We have investigated seasonal turbulence variation with altitude above the Siding Spring Observatory using the 24" telescope facility and interchangeable SCIDAR (Scintillation Detection and Ranging) and SLODAR (Slope Detection and Ranging) techniques. The latter proposed by Wilson triangulates the correlations through image motion of and between images of binary stars when imaged through multiple sub-pupils in a Shack-Hartmann configuration, so to determine the C²_N(h) profile as a function of height above the telescope, and temporal evolution from subsequent short exposure, fast frame rate images. The simplicity of SLODAR pertains to the lack of restriction in coherence or fringe visibility (scintillation index) that underlies the SCIDAR technique, and that the available light is divided into N sub-pupils to be condensed to speckle star images, rather than spread across the full imaging array. However, with the like of f18 telescope being reduced in each sub-pupil to f60, using a 1-4 ms exposure intensified imager, we are still limited to magnitude 5-7 star pairs, of which there are precious few, and their associated angular separations limit the altitude resolution of the technique accordingly. To overcome some of these restrictions we have obtained data, and propose methods to process such, using the Galilean satellites of Jupiter (each mag 5-6), which change separation over the observing cluster of nights, and hence offer a changeable altitude sampling. These are unresolvable in the sub-pupil imaging system, but suffer less from the speckling effects of a scintillated point source. We present results to reinforce these premises.

Obtaining a high-resolution image of an object or scene from a long distance away can be very problematic, even with the best optical system. This is because atmospheric blurring and distortion will limit the resolution and contrast of high-resolution imaging systems with substantial sized apertures over horizontal and slant paths. Much of the horizontal and slant-path surveillance imagery we have previously collected and successfully enhanced has been collected at visible wavelengths where atmospheric effects are the strongest. Imaging at longer wavelengths has the benefit of seeing through obscurants or even at night, but even though the atmospheric effects are noticeably reduced, they are nevertheless present, especially near the ground. This paper will describe our recent work on enhanced infrared (IR) surveillance using bispectral speckle imaging. Bispectral speckle imaging in this context is an image post-processing algorithm that aims to solve the atmospheric blurring and distortion problem of imaging through horizontal or slant path turbulence. A review of the algorithm as well as descriptions of the IR camera and optical systems used in our data collections will be given. Examples of horizontal and slant-path imagery before and after speckle processing will also be presented to demonstrate the resolution improvement gained by the processing. Comparisons of IR imagery to visible wavelength imagery of the same target under the same conditions will be shown to demonstrate the tradeoffs of going to longer wavelengths.

When imaging through the atmosphere, the resulting image contains not only the desired scene, but also the adverse effects of all the turbulent air mass between the camera and the scene. These effects are viewed as a combination of non-uniform blurring and random shifting of each point in the received short-exposure image. Corrections for both aspects of this combined distortion have been tackled reasonably successfully by previous efforts. A potentially more robust method of restoring the geometry is presented, which is also better suited to real-time implementation. The improvements were achieved by replacing the concept of prototype frame with the sequential registration of each frame with its nearest neighbour and the accurate accumulation of shiftmaps from any one frame to another without redundant calculations.

Diffraction tomography (DT) is an established imaging technique for use with diffracting wavefields, which represents a generalized form of x-ray tomography. In this work, we revisit the three-dimensional reconstruction problem of DT for variable density acoustic media. Novel reconstruction algorithms are developed for reconstructing separate images that depict a weakly scattering object's compressibility and density variations. If tomographic measurement data are acquired at four distinct temporal frequencies, we demonstrate that the effects of object dispersion can be accounted for completely by use of analytic reconstruction formulas. Computer-simulation studies are conducted to demonstrate the developed image reconstruction methods.

Laguerre-Gaussian beams are considered as basis functions for inverse scattering applications. First order perturbation theory is applied to paraxial higher order Gaussian beams. Information about the scattering potential is deduced from the coupling coefficients between otherwise orthogonal modes. This leads to a theoretical description analogous to plane wave diffraction tomography. Differences between the plane wave model and the Laguerre-Gauss formalism highlight both limitations as well as opportunities for applying singular Gaussian beams to the inverse scattering problems. The perturbation analysis is applied to a number of examples illustrating how information about the scattering object can be deduced from measurements of the scattered paraxial field.

