Showing papers on "Point spread function published in 1979"
TL;DR: In this paper, a backprojection method for reconstructing cross-sectional images of ultrasonic reflectivity from scattering measurements is presented, and the point spread function (PSF) for each case is derived and is shown to depend on the shape of the acoustic pulse used.
159 citations
TL;DR: It is found, by performing an important coordinate transformation, that the projection data of many three-dimensional radiographic imaging systems can be transformed to a form amenable to analysis by the central-slice theorem.
Abstract: The properties of many three-dimensional radiographic imaging systems are examined within a common analytic framework. It is found, by performing an important coordinate transformation, that the projection data of these systems can be transformed to a form amenable to analysis by the central-slice theorem. Therefore, a clear relationship between the measured data set and the three-dimensional Fourier transform of the object can be established. For the Fourier aperture system, each measurement in the detector plane gives directly one point in the three-dimensional Fourier transform of the object. The limited view angle of these systems manifests itself in the incomplete collection of the Fourier transform of the object. This “missing cones” region in the Fourier space produces a point-spread function that has long-range conical ridges radiating from the central core. It is shown that degradations in linear reconstructions of extended objects are not as disastrous as might have been expected.
72 citations
TL;DR: In this paper, an analytical expression for the point spread function (PSF) generated by the backprojection process has been derived for several different choices of the acoustic pulse: a narrowband pulse, wideband pulse and two analytically derived optimum pulses which provided the best sidelobe response and a mainlobe width equal to approximately 0.4λ c, where λ c is the wavelength corresponding to the upper cutoff frequency of the pulse.
70 citations
43 citations
TL;DR: An improvement in resolution in a conventional microscope has been shown to result if an annular condenser is employed, and Fourier imaging with defocus and spherical aberration is considered, resulting in an imaginary part being introduced into the transfer function.
Abstract: An improvement in resolution in a conventional microscope has been shown to result if an annular condenser is employed. Here Fourier imaging in the presence of defocus and special aberration is considered, and the image of a straight-edge calculated. Imaging in confocal microscopes is superior to that in conventional microscopes and may be further improved by the use of one lens with annular aperture. Again Fourier imaging with defocus and spherical aberration is considered, resulting in an imaginary part being introduced into the transfer function. The straight edge response is very sharp.
41 citations
TL;DR: Four variations on Linnik's design are discussed, one of which avoids the use of transmitting optics and normal incidence reflections altogether and could therefore be used at ultraviolet or soft x-ray wavelengths.
Abstract: A simple interferometric method capable of displaying quantitatively the wave front aberration of any image-forming optical system is described. Its application for testing and aligning grazing incidence reflection optics at the same conjugates as those of short-wavelength use is demonstrated. The image-forming wave front from the system being tested is compared with a true spherical wave front generated within the interferometer from a point at the intended focus. The differences are displayed as a fringe pattern superimposed on an image of the exit pupil. Each fringe corresponds to one wavelength of separation between the actual image-forming wave front and the Gaussian reference sphere. The principle originates from a paper by W. P. Linnik published in Russian and German in 1933. A translation is included as an appendix. Four variations on Linnik’s design are discussed, one of which avoids the use of transmitting optics and normal incidence reflections altogether and could therefore be used at ultraviolet or soft x-ray wavelengths.
32 citations
TL;DR: The concepts of generalized projection and generalized Radon transform are introduced and point-spread functions are given for cases involving piecewise-uniform symmetrical source distributions and uniform detectors.
Abstract: Tomographic reconstruction has ordinarily assumed that the measurement data can be regarded as line integrals, but the finite width of the X-ray beam invalidates this assumption. The data can however be expressed in the form of integrals over a strip rather than a line. The strip integral kernel is calculated allowing for extended source and detector, as well as for nonuniform photon emission and detector sensitivity. Strip eccentricity, which occurs in practice, is also taken into account. Even if the measurement data were to cover all scanning angles, there would be imperfect reconstruction expressible as a space-variant point spread function deducible from the strip integral kernel. To deal with this it is convenient to introduce the concepts of generalized projection and generalized Radon transform. Point-spread functions are given for cases involving piecewise-uniform symmetrical source distributions and uniform detectors.
32 citations
TL;DR: The second moment of the point spread function is related to the second derivative of the optical transfer function at the origin by the moment theorem as discussed by the authors, which is the sum of a contribution of the aperture amplitude distribution, which yields a sometimes infinite term, and a term that is directly related to wave front aberrations.
