Showing papers on "Point spread function published in 1980"
TL;DR: Fully three-dimensional positron emission tomography is considered and a reconstruction algorithm derived that is computationally feasible and results in accurate reconstructions.
Abstract: Fully three-dimensional positron emission tomography is considered and a reconstruction algorithm derived. The reconstruction problem is formulated mathematically as a three-dimensional convolution integral of a point spread function with an unknown positron activity distribution and is solved by Fourier transform methods. Performance of the algorithm is evaluated using both simulated phantom data produced by a Monte Carlo computer program and phantom data obtained from the University of Chicago/Searle Positron Camera. It is concluded that the method is computationally feasible and results in accurate reconstructions.
229 citations
TL;DR: A theoretical approach has been developed that allows the geometric transfer function component for conventional scintillation camera collimators to be predicted in closed form and Monte Carlo simulations and experimental measurements have shown these theoretical expressions to be highly accurate.
Abstract: A theoretical approach has been developed that allows the geometric transfer function component for conventional scintillation camera collimators to be predicted in closed form. If transfer function analysis is to be useful in describing imaging system performance, the image of a point source must not depend on source position in a plane parallel to the detection plane. This shift invariance can be achieved by analysis of system response in terms of an effective point spread function, defined as the normalised image of a point source that would be obtained if the camera collimator were uniformly translated (but not rotated) during image formation. The geometric component of the corresponding effective transfer function is shown to be expressed simply by the absolute square of the two-dimensional Fourier transform of a collimator hole aperture, with the spatial frequency plane scaled by a factor which depends on collimator length, source-to-collimator distance, and collimator-to-detection plane distance. Closed form algebraic expressions of the geometric transfer function have been obtained for all four common hold shapes (circular, hexagonal, square and triangular). Monte Carlo simulations and experimental measurements have shown these theoretical expressions to be highly accurate.
154 citations
TL;DR: In this paper, the authors present a theory for ultrasonic B-scan image formation based on the assumption that imaging is done using broad-band signals and that all the information in the returned echos is utilized for image formation, as opposed to only the detected envelopes.
128 citations
TL;DR: In this article, a general imaging theory is developed from which the performance of scanning and conventional microscopes may be investigated, including the effects of defocus, Zernike phase contrast, and interference and resonant microscopy.
Abstract: The imaging performance of scanning microscopes may be improved by introducing a pinhole in the detector plane, thus forming a confocal (or type 2) scanning microscope. A general imaging theory is developed from which the performance of scanning and conventional microscopes may be investigated. Various methods of obtaining phase imaging are considered, including the effects of defocus, Zernike phase contrast, and interference and resonant microscopy.
58 citations
TL;DR: It is shown that it is always desirable to make the sample spacing as small as possible, and that an attempt to avoid the volcano effect by means of inadequate sampling can have disastrous consequences for the reconstructed image.
36 citations
01 Jan 1980
15 citations
TL;DR: A method of deblurring an image is described that uses an achromatic, coherent optical-processing system and either one or two diffraction gratings to serve as a reference function that is cross correlated with the blurred image.
Abstract: A method of deblurring an image is described that uses an achromatic, coherent optical-processing system and either one or two diffraction gratings. One grating, after differentiation, serves as a reference function that is cross correlated with the blurred image.
10 citations
TL;DR: In this article, the authors proposed a new norm of restoration that restores the ideal object which, had it existed, would have maximized the throughput of information from object to image planes.
Abstract: Image interpreters often express the desire to extract a "maximum of information" from a given picture. We have devised a new norm of restoration that, in fact, realizes this aim. The image data are forced to contain a maximum of information about the object, through variation of the object estimate. This maximum information (MI) norm restores the ideal object which, had it existed, would have maximized the throughput of information from object to image planes. Or, the object estimate achieves the "channel capacity" of the image-forming medium. The following simple model for image formation is used. The imaging system is regarded as a transducer of photon position, from x in the object plane toy in the image plane. Then the conditional probability p(y1 x) is just s(y-x), the point spread function for the imagery, plus an unknown noise probability law n(y) independent of x (signal) for those transitions to y that are due to noise. The average information per photon transition x-y may then be calculated, using the correspondence of probability law p(x) with the object and p(y) with the image. When the image law p(y) is constrained to equal the data, the only set of unknowns remaining is the object, which may be varied to maximize the information. Restorations by this method are compared with corresponding ones by maximum entropy and show some advantage over the latter.
