The method presented is aimed at identifying the shape of an axially symmetric, sound soft acoustic scatterer from knowledge of the incident plane wave and of the scattering amplitude. The method relies on the approximate back propagation (ABP) of the estimated far field coefficients to the obstacle boundary and iteratively minimizes a boundary defect, without the addition of any penalty term. The ABP operator owes its structure to the properties of complete families of linearly independent solutions of Helmholtz equation. If the obstacle is known, as it happens in simulations, the theory also provides some independent means of predicting the performance of the ABP method. The ABP algorithm and the related computer code are outlined. Several reconstruction examples are considered, where noise is added to the estimated far field coefficients and other errors are deliberately introduced in the data. Many numerical and graphical results are provided.

The wave field splitting/invariant imbedding/phase space approach to direct and inverse wave propagation in the frequency domain is outlined. The properties and subsequent applications of the reflection and Dirichlet-to-Neumann operator symbols are briefly illustrated by an exact solution case.

A random medium model is applied to study propagation and multiple scattering of laser beams in nonlinear media containing microparticles. Refractive indices of these nonlinear media are considered to be isotropic and intensity-dependent. After applying a probabilistic model, we obtain an autocorrelation function with exponential-decay shape for the random medium assuming a two-phase mixture. Using the parabolic approximation, we have calculated the mean value of the intensity-dependent part of refractive index from the mutual coherence function. The Feynman diagrammatic technique, bilocal, and distorted-wave Born approximations are then invoked to formulate a Fourier relationship between the autocorrelation function and the forward scattered field of the incident light beam. Finally, our Fourier-based inversion algorithm is employed to extract information about the medium from the measured scattered field data.

We introduce a novel approach to the inversion of 2D distributions of electrical conductivity illuminated by line sources. The algorithm stems from the newly developed extended Born approximation, which sums in a simple analytical expression an infinitude of terms contained in the Neumann series expansion of the electric field resulting from multiple scattering. Comparisons of numerical performance against a finite-difference code show that the extended Born approximation remains accurate up to conductivity contrasts of 1:1000 with respect to a homogeneous background, even with large-size scatterers and for a wide frequency band. Similar comparisons indicate that the new approximation is nearly as computationally efficient as the first-order Born approximation. We show that the mathematical structure governing the extended Born approximation allows one to express the nonlinear inversion of electromagnetic fields scattered by a line source as the sequential solution of two Fredholm integral equations. We elaborate on this procedure and compare it against a more conventional iterative approach applied to a limited-angle tomography experiment. Preliminary numerical tests show excellent performance of the two-step linear inversion process.

A recovery algorithm is given for the 2 X 2 X 2 problem in diffuse tomography. This three dimensional algorithm is computationally more complex and yields relatively more information than its two dimensional counterpart.

Methods for inverse scattering, i.e. imaging from scattered field data such as diffraction tomography, typically require that the object be weakly scattering. Under this assumption the inversion methods based on adopting the first-order Born and the Rytov methods become straightforward Fourier inversion procedures. More general methods or `exact' inversion procedures have proved extremely difficult if not impossible to implement. In this paper, we exploit a differential cepstral filter in order to produce images of the scattering potential from strongly scattering objects.

Neutron specular reflectivity data obtained with a new grazing angle neutron spectrometer (GANS) from a NiC/Ti-multilayer sample were analyzed and modeled for reconstructing the scattering length density profile as a periodic step potential for the layered material. There is some ambiguity in the results due to the uniqueness problem with missing phase information. For more complex layered materials, there is often insufficient knowledge about the layers to use modeling reconstruction without phase information. In the second part, we present a method in which this problem is solved for diffraction data from lipid multilayers: due to changes in chemistry (isomorphous heavy atom method) the phases are determined directly and therefore the density profile of the lipid bilayer can be uniquely determined.

Noninvasive methods of obtaining the real-time data of internal structure of light emitting objects from their parts are considered to be rather significant for investigation of various high-speed processes such as flames, exposition, plasma, and jets. The method of dynamic operation (DPO) should be based on the spectral emission tomography. The DPO method essentially consists in treating the substrate surface by a high-enthalpy complex configuration plasma flow. We have constructed a light emission computed tomography system (LECT) and a light emission integrative tomography system (LEIT) for obtaining the real-time data.

