Showing papers on "Point spread function published in 1990"
01 Apr 1990
TL;DR: It is shown that the introduction of the concept of coarray provides a convenient and elegant framework within which many apparently isolated techniques for point-spread function or aperture synthesis can be understood.
Abstract: Systems of two-dimensional (2-D) imaging arrays and apertures are considered from the point of view of their performance in the imaging of spatially incoherent as well as coherent source distributions. Such systems find applications in radar, sonar, and ultrasound imaging, as well as in applications such as seismology and radio astronomy. For linear imaging techniques related to beamforming and based on the Fourier transform relationship between the source distribution and the aperture plane measurements, the point spread function of the system completely characterizes its performance. This function is determined by the geometry of the physical aperture or array as well as the weighting that can be applied to measurements. It is shown that the introduction of the concept of coarray, both for receive apertures in incoherent imaging and for transmit/receive systems in reflection-mode coherent imaging, provides a convenient and elegant framework within which many apparently isolated techniques for point-spread function or aperture synthesis can be understood. In addition to this unifying role, coarray concept gives new insight into the aperture synthesis process, which allows interesting new imaging techniques to be developed, especially in coherent imaging. >
431 citations
TL;DR: Understanding the optical behavior of the microscope system has indicated how to optimize specimen preparation, data collection, and processing protocols to obtain significantly improved images.
264 citations
TL;DR: A Monte Carlo simulation of photon transport which includes collimator scatter is developed and Comparisons of measured and simulated PSFs demonstrate the validity of the model and the significance of collimators scatter in the degradation of image quality.
Abstract: The geometric component of the point spread function (PSF) of a gamma camera collimator can be determined analytically, and the penetration component can be calculated readily by numerical ray-tracing. A Monte Carlo simulation of photon transport which includes collimator scatter is developed. The simulation was implemented with an array processor which propagates up to 1024 photons in parallel, allowing accurate estimates of the total radial PSF in less than a day. The simulation was tested by imaging monoenergetic point sources of Tc-99m, Cr-51, and Sr-85 (140, 320, and 514 keV, respectively) on a General Electric Star Cam with low-energy, general-purpose, and medium-energy collimators. Comparisons of measured and simulated PSFs demonstrate the validity of the model and the significance of collimator scatter in the degradation of image quality. >
122 citations
TL;DR: In this article, the imaging properties of a confocal fluorescence microscope are considered on the basis of a theoretical model, which takes into account high-aperture objectives, the polarization state of the excitation light and a finite detector pinhole.
Abstract: SUMMARY
The imaging properties of a confocal fluorescence microscope are considered on the basis of a theoretical model. The model takes into account high-aperture objectives, the polarization state of the excitation light and a finite detector pinhole. Electromagnetic diffraction theory of the field near focus as developed by Richards and Wolf is used to compute the optical properties of the model. These are shown to be dependent on the polarization of the light. With the resulting three-dimensional point spread function we have studied the imaging of point, line and plane objects as a function of their orientation with respect to the confocal plane. In addition, the effect of the pinhole size on the image formation of these objects is discussed.
The results indicate the necessity to take object orientation into account during image processing activities such as segmentation or analysis.
115 citations
TL;DR: The problem of identifying the image and blur parameters and restoring a noisy blurred image is addressed and two algorithms for identification/restoration, based on two different choices of complete data, are derived and compared.
Abstract: In this paper, the problem of identifying the image and blur parameters and restoring a noisy blurred image is addressed. Specifying the blurring process by its point spread function (PSF), the blur identification problem is formulated as the maximum likelihood estimation (MLE) of the PSF. Modeling the original image and the additive noise as zeromean
Gaussian processes, the MLE of their covariance matrices is also computed. An iterative approach, called the EM (expectation-maximization) algorithm, is used to find the maximum likelihood estimates ofthe relevant unknown parameters. In applying the EM algorithm, the original image is chosen to be part of the complete data; its estimate is computed in the
E-step of the EM iterations and represents the restored image. Two algorithms for identification/restoration, based on two different choices of complete data, are derived and compared. Simultaneous blur identification and restoration is performed by the first algorithm, while the identification of the blur results from a separate minimization in the second algorithm. Experiments with simulated and photographically blurred images
are shown.