In the cryo-EM tomography, the projection and back-projection are essential steps in reconstruction the 3D structure of the virus and macromolecules. Distance driven method (DD) is the latest projection /backprojection algorithm originally employed for x-ray computed tomography. This paper is mainly concerned about employing this algorithm to the cryo-EM tomography for reconstruction performance improvement. Existing algorithms used in cryo-EM are pixel-driven and ray driven projection/backprojection, etc. These methods are generally quite time consuming because of their high computational complexity. Furthermore, interpolation artifacts are usually noticeable when the sufficient view and detector samples are not available. The DD is originally proposed to overcome these drawbacks. The interpolation process in DD is done by calculating the overlap area between the detector and pixel boundaries. This procedure largely removes the interpolation artifacts, and reduces the computational complexity significantly. Furthermore, it guarantees that the projection and backprojection are adjoint to each other - a desired property to guarantee the convergence of the iterative reconstruction algorithm. However, unlike the x-ray computed tomography, the cryo-EM tomography problem generally has limited number of the projections, and projection angles are randomly distributed over 4pi steradian. Therefore, the conventional DD should be modified. Rather than computing the boundary overlap in the previous 3-D DD method, we propose a novel DD algorithm based on volume overlap. CCMV virus model is used as testing example. Results are visualized using AMIRA software. Analysis is made upon the advantages and drawbacks of both the existing approaches and distance driven method.

Intensity diffraction tomography (I-DT) is an imaging method that reconstructs the complex-valued refractive index distribution of a weakly scattering object without explicit knowledge of the wavefield phase. In this work, a novel scanning protocol for I-DT is proposed that involves the use of plane-wave and spherical wave probing wavefields. A useful feature of the scanning protocol is that two in-line intensity measurements are acquired on a detector-plane whose distance from the object remains fixed. Accordingly, the translation of the detector that is required in classic in-line measurement geometries is avoided. A reconstruction algorithm that exploits tomographic symmetries is developed and demonstrated by use of computer-simulation studies.

Patient motion during magnetic resonance imaging (MRI) can produce significant artifacts in a reconstructed image. Since measurements are made in the spatial frequency domain ('k-space'), rigid-body translational motion results in phase errors in the data samples while rotation causes location errors. A method is presented to detect and correct these errors via a modified sampling strategy, thereby achieving more accurate image reconstruction. The strategy involves sampling vertical and horizontal strips alternately in k-space and employs phase correlation within the overlapping segments to estimate translational motion. An extension, also based on correlation, is employed to estimate rotational motion. Results from simulations with computer-generated phantoms suggest that the algorithm is robust up to realistic noise levels. The work is being extended to physical phantoms. Provided that a reference image is available and the object is of limited extent, it is shown that a measure related to the amount of energy outside the support can be used to objectively compare the severity of motion-induced artifacts.

A method is described for reconstructing images from incomplete data sets if subsets of the data are obtained with different data acquisition systems. The proposed method is able to incorporate prior information about the object into the reconstruction process. The general scheme is applied to construct improved images from multiple low resolution frames of the same scene, where each frame is obtained with an imaging system characterized by a different response function. The working principle is demonstrated with synthetic data for a set of generic imaging systems. Additional attention is given to the potential of the inherent superresolution capabilities of this method in the context of compressed image representations.

Extended interpolatory approximation is discussed for some classes of n-dimensional vector signals. Firstly, we present two sufficient conditions of the optimum approximation and prove that the proposed optimum approximation using fixed finite number of sample values satisfies these two conditions. Secondly, we discuss the optimum running approximation of n-dimensional time-limited vector signals based on a certain one-to-one correspondence between a vector signal and the corresponding vector error signal of approximation. The proposed optimum approximation has the minimum measure of error among almost all the linear and the nonlinear approximations using the same measure of error and generalized sample values. Note that the proposed optimum approximation can be realized by flexible FIR filter bank. The term "flexible" means that we can widely choose the number of paths and frequency response of time-invariant FIR analysis filters. Moreover, we can use sample points that are distributed on an arbitrary periodical pattern.

The size and shape of the stones in dry gravel river beds are of interest in geology and river hydraulics. The topography of a bed surface can be measured by three-dimensional laser scanning. A method is described for fitting ellipsoids to the surfaces of individual stones to estimate their size, shape and orientation in the river bed. Different cost functions are evaluated and the methods are applied to data from a gravel river bed in the South Island of New Zealand.

Frontal chest radiographs ("chest X-rays") are routinely used by medical personnel to assess patients for a wide range of suspected disorders. Often large numbers of images need to be analyzed. Furthermore, at times the images need to analyzed ("reported") when no radiological expert is available. A system which enhances the images in such a way that abnormalities are more obvious is likely to reduce the chance that an abnormality goes unnoticed. The authors previously reported the use of principal components analysis to derive a basis set of eigenimages from a training set made up of images from normal subjects. The work is here extended to investigate how best to emphasize the abnormalities in chest radiographs. Results are also reported for various forms of image normalizing transformations used in performing the eigenimage processing.

