Showing papers on "Point spread function published in 1984"

Characterization of the veiling glare PSF in x-ray image intensified fluoroscopy

Abstract: A theoretical derivation for the point spread function (PSF) which describes the veiling glare in x-ray image intensifiers (II) is presented. The PSF is dependent on two parameters which can be determined experimentally for a given II. An experimental investigation of the linearity of veiling glare phenomenon is undertaken. The experimental results indicate that veiling glare could be described as a linear process to a high degree of accuracy.

Depth Transfer by an Imaging System

Abstract: In many applications such as three-dimensional (3-D) data acquisition, the scanning of 3-D objects or 3-D display, it is necessary to understand how an imaging system can be used to obtain information on the structure of an object in the direction perpendicular to the image plane, i.e. depth information. In certain cases the formation of a 3-D image can be described by a theory based on optical transfer functions (OTF): the image intensity distribution is given by the 3-D convolution of the object and a 3-D point spread function (PSF); equivalently, in 3-D Fourier space the image spectrum is the product of the object spectrum and a 3-D OTF. This paper investigates the 3-D PSFs and OTFs that are associated with different pupil functions of the imaging system.

Image gathering and processing for enhanced resolution

Abstract: Traditional approaches to optical resolution enhancement have involved either the design of appropriate image-formation systems or some type of postprocessing of an image that has already been formed. Results presented in this paper suggest that improved images can be obtained if the image-gathering system is designed specifically to enhance the performance of the image-restoration algorithm to be used. We consider a class of problems in which the total available spatial bandwidth is fixed but the location of this bandwidth along the spatial-frequency axis is to some extent under our control. For example, we might consider either a low-pass system or a bandpass system of the same total bandwidth. We show that system performance can be substantially improved by proper allocation of the available bandwidth in the spatial-frequency domain. The optimum allocation is shown to be a function of the signal-to-noise ratio. We also describe coherent and incoherent optical image-gathering systems that can achieve the desired spatial-frequency passbands.

Multiple scattering effects in spatial frequency filtering

Abstract: The existing theory of imaging through an aerosol medium based on the small-angle approximation to radiative transfer is extended to the general case of multiple scattering with an arbitrary degree of anisotropy. By applying the discrete-ordinates finite-element radiation transport code twotran, we compute the modulation transfer function for a medium characterized by optical depth, single-scattering albedo, and asymmetry parameter. To partially suppress the ray effect in the discrete-ordinates solution to the transfer equation, the first-collision source approach is employed. The results of our modeling which apply to the case of incoherent imaging indicate a strong dependence on the angular divergence of an isotropic source of radiation. Distinctions between the coherent and incoherent illumination cases are stressed, and the earlier small-angle approximation results are rederived.

Resolution enhancement and zoom

Abstract: The resolution is enhanced first by effectively decreasing the scan angle subtended between adjacent samples significantly below that of the Rayleigh limit to obtain an image blurred by the point spread function (or diffraction pattern) of the aperture. The next step is to process this blurred image at least to partially remove the blur. The unblurring process consists of correlating each small segment of the blurred image with blurred images of preconstructed image primitives and then synthesizing a new image comprising a mosaic of spatially correlated original (unblurred ) primitives. The blurred images of the primitives are obtained from a complete set of image primitives comprising, ideally, all possible unblurred primitive shapes. These primitives are then blurred by convolution with the point spread function of the aperture of the imager.

Resolution enhancement and zoom by degradation estimates.

Abstract: The resolution is enhanced by first effectively decreasing the scan angle subtended between adjacent samples significantly below that of the Rayleigh limit to obtain an image blurred by the point spread function (or diffraction pattern) of the aperture. The next step is to process this blurred image to at least partially remove the blur. The unblurring process consists of convolving this finely sampled blurred image with a specially designed convolution mask. This mask effectively outputs an enhanced pixel at each step of the convolution. The mask simultaneously performs the equivalent of the following operations: 1) blur the image again; 2) subtract this reblurred image from the original image to form degradation estimates; and 3) add the estimates of the losses back into the original image.

Topics in the two-dimensional sampling and reconstruction of images

Abstract: Mathematical analysis of image sampling and interpolative reconstruction is summarized and extended to two dimensions for application to data acquired from satellite sensors such as the Thematic mapper and SPOT. It is shown that sample-scene phase influences the reconstruction of sampled images, adds a considerable blur to the average system point spread function, and decreases the average system modulation transfer function. It is also determined that the parametric bicubic interpolator with alpha = -0.5 is more radiometrically accurate than the conventional bicubic interpolator with alpha = -1, and this at no additional cost. Finally, the parametric bicubic interpolator is found to be suitable for adaptive implementation by relating the alpha parameter to the local frequency content of an image.

