Showing papers on "Point spread function published in 1992"

Tandem linear scanning confocal imaging system with focal volumes at different heights

Abstract: A confocal imaging system utilizes an opaque mask with a slit and a row of pinpoint sensors or utilizes an opaque mask with a skewed pattern of pinholes and an array of isolated pinpoint sensors in a matching pattern in order to obtain sufficient data to provide a complete image for imaging and/or inspecting an object such as electronics in a single one-dimensional scan. The system also simultaneously produces multiple images at different heights in the single one-dimensional scan of the viewed object, and also simultaneously produces images taken in different spectral bands in the same one-dimensional scan of the object to be imaged and/or inspected. The relative height or depth of the different images can be modified by simply adjusting the inclination between the confocal imaging system and a path followed by the object that is to be imaged and/or inspected during the one-dimensional scan. The optical confocal imaging system requires no moving parts and the only moving parts of the system are for motorized conveying of the object to be imaged and/or inspected along the path. In one arrangement of the confocal imaging system, color imaging and/or inspecting of the object can be performed. In another arrangement of the confocal imaging system, simultaneous brightfield and darkfield imaging and/or inspecting of an object can be performed.

The loss of small objects in variable TE imaging: implications for FSE, RARE, and EPI.

Abstract: The importance to MR image quality of the order of acquisition of different phaseencoded views with sequences that have variable TR and TE has been recently reported. It has been shown that the effective point spread function (PSF) may be manipulated by varying TE or TR, or both, with each phase-encoding step. This paper explores the behavior of the PSF in a variable TE sequence and its dependence on both imaging and tissue parameters. It is shown that the PSF is different for each tissue type and that its effect on tissue contrast is a function of both the shape and size of the structure. The important problem of signal loss from small objects that arises when the effective PSF is broad and the difficulty in detecting this phenomenon in practical MR images is illustrated. It is shown that the PSF can produce significant blurring and loss of object contrast in fast spin-echo images but that this blurring may be not be obvious in practice because the noise is unaffected by the PSF. It is also shown that the signal from small lesions with short T2 can easily be lost through this blurring mechanism. The importance of signal loss from small objects and its implication for the clinical use of such sequences as fast spinecho or rapid acquisition relaxation-enhanced and echo planar imaging is stressed.© 1992 Academic Press,Inc.

Deblurring for non-2D Fourier transform magnetic resonance imaging.

Abstract: For several non-2D Fourier transform imaging methods, off-resonant reconstruction does not just cause geometric distortion, but changes the shape of the point spread function and causes blurring. This effect is well known for projection reconstruction and spiral k-space scanning sequences. We introduce here a method that automatically removes blur introduced by magnetic field inhomogeneity and susceptibility without using a resonant frequency map, making these imaging methods more useful. In this method, the raw data are modulated to several different frequencies and reconstructed to create a series of base images. Determination of degree of blur is done by calculating a focusing measure for each point in each base image and a composite image is then constructed using only the unblurred regions from each base image. This method has been successfully applied to phantom and in vivo images using projection-reconstruction and spiral-scan sequences.

Identification and restoration of spatially variant motion blurs in sequential images

Abstract: Sequential imaging cameras are designed to record objects in motion. When the speed of the objects exceeds the temporal resolution of the shutter, the image is blurred. Because objects in a scene are often moving in different directions at different speeds, the degradation of a recorded image may be characterized by a space-variant point spread function (PSF). The sequential nature of such images can be used to determine the relative motion of various parts of the image. This information can be used to estimate the space-variant PSF. A modification of the Landweber iteration is developed to utilize the space-variant PSF to produce an estimate of the original image. >

Imaging through fog and rain

Abstract: The main aerosol effect on imaging performance is brightness reduction through scattering losses. This is fairly well understood and modeled. However, one phenomenon that is almost always overlooked is the blurring of images that can result from forward-scattered radiation, i.e., the radiation reaching the image plane after being scattered by airborne particles. The paper describes a new and efficient method of calculation of the forward-scattering effect on the point spread and modulation transfer functions. Solutions are presented that show the dependence of the aerosol blurring effect on particle concentration, particle size, geometry, and size of object features. The paper also reports on a simple experiment for measuring the visible point spread function through fog and rain. In most cases, the measurements are in good agreement with the model predictions. As it turns out, our measurements performed at ranges of 500 and 900 m and optical depths of up to seven show significant aerosol blurring effects only for rain and for some advection fogs with a sufficient number of particles in the size range of about 100 μm.

Thin-section ratiometric Ca2+ images obtained by optical sectioning of fura-2 loaded mast cells.

Abstract: The availability of the ratiometric Ca2+ indicator dyes, fura