Myosin filaments are important components of striated muscle and pack in a semi-ordered, two-dimensional array. The array can be imaged by electron microscopy of thin cross-sections which indicates, for many species, that the filaments adopt two orientations that are distributed with short-ranging order. We describe analysis and modelling of this substitution disorder based on the micrographs and an Ising model.

Phase retrieval has seen a resurgence of interest in the last ten years as a result of some serendipitous developments in instrumentation (high flux x-ray sources) for molecular and nano-particle imaging. This has led to new applications, new formulations of iterative phase retrieval algorithms, and some new algorithms. These new developments are reviewed.

X-ray coherent diffractive imaging is attracting interest within the x-ray community because it promises wavelength-limited resolution for imaging nonperiodic objects. It is well known that a wave diffracted or scattered by an object can be described simply by the Fourier transform of the object's electron density distribution. However, this result is general only in the so-called far-field regime, where most practical work is done. In the near-field regime, evaluations of wave field amplitudes become more complicated, and Fresnel diffraction and imaging effects have to be taken into account. In this paper, we present an algorithm that can be used to reconstruct an object from a near-field diffraction pattern. The algorithm uses the concept of a 'phase-chirped' distorted object, where a Fresnel-zone construction is embedded on an original object. This algorithm can eliminate the twin image ambiguity in phase retrieval and will therefore improve the convergence of retrieval. Our algorithm is a unified algorithm, consistent with those used in far-field experiments. Our algorithm extends the applicability of Fourier-based iterative phasing algorithms that are already established for far-field diffraction into the near-field holographic regime where phase retrieval has traditionally been difficult.

We have developed a test method using parametric phase retrieval to estimate the wavefront of a cryogenic infrared spectrometer. The phase retrieval algorithm accounts for optical system obscurations, apodization, noisy detector pixels, polychromatic sources, and spectrometer dispersion. This tool was used in establishing the optimal alignment and focus for a two channel infrared spectrometer operating in a cryogenic environment. This paper provides an overview of the technique and test implementation.

Multiple scattering imposes severe challenges for inverse scattering and inverse synthesis applications. We have been pursuing a relatively simple nonlinear filtering technique that could provide an estimate of the scattering structure from scattered far-field data. This cepstral filtering method assumes that one can obtain an estimate of the secondary source distribution and that under certain conditions this is well approximated by a product of the scattering potential and terms representing the total internal field. Preprocessing of this estimated function can render it a minimum phase function, and its logarithm is then well behaved and amenable to spectral filtering that allows an estimate of the scattering potential to be obtained. We have applied this to real and simulated scattering data with some success. The deliberate manipulation of scattered field data mapped into in reciprocal or k-space allows one to define certain scattering characteristics at specific wavenumbers and scattering angles. Inversion of these data using the inversion method described generates a possible structure that exhibits these properties in practice. We show some examples of this and consider its usefulness for the design of rough surfaces with prescribed optical properties.

Sinogram truncation is a common problem in tomographic reconstruction. Authors expand their previously published method of sinogram extension using decomposition into sinogram curves by using the adaptive convex filter. The main idea is to estimate the truncated parts of the projections of some object or patient using measured projections at different projection angles. This technique provides good estimation of the missing data near the edge of truncation. However, it is hard to estimate the outer edges of the truncated sinogram; in other words, the outer edge of the sinogram, and, consequently, reconstructed object, is invisible. To overcome this problem we introduce the adaptive convex filter that rounds off the outer portions of the extended sinogram, which tend to have a form of peak directed outwards. Here we assume that the truncated part of the reconstructed object has a round or elliptic shape, which holds with most clinical applications. The method automatically adjusts to the size of the truncated object, whether it is an arm or a part of torso.

Intensity diffraction tomography (I-DT) is an in-line holographic imaging method for reconstructing the three-dimensional complex refractive index distribution of a weakly scattering object. Because it circumvents the phase retrieval problem of diffraction tomography, I-DT reconstruction methods may benefit a range of imaging problems involving optical and coherent X-ray radiation. In this work, we investigate the use of statistically complementary data, provided by multiple (> 2) in-line intensity measurements, for effective suppression of image noise in I-DT. The noise properties of the reconstructed images are demonstrated to depend strongly on the specification of measurement geometry. The effects of experimental uncertainties on the performance of I-DT is investigated also. Computer-simulation studies that are representative of a tomographic microscopy implementation of I-DT are presented.

The Wigner distribution function is used to display data obtained from a bistatic radar imaging setup. In particular, a scheme is developed to exploit the properties of the Wigner function for subsurface detection. Based on heuristic considerations it is argued that in the Wigner domain a separation of surface scattering and target signal is possible depending on the properties of the respective local plane wave spectra. An intuitive understanding of the phase space approach is developed from the case of a point target located underneath a planar dielectric interface. In addition, data based on rigorous computations of rough surface scattering are used to validate the method.