We review several algorithms for obtaining quantitative reconstructions of weakly scattering objects from measured intensity data. These algorithms represent an extension of the usual techniques of diffraction tomography to cases where phase information cannot be measured or is otherwise unavailable, such as in the optical regime. The algorithms we present take advantage of the holographic recording geometry of diffraction tomography -- where the interference of the scattered wave with the incident wave is measured -- and generate a quantitative reconstruction of the scattering object by numerically recovering the phase of the scattered field prior to the tomographic reconstruction step. Phase recovery is performed non- iteratively using two intensity measurements. We compare this algorithm to a direct reconstruction algorithm within the Rytov approximation for the tomographic reconstruction of the index of refraction distribution of an optical fiber from simulated intensity data. These algorithms extend the practical range of diffraction tomography and inverse scattering by allowing reconstruction from phase-less scattering data using support constraints or additional measurements.

We discuss a 3D imaging modality called pulsed heterodyne-array imaging (PHI). The relationship between PHI and stepped-frequency methods for 3D coherent image formation is derived. For both cases, we consider flood-illumination of the object and detection with a 2D array of coherent receivers located in the pupil plane. It is shown that PHI can recover the same coherent 3D image as a stepped-frequency method such as holographic laser radar.

Three-dimensional imaging provides profile information not available with conventional 2D imaging. Many 3D objects of interest are opaque to the illuminating radiation, meaning that the object exhibits surface, as opposed to volume, scattering. We investigate the use of an opacity constraint to perform 3D phase retrieval. The use of an opacity constraint in conjunction with frequency-diverse pupil-plane speckle measurements to reconstruct a 3D object constitutes a novel unconventional-imaging concept. This imaging modality avoids the difficulties associated with making phase measurements at a cost of increased computations.

We describe two new methods for phasing arrays of heterodyne receivers. Both can be used when the arrays are sparse and distributed. One is based on the iterative transform algorithm using a support constraint and the other on maximizing image sharpness. Both work well; they require a modest number of speckle realizations with the same aberrations and are relatively immune to measurement noise.

New methods are needed to analyze and monitor multicomponent unknown environments or media (an object), for example, air toxic mixtures or protein mixtures. The existing methods are basically a single-pass measurement and do not provide enough information. We propose an optical exploration approach, a multistep feedback controlled architecture that includes multiple measurements with systematic modification of an object to get additional data. We discuss various optical techniques to modify and probe the object. The data obtained from the multiple measurements allow the object properties (say, individual concentrations) to be evaluated. Experimental data on air toxic mixtures are presented.

The blind image restoration method based on equivalent power spectrum is especially suitable to the restoration with the point spread functions (PSFs) of random characters. The problem is to identify the power spectrum of the original image in the filter transfer function expression. In this paper, a recognition method for the power spectrum of an ideal image was proposed through exploring a spectrum of the degraded image. This method is simpler and more practical than the other methods of identifying PSF parameters, and it is applicable to both cases with and without frequency domain zero-crossings in the observed image. In this paper we discuss the case with zero-crossings.

Confocal scanning laser microscopy is a powerful tool for nondestructive investigations. We introduce it to characterize active semiconductor devices. Due to the high resolution of this type of optical microscope, objects are identified with dimensions less than 0.1 micrometers . At this range, the fundamental physical concepts prevent readable images with conventional microscopes. In fact, at these dimensions the diffraction becomes very effective, so that we obtain a noncomprehensible pattern unless we numerically process it. In order to get a readout of the detected signal we use, instead of the deconvolution or Fourier Transforms, a direct method that consists of an explicit calculation of the electrical field of the electromagnetic wave. The amplitude is calculated in all functional planes of the microscope: from the laser source to the object and from this to the CCD camera. We focused our attention on polycrystalline silicon textures and roughness obtained after an anisotropic etching.

This paper presents a new method of analyzing intensity correlation data obtained in dynamic light scattering measurements of particles in Brownian motion in a colloid. A second-order linewidth distribution is obtained directly from the intensity autocorrelation by the method of regularized inversion with a nonnegativity constraint, based on the regularization method of Tikhonov. The linewidth distribution, and consequently a particle size distribution, is obtained by deconvolving the second order linewidth. The method is illustrated using a variety of data obtained using a compact optical fiber based instrument developed by Dhadwal. It is shown that regularized inversion of intensity data, followed by a deconvolution to obtain the first order linewidth distribution, is superior in performance to the inversion of reduced first order data. The reduction of second order data by subtracting a baseline and taking the square root of the difference results in increased noise, and in distortion. Noise and distortion cause inaccurate or even completely spurious inversions. The method can resolve very narrow monomodal size distributions or much broader multimodal distributions.