Germanium-Scintillation Camera Coincidence Detection Studies for Imaging Single Photon Emitters

Abstract: A prototype system has been used to measure the point spread function (PSF) and sensitivity characteristics of a germanium-scintillation camera (GSC) system for imaging single photon emitters. A detector consisting of two 5mm × 5mm × 6 mm elements, fabricated on a single piece of high purity germanium, and a Pho/gamma HP scintillation camera were used. Experiments were conducted with a point source of Tc-99m to specify the threshold and energy resolution required in the germanium detector and to study the timing characteristics of coincidence detection.

Reconstruction of an object from its coded image and object constraints.

Abstract: In coded-aperture imaging, a technique useful in nuclear medicine, a coded image of dimensionality one less than that of the object is recorded. It is possible to obtain a crude reconstruction of the object with the use of a form of correlation decoding of the coded image, but to date these methods have been unsatisfactory. We present an iterative reconstruction algorithm that makes use of a priori knowledge of object border and object postivity. Reconstructions obtained in simulations are consistent with the constraints and coded image and are surprisingly accurate in light of the extensive information loss involved in the image-formation process.

Nonstationary image-plane speckle statistics

Abstract: The properties of the image of a nonuniform transparency degraded by speckle noise are studied. Attention is focused on the spatial details of an object that cannot be resolved by a coherent system. Analysis of the power spectrum of the noisy spatial-intensity distribution in the image plane confirms that the bandwidth for coherent diffuse illumination corresponds to the incoherent transfer function of the system. Experimental verification is presented using a Ronchi ruling as a test object.

Wiener Filtering For Deconvolution Of Geometric Artifacts In Limited-View Image Reconstruction

Abstract: Computed Tomography (CT) images reconstructed using a limited number of projections, measured over a narrow angle range, are characterized by approximately elliptical distortion along the view angles used, and poor contrast at angles not used. This systematic geometric distortion is caused by the two dimensional point spread function of the reconstruction process. In this paper, we show that such geometric distortion and other artifacts introduced in the reconstruction process can be reduced substantially by deconvolution performed via Wiener filtering using a priori knowledge derived from the given projections. The two-dimensional system transfer function used in the deconvolution is obtained from the reconstruction of a test image by a linear reconstruction algorithm (unconstrained multiplicative Algebraic Reconstuction Technique).

Resolution and contrast in confocal optical scanning microscopes

Abstract: A theoretical study is made of a simple method of obstructing an amplitude pupil which results in improved microscope resolution with only a little degradation of the image contrast. Using a confocal scanning optical microscope the resultant point spread function is calculated, from which the image of a point object is deduced. The calculations are made for two different apertures — the first has four-fold symmetry and the second has eight-fold symmetry — and are compared with full circular and annular apertures.

Image Analysis -Topological Methods

Abstract: The aim of image analysis is to provide a symbolic description of the image structure, that can serve to supply information about the image for all kinds of different tasks

Point spread and transfer functions for the rainbow holographic process.

Abstract: By using Fourier optics a theoretical analysis of the rainbow holographic process is made. The monochromatic and the polychromatic point spread functions, the monochromatic and the polychromatic transfer functions are derived. From these functions the real resolution (including monochromatic resolution and color blur) of the rainbow holographic image for different limiting apertures and the cutoff spatial frequency of the transfer function are calculated. These calculations are less laborious in contrast to the tedious evaluation of the diffraction theory. The formulas are general and applicable to the conventional hologram. The imaging plane hologram is first explained as a specific case of the rainbow hologram in this paper.

Multifrequency Acoustical Holography Using a Narrow Pulse

Abstract: Absmct-A multifrequency hologram is obtained by use of a single narrow pulse to reduce data acquisition time. Imaging properties of the method are analyzed theoretically by deriving a point spread function. Analytical expressions of radial and azimuthal resolutions are also derived. Numerical images are reconstructed by the calculation similar to the beam-formed imaging method (BIM). Experiments are made to compare the new method with the BIM. Results demonstrate that the new method reconstructs much clearer images, since it equalizes frequency components of the pulse signal within the effective bandwidth, which sharpens pulse waveforms and removes noises outside the bandwidth.

Aberrations in gamma-ray coded aperture imaging.

Abstract: Laboratory tests have been performed to investigate the quality of γ-ray images which may be obtained using the coded aperture mask technique. A number of potential sources of image defects are examined both theoretically and experimentally, and the methods in which these may be minimized or eliminated are studied. It is shown that good quality γ-ray images may be produced by efficient design and control of the imaging system.

Edge detection in micrometrology with nearly confocal microscopy.