10 citations
TL;DR: The rotating slit is a time-varying coded aperture that can be used advantageously with a scintillation camera in imaging of static radioactive objects and can be brought in focus by shift operations and a computed-tomography algorithm.
Abstract: The rotating slit is a time-varying coded aperture that can be used advantageously with a scintillation camera in imaging of static radioactive objects. The coded image obtained from an on-axis slit conveys no tomographic information, but when the slit is displaced away from the axis of rotation, tomographic information can be obtained. From one set of coded images, each plane of a 3-D object can be brought in focus by shift operations and a computed-tomography algorithm. Inverse filtering is necessary to remove the side lobes of the point spread function. The intrinsic resolution of the camera, the slit width, the filter function, and the display all affect the lateral resolution, while the object distance, the off-axis distance of the slit, and the lateral resolution determine the longitudinal resolution of the system.
10 citations
01 Jan 1980
TL;DR: The theory to predict the imaging performance of the two aperture geometries is developed and the respective Point Spread Functions are simulated and agree well with theoretical results.
Abstract: Synthetic focus imaging techniques suitable for reconstructing 3-D acoustic images of flaws inside silicon nitride are described. A 50 MHz imaging system consisting of a precision scanner, a microcomputer controller, and a minicomputer image processor has been developed for this purpose. A square synthetic aperture is used to image flaws in flat disc samples and a cylindrical synthetic aperture is used in the cylindrical rod case. We have developed the theory to predict the imaging performance of the two aperture geometries. The respective Point Spread Functions are simulated and agree well with theoretical results. Special attention is given to reconstructing images of specular reflectors. Computer simulations based on theoretical flaw models have been carried out.
9 citations
01 Jan 1980
TL;DR: In this article, the Anger camera is described in Chapter 4, where the pinhole aperture or the multihole collimator performs the imaging operation while a detector system consisting of a scintillation crystal and an arrangement of photomultiplier tubes detects the image.
Abstract: In a photographic camera, the camera lens forms an image of the object and the image is detected by the photographic film. In the Anger camera described in Chapter 4, the pinhole aperture or the multihole collimator performs the imaging operation while a detector system consisting of a scintillation crystal and an arrangement of photomultiplier tubes detects the image. The detector system in the Anger camera is very efficient and records almost every X-ray or γ-ray photon that arrives with an energy within the preselected energy window. Unfortunately, the imaging system severely limits the number of photons that arrive. A collimator typically passes only 0.01% of the radiation emitted by the object. Since the statistical quality of the images formed in this way is dependent on the number of photons collected from a single element of the object, one needs to collect as many photons as possible. Patient-dose restrictions limit the number of photons available, while exposure time is limited by temporal-resolution requirements in a dynamic study, by image degradation due to patient motion, by patient fatigue, or by the expense involved in tying up a clinical instrument for extended periods.
TL;DR: Restoring the reconstructed image to provide higher resolution is a nontrivial operation, which however greatly benefits from experience already gained in dealing with optical imagery degraded by the aberrations of astigmatism and curvature of field.
Abstract: A loss of resolution in tomographic images is due to the well‐known bimodal spatial variations in photon emission across the x‐ray focal spot combined with the finite width of the x‐ray detector. Such departures from the ideal infinitely narrow beams which are usually considered can be taken into account by replacing the customary line integrals by suitably chosen integrals over strips. The image degradation resulting from using those strip integrals as ingredients in conventional reconstruction formulas is expressible as a complicated point spread function, which can always be computed in any given situation. Restoring the reconstructed image to provide higher resolution is a nontrivial operation, which however greatly benefits from experience already gained in dealing with optical imagery degraded by the aberrations of astigmatism and curvature of field. Typical point spread functions are shown for a simple bimodal source intensity distribution of primordial importance.
