The high resolution in synthetic aperture radar (SAR) systems is reduced by the speckle appearing in the images. This speckle noise is generated by the coherent processing of radar signals and exists in all types of coherent imaging systems. We study the statistical properties of speckle noise in a four-look SEAS AT SAR image to show evidence of correlation between underlying looks resulting in correlated values for adjacent pixels in the final image. Concentrating on homogeneous areas of the image, experimental determination of the SNR and of the probability density of the recorded intensity is performed. It is shown that the intensity fluctuations due to speckle noise in homogeneous areas are not gamma distributed. A model incorporating the empirical correlation coefficient is extracted from experimental data.

The presence of speckle in Synthetic Aperture Radar (SAR) images makes segmentation of such images difficult either by gray levels or by texture. A natural way to segment an image by gray level is to select thresholds at the valleys of its multi-modal histogram if it exists. This paper will investigate the existence of histogram valleys in SAR images, the classification errors and devise a procedure for multi-level thresholding of SAR images.

The L-band synthetic aperture radar (SAR) aboard the space shuttle Challenger succeeded in imaging the surface wave field produced by Hurricane Josephine. A fresh wind sea travelling across the SAR ground track was recorded approximately 100 kilometers from the storm center under the influence of a large ocean swell generated approximately 20 hours earlier when hurricane winds were at their maximum intensity. Such a dynamic sea state accentuates the role of specular reflection by surface facets in the SAR imaging process and serves as a unique test of the Doppler clutterlock and autofocus algorithms employed by ground scene correlators. Along track image resolution is defined in terms of the average number of specular facets per meter and a random number of specular events per radar cell. Speckle correlation statistics computed from Shuttle Imaging Radar scenes of the hurricane are used to approximate the dynamic wavenumber response of the SAR instrument. Observations of exponential trends in two-dimensional autocorrelations of speckled image data support an equilibrium theory model of sea surface hydrodynamics. The concepts of correlated specular reflection, surface coherence, optimal Doppler parameterization and spatial resolution are discussed within the context of a Poisson-Rayleigh statistical model of the SAR imaging process.

The correlation time of each Doppler or cross-range resolution cell of a rotating target is derived as the time duration required for the surface roughness elements within the illuminated cell to rotate out of it. Thus, for a fully range-resolved rotating target, each Doppler resolution cell has its associated cross section and correlation time. However, the effective speckle correlation time of the target is weighted towards an effective average over the correlation times of the dominant scattering elements.

Researchers have shown that aberrations in incoherent optical systems can be corrected through the use of an image-sharpness criterion [1]. An analogous image-sharpness criterion is defined for the case of speckled imagery derived from coherent imaging of diffuse objects. By appealing to a multiplicative noise model we show that this speckled-image sharpness criterion is a random variable with an expected value proportional to the sharpness criterion for the associated incoherent image. Thus, aberration correction can be accomplished by maximizing the speckled-image sharpness criterion. A variety of computer simulation experiments designed to test the performance of the image-sharpness criterion applied to speckled imagery are presented. These experiments model the problem of imaging moving targets with synthetic aperture radar (SAR). Target motion introduces one-dimensional (azimuthal) phase aberrations in SAR Fourier data producing a one-dimensional blur in the image. These aberrations can be represented as a linear sum of orthogonal polynomials and the coefficients of such a representation serve as optimization parameters. The sharpness criterion is maximized with respect to the aberration parameters through the use of a conjugate-gradient algorithm. The problem of entrapment by local minima can be overcome by using multiple initial estimates. We demonstrate that quadratic, cubic, and quartic polynomial coefficients are successfully sensed through this technique. The method is shown to succeed for both extended images and point-like images that more closely resemble SAR images of cultural targets.

We investigate the way errors arise in photon-limited, coherent imaging systems and how such errors fundamentally limit the quality of images formed. To reflect the best possible imaging performance with a given optical system, we utilize a continuous detection model to describe the operation of the image recording mechanism, where the image plane camera records the exact x- and y-position of each photoevent produced by the detected coherent field intensity. Using this continuous detection model and well-known statistical properties of laser-speckle patterns, we compute the signal-to-noise ratio of the complex Fourier amplitudes estimated by the detected coherent image. We explore physical insights provided by this expression and illustrate key points with the help of computer-simulated coherent imagery.

The averaged speckled images of coherently illuminated objects consisting of a diffuser in contact with a transparency are analysed taking into account the structure of theaffuser. Averaged images for sinusoidal amplitude gratings are calculated for both, strong and weak phase diffusers. For strong diffusers the mode of image formation is in general a partially coherent one, and departures from linearity become important when the correlation areas of the diffuser and of the resolution cell are comparable. For weak diffusers the resulting average image can be expressed mathematically as the incoherent sum of two images: one formed in a coherent mode and due to the direct component, and another one produced in a partially coherent mode and due to the diffuse component.