Abstract: The second moment of the point spread function is related to the second derivative of the optical transfer function at the origin by the moment theorem. The second moment is the sum of a contribution of the aperture amplitude distribution, which yields a sometimes infinite term, and a term that is directly related to the wave front aberrations. In practical applications it is possible to redefine the second moment such that a quality parameter, identical to one successfully used in lens design, is obtained.
24 citations
TL;DR: It is shown that restorations computed point by point appear the same as global restorATIONS produced by Fourier techniques, and parameters that are related to noise, point-spread functions, or object texture can be varied easily from pixel to pixel, allowing flexibility that is achieved only with computational difficulty in global restoration techniques.
Abstract: Restoration of individual image points by the method of least squares is investigated. We show that restorations computed point by point appear the same as global restorations produced by Fourier techniques. Moreover, parameters that are related to noise, point-spread functions, or object texture can be varied easily from pixel to pixel, allowing a flexibility that is achieved only with computational difficulty in global restoration techniques. To restore individual pixels, only a few points in their neighborhood, need to be considered, and the matrices that must be inverted are small enough for practical computation. The sizes of these matrices can be reduced especially if the blurring point-spread function has symmetries.
23 citations
TL;DR: A time-delay filter is described that transforms the phase-modulated beam into an amplitude- modulated beam and compares the proposed method with other demodulation schemes described in the literature.
Abstract: Several acousto-optical imaging systems are described in the literature where the image information is obtained by scanning a focused beam over a flexible mirror located at the acoustical image plane. The small dynamic deformation of the mirror induces a shallow phase modulation in the scanning beam. This paper describes a time-delay filter that transforms the phase-modulated beam into an amplitude-modulated beam and compares the proposed method with other demodulation schemes described in the literature. Specifically, stability, resolution, sensitivity, and frequency responses are considered.
23 citations
TL;DR: The noise-suppression characteristics of an achromatic optical processing system when operated with a broad-spectrum light source are analyzed and it is shown that such systems produce considerable noise improvement.
Abstract: The noise-suppression characteristics of an achromatic optical processing system when operated with a broad-spectrum light source are analyzed. It is shown that such systems produce considerable noise improvement. Both signal-dependent and signal-independent noise are considered. In each case, we find that the achromatic coherent system behaves much like an incoherent imaging system.
TL;DR: In this article, the authors describe a recently developed shearing interferometer that is designed for general purpose laboratory use, including a description of the instrument characteristics and principle of operation as well as a comparison of measured and theoretical accuracy limits.
Abstract: The fundamental measurement required for proof of quality of an optical system is the shape of its transmitted wavefront. A knowledge of wavefront error and the transmission characteristics of an optical system allow calculation (at the measurement wavelength) of all commonly used quality factors such as optical transfer function, point spread function, Strehi ratio, etc. This paper describes a recently developed shearing interferometer that is designed for general purpose laboratory use. Included is a description of the instrument characteristics and principle of operation as well as a comparison of measured and theoretical accuracy limits.
01 Jan 1979
TL;DR: In optical astronomy, images are highly degraded by atmospheric turbulence as discussed by the authors and the diameter of the seeing disk may vary from 0.2 arcseconds to 10 arcseconds or more according to weather conditions.
Abstract: In optical astronomy, images are highly degraded by atmospheric turbulence. The diameter of the seeing disk may vary from 0.2 arcseconds to 10 arcseconds or more according to weather conditions. A typical diameter is of the order of 2 arcseconds which is the angular resolution of a 6cm lens at the diffraction limit.
TL;DR: The method of least squares is presented, which opens a large field of applications including image restorations without deterministic knowledge about the point spread function and the object, or with spatially varying point spread functions.
TL;DR: The collimator function is developed into a Fourier series and the intensity distribution in the detector plane for a point source is given by a mathematical expression that depends on the object position and on the collimators parameters.
Abstract: A new technique for evaluating the point spread function of parallel hole collimators in scintillation cameras is studied. The collimator function is developed into a Fourier series and the intensity distribution in the detector plane for a point source is given by a mathematical expression that depends on the object position and on the collimator parameters. The septal penetration effect is considered. The technique is applied to obtain the general formulae for collimators with hexagonal holes and the PSF is evaluated.
TL;DR: The proposed deconvolution method (due to Biraud) is shown to work satisfactorily on a 1-D scintigraphic signal which is a particular cross-section of a 2-D image.