TL;DR: A novel omnidirectional spatial filter, which has bandpass characteristics, is designed to block all the repetitive periodic regular pattern spectra and pass the defect information carrying spectra, and is characterized by its ability to detect defects at any location and rotation and be insensitive to object magnification by the frequency domain operation characteristics.
Abstract: Defects in rectangular x-y axis decomposable periodic patterns are found to be detected by an omnidirectional (r-θ axis decomposable) spatial filter optical system, where use is made of the spectral difference between periodic patterns and defects. A novel omnidirectional spatial filter, which has bandpass characteristics, is designed to block all the repetitive periodic regular pattern spectra and pass the defect information carrying spectra. According to a computer simulation, the minimum detectable defect size using this optical system is about one-twentieth that of the periodic pattern pitch. This novel optical system is characterized by its ability to detect defects at any location and rotation (shift and rotation immunity of the optical system) and also to be insensitive to object magnification by the frequency domain operation characteristics. This filter application is not limited to 2-D rectangular periodic-pattern-defects detection, but defects in 1-D or skew periodic patterns are also detected by the same filter.
01 Aug 1980
TL;DR: In this article, a NFOV scanner can be approximated by a spatially invariant system whose point spread function depends on the detector shape and angular characteristics and electrical filter transfer function for given patches at the top of the atmosphere.
Abstract: Starting from the general measurement equation, it is shown that a NFOV scanner can be approximated by a spatially invariant system whose point spread function depends on the detector shape and angular characteristics and electrical filter transfer function for given patches at the top of the atmosphere. The radiometer is modeled by a detector, electrical filter, analog to digital converter followed by a reconstruction filter. The errors introduced by aliasing and blurring into a reconstruction of the input radiant exitance are modeled and analyzed for various detector shapes, sampling intervals, electrical filters and scan types. Quantitative results on the errors introduced are presented showing the various tradeoffs between design parameters. The results indicate that proper selection of detector shape coupled with electrical filter can reduce aliasing errors significantly.
TL;DR: In this article, the visibility of the interference terms over the image irradiance of a complex amplitude object immersed in a uniform background is described by an interference transfer function (ITF), which is the linear transfer function for coherent optical systems with quadratic detection when the test object either has low contrast or is periodic.
Abstract: The visibility of the interference terms over the image irradiance of a complex amplitude object immersed in a uniform background is described by an interference transfer function (ITF). It is shown that the ITF is the linear transfer function for coherent optical systems with quadratic detection when the test object either has low contrast or is periodic.
01 Jan 1980
TL;DR: In this article, a high-resolution 3D passive acoustical imaging system is realized by using array detectors arranged hemispherically covering the object, and cross power or bispectral analyses of the detected signals are carried out so that images of the distributions of power of single frequency component or coherence among three frequency components are obtained.
Abstract: A High resolution three dimensional passive acoustical imaging system is realized by using array detectors arranged hemispherically covering the object. Auto and cross power or bispectral analyses of the detected signals are carried out so that images of the distributions of power of single frequency component or coherence among three frequency components are obtained. One of the most significant features of the system is the ability to display high quality images of any desired cross sections of three dimensional noise emitting objects simply by the choice of parameters at the stage of image reconstruction. Three dimensionally high resolutions, for instance resolution volume of 3cm × 3cm × 5cm for waves at 10 kHz over the observation volume of 60cm×60cm×60cm, are achieved. An image is obtained within five minutes and it is displayed on a color TV monitor or printed out graphycally. Moreover, to obtain structures which are much smaller than the wave length a new image reconstruction process which uses the matrix correspondence between the detected hologram and the complex amplitudes of mesh points on the object’s surface is proposed. The system is a powerful means for precise analysis and control of noise sources.