In this paper we report on research concerning triple correlation of laser speckle patterns produced by illuminating a distant rough object with coherent light. Triple correlation of these speckle patterns is known to contain Fourier phase information. In our work the Fourier phase of an object is extracted by treating the phase triplet in the factorized form of the triple correlation as a binary quantity. The Fourier phase along with the Fourier magnitude, obtained by second order correlation, yields an image via inverse transformation.

Imaging correlography is a technique for obtaining images of laser illuminated objects. The results of a laboratory experiment and a corresponding computer simulation of the imaging technique are presented in this paper. Power spectrum estimates for an imaging target, obtained both in the laboratory and through simulation, are compared with the true spectrum of the target. Differences between the laboratory and simulation results are also discussed. A, theoretical expression for the signal�to�noise ratio (SNR) of the power spectrum estimate applicable to our implementation of the imaging correlography technique is considered. It is illustrated that the SNR expression provides a reasonable means for estimating the recoverable spatial frequency content of a simple target.

The problem of reconstructing a signal or image from a finite number of spectral data is the problem of finding an optimal approximation to one function by another. We describe here methods for signal recovery and phase retrieval based on the theory of best approximation in weighted Hilbert spaces 1. These methods have been under development for some time for use in a variety of 1-D and 2-D spectral estimation problems. A new interpretation of these methods will be discussed based on the close analogy between the reconstruction of a non-negative function from finitely many values of its Fourier transform, and the design of approximate Wiener filters2. We also describe the relationship between these methods and other spectral estimation procedures. The Wiener filter produces as an output an estimate of a signal when presented with an input of signal plus noise. Its design, under restrictions of limited data, gives a clear picture of the role of the prior estimate for both linear and non-linear signal recovery procedures, and the significance of this is discussed.

The ideal observer signal-to-noise ratio is used to derive the multiplex penalty associated with line-integral-projection imaging modalities. This penalty explains the high exposures required in computed tomography. The same multiplexing phenomenon applies to diffraction tomography--the radiofrequency inverse problem, or holography of semi-transparent objects. For the planar case the multiplex penalty enters to the second power, i.e., it is an areal penalty. We show that the approach of compound B-scanning--which avoids multiplexing by conventional ranging--remains quite competitive in the face of the more general tomographic approach.

Recent studies by others in maximum-likelihood (ML) image restoration have shown the feasibility of restoring positron-emission tomography images to a point beyond the classical limitation in resolution. These results have prompted a parallel study reported herein to determine if a similar method might provide superresolving image-restoration in quantum-photon limited noncoherent imaging systems. The challenge posed in this study is that of restoring Fourier components in the image that have been removed by the optical system. For clarity we summarize in this paper the derivation of the ML-based algorithm, which is an adaptation of the developments in 1,2. Computer simulations are presented which show the feasibility of superresolution and the property of restoring missing Fourier components. Also shown are the results of a preliminary experiment of restoring the image from a defocused camera. Several potential applications that fit this model include fluorescence microscopy, astronomical imaging and infrared imaging.

The operation of a novel radio interferometer is described and then analyzed using coherence theory techniques.

A derivation of the temporal spectrum a the far zone field diffracted by a uniformly translating planar aperture in front of a quasimonochromatic, temporally stationary, spatially homogeneous, incoherent, primary source is performed and numerical examples are provided. It is shown that the diffracted field spectrum can be expressed as the convolution of the spectrum of the source with a "modulating spectrum" determined by the shape and velocity of the aperture, as well as the direction of observation in the far zone.

A new method for modulating spectra by correlating source fluctuations is discussed. Potential advantages and limitations of this method are considered for both scalar and electromagnetic sources.

The mutual intensity of the optical field in the Fraunhofer diffraction region from the end of an optical fiber is analyzed theoretically by using a fiber-end source model. Tn this source model, the optical field at the end of the fiber is expressed as a sum of independent plane waves with random directions and phases since the guided modes propagating through an optical fiber may be regarded as a stochastic process. It is found that the spatial coherence property of the optical field in the diffraction region is not homogeneous but quasihomogeneous in a statistical sense. This property is discussed in connection with the V number of the fiber and in comparison with that of the optical field, obeying the van Cittert-Zernike theorem, produced by the incoherent source.

We discuss fast numerical calculation of the radiation patterns produced by sources of arbitrary states of spatial coherence, and report on experimental results that verify predictions of generalized radiometry. Examples considered include evaluation of the effects of obstructions and aberrations on far-field diffraction patterns of gaussian-correlated sources.

