The Air Force Office of Scientific Research (AFOSR) is launching a research program in imaging physics planned to start in fiscal year 1997 (FY97). Both active (man made illumination sources) and passive (solar illuminated) imaging methods will be included in the program. The purpose of the program is to develop a national thrust for imaging science which will lay the foundation for future Air Force imaging systems. The new imaging physics program will be jointly administered from the Directorate of Physics and Electronics (AFOSR/NE) and the Directorate of Mathematics and Geosciences (AFOSR/NM) with collaborations with the Directorate of Life Sciences. The combined NE, NM, and NL imaging program will apply innovative mathematical formalisms (wavelets, non-linear partial differential equations, inverse methods, statistical techniques, optimization methods . . .) to the imaging problem (object representation, atmospheric turbulence compensation and noise modeling, innovative imaging techniques, multi- spectral imaging, data and sensor fusion, smart sensors, imaging neural nets, phase retrieval, . . .). The electronic emulation of biological vision processes for intelligent information identification and extraction in a timely manner are also of interest. A description of AFOSR and the current and planned imaging physics program are presented.

From an information theoretic point of view, the inverse problem and the problem of data compression are intimately related. Optimal compression seeks the most concise representation of a data set, while Bayesian probability theory favors image reconstruction algorithms which minimally model the information present in the data. This should not be surprising. It is in keeping with a scientist's intuitive need to satisfy the precepts of Occam's Razor, i.e. not to over interpret one's data. Information scientists might describe this process as quantifying the algorithmic information content (AIC) of the image, and then using this 'coordinate system' for optimal image reconstruction. The present paper describes pixon- based image reconstruction, a technique based upon AIC minimal image models. Because AIC is language dependent (description length and language complexity are inversely related) we have based the practical implementation of our method on concise (descriptive) languages for generic images, e.g. multiresolution basis functions. The present paper describes both the theory of pixon-based reconstruction and presents practical examples demonstrating that pixon-based reconstruction produces results consistently superior (often by large factors) to those of other methods, including the best examples of maximum likelihood and maximum entropy image reconstruction.

In phase diverse speckle imaging, one collects a time series of phase-diversity image sets. From these data it is possible to jointly estimate the object and each realization of the aberrations. Current approaches model the total aberration phase screen in some deterministic, parametric fashion. For a typical scenario, however, one has more information than this. Specifically, the total aberration phase screen is caused by fixed aberrations combined with dynamic (time-varying), turbulence-induced aberrations for which we have some knowledge about the stochastic behavior. One important example is where the dynamic aberrations derive from Kolmogorov turbulence. In this context, utilizing this extra information has the potential for being a powerful aid in the joint aberration/object estimation. In addition, such a framework would provide a relatively simple method for calibrating fixed aberrations in an imaging system. The natural framework for utilizing the stochastic nature of the wavefronts is that of Bayesian statistical inference, where one imposes an a priori probability distribution on the turbulence-induced wavefronts. In this paper, we present the general Bayesian approach for this joint-estimation problem of the fixed aberrations, the dynamic aberrations, and the object from phase-diverse speckle data. We then discuss issues related to theoretical performance, numerical implementation, and applications. Finally we provide simulation results which demonstrate improvement in PDS image reconstructions resulting from the Bayesian estimation approach.

An estimate of the transmittance of an object is examined in a twin-photon beam setup. The estimate is based on observing both the photons of one beam and the photons of the twin beam after passage through the object. The performance of the estimate (bias, variance, and mean-square error) is compared to the conventional single-beam measurement. The improvement depends on the photon flux, the counting time, the quantum efficiencies of the detectors, and the value of the measured transmittance itself. In general, a performance advantage is achieved for sufficiently high photon flux or long counting time.

Michelson stellar interferometers with long baselines have been proposed as a means for obtaining high resolution images of space objects. The fringes measured in such interferometers move randomly due to atmospheric turbulence effects. To overcome turbulence effects the fringe phase at any instant is summed around groups of three or more aperture pairs to create the so-called closure phase. For small apertures, the closure phase is insensitive to atmospheric turbulence effects. However, the closure phase is corrupted by photon noise effects. In a recent paper the probability density function of the error in the closure phase estimate due to photon noise was derived as a function of the fringe visibility and light level, and evaluated. In this paper we apply this theoretical result to the practical problem of measuring the closure phases associated with an Earth orbiting satellite.