Certain wavelet transforms based on orthogonal wavelets are used to reduce the noise and then to invert noisy, bandlimited elastic wave scattering signals in stainless steel for nondestructive evaluation (NDE). An empirical technique that is based upon treating the noise differently at different frequency scales is presented. In this approach the amount of pruning of small coefficients depends nonlinearly on their frequency scales. One somewhat surprising consequence of the analysis is that information etalons in phase space exist that must not be changed at all because they pass almost pure information on the radius of the flaw. This suggests the presence of islands of information in phase space for other attributes of flaws such as location, material properties, and boundary shape which are being addressed in other work.

In medical imaging applications, the expectation maximization (EM) algorithm is a popular technique for obtaining the maximum likelihood estimate (MLE) of the solution to the inverse imaging problem. The Richardson/Lucy (RL) method, derived under different assumptions, is identical to this particular EM algorithm. The RL method is commonly used by astronomers in image deconvolution problems from astronomical data. A closely related algorithm, which we shall refer to as the Poisson MLE, was proposed recently in the context of image superresolution. These algorithms can be grouped under minimum Kullback-Leibler distance methods (minimum cross-entropy methods) as opposed to the standard least-squares methods. The purpose of this paper is twofold. In the first part we explore a common underlying conceptual similarity in the algorithms, even though they were derived under varying assumptions. In the second part, we empirically evaluate the performance of this class of algorithms via experiments on simulated objects, for the image superresolution problem. One set of experiments examines the data consistency performance of the algorithms. A second set of experiments evaluates the performance on the addition of simple constraints on the estimate.

The extent of bandwidth extrapolation obtainable in a superresolution algorithm depends on the spatial extent of the object. However, in most of the problems encountered in real-world applications, the object is not spatially limited. To circumvent this problem, one can decompose the estimation problem into estimating the smooth background and then incorporating this knowledge to estimate the `sparsely distributed' detailed portion of the object. For example, in astronomical applications, the low photon count background is estimated initially, followed by the binary stars embedded in the background. In this paper we propose an iterative method to implement the two-step estimation technique. Further, we propose a modified version of the Richardson/Lucy algorithm to incorporate this two-step estimation. Some preliminary results on one-dimensional objects for the proposed algorithms are included.

Halftoning (intensity-to-area modulation) is used to implement nonlinear gray-scale transformations in optical information processing and in the graphic arts. Dynamically variable halftoning can be achieved by recording the intensity distribution of cross-line grating diffraction patterns onto a high contrast photosensitive medium. The input image information thus becomes an array of opaque periodic structures whose areas are related to the input image intensity. To achieve a required halftone mapping from intensity to area, we pose an inverse problem: given the area of the periodic structures as a function of input intensity, synthesize an optical system that implements this function. This ill-posed problem is solved using a class of symmetric functions with separable variables.

We describe a class of nonlinear optical field cross-correlation processes capable of producing a high contrast subpicosecond optical gate with long broadband laser pulses. Two of the techniques, coherent anti-Stokes Raman scattering and coherently amplified Raman polarization gating, were used to produce an image of an object hidden behind a strong scattering media. We also demonstrate the capability of three-dimensional imaging using optical gating with the reflected light. The temporal resolution of these techniques is on the order of the inverse bandwidth of the laser.

Assuming that 2D bandlimited functions are always nonfactorizable, one can use this property to separate the product of two bandlimited functions into its respective factors. The contour in C² on which each bandlimited function is zero typically intersects with the real plane at isolated points and the location of these zeros can be used to write a factorizable approximation to the original irreducible complex spectrum. From two differently blurred images, the point zero set from the object's spectrum can be separated from those of the blurring functions by inspection, allowing the object to be reconstructed; examples are given and the importance of this for Fourier phase retrieval is also discussed.

In this paper we consider the blind deconvolution of an image from an unknown blurring function using a technique employing two nested Hopfield neural networks. This iterative method consists of two steps, first estimating the blurring function followed by the use of this function to estimate the original image. The successive inter-linked energy minimizations are found to converge in practice although a convergence proof has not yet been established.

Unconventional imaging techniques obtain high resolution images of objects at very long ranges without the use of large diameter primary optical elements. Cost and weight constraints lead us to consider methods for using sparse arrays of subapertures. In this paper, we present a genetic algorithm method for designing sparse arrays of subapertures for an unconventional imaging technique known as correlography. We have compared the solutions found using genetic algorithms to other techniques for generating arrays with filled autocorrelations. The results of this comparison are presented in this paper.

New mathematical results about extrapolation of an image spectrum yield an efficient algorithm for superresolution in image processing. A significant power resolution is gained with the help of a new nonlinear interpolation method. The principle of this new method is described and illustrated by the treatment of (small) real images.