TL;DR: It is shown how to apply a truncated eigensystem expansion in the solution of image restoration problems for the case of space invariant point spread functions and how this algorithm compares favorably with other existing methods.
Abstract: We show how to apply a truncated eigensystem expansion in the solution of image restoration problems for the case of space invariant point spread functions. The solution is obtained directly from the system of linear equations, which result from the discretization of the Fredholm integral equation of the first kind. Fast Fourier transform techniques are used in obtaining this solution. A procedure is devised to estimate the rank of the coefficient matrix that gives a best or near best solution. It is demonstrated that this algorithm compares favorably with other existing methods. Numerical results using spatially separable point spread functions are given.
TL;DR: In this article, an interferometric approach to the calculation of the two-dimensional MTF of an optical system is proposed based on the computation of the second-order spatio-temporal statistics of a fluctuating speckle pattern.
Abstract: An interferometric approach to the calculation of the two-dimensional MTF of an optical system is proposed. The technique is based on the computation of the second-order spatio-temporal statistics of a fluctuating speckle pattern. The theorem of Van Cittert-Zernike is invoked to relate the speckle, due to the illumination of a perfect diffuser by the point spread function of an optical system, to the two-dimensional MTF of the system. The computed MTF is displayed in the form of a contour map and can also be represented in the conventional form of a one-dimensional vertical cut. Preliminary measurements have yielded qualitatively useful results and clearly illustrate the suitability of two-dimensional maps for the detection of transfer function anisotropies.
TL;DR: By using an expansion of the correlation function of the source and by means of linear operator techniques, necessary and sufficient conditions for determining the behavior of the object when the source is extended and quasi-monochromatic are stated.
Abstract: By using an expansion of the correlation function of the source and by means of linear operator techniques, we have stated necessary and sufficient conditions for determining, in a unique way, the behavior of the object when the source is extended and quasi-monochromatic.
03 Dec 1980
TL;DR: In this article, the effects of non-isoplanatic conditions and telescopic aberrations on speckle imaging are analyzed and the combined effects of second-order statistics of a set of images are examined.
Abstract: The combined effects of non-isoplanatic conditions and telescopic aberrations on speckle imaging are analyzed. The general form of the two-point source wave-structure function for upward viewing through the turbulent atmosphere is used as a basis for developing descrip tions of the second-order statistics used in speckle imaging. An analysis of the informa tion recoverable from astronomical speckle imagery shows that diffraction limited resolu tion can be obtained. Two important assumptions which are usually satisfied have been made :1) the isoplanatic patch encompasses the average spread function;2) the greatest contribution to the atmospheric distortion comes from turbulence at lowaltitudes .Under these conditions, the aberrations of the telescope do not affect the second-order statistics and the integral equation relating the object and measured second-order statis tics is well conditioned.IntroductionThe removal of atmospheric turbulence effects from telescopic imagery has been a subject of continuing interest. A variety of methods have been proposed and demonstrated. Most of these methods involve second-order statistics of the atmospherically degraded imagery. The combined effects of non-isoplanatic conditions and telescopic aberrations on second-order statistics will be examined.This paper describes a continuation of our efforts previously reported-*- ' 2 . The restora tion of diffraction limited resolution with astronomical data was demonstrated under iso planatic conditions. The research reported here is the first step in an effort to broaden the range of conditions under which these methods can be applied. First, models for inco herent imaging and for atmospheric disturbance will be given for non-isoplanatic conditions and telescopic aberrations. Next, the first-order and second-order statistics of a set of images will be developed. Finally, the effects of aberrations and non-isoplanatism will be examined.Non-isoplanatic imaging equationsUnder general non-isoplanatic conditions, the image is given by a superposition integralKx) =_// 0(y) S(x,y) d y (1)x is the angular position in the image plane y is the angular position in the object plane I(x) is the image intensity function 0(y) is the object intensity function S(x,y) is the point spread function.The point spread function can be expressed in terms of the phase and amplitude distur bance at the aperture. To simplify the analysis, Faunhofer diffraction is assumed so that the object and aperture planes, and the aperture and image planes are related by Fourier transforms. The coherent Green's function for a point source at y for the configuration of Figure 1 is the two-dimensional Fourier transform of the product of F(z,y) and the phase due to the point source
22 Aug 1980
TL;DR: In this paper, the point spread function is also sharper and the outer rings weak, resulting in a response to a step object without fringes, and an arrangement in which the beam traverses the object more than once is discussed.