109 citations
TL;DR: In this paper, a method for optimizing the aperture size in emission imaging is presented that takes into account limitations due to the Poisson nature of the detected radiation stream as well as the conspicuity limitation imposed by a spatially varying background.
Abstract: A method for optimizing the aperture size in emission imaging is presented that takes into account limitations due to the Poisson nature of the detected radiation stream as well as the conspicuity limitation imposed by a spatially varying background. System assessment is based on the calculated performance of two model observers: the best linear observer, also called the Hotelling observer, and the nonprewhitening matched-filter observer. The tasks are the detection of a Gaussian signal and the discrimination of a single from a double Gaussian signal. When the background is specified, detection is optimized by enlarging the aperture; an inhomogeneous background results in an optimum aperture size matched naturally to the signal. The discrimination task has a finite optimum aperture for a flat background; a nonuniform background drives the optimum toward still-finer resolution.
85 citations
TL;DR: Tissue characterization is feasible if these characteristics are analyzed by statistical methods and structural order in tissues can be quantified by autocorrelation analysis and clinical studies on diffuse liver diseases support this conclusion.
Abstract: Models of biological tissues are described in terms of acoustic parameters and of structure. Beam formation is discussed for continuous wave and pulsed modes of transducer operation and the concept of the point spread function (PSF) is introduced. The PSF is equivalent to the resolution cell, or the sampling volume, of echographic equipment. The generation of echograms from parenchymal tissues is described in terms of speckle formation due to interference at reception on the transducer. The speckle dimensions are quantitatively compared to the sampling volume of the employed transducer. It is shown that for fully developed speckle the tissue characteristics are exclusively reflected in the mean echolevel and not in the speckle size. The speckle size is, however, greatly dependent on the bandwidth, the frequency, and the geometry of the employed transducer. The attenuation by the insonated tissue yields a depth-dependent increase of mainly the lateral speckle size, in addition to the depth dependence caused by the beam formation. If the number density of scattering sites within the tissue is relatively low, the speckle characteristics are dependent on this density and, hence, tissue characterization is feasible if these characteristics are analyzed by statistical methods. These methods are gray level histogram analysis and the estimation of the autocorrelation function, ie, first and second order statistics, respectively. Structural order in tissues can be quantified by autocorrelation analysis and clinical studies on diffuse liver diseases support this conclusion. The effects of pre- and postprocessing on the detectability of focal lesions are outlined. The impact of multifocus systems and of the acquisition of radio frequency echograms on further developments of clinical echography is discussed.
50 citations
TL;DR: The three-dimensional optical transfer function of a confocal fluorescence microscope is derived, which has no missing cone and provides tomographic images of the sample and the diffraction limitation by an objective lens is verified.
Abstract: The three-dimensional optical transfer function of a confocal fluorescence microscope is derived. It has no missing cone and provides tomographic images of the sample. The derivation is based on the dispersion equation of spherical waves and the diffraction limitation by an objective lens. Experimental results are shown to verify the derivation.
48 citations
01 Jan 1990
TL;DR: The conventional (wide-field) light microscope accepts light from planes above and below the plane of focus and rejects out-of-focus light with the confocal pinhole, which makes it attractive for 3D optical sectioning microscopy.
Abstract: The conventional (wide-field) light microscope accepts light from planes above and below the plane of focus. This lack of depth discrimination is the main limitation of the wide-field microscope for 3D imaging. The confocal microscope rejects this out-of-focus light with the confocal pinhole and provides greater resolution than the wide-field microscope. This depth discrimination of the confocal microscope makes it attractive for 3D optical sectioning microscopy. This advantage of the confocal microscope is balanced by inherent signal losses from the confocal pinhole (see also Chapter 2: Pinhole) and by the use of detectors in current commercial confocal microscopes that have substantially lower quantum efficiency than the cooled CCD cameras used in wide-field digital imaging microscopes. These additional losses of current commercial confocal instruments are especially important in 3D fluorescence imaging of single cells.