An estimation-based method for accommodating nonuniform flat-field response of a focal-plane array is described. This method employs image data directly for performing the flat-field correction and does not rely on a separate flat- field calibration-measurement. This is accomplished by dithering the camera so that the object's focal-plane images acquired in a series of snapshots appear in different positions against the fixed-pattern artifacts caused by nonuniformity of the focal-plane array.

Current methods for estimating the wavefront slope at the pupil of a telescope using a Hartmann wavefront sensor (H- WFS) are based on a simple centroid calculation of the irradiance distributions (spots) recorded in each subaperture. The centroid calculation does not utilize knowledge concerning the correlation properties of the slopes over the subapertures or the amount of light collected by the H-WFS. This paper presents the derivation of a maximum a priori (MAP) estimation of the irradiance centroids by incorporating statistical knowledge of the wavefront tilts. Information concerning the light level in each subaperture and the relative spot size is also employed by the estimator. The MAP centroid estimator is found to be unbiased and the mean squared error performance is upper bounded by that exhibited by the classical centroid technique. This error performance is demonstrated using Kolmogorov wavefront slope statistics for various light levels.

The Super-SVA algorithm has been shown effective for improving the resolution of microwave synthetic-aperture radar (SAR) images. In this paper we review the Super-SVA algorithm and demonstrate its application to optical imaging systems using coherent laser illumination. Examples of such imaging systems include heterodyne-array imaging, holographic laser radar, laser synthetic-aperture radar, coherent phase retrieval from pupil-plane intensities, and SCIP (sheared-beam imaging). We consider the case of a bright object on a dark background. We show the difference in performance for different features of the image -- prominent points versus extended, diffuse areas.

Phase reconstruction algorithms, which determine phase from measured phase differences, are used in several areas, such as adaptive optics and speckle imaging. The purpose of this study is to examine the effects of noisy phase difference measurement inputs on reconstructor output phase noise. An analytic procedure for finding the probability density function, and hence the variance and gain, of the output noise in a general phasor-based path averaging operation is given. Also, noise performance comparisons between the phasor-based and optimal linear techniques are shown.

A laboratory investigation into Doppler heterodyne imaging is presented. Heterodyne detection involves beating a temporally modulated laser beam with a local oscillator. The primary advantage of this technique is that it allows measurements to be taken at low SNR levels. In heterodyne imaging, a series of temporally modulated far-field speckle patterns is measured, and demodulated to form the 2- dimensional complex field. The complex field data is inverse Fourier transformed to create a speckled image of the coherently illuminated target. Rotating targets cause the beat frequency to be Doppler broadened, and target information is encoded into temporal frequencies determined by the associated Doppler shift from which velocity information can be recovered. A significant limitation of heterodyne array imaging is that, in its fundamental form, it is sensitive to phase aberrations in the propagation path. We investigate a method whereby information on the imaging system aberrations may be obtained, and good images recovered in the presence of phase aberrations. Recoveries of laboratory data using Doppler heterodyne at high and low SNR levels are presented.

The recovered object in speckle imaging is generally an accumulated average of instantaneous speckled image frames. Misregistration of individual frames with respect to each other degrades image quality by blurring the average resultant image. In particular, atmospheric perturbations can cause random tilts in the phase of the detected speckle pattern, which tilts in turn induce random translations in each reconstructed image. Various techniques have been proposed to deal with this registration problem. We present here a maximum likelihood estimator to estimate and correct for the random tilts when each speckle frame is further corrupted by shot noise. The noise is modeled as a Poisson- distributed random variable. Results of this correction technique are compared with the performance of previous registration routines.

Three methods for reconstructing icosahedrally-symmetric particles from solution x-ray scattering data are described. Such data is the spherical average of the magnitude-squared of the Fourier transform of the electron density in the particle and therefore is only one dimensional. Because of the limited amount of data, a priori information about the particle is crucial and the three methods differ in the description of the particle that is used. This type of reconstruction problem is important in the structural biology of spherical viruses, and example reconstructions from one such virus are described.

An eight-view tomographic system based on one-dimensional Hartmann sensors is currently in use to image heated air flows. The system produces two-dimensional maps of refractive index at rates of several kilohertz. The high rate and good resolution enable comparison of measured results to expected results from fluid flow models. However, the novel nature of the application complicates validation of the system's performance. This paper describes computer simulations and experimental results quantifying the performance of the tomographic system at resolving spatial and temporal structures within the flow. The computer simulations model the physics and noise sources inherent in the wavefront sensing and tomographic imaging systems. An error budget for the system and an effective resolution metric allow quantitative comparison of performance against a given model of the flow. However, the accuracy of the simulation's predictions depends upon the accuracy of the disturbance model. By combining computer models of fluid flow, time averaged measurements such as temperature across the flow, and intrusive measurements such as smoke visualizations, we refine our flow model and improve the simulation. Experimental results show good agreement with this model, and the model allows us to discriminate and remove reconstruction artifacts from the imaged flow.