Abstract: Scanning image processing systems have the advantage that the image is in a form suitable for further electronic processing, and a particular class of these is the confocal scanning systems which exhibit superior imaging properties compared with conventional systems. Imaging is coherent thus allowing coherent processing to be performed with twice the spatial-frequency cut-off of a conventional processor. The point spread function is also sharper and the outer rings weak, resulting in a response to a step object without fringes. The important feature of the confocal system is that two lenses are involved in the imaging process. An arrangement in which the beam traverses the object more than once is therefore also discussed. This produces an extremely sharp point spread function and interesting optical properties.
TL;DR: In this paper, the authors studied coherent diffraction images formed by a polarizing microscopy with crossed polarizers and obtained closed form solutions for the cumulative point spread function, the line spread function and the edge spread function.
Abstract: Incoherent diffraction imagery formed by a polarizing microscopy with crossed polarizers is studied. Closed form solutions are obtained for the cumulative point spread function, the line spread function, and the edge spread function. Representative numerical results are displayed. The image of a bar target is also evaluated.
TL;DR: In this paper, a radio application is described for imaging a confined region using projections or ring scans around concentric arcs centered at the image field periphery, in common with other forms of reconstruction in radioastronomy, computerized tomography, and elsewhere.
Abstract: A reconstruction technique is reconsidered and a radio application is described for imaging a confined region using projections or ring scans around concentric arcs centered at the image field periphery. The point-spread function varies across the image, in common with other forms of reconstruction in radioastronomy, computerized tomography, and elsewhere. The more common reconstruction from parallel projections is seen as a limiting case of either ring scan synthesis or fan beam synthesis. These various projections are combined in a general view of image synthesis based on polar coordinate descriptions of a circular imaging region.
01 Dec 1980
TL;DR: In this paper, the Euler-Lagrangian variational approach instead of the conventional gradient method was used to solve the Bojarski-Lewis inverse scattering problem.
Abstract: Single frame image processing with noise can be cast into the Fredholm integral equation of the first kind. Its inversion for object reconstruction is known to be increasingly unstable when the ratio of the maximum and minimum eigenvalues (of the square of the point spread function) increases as the number of discrete samples increases. Therefore single‐frame image processing belongs to the class of ill‐posed inverse problems. The root of instability is identified to be the singularity of the ratio of noise power spectrum and modulation transfer function. Such an over amplification of noise at high spatial frequency is well known1 in optics2,3 and the image extrapolation problems.7,8,9,10 Ad hock procedures have been casually taken to suppress it. Recently an entirely different approach in a geological inversion problem has been applied to the ad hoc procedure in trading off noise and resolution in image problems. However, the ad hoc combination procedure can be simplified using the Euler‐Lagrangian variational approach instead of the conventional gradient method. This will be shown to be rigorously achieved. Qualitative illustrations will be presented which give insight to the present method of dynamical regulation for the illposed inverse problem. Two exact solutions of the Bojarski‐Lewis inverse scattering problem will be obtained showing different noise behaviors in the reconstructed object profile. Its impact in the super resolution and the image extrapolation problems will be indicated using an optical implementation of iteration algorithm for image restoration.
TL;DR: This chapter presents a review of image intensification and conversion, and an interesting example of an image intensifier being used for image processing was described by Geluk.