Two-stage template matching using quantum-limited images is investigated. A high-light-level input scene is searched using a small window function that is moved to various offsets within the input scene. The cross-correlation between the reference function and the input scene at a given offset is estimated by sampling the input scene using a small number of detected photoevents. The photon-limited correlation signal is used as a similarity criterion for comparing the input with the reference function. In the first stage, a small number of detected photoevents is used to find probable locations for the reference function. In the second stage, likely locations are examined using a sufficient number of detected photoevents to provide a recognition decision within a specified error. Results are presented for a simple inspection problem, and for scene matching in a satellite image.

We discuss the importance of the temporal fluctuation of images viewed through atmospheric turbulence in the determination of their spatial correlation functions. If the basic data is considered to be divided into time-frames, then the temporal characteristics simply determine the exposure or integration time per frame. However, it is more fundamental and better from the point of view of signal-to-noise ratio to treat the data as a set of photon coordinates in space and time. For either approach, the temporal correlation function of the image intensity is of great importance and new measurements of this quantity and its wavelength dependence recorded at La Palma, Canary Islands are given.

Three different pinholes are imaged onto the microchannel-plate imaging detector to observe the dependence of the dead-time effects on the size of the area of illumination. The independent paralyzable-counter model is used to compare with experimental results. It is seen that the dead time increases rapidly as the area of illumination increases. This indicates that the coupling between channels in the microchannel plate is rather important. Therefore a model which assumes that the whole detector behaves as a single paralyzable counter is also examined. Both models give good agreement with the experimental mean, however they do not fit well with experimental values obtained for the variance of photocounts except for low count rates.

Measurements of the temporal correlation of both co- and cross-polarised returns around the enhanced backscat-tering cone of a dense collection of latex spheres are presented. The correlation time shows completely different variation with angle in the two cases and an explanation of this is given. The photon statistics have also been measured for co- and cross-polarised intensities. The normalised factorial moments of the photon counts (which equal to normalised intensity moments) are independent of angle (for angle within 15mrad of backscatter) and detecting polarisations, and they are in agreement with those derived from gamma intensity distribution with the descriptive parameter u=1.20.

We study the speckle contrast produced by gamma-distributed diffusers in the far field as a function of the point of observation, the number of uncorrelated areas illuminated, and the statistics of the diffuser. It is found that the speckle contrast and the strength of the specular component are extremely sensitive to the detailed form of the probability density function of the phase variations introduced by the diffuser. This makes it difficult to infere roughness related parameters from measurements of these quantities.

The infrared imager currently in use at the National Optical Astronomy Observatories (NOAO) has been adapted for use as a two-dimensional infrared speckle camera operating at wavelengths of 1μm 5μm. Data have been obtained at the Kitt Peak National Observatory (KPNO) Mayall telescope (effective aperture ti 3.8m) for a number of different sources. Diffraction-limited images are presented for two objects, the "Red Rectangle" and NML Cygnus, using the Knox-Thompson algorithm to recover the Fourier phases. A comparison of phase-relaxation techniques applied to the integrated phase differences is presented using both the Hudgin method and successive over-relaxation.

A new wavefront sensing method based on local wavefront curvature measurements rather than tilt measurements is investigated. Performances are compared to that of a Shack-Hartmann sensor. Examples of experimentally reconstructed wavefronts are presented and several applications are discussed.

A method using the speckle contrast for the determination of both the roughness and the correlation length of surface height variations of a rough surface object is studied on the basis of the statistical properties of the Gaussian speckle field in the diffraction region. The speckle contrast is theoretically derived as a function of the illuminating condition for the object and the surface parameters of the object. It is found that the roughness depends almost only on the ratio of the two speckle contrasts obtained under the two different illuminating conditions for the object. By solving the equations expressing these two speckle contrasts, it is also found that an unique solution exists for the roughness and the correlation length. Therefore, the correlation length can also be determined from the two speckle contrasts. Experiments are performed to verify the present method. This method has an advantage of the simplicity in a measuring procedure where only two speckle contrasts are required to determine the surface parameters.

This paper reports the experimental study on the velocity dependence of dynamic speckles produced by diffuse plates in layers. The experiments were performed to measure the auto-correlation functions of speckle intensity fluctuation detected in the image plane, mainly in the reflection and briefly in the transmission optical systems. The results show that the linear velocity dependence of speckle movements is usually obtained although the non-linear velocity dependence and the saturation tendency are found in the specific diffusing condition in the reflection optical system. These phenomena do not occur in the transmission optical system.

The S11 light scattering matrix element is a measurement of the total intensity of light scattered into a particular direction as a function of scattering angle. The S11 matrix element is peaked in the forward (specula') direction. Changes in the shape of the S11 curve may be used to detect the presence of micron-sized surface cracks in metals stretched beyond their elastic limit prior to failure. Shape changes are quantitatively monitored by studying changes in the kurtosis, or "flatness', of the Sii curve.