Abstract: It is shown that an Anger-type gamma camera can be considered as a linear filter. The image is therefore the convolution of the object by the camera point spread function. An important property of the objects is the fact that they are basically positive (count-rates as a function of space variables). The proposed deconvolution method (due to Biraud) is shown to work satisfactorily on a 1-D scintigraphic signal which is a particular cross-section of a 2-D image. This is a preliminary study of the enhancement of real scintigraphic images.
TL;DR: The centroid, variance, eccentricity, and angle of the principal axes are suggested as pertinent parameters, and an image chopping technique for fast measurement of these parameters is described.
Abstract: In several applications it is necessary to get a fast evaluation of the shape and quality of an image of a point source. Since a complete description by means of the point spread function involves time-consuming data processing, it is necessary to limit the evaluation to a set of parameters which can be measured at high rates. Such a set can be defined in terms of the first and second moments of the distribution. In this article the centroid, variance, eccentricity, and angle of the principal axes are suggested as pertinent parameters, and an image chopping technique for fast measurement of these parameters is described.
TL;DR: It is shown that, within the limits of geometrical optics, it is possible to specify a pure-phase pupil function that will produce any desired optical transfer function (OTF) or point spread function (PSF) in an incoherent optical processing system.
Abstract: It is shown that, within the limits of geometrical optics, it is possible to specify a pure-phase pupil function that will produce any desired optical transfer function (OTF) or point spread function (PSF) in an incoherent optical processing system. A general prescription for finding the pupil function is presented, and specific analytical results are given for simple power-law PSFs. As an example, the fabrication and testing of a logarithmic phase plate that produces an appropriate PSF for incoherent optical processing of transaxial tomography data are discussed.
TL;DR: In this article, the authors proposed to use a narrowness measure for the composite point spread function of a blurring-restoration operation that is the ratio of the energy of the composite PSF in a fixed interval around the origin to its total energy.
Abstract: Development of restoration filters based on the use of a narrowness measure for the composite point spread function of a blurring-restoration operation that is the ratio of the energy of the composite PSF in a fixed interval around the origin to its total energy, is discussed. For a continuous-continuous model, this leads to composite PSF's that belong to the family of prolate spheroidal wave functions. For a continuous-discrete model, the solutions do not have simple analytical forms but resemble those of the continuous model. Filters of this type have been found to be superior to those with a radius-of-gyration narrowness measure for the control of sidelobes in the case of a Gaussian blurring function and for restoration of images degraded by linear motion blurring. Details of filter construction and examples of image restoration performance are presented.
TL;DR: The PSF's and MTF's calculated in the singlescattering approximation are compared with the corresponding functions obtained considering multiple scattering of optical radiation under conditions of varying meteorological range and an interpretation of the obtained dependences is suggested.
Abstract: We consider the results of calculating the point-spread functions (PSF's) and modulation-transfer functions (MTF's) in the observation of the earth's surface from outer space. The PSF's and MTF's calculated in the singlescattering approximation are compared with the corresponding functions obtained considering multiple scattering of optical radiation under conditions of varying meteorological range. We give the PSF and MTF calculation results for various wavelengths of optical radiation (0.5, 0.7, and 1.0 microm) and suggest an interpretation of the obtained dependences.
TL;DR: In this article, the point spread function associated with the combined encoding-decoding process is derived and a least-squares procedure is then used to determine the decoding function which, for a given aperture code, minimises the mean square magnitude of the sidelobes.
Abstract: The method of coded aperture imaging with a one-dimensional aperture coding mask is applied to the problem of imaging a two-dimensional axial slice through a three-dimensional source distribution. A rigorous expression for the point spread function associated with the combined encoding-decoding process is derived. A least-squares procedure is then used to determine the decoding function which, for a given aperture code, minimises the mean square magnitude of the sidelobes of the point spread function. Replacement of the initial decoding function by its optimised counterpart is seen, by means of an example, to produce a point spread function which not only oscillates rapidly in sign (thus minimising the build-up of background), but also has substantially smaller mean square sidelobe magnitudes. Finally, the analysis is extended to the case of imaging with multiple views. An example demonstrates that the use of multiple views can further improve the suppression of sidelobes in the point spread function. Computer-generated plots of point spread functions accompany the analysis.
TL;DR: The significant atmospheric effects in stellar speckle interferometry may be simulated in a controlled laboratory experiment by imaging through appropriate photographic phase plates.
Abstract: The significant atmospheric effects in stellar speckle interferometry may be simulated in a controlled laboratory experiment by imaging through appropriate photographic phase plates. Coupling such an imaging facility to a speckle camera with a video detector and processing image data by digital means have aided in technique and instrument development and verification. Laboratory results for system transfer functions and nonisoplanatic effects are presented.