48 citations
TL;DR: In this article, the concept of the zero sheet (of the spectrum of a compact image) and its application in deconvolution and phase retrieval are discussed. But, the authors do not consider the problem of phase retrieval for complex-valued images.
Abstract: The insight into deconvolution and phase retrieval afforded by the concept of the zero sheet (of the spectrum of a compact image) is summarized. Difficulties associated with practical implementation of the zero-sheet concept are outlined. Possible means for overcoming these difficulties are suggested and are illustrated with selected examples for several types of deconvolution, i.e., standard, ensemble blind (i.e., blind deconvolution in Stockham’s sense), and pure blind (i.e., deconvolution of a single blurred image without prior knowledge of the point-spread function). A specialized procedure is described for blindly deconvolving a blurred image when the spectrum of the point-spread function is an unknown pure phase function. It is indicated how this procedure may facilitate phase retrieval for spectra of complex-valued images. Possible effects on Wiener filtering and on astronomical speckle imaging are discussed.
48 citations
Patent•
20 Mar 1990TL;DR: In this paper, an image restoration device restores images which are viewed through an optical member and stored in a data processor by processing means associated with the data processor iteratively determine, for each point in a viewed image, a factor which minimizes noise and distortion at that point.
Abstract: An image restoration device restores images which are viewed through an optical member and stored in a data processor. Processing means associated with the data processor iteratively determine, for each point in a viewed image, a factor which minimizes noise and distortion at that point. The factor is iteratively determined through a division operation of a transform of a first function of a response function of the optical member and a transform of a second function of the response function. Preferably, the transform is a Fourier transform and the response function is the point spread function of the optical member. The processing means displays the restored image on a suitable display unit (e.g. a CRT).
TL;DR: This instrument uses a CCD solid state camera to measure the angular radiance field due to a pulsed Lambertian source, which means the PSF can be measured easily at sea, when precise alignments over ranges >10 m cannot be maintained.
Abstract: A new instrument to measure the point spread function (PSF) in the ocean is described. This instrument uses a CCD solid state camera to measure the angular radiance field due to a pulsed Lambertian source. In this way the PSF can be measured easily at sea, when precise alignments over ranges >10 m cannot be maintained. With the large dynamic range of the camera system, the PSF can be measured over short ranges (10 m), and the variation of the PSF with depth, or range, can be investigated.
TL;DR: A model that allows any imaging system to be modeled as an afocal telecentric imaging system preceded and succeeded by simple coordinate transformation operators is presented, derived for diffraction-limited imaging systems where the Fresnel approximation is valid.
Abstract: Streibl [Optik 66, 341-354 (1984)] has shown that afocal telecentric imaging systems are shift invariant in three dimensions. We show that afocal telecentric imaging systems are the only imaging systems that are shift invariant in three dimensions. In addition, we present a model that allows any imaging system to be modeled as an afocal telecentric imaging system preceded and succeeded by simple coordinate transformation operators. The model is derived for diffraction-limited imaging systems where the Fresnel approximation is valid. It is assumed that the object distribution is incoherently radiating and that multiple scattering and absorption within the object distribution are negligible. A physical analogy is given that provides insight into the mathematical model. Finally, a comparison with the work of Frieden is given.
TL;DR: In this article, measurements of an object viewed at low-light levels through weak atmospheric turbulence are modeled mathematically as a time-space doubly stochastic Poisson process in which the intensity function moves randomly in time but is otherwise undistorted.
Abstract: Measurements of an object viewed at low-light levels through weak atmospheric turbulence are modeled mathematically as a time-space doubly stochastic Poisson process in which the intensity function moves randomly in time but is otherwise undistorted. This model is used with the maximum-likelihood method of statistics to derive a new method for forming an image of the object. A simple computer simulation of a moving one-dimensional binary star suggests that improved images may be produced by this method in comparison with others that have been suggested in the literature, but it remains to be demonstrated that this improvement is realized in practice with real imagery data.