The AMOS daylight optical near-infrared imaging system, acronym ADONIS, is a sensor system designed for collecting satellite images under daylight conditions and employing speckle post-processing for enhancement of the resulting images. This paper presents our solution (the ADONIS system) to the daylight observation problem by first establishing the issues related to radiometry, daylight detection, and incoherent speckle imaging. System design resolution optimization results are presented. ADONIS imaging results and conclusions based on these results also are presented.

The utility of a blind deconvolution algorithm used in conjunction with the Knox-Thompson algorithm is demonstrated with day time observations of the MIR space station. We also investigate the convergence properties of the Richardson- Lucy Blind deconvolution algorithm when used in conjunction with the Knox-Thompson algorithm.

In this paper the problem of optimally using object model information in image reconstruction is addressed. A closed form solution for the estimated object spectrum is derived using the Lagrange multiplier technique which assumes a measured image, knowledge of the optical transfer function, statistical information about the measurement noise, and a model of the object. This reconstruction algorithm is iterative in nature for two reasons: (1) because the optimal Lagrange multiplier is not generally known at the start of the problem; and (2) we can use the object estimate obtained from one step of the algorithm as the model input for the next step. In this paper we derive the estimator, describe one technique for determining the optimal Lagrange multiplier, demonstrate a stopping criterion based on the mean squared error between a noise free image and the photon-limited version of the image, and show representative results for a sparse aperture imaging application.

Restoration of images blurred by an optical transfer function (OTF), or additive Gaussian noise which affect the Fourier transform amplitude and phase of the image, are considered. A method for reconstructing a two-dimensional image from power spectral data is presented. It is known that the spatial frequencies at which the Fourier transform F(u,v) of an image equals zero are called the real-plane zeros. It has been shown that real-plane zero locations have a significant effect on the Fourier phase in that they are the end points of phase function branch cuts, and it has been shown that real-plane zero locations can be estimated from Fourier transform magnitude data. Thus, real-plane zeros can be utilized in phase retrieval algorithms to help constrain the possible Fourier transform phase function. The purpose of this research is to recover the Fourier transform phase function from the knowledge of the power spectrum itself. By locating the points at which the Fourier transform intensity data are zero, we approximate a nonfactorizable function by its point-zero factors to recover an estimate of the object. A simple iterative method then successfully refines this phase estimate. The basic idea for the restoration is to separate the point-zeros of the modulation transfer function (MTF) or the additive noise from the point-zeros of the original image. Image restoration results according to the method of phase function retrieval for images degraded by additive noise and linear MTF are also presented.

A new method of calculating the optical transfer function (OTF) for image blur caused by arbitrary motion is introduced. Previous methods, except for a few specific types of motion, were numerical rather than analytical. This new method makes it possible to obtain analytical expressions for OTF, deriving from any kind of motion, by means of the statistical moments of the motion function. Analytical OTF expression are derived for high and low- frequency vibrations. An example of implementation of the method in restoration of images blurred by motion is presented.

Image restoration techniques, iterative and non-iterative, are applied to high-speed infrared images from a ground based telescope of objects at altitudes to reduce the degradation of the images caused by atmospheric turbulence, vibration, and systematic aberrations. Comparisons are made among the following: The Wiener filter, the Richardson-Lucy method, the CLEAN algorithm, and the maximum entropy method. The Wiener and Richardson-Lucy filters are found to have the best overall performance and flexibility when the PSF is known. The Wiener filter consistently provides the shortest restoration time for each set of test images. A good estimate of the PSF, obtained using Tatians's method, is used as an input parameter for each of the restoration algorithms.

The mathematics of emission computed tomography is applied to the three-dimensional reconstruction of the optical emission within an auroral arc. According to general experimental conditions, a very limited angular range and a small number of observers require an iterative back projection method. Parameters for the quantitative correspondence between the original and reconstructed volumes and between the images are defined and using this method, a theoretical arc can be reconstructed with root- mean-square errors of the images of less than 2%. The reconstruction accuracy of the volume can be improved with an increasing number of observers to root-mean-square errors of about 15%. Different geometries are tested but the best results are obtained as long as one observer looks along the magnetic field line through the auroral arc. The calculations confirm the range of suitable observation geometries to within 20 km from the field line through one of the observers.