01 Jan 1979
TL;DR: In this paper, the authors proposed to use a narrowness measure for the composite point spread function of a blurring-restoration operation that is the ratio of the energy of the composite PSF in a fixed interval around the origin to its total energy.
Abstract: Development of restoration filters based on the use of a narrowness measure for the composite point spread function of a blurring-restoration operation that is the ratio of the energy of the composite PSF in a fixed interval around the origin to its total energy, is discussed. For a continuous-continuous model, this leads to com- posite PSF's that belong to the family of prolate spheroidal wave func- tions. For a continuous-discrete model, the solutions do not have simple analytical forms but resemble those of the continuous model. Filters of this type have been found to be superior to those with a radius-of-gyration narrowness measure for the control of sidelobes in the case of a Gaussian blurring function and for restoration of images degraded by linear motion blurring. Details of filter construction and examples of image restoration performance are presented.
TL;DR: In this paper, a general theory of imaging a randomly aberrated wave is presented and a special emphasis is placed upon identifying parameters and characteristics necessary to simulate imaging through the turbulent atmosphere.
Abstract: A general theory of imaging a randomly aberrated wave is presented Special emphasis is placed upon identifying parameters and characteristics necessary to simulate imaging through the turbulent atmosphere Two components are found in the average image and optical transfer function Energy and intensity ratios are calculated Special cases studied include wave amplitude and phase fluctuations alone and in combination, image contrast, predetection compensation, and stellar speckle interferometry Observations of cores in star images and laboratory simulations give support to our calculation of an additional term in the long exposure image and optical transfer function
TL;DR: Several optimal spatial filters that could be used in a coherent imaging system to remove post-detection linear distortions are obtained and their performance assessed.
Abstract: Several optimal spatial filters that could be used in a coherent imaging system to remove post-detection linear distortions are obtained and their performance assessed. It is shown that the minimum mean square error filter approximates the usual inverse filter for low-contrast images. The performance of these compensation filters is illustrated by use of examples of one-dimensional signals.
28 Dec 1979
TL;DR: In this article, the spectral magnitude of the image was smoothed by averaging over an ensemble of similar images, and the estimated magnitude was then adjusted to obtain zero crossings and adjust the phase accordingly.
Abstract: Frequently an image may be blurred by a point spread function whose details are not known exactly. In such a case it is necessary to estimate the point spread function before deconvolving the blurred image. This paper presents a new technique for estimating a zero phase blurring function when its optical transfer function is smooth. The estimate is obtained by smoothing the spectral magnitude of the image and comparing it to an average magnitude that is also smoothed. The average magnitude is obtained by averaging over an ensemble of similar images. The estimation can be extended to degradations such as a defocused lens by thresholding the estimated magnitude to obtain zero crossings and adjusting the phase accordingly. In particular, this technique can be applied to a circularly symmetric Gaussian or a defocused lens with a circular aperture.© (1979) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
TL;DR: It is demonstrated that the Gauss LU decomposition method compares favorably with other existing methods as a powerful tool for the solution of image restoration problems.
Abstract: It is demonstrated that the Gauss LU decomposition method compares favorably with other existing methods as a powerful tool for the solution of image restoration problems. A computer simulation example, using a spatially separable point spread function, is given.
25 Dec 1979
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, in some ways analogous to that of speckle interferometry used in astronomical situations, is based on the computation of the second-order spatio-temporal statistics of a fluctuating speckle pattern. The theorum of Van Cittert-Zernike is invoked to relate the speckle, due to 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.© (1979) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
TL;DR: In this paper, an expression for the contrast of time-averaged speckle patterns formed at a defocused image plane by an out-of-plane vibrating diffuse object is derived with the assumptions that circular Gaussian statistics hold for the formation of speckles and the object surface is approximated by the deep phase screen.
Abstract: An expression for the contrast of time-averaged speckle patterns formed at a defocused image plane by an out-of-plane vibrating diffuse object is derived with the assumptions that circular Gaussian statistics hold for the formation of speckles and the object surface is approximated by the deep phase screen. The theoretical result shows that the contrast degradation occurs at all the positions of the observation plane and increasingly proceeds with the increase of both the vibration slope of the object and the aperture width of pupil used. It is also found that the contrast variation due to the object vibrations becomes particularly noticeable at a defocused plane taken close to the focal plane.