TL;DR: In this article, a general technique for designing the thick apertures required to image penetrating radiation with high resolution was presented, which is used to design a high-resolution neutron penumbral-aperture microscope planned for the Nova laser.
Abstract: A general technique is presented for designing the thick apertures required to image penetrating radiation with high resolution. The new apertures are tapered in such a way that the radius of curvature varies inversely with distance from the source plane. The technique is used to design a high-resolution neutron penumbral-aperture microscope planned for the Nova laser. The design provides a resolution (determined by the sharpness of the aperture point-spread function) of >
TL;DR: The imaging properties of a fluorescent scanning optical microscope with a slit detector are investigated by calculating the 3-D optical transfer function (3-D OTF), which varies with the slit direction.
Abstract: The imaging properties of a fluorescent scanning optical microscope (SOM) with a slit detector are investigated by calculating the 3-D optical transfer function (3-D OTF). The bandwidth of the 3-D OTF in the lateral direction varies with the slit direction. The widest bandwidth corresponds to the confocal SOM with an extremely small pinhole detector. The widest longitudinal bandwidth also corresponds to the longitudinal one for the confocal SOM. The contrast for the microscope with the slit is lower than that for the confocal SOM. When the slit width increases, the imaging properties approach those of the conventional optical microscope.
TL;DR: In this paper, the authors describe techniques for data acquisition and processing, which permit accurate photometry at a level of 10−4 of the background night-sky level, are described.
Abstract: Techniques for data acquisition and processing, which permit accurate photometry at a level of 10−4 of the background night-sky level, are described. High quantum efficiency, excellent linearity, and low noise make frame-transfer silicon charge-coupled devices (CCD’s) nearly ideal imagers at ultralow-light levels in the UV to 900-nm range. Scientific-grade CCD’s are now available with less than 10-electron noise from several manufacturers. In astronomy these CCD’s permit studies of objects that are 100 times fainter than is possible by using photographic or video-camera techniques. Detection levels of 2 × 10−5 photons m−2 nm−1 sec−1 pixel−1 have been achieved. The efficiency of telescopes of all apertures has increased to the point at which observations that were unthinkable a decade ago are now becoming routine. New techniques for ultradeep imaging with CCD’s are described. The telescope is moved randomly between exposures, producing 30–100 disregistered images. Automated image processing on a workstation yields the final image, corrected for CCD imperfections and sky + optics systematics. Faint galaxies and stars of 30th magnitude are detected in 10-h integration on a 4-m telescope, corresponding to 0.02 photon sec−1 pixel−1. These techniques may be applied to longer-wavelength imagers with similar problems of bad pixels, bad lines or columns, background variations, etc. Application to faint-galaxy photometry is reviewed, and mosaic CCD imagers are discussed.
TL;DR: In this article, rotational shear interferograms are used to reconstruct unknown objects through fixed unknown aberrations, where the objects are assumed to be fully incoherent and no reference point source is used to calibrate the effects of aberration.
Abstract: Diffraction-limited imaging of unknown objects through fixed unknown aberrations is demonstrated using rotational shear interferograms. Objects are assumed to be fully incoherent. No reference point source is used to calibrate the effects of aberrations. Several algorithms are described, and two are successfully used to reconstruct extended objects. Best results are obtained by combining the two successful ones.
01 Jan 1990
TL;DR: In this paper, a class of imaging, condensing, and collimating devices for x rays is investigated which is based on the use of an array of small channels of square cross section.
Abstract: A class of imaging, condensing, and collimating devices for x rays is investigated which is based on the use of an array of small channels of square cross section. The focusing and collimating effect arises from external reflection of near‐grazing‐incidence rays at the interior channel surfaces. Rays are redirected by being singly reflected from two orthogonal channel surfaces and are imaged from a source point to a square region with a side length MT+1 times that of the channel side length, where MT is the transverse magnification. The image and source locations are related by a thin‐lens formula. The point spread function and the efficiency of these focusing devices are calculated. Two energy regimes with different channel reflectivity characteristics are examined in detail: the hard x‐ray regime (E>8 keV) and the soft x‐ray regime (E<200 eV). For these cases the efficiency of focusing x rays depends only on the channel aspect ratio and reflectivity parameters. A discussion is made of channel plates of ...
