Image reconstructions from two orthogonal projections

A vector entropy optimization‐based neural network approach is presented to handle image reconstructions from two orthogonal projections. An accurate and parallel reconstruction is attained with this method allowing parallel implementation. This is an attempt to extract the image information from two projections. It is especially meaningful for clinical applications and three‐dimensional modeling of the coronary arteries. © 2003 Wiley Periodicals, Inc. Int J Imaging Syst Technol 13, 141–145, 2003; Published online in Wiley Inter‐Science (www.interscience.wiley.com). DOI 10.1002/ima.10036     

Calculation of tomographic projections

The article suggests a method of calculating tomographic projections.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 50, No. 1, pp. 126–128, January, 1986.     

Synthetic scanner arrays in tomographic reconstructionsfrom fan- and cone-beam projections

A deterministic method for artifact-free reconstruction from truncated sets of fan-beam projections thatextends the artifact-free zone of fan-beam scanners is presented. Truncated partial sets of projectionsare merged into a complete virtual set of projections before reconstruction through synthetic scannerarrays. The reconstruction from the virtual set of projections yields the artifact-free representation ofthe whole object needed for evaluation of its global structure. The extent of the artifact-free zone in reconstructions from cone-beam projections is evaluated. The concept of synthetic linear and circular scanner arrays for reconstruction from truncated sets of projections is extended to cone-beam geometry. It is shown that linear scanner arrays are not directly applicable to cone-beam geometry but yieldreasonable approximations if the partial sets of projections are resorted into a virtual set of wedge-beam projections before reconstruction. The presented solution constitutes a practical and exact det rministic method of horizontally extending the artifact-free zone in cone-beam geometry. The extension of the vertical limits of the artifact-free zone is discussed. The proposed methods provide a practical low-cost approach to artifact-free reconstruction of large objects. Illustrative examples are provided.     

Periodic image artifacts from continuous-tone laser scanners

Continuous-tone images produced by mechanically scanned analog modulated laser beams are susceptible to image artifacts in the form of spatially periodic density variations due to machine errors in film transport velocity, raster scan-line placement, and scan-line intensity. The human eye is particularly sensitive to periodic patterns and, in ideal conditions, can detect peak-to-peak density variations as small as approximately 0.005 for spatial frequencies around 2-5 cycles/deg. The stringent requirements that this implies for the scanner hardware are derived. Particular attention is paid to the rotating polygon-type scanner, since this device currently provides the best combination of speed, image quality, and cost.     

Compression defects in different reconstructions from phase-shifting digital holographic data

Three principal strategies for the compression of phase-shifting digital holograms (interferogram domain-, hologram domain-, and reconstruction domain-based strategies) are reviewed and their effects in the reconstruction domain are investigated. Images of the reconstructions are provided to visually compare the performances of the methods. In addition to single reconstructions the compression effects on different depth reconstructions and reconstructions corresponding to different viewing angles are investigated so that a range of the 3D aspects of the holograms may be considered. Although comparable at low compression rates, it is found that depth and perspective information is degraded in different ways with the different techniques at high compression rates. A hologram of an object with sufficient details at different depths is used so that both parallax and depth effects can be illustrated.     

On geometric phase from pure projections

Abstract

The relation between three recent experiments aimed at demonstrating a strictly geometric phase using pure projections is clarified in the light of a recent claim to such a measurement. The possibility of observing & ± 2π phase jumps in an optical interference experiment is pointed out.     

Gradient-based microstructure reconstructions from distributions using fast Fourier transforms

Reconstructions are an important step in analyzing the statistics of local state distributions in the internal structure of heterogeneous material systems and in estimating their effective properties using deterministic models. In this paper, we demonstrate the use of fast Fourier transforms (FFTs) and gradient-based algorithms for the reconstruction of microstructure realizations from 2-point statistics. The FFT method greatly improves the computational efficiency of the algorithm, facilitating use of the full set of 2-point statistics in the reconstruction. This approach introduces periodic boundary conditions naturally into the model. The reconstruction of several two-phase 2D structures is demonstrated, resulting in exact replicas of the original microstructures. The limitations of the technique, especially for more complex structures, are also discussed.     

Image reconstructions in diffraction tomography from limited transmitted field data sets

Diffraction tomography reconstructions of objects from limited transmitted field data sets are discussed together with theoretical analyses and results of numerical experiments. It is shown that limited data sets, representing only a small part of the complete data sets, can be used for reconstructions in diffraction tomography with satisfactory accuracy. We also find that, in diffraction tomography based on the hybrid filtered backpropagation and the first-Rytov approximation, the use of limited data sets can provide a larger range of validity than the use of complete data sets, the reason being that limited data sets pose less-severe phase-unwrapping problems.     