Abstract: Publisher Summary This chapter presents a review of image intensification and conversion. An interesting example of an image intensifier being used for image processing was described by Geluk. This image intensifier was used to sharpen blurred images by deflecting them across a mask corresponding to the point spread function of the degrading system in the manner of an image dissector. The mean output current from a photomultiplier placed behind the mask generated the video signal for the sharpened image which was displayed on a picture monitor. Various X-ray applications of image intensification and conversion are also discussed in the chapter. These applications include X-ray crystallography, conventional X-ray radiology, and X-ray computer tomography. There has been very little change in recent years in the methods of fabrication of the fluorescent screens in image intensifiers. The phosphors used in fabrication have been predominantly P.11 and P.20 types. The former type has mainly been used for photographic recording, whereas the latter has been used for direct observation. Both types can be efficiently coupled to suitable photocathodes. High resolution, high efficiency screens are still produced by the deposition of phosphor grains; other deposition techniques have suffered from loss of either resolution or efficiency, or both.
26 Nov 1980
TL;DR: In this paper, computer programs were developed to create a digital scene and to simulate the effect of the sensor point spread function (PSF) on the transfer of modulation from the scene to an image of the scene.
Abstract: The underlying factors affecting the detection and identification of nonurban to urban land cover change using satellite data were studied. Computer programs were developed to create a digital scene and to simulate the effect of the sensor point spread function (PSF) on the transfer of modulation from the scene to an image of the scene. The theory behind the development of a digital filter representing the PSF is given as well as an example of its application. Atmospheric effects on modulation transfer are also discussed. A user's guide and program listings are given.
21 Nov 1980
TL;DR: In this article, the point spread function (PSF) is derived from the intensity data, and fitting it via chisquare minimization techniques to either single or multiple stellar images.
Abstract: Software available at KPNO for performing stellar photometry on digital images is summarized. Aperture sum and two dimensional fitting techniques are described and compared in terms of accuracy, versatility, and computational efficiency. Algorithms are presented for deriving the point spread function (PSF) from intensity data, and fitting it via chisquare minimization techniques to either single or multiple stellar images. The results of tests performed on artificial starfields are summarized and evaluated. Two dimensional psf fitting techniques are seen to be a versatile and accurate tool even in fairly crowded fields, though computationally quite expensive compared to aperture sum techniques.
24 Jun 1980
TL;DR: A simulation model has been developed to analyze Infrared Imaging systems that synthesizes an optical point spread function and convolves it with target and detector configurations to produce a target signal.
Abstract: A simulation model has been developed to analyze Infrared Imaging systems. This model synthesizes an optical point spread function and convolves it with target and detector configurations to produce a target signal. The model includes the effects on the signal of detector responsivity contours, varying target shapes, noise and various electronic filtering and signal processing methods. The model runs on CDC 6600/7600 computers and requires about 40 seconds processor time per run when exercising all options. Outputs are in the form of tables, printer plots and calcomp plots.© (1980) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
01 Jan 1980
TL;DR: In this paper, coded aperture imaging is used in microimaging for laser induced plasmas diagnosis and the first results obtained in this field show a resolution of 10 μm and they hope rapidly a gain of 2 to 4 with regard to this number.
Abstract: As we say at the begining, coded aperture imaging is a general method not limited to nuclear medicine. It can be used in several domains such as neutrons, a particles imaging. We begin to develop it in microimaging for laser induced plasmas diagnosis. The first results that we obtained in this field show a resolution of 10 μm and we hope rapidly a gain of 2 to 4 with regard to this number.
01 Jan 1980
TL;DR: A computer simulation test showed that this method could determine the location of each of three objects within the resolution limit when a 41-element array was used and the original S/N amplitude ratio at each array receiver was greater than 20 dB.
Abstract: A technique for accurate estimation of the positions of objects separated by less than the classical resolution distance is described, where the main emphasis is on rapid processing and noisetolerance, The technique consists of three steps: signal pre-cleaning (or filtering), deconvolution, and the use of spatial null processing. A computer simulation test showed that this method could determine the location of each of three objects within the resolution limit when a 41-element array was used and the original S/N amplitude ratio at each array receiver was greater than 20 dB. Detailed results of the simulation are discussed.