TL;DR: It is found that the gradient of the image of a straightedge is 17.8% sharper than in a traditional confocal microscope, and theoretical imaging calculations are often possible in terms of simple analytic functions.
Abstract: We consider the imaging of line structures in confocal imaging systems and show that some advantages result if we employ a slit pupil function in one of the lenses. As an example it is found that the gradient of the image of a straightedge is 17.8% sharper than in a traditional confocal microscope. Another attraction is that theoretical imaging calculations are often possible in terms of simple analytic functions. Experimental results and images are presented which are compared with traditional confocal systems as well as those employing incoherent slit detectors.
01 Nov 1990
TL;DR: In this article, the principles of image formation using a dilute, multiple- telescope interferometer were considered and the requirements for an instrument capable of providing a unique reconstruction of object Fourier phases and instrumental phase errors from a single'snapshot' of data were examined.
Abstract: The principles of image formation using a dilute, multiple- telescope interferometer will be considered. In particular, the requirements for an instrument capable of providing a unique reconstruction of object Fourier phases and instrumental phase errors from a single 'snapshot' of data will be examined. The roles of redundancy in the telescope array, the imposition of the positivity requirement in data inversion, the quality of the instrument point spread function and the stability of the data inversion will be taken into account.
TL;DR: With a suitable noise analysis and a relative Wiener filter, utilizing a Point Spread Function in analogy with optical cases, a good restoration of noisy fast-STM images can be achieved.
01 May 1990
TL;DR: In this paper, an estimation method based on the constrained least squares principle is presented for the restoration of images distorted by a random point spread function and additive measurement noise, which can be constructed in the discrete frequency domain and its overall computation can be carried out using the fast Fourier transform.
Abstract: An estimation method based on the constrained least-squares principle is presented for the restoration of images distorted by a random point spread function and additive measurement noise. The proposed filter modifies the conventional constrained least-squares filter by incorporating additional statistical characteristics about the randomness of the point spread function. Simulation results show that the proposed method outperforms the conventional constrained least-squares method, which neglects the randomness of the point spread function. For space-invariant systems, the modified constrained least-squares filter can be constructed in the discrete frequency domain and its overall computation can be carried out using the fast Fourier transform. >
Patent•
30 Apr 1990
TL;DR: In this paper, the authors proposed an imaging optical system that includes an imaging lens system for forming an image of an object on a given image plane, which can have different magnifications without changing the positional relationship between the object and the image plane and includes a varifocal lens portion and a front lens portion arranged on the object side of the front lens.
Abstract: An imaging optical system suitable for imaging an object having a large spectral component at a certain spatial frequency. The imaging optical system includes an imaging lens system for forming an image of an object on a given image plane. The imaging lens system can have different magnifications without changing the positional relationship between the object and the image plane and includes a varifocal lens portion and a front lens portion arranged on the object side of the varifocal lens portion. The imaging lens system satisfies the following condition: |φ.sub.3T |-|φ.sub.3W |≧0.8|(Z-1)SA31| where Z is the ratio of the maximum value to the minimum value of the magnification of the imaging lens system; SA31 is the third-order coefficient of spherical abberation of the front lens portion; |φ 3T | is the sum of the third-order coefficients of spherical abberation of the respective lens surfaces of the imaging lens system in the state of the maximum magnification; and |φ 3W | is the sum of the third-order coefficients of spherical aberration of the respective lens surfaces of the imaging lens system in the state of the minimum magnification. In this imaging optical system, when the image magnification is varied, the magnitude of the spherical aberration caused by the imaging lens system varies with the magnification. Therefore, the variation of the spatial frequency response of the imaging lens corresponding to the variation of the image magnification is smaller than that of usual varifocal lenses so that the effect of spurious signal elimination remains unchanged even if the magnification is varied.
01 Oct 1990
TL;DR: In this paper, the effects of scatter on image quality and susceptibility to bright off-axis sources were evaluated for planar windows having arbitrary orientations with respect to the optical axis, including A1203 (ordinary ray), Y203, LaO3-doped Y203 and MgAL2O4, and ALON.
