due to a set frequency difference between beams. In this way the target spatial frequency components are encoded in the temporal signal that is reflected from the target. The FT receiver can then be composed of a large area "light bucket" collector, since only the integrated temporal signal is necessary to reconstruct the target image. The GEO Light Imaging National Testbed (GLINT) system was previously designed to obtain satellite images at geosynchronous ranges by using this technique. The "light bucket" receiver was designed use forty heliostats, each having a collection area of ten meters square, and composed of a 16 x 16 grid of two foot square mirrors. The heliostats would redirect the return light from the target onto a large spherical concentrator array composed of hexagonal mirror segments. This concentrator would then focus the return light onto a photomultiplier tube (PMT) detector. The FT Field experiment presented in this paper uses one 10-meter square heliostat and a single PMT, plus a scaled down secondary array to provide the optical elements of the receiver for the FT field experiment. In this paper, we will describe the performance characteristics of the heliostat, secondary, and PMT detector. Performance characteristics include optical wavefront, alignment, and alignment stability of the optical elements. Finally, results will be presented after the receiver was integrated with a transmitter system that provided the modulated FT signal from various targets. Image reconstructions will show that even using low quality "Light bucket" receiver optics and a 1.5 km horizontal path through the atmosphere, the modulated signal can still produce good image quality of the targets. Image reconstruction will also be presented for different SNR values in the received signal.

Multi-aperture systems allow a natural method of implementing phase diversity for the joint estimation of both pupil aberrations and an image of the object. Instead of creating diversity images by means of focus adjustments, one can actuate the individual sub-apertures of the system (e.g., with a piston phase) to introduce known phase diversity. Implementation of a nonlinear optimization routine is discussed. Through digital simulation, this paper investigates the performance of a sub-aperture piston diversity algorithm by tracking Strehl ratio and the probability and speed of convergence of the nonlinear optimization routine.

Ideally phase diversity determines the object and wavefront that are consistent with two images taken identically except that the wavefront of the diversity channel is perturbed by a known additive aberration. In practice other differences may occur such as image rotation, magnification, changes in detector response, and non-common image motion. This paper develops a mathematical forward model for addressing magnification changes and a corresponding maximumlikelihood implementation of phase diversity. Performance using this physically correct forward model is compared with the more simple approach of resampling the data of the diversity channel.

In this paper, we will study the optimum bounds for various diversity polynomials. For the Poisson or Gaussian noise cases studied, we have found that the optimum bound for extended scenes does not depend on the nature of the noise statistics. There is a slight dependence of optimum diversity for point sources, however. We will show, further, that the bound for Gaussian noise sources is larger than that for Poisson noise for large scenes. This behavior is reversed for point sources.

Three-dimensional imaging techniques are very attractive for many applications. We develop the basic principle of coded aperture imaging used in invisible imaging realm to visible imaging realm, propose a three-dimensional imaging method. The object is captured by a cameras array. Then captured photographs of the object are integrated into an image named coded image. Finally coded image is computationally decoded to obtain a series of longitudinal layered surface images of the object. For good reconstructed images fidelity, we make use of correlation decoding method. With the use of correlation decoding, the distribution of cameras in array is crucial for the quality of reconstructed images. We investigate some typical two-dimensional arrays, choose non-redundant array for its proper imaging property. Experiments have been done to test and verify the performance of the proposed method. We choose a simple discontinuous object. The object is composed of two digit models, digit "1" and "2". Two digit models are displaced from each other. The distance between them is 10cm. Cameras array includes 9 cameras arranged as non-redundant array. The object is placed at the center axis of the cameras array, face to face with the array. After capturing, photographs integrating, computational decoding etc. procedures, we obtain high-quality reconstructed images of digit "1" and "2". The results of experiments show that the proposed method is feasible.

A method using the phase-space representations, i.e. the ambiguity function or Wigner distribution function to compute the optical transfer function (OTF) for an optical system with circularly symmetrical pupils under polychromatic illumination is presented. The phase-space representations is a very convenient tool for display the optical transfer function with varying aberrations such as the longitudinal chromatic aberration and defocus in a single picture, and the monochromatic OTFs can be easily determined from these joint representations. The polychromatic OTFs are computed by synthesizing a suitable number of monochromatic OTFs weighted by the spectral distribution of source and the color sensitivity of the receiver at fixed wavelength. Since the ambiguity function or the Wigner distribution function can be previously obtained by optical method or digital computation, the computational efficiency is greatly improved compared with traditional method, in which every monochromatic OTF need to be determined along. We computed the polychromatic OTFs for an optical system with a clear circular pupil and an annular ring pupil in detail and show some primary applications of the computations in spatial filter designing for color-blur reduction.