Abstract: In the confocal microscope a diffraction-limited focused laser spot is arranged to coincide with the backprojected image of a point detector and the object scanned relative to this confocal spot to build up an image. This results in an improvement in resolution: for example, the point spread function is sharper and exhibits extremely weak outer rings. In a previous paper it was shown that if the point detector, achieved in practice by placing a pinhole in front of the detector, is displaced slightly the point spread function is sharpened even more. This is accompanied by a relative increase in the value of the transfer function at higher spatial frequencies. The price of this improvement is an increase in the strength of the outer rings and a fall in the total power in the image. In general this.strengthening of the outer rings is deleterious as it may result in optical artifacts, but there are circumstances where the improved resolution overweighs this disadvantage. One example is in the metrology of line structures as result in semiconductor microlithography, where the form of the object is known and all that is required is to make a particular measurement. Unfortunately, an error appeared in the previous paper in Eqs. (14) and (15) and also in Fig. 7. The purpose of the present paper is to give correct expressions and theoretical profiles for the image of an opaque edge and to compare these two experimental results. Imaging in a confocal system is coherent so that the image may be written Fig. 1. (a) Normalized intensity image of a straight edge in a confocal microscope with various offsets; (b) offset to give dark-field image.

Ultraviolet resolution of large mirrors via Hartmann tests and two-dimensional fast Fourier transform analysis

Abstract: Large mirrors appear to be limited in resolution by their medium scale defects (mirror surface "ripples" of small amplitude and of 4 to 12 cycles per diameter). The ultraviolet resolutions of the Pic du Midi (PDM) 2 m mirror, the Canada-France-Hawaii (CFH) 3.6 m mirror, and the Space Telescope (ST) 2.4 m mirror have been studied. Hartmann screen tests were used to determine the wavefront error of the PDM and CFH mirrors, while only semiquantitative reports were used in the case of the ST mirror. Point spread function and modulation transfer function were determined by two-dimensional fast Fourier transform analysis, a necessary technique in the ultraviolet, where the small phase defects of mirrors are no longer negligible (and also because the mirrors' irregularities do not possess a particular arrangement or a given symmetry). If the three mirrors appear to be nearly limited by diffraction in the visible (except the CFH), in the ultraviolet at Lyman a 121.6 nm the resolution is inferior by more than a factor of 10 to the diffraction-limited resolution. While the ultra-violet wavelength range and very high resolution (0.014 arcsec with a diffrac-tion-limited Space Telescope at Lyman a) are highly desirable, such a limitation imposed by mirror surface quality has to be mentioned. The effects of the correlation length, amplitude of defects, and Hartmann screen sampling are presented, as well as some comments on the inadequacy in the ultraviolet of analytical methods compared to two-dimensional numerical simulations.

Transfer characteristic for a projection-type imaging system with an extended incoherent source

Abstract: A new transfer characteristic is proposed for the analysis of projection-type imaging systems when the source is an extended incoherent one and the Fresnel approximation can be applied among source, object, and detector. This characteristic represents the propagation of the mutual power spectrum from the object plane to the detection plane and, once the imaging scheme is fixed, it can be derived uniquely regardless of the object’s structure. The image for given objects and the quality of the imaging system can be estimated from this characteristic. Numerical analyses to demonstrate the effectiveness of this method were carried out assuming a high-resolution x-ray imaging system.

Speckle interferometry image reconstruction from the Fourier transform phase.

Abstract: A method suggested earlier for the restoration of speckle images from the average phase of the spectrum is described and investigated in detail. Much attention is concentrated on the reconstruction ambiguity that arises because of inexact knowledge of the spectrum phase, uncertainty about the position and the size of the object, and the probable presence of symmetric factors in the spectrum. Several algorithms that permit unambiguous object image reconstruction (to within arbitrary symmetric factors) have been developed. Results of model calculations for simple one- and two-dimensional images are given.

Linear restoration of projections obtained by an extended incoherent source.

Abstract: A new image-restoration method is proposed for a projection-type imaging system with an extended incoherent source. First, linearization of the system is carried out using the new transfer characteristic of the mutual power spectrum proposed earlier1; then the conventional linear restoration process is applied. Numerical analyses for a high-resolution x-ray imaging system are shown; these results demonstrate the effectiveness of this method.

Circularly coded x-ray tomography.

Abstract: A 3-D radiographic transmission tomography technique based on coded-aperture imaging is described. In this technique an x-ray source moving on a circular path parallel to the film projects an image of the object onto the film and convolves this image with a circle. By applying the matched filter of the circle to the image recorded on the film, any selected plane of the 3-D object can be reconstructed. The performance of this technique is analyzed by computer simulation and preliminary physical experiments. This technique may be particularly useful for 3-D reconstruction of high spatial frequency objects such as a 3-D angiogram.

Coded-aperture imaging system for reconstructing tomograms of human myocardium.