Abstract: Knowledge of the scatter characteristics of candidate infrared sensor dome materials is necessary for the evaluation of
image quality and susceptibility to bright off-axis sources. For polycrystalline materials in particular, the scattering levels
are high enough to warrant concern. To evaluate the effects of scatter on image quality, estimates of the window Point
Spread Function (PSF), or its transform, the Optical Transfer Function (OTF) are required. Additionally, estimates of the
material scatter cross-section per unit volume are essential for determining flare susceptibility. Experimental procedures and
models in use at JHU/APL allow the determination of each.
Measurement results are provided for samples of A1203 (ordinary ray), Y203, LaO3-doped Y203, MgAL2O4, and ALON.
Applications of these results are illustrated for planar windows having arbitrary orientations with respect to the optical axis.
TL;DR: In this article, a new approach of imaging based on computer processing is proposed, which is a typical "inverse problem" solution which can be valuably and unambiguously derived in the present situation of point images.
TL;DR: The two-dimensional modulation transfer function (MTF) provides a method for describing resolution in panoramic x-ray systems where the process of image formation differs in the horizontal and vertical dimensions.
Abstract: The two-dimensional modulation transfer function (MTF) provides a method for describing resolution in panoramic x-ray systems where the process of image formation differs in the horizontal and vertical dimensions. As an example, two-dimensional MTFs for the Philips OrthOralix SD machine were calculated from point spread functions (PSF) describing the various sources of unsharpness within the system. The PSF for the focal spot was measured using a pinhole camera. The PSF for the screen-film combination was calculated from data supplied by the manufacturer. The PSF for the motion blurring that is inherent in rotational panoramic radiography was derived from standard mathematical models. The three functions were convolved together to obtain the PSF of the entire system and the two-dimensional MTF was derived from the system PSF by Fourier transformation. The two-dimensional MTF provides a tool which should be useful in the future for the evaluation of existing systems, for the design of improved equipment, and for the implementation of image processing algorithms.
TL;DR: In this paper, an experimental investigation on image quality improvement using J2 synthesis has been conducted, which is known to be an effective method in radio astronomy to generate an appropriate PSF.
TL;DR: In this investigation, a new technique employing wavefront superposition has been proposed to implement an optical half-adder and the experimental results are presented.
Abstract: Wavefront superposition is a powerful technique for performing optical logic operations. In this investigation, a new technique employing wavefront superposition has been proposed to implement an optical half-adder; the experimental results are presented. Multiplexing these half-adders to perform any additions and potential hardware specifications are also discussed.
TL;DR: The WINKLER spectrometer as discussed by the authors is a matrix of nine high-purity n-type germanium detectors developed for astrophysical observations and terrestrial monitoring and is fitted with a set of modulation collimator grids designed for imaging hard X-ray and gamma-ray sources by the Mertz, Nakano, and Kilner (1986) method.
Abstract: The WINKLER spectrometer is a matrix of nine high-purity n-type germanium detectors developed for astrophysical observations and terrestrial monitoring. The spectrometer has been fitted with a set of modulation collimator grids designed for imaging hard X-ray and gamma-ray sources by the Mertz, Nakano, and Kilner (1986) method. This technique uses a pair of gridded collimators in front of each detector with the number of grid bars varying from one to N, where N is the number of detectors. When the collimator pairs are rotated through a full 360 degrees angular range, the detector signals provide the information for a two-dimensional bandlimited Fourier reconstruction of order N. Tests of the spectrometer with single and multiple point sources as well as continuous source distributions are reported. The spectrometer's field of view is 20 degrees , and the observed FWHM of the point spread function is 1.6 degrees , in good agreement with simulation results. Images have been obtained for gamma-ray energies from 60 keV to 1.3 MeV, although transmission through the grids reduces contrast at the higher energies. Potential capabilities of the spectrometer for locating the position of single point sources or resolving structure in closely spaced source distributions are discussed, as well as proposed upgrades to improve angular resolution. >