Removing aperture-induced artifacts from Fourier transform infrared intensity values

Two Fourier transform infrared intensity artifacts have been observed at moderately high (0.1 cm(-1)) spectral resolution: Light reflected off the aperture was double modulated by the interferometer, producing a 2f alias, and the warm (approximately 310 K) annulus of the aperture seen by a cooled detector resulted in distorted line shapes and anomalous intensities in the fingerprint region. Although the second artifact has been alluded to previously, we report corrections to remove both of these anomalies and to demonstrate the efficacy of these corrections. Prior to correction, integrated-band intensities were found to be in error by up to 12%.     

Tomographic image reconstruction from optical projections in light-diffusing media

The recent developments in light generation and detection techniques have opened new possibilities for optical medical imaging, tomography, and diagnosis at tissue penetration depths of ~10 cm. However, because light scattering and diffusion in biological tissue are rather strong, the reconstruction of object images from optical projections needs special attention. We describe a simple reconstruction method for diffuse optical imaging, based on a modified backprojection approach for medical tomography. Specifically, we have modified the standard backprojection method commonly used in x-ray tomographic imaging to include the effects of both the diffusion and the scattering of light and the associated nonlinearities in projection image formation. These modifications are based primarily on the deconvolution of the broadened image by a spatially variant point-spread function that is dependent on the scattering of light in tissue. The spatial dependence of the deconvolution and nonlinearity corrections for the curved propagating ray paths in heterogeneous tissue are handled semiempirically by coordinate transformations. We have applied this method to both theoretical and experimental projections taken by parallel- and fan-beam tomography geometries. The experimental objects were biomedical phantoms with multiple objects, including in vitro animal tissue. The overall results presented demonstrate that image-resolution improvements by nearly an order of magnitude can be obtained. We believe that the tomographic method presented here can provide a basis for rapid, real-time medical monitoring by the use of optical projections. It is expected that such optical tomography techniques can be combined with the optical tissue diagnosis methods based on spectroscopic molecular signatures to result in a versatile optical diagnosis and imaging technology.     

Data from orbiting navigation satellites for tomographic reconstruction

So far, orbiting navigation satellites are the only source for primary data in ionospheric tomography. Phase difference measurements give the input for tomographic reconstruction. Except for a constant, the initial phase difference value, the data can be considered to be the line integral of electron density along the straight line from the satellite to a ground based receiver (“slant electron content”). In ionospheric physics a projection onto the vertical is used: (vertical) electron content (TEC). Many investigations have been based on this quantity alone. This work discusses some of the propeties of the measured data (instrumental and “ionospheric” limitations in section II), and the role of TEC evaluation assumptions (“mean ionospheric height” and initial phase constant, in section III). Some of the problems inherent in ionospheric tomography using orbiting navigation satellites are discussed by means of model calculations (section IV). The models are mathematically defined two-dimensional electron density distributions that are used to calculate the latitude dependence of both slant and vertical TEC. Among others, the model calculations are useful in showing that strongly different electron density distributions can lead to similar electron contents. Tomographic reconstruction would probably not be able to distinguish between the different distributions, which leads to the recommendation to incorporate additional data in the reconstruction process. It is well known, and reflected in the model electron contents, that without additional data tomographic reconstruction is not accurate in height determination. Layer height variations with latitude, however, can have a strong influence on slant and vertical electron content.©1994 John Wiley & Sons Inc     

Neural network approach to image reconstruction from projections

In this article, we formulate the image reconstruction problem in terms of a multicriteria optimization-based neural network model, and study its performance. The value of neural network as a computational device is to be shown. We also demonstrate the efficiency of our implementation of neural net processing and compare its performance with respect to the convolution-backprojection reconstruction techniques based on computer-generated noisy projections. The method presented here has the particular ability to solve ill-posed reconstruction problems. The algorithm described was implemented on a serial PC/Intel 586 microcomputer, but was cast in a form which is ideally suited for parallel processing. © 1998 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 9, 381–387, 1998     

Illumination artifacts in hyper-NA vector imaging

Off-axis polarized monopole illumination is applied to a hyper-numerical-aperture (NA) (NA>1) microscopic system. Illumination artifacts due to vector effects are observed, which are asymmetric and depend on illumination conditions. A model based on rigorous coupled wave theory is used to simulate image profiles for dielectric, semiconductor, and metal gratings with different monopole locations and polarization states. A solid immersion lens microscope is used to image different types of samples including MoSi photomask, patterned silicon wafer, and chrome photomask. The experimental images are in good agreement with simulation results.     