Abstract: To increase the detection efficiency and improve the spatial resolution, a coded-aperture imaging method is applied to nuclear medicine. The aperture consists of nine pinholes arranged in a square grid. Three kinds of coding are sequentially used to record the same number of projections including parallax and overlap. The overlapped images are partially separated, and good tomograms of a ring phantom and a human myocardium are reconstructed using a modified backprojection algorithm with variable damping factor.

Methods and Algorithms Toward 3-D Volume Image Reconstruction with Projections

Abstract: Since the introduction of computerized tomography (1), many reconstruction algorithms (2–4) have been suggested using various mathematical techniques. Especially, in 3-dimensional volume imaging, the Fourier transform approach (5) is usually preferred. This Fourier technique can be categorized into conventional 2-D slice by slice technique (6–8) or direct true 3-D image reconstruction (9–11) and also depending on the mode of data collection, i.e., parallel (6,7,9,10) or fan (cone for 3-D) beam (8, 12–16). Reconstruction procedure can also be classified depending on the mode of processing; namely filtered backprojection (FB) (7, 10), backprojection filtering (BF) (17, 51), or direct Fourier transform reconstruction (DFR) (18–20). Each method has its own characteristics and preference depends on the kind of tomographic system being employed and computational hardware involved.

A generalized deconvolution algorithm for image reconstruction in positron emission tomography with time-of-flight information (TOFPET)

Abstract: Positron emission tomographic systems capable of time-of-flight measurements open new avenues for image reconstruction Three algorithms have been proposed previously: the most-likely position method (MLP), the confidence weighting method (CW) and the estimated posterior-density weighting method (EPDW) While MLP suffers from poorer noise properties, both CW and EPDW require substantially more computer processing time Mathematically, the TOFPET image data at any projection angle represents a 2D image blurred by different TOF and detector spatial resolutions in two perpendicular directions The integration of TOFPET images over all angles produces a preprocessed 2D image which is the convolution of the true image and a rotationally symmetric point spread function (PSF) Hence the tomographic reconstruction problem for TOFPET can be viewed as nothing more than a 2D image processing task to compensate for a known PSF A new algorithm based on a generalized iterative deconvolution method and its equivalent filters (''Metz filters'') developed earlier for conventional nuclear medicine image processing is proposed for this purpose The algorithm can be carried out in a single step by an equivalent filter in the frequency domain; therefore, much of the computation time necessary for CW and EPDW is avoided Results from computer simulation studies show thatmore » this new approach provides excellent resolution enhancement at low frequencies, good noise suppression at high frequencies, a reduction of Gibbs' phenomenon due to sharp filter cutoff, and better quantitative measurements than other methods« less

Accurate Assessment Of The Optical Quality Of Infrared Systems

Abstract: The development and operation of a 300 mm aperture, high precision scanning interferometer with associated software for the semiautomatic testing of far-infrared lenses and system are described. The instrument is capable of analyzing and evaluating systems in terms of the optical transfer function (OTF), point spread function (PSF), wavefront aberration, ray intersection patterns, polynomial fitting, aberration contouring, and refractive index variation mapping and of providing a large range of representatives of data. The speed of the analysis is commensurate with established techniques with an improvement in the accuracy and flexibility of use of the instrument over alternative measuring systems. The introduction of this instrument has allowed the complete diagnosis of system defects, along with an accurate measure of any error and its effect on system performance in terms of wavefront error, modulation transfer function (MTF), etc. Results on a variety of systems which exhibit errors are presented, and their root cause and subsequent cure are discussed. The value of such an instrument for both prototype building and production runs is described.

An Iterative Spatial Algorithm For Three-Dimensional Reconstruction In Single Photon Emission Computed Tomography

Abstract: Two major problems in the reconstruction of spatial distribution of radioisotope in single photon emission computed tomography (SPECT) are tissue attenuation and resolution degradation with distance. In order to describe the projection process in SPECT more accurately, a three-dimensional linear model which takes into consideration the medium attenuation effect and the point spread function (PSF) of the imaging system is presented. Based on this model, an iterative spatial reconstruction algorithms, i.e., the Spatially Modified Algebraic Reconstruction Technique (SMART) is proposed and tested by computer simulation and phantom study. Comparison of the result with other conventional SPECT algorithms indicates that SMART has better performance in attenuation effect compensation and discrimination of spatial features in phantom. Key Words: (1) Single photon emission computed tomography (2) Spatial iterative algorithm (3) linear model (4) evaluation of computer algorithms

Selection of the optimum wavelength for an x-ray tomography system.

Abstract: A means of selecting the optimum x-ray wavelength for an x-ray tomographic imaging system is proposed. In the evaluation, both the detection process and the image reconstruction algorithm are taken into account. The optimum wavelength is selected so that the stability of the reconstructed images is maximized. A concrete means of getting the optimum wavelength in connection with the detectable projections is also shown.