Optical tomographic image reconstruction from ultrafast time-sliced transmission measurements

Optical imaging and localization of objects inside a highly scattering medium, such as a tumor in the breast, is a challenging problem with many practical applications. Conventional imaging methods generally provide only two-dimensional (2-D) images of limited spatial resolution with little diagnostic ability. Here we present an inversion algorithm that uses time-resolved transillumination measurements in the form of a sequence of picosecond-duration intensity patterns of transmitted ultrashort light pulses to reconstruct three-dimensional (3-D) images of an absorbing object located inside a slab of a highly scattering medium. The experimental arrangement used a 3-mm-diameter collimated beam of 800-nm, 150-fs, 1-kHz repetition rate light pulses from a Ti:sapphire laser and amplifier system to illuminate one side of the slab sample. An ultrafast gated intensified camera system that provides a minimum FWHM gate width of 80 ps recorded the 2-D intensity patterns of the light transmitted through the opposite side of the slab. The gate position was varied in steps of 100 ps over a 5-ns range to obtain a sequence of 2-D transmitted light intensity patterns of both less-scattered and multiple-scattered light for image reconstruction. The inversion algorithm is based on the diffusion approximation of the radiative transfer theory for photon transport in a turbid medium. It uses a Green s function perturbative approach under the Rytov approximation and combines a 2-D matrix inversion with a one-dimensional Fourier-transform inversion to achieve speedy 3-D image reconstruction. In addition to the lateral position, the method provides information about the axial position of the object as well, whereas the 2-D reconstruction methods yield only lateral position.     

Peculiarities of the electron diffraction from nanostructured objects in high-symmetry projections

The crystals of M_1−x R_xF_2+x (where M = Ca, Ba, Cd and R is a rare earth element, Ga, or In) are susceptible to phase separation on a nanometer scale (nanostructurization), which determines to a considerable degree the properties of these materials. The patterns of electron diffraction from such nanostructured crystals exhibit reflections corresponding to unknown structural features, but these reflections may completely disappear when the sample is tilted within <1°. It is shown that suppression of the nonmatrix reflections is related to peculiarities of the electron diffraction from such objects rather than to any structural features.     

Ghosts and artifacts in Fourier-transform spectrometry

Ghosts in Fourier-transform spectrometry are important for three reasons: they can give rise to spurious coincidences of frequency differences in spectral analysis, distort the phase correction, and set a limit to the attainable signal-to-noise ratio. The various types of ghost, originating from amplitude modulation, phase modulation, and intermodulation, are described and discussed, together with some hardware and software artifacts. Recipes are given for identifying these features and, where possible, avoiding harmful effects from them.     

Truncation error in mesh‐free particle methods

A truncation error analysis has been developed for the approximation of spatial derivatives in smoothed particle hydrodynamics (SPH) and related first‐order consistent methods such as the first‐order form of the reproducing kernel particle method. Error is shown to depend on both the smoothing length h and the ratio of particle spacing to smoothing length, Δx/h. For uniformly spaced particles in one dimension, analysis shows that as h is reduced while maintaining constant Δx/h, error decays as h² until a limiting discretization error is reached, which is independent of h. If Δx/h is reduced while maintaining constant h (i.e. if the number of neighbours per particle is increased), error decreases at a rate which depends on the kernel function's smoothness. When particles are distributed non‐uniformly, error can grow as h is reduced with constant Δx/h. First‐order consistent methods are shown to remove this divergent behaviour. Numerical experiments confirm the theoretical analysis for one dimension, and indicate that the main results are also true in three dimensions. This investigation highlights the complexity of error behaviour in SPH, and shows that the roles of both h and Δx/h must be considered when choosing particle distributions and smoothing lengths. Copyright © 2005 John Wiley & Sons, Ltd.     

Reduction of polarization-induced artifacts in grating-based spectrometers

An optical device that converts unpolarized light into a single polarization state is described. The device is based on a polarizing beam splitter that separates the two polarization directions. The beam splitter is combined with two pairs of equilateral prisms that are used to collimate the two beams in terms of both propagation and polarization directions. When it is used in combination with a blazed diffraction grating, this device is shown to effectively remove the polarization dependence of the first-order diffracted power. The device has an insertion loss of approximately 14% for purely s-polarized light. However, for unpolarized light incident upon the two gratings studied here, the increased throughput of the p-polarized component leads to an average relative gain in overall efficiency of 13%-19%, depending on the grating. In collimating the two polarization directions, the device may cause a reduction in spectral resolution for a rectangular entrance slit. As a result, the device is more likely to find use in spectrometers that have a circular aperture, such as that provided by an optical fiber.     

Resolution enhancement in computerized tomographic imaging

We consider the problem of reconstructing an object function f(r) from finitely many linear functional values. In our main application, the function f(r) is a tomographic image, and the data are integrals of f(r) along thin strips. Because the data are limited, resolution can be enhanced through the inclusion of prior knowledge. One way to do that, a generalization of the prior discrete Fourier transform (PDFT) method, was suggested in 1982 [SIAM J. Appl. Math.42,933 (1982)] but was found to be difficult to implement for the tomography problem, and that application was not pursued. Recent advances in approximating the PDFT make it possible to achieve the desired resolution enhancement in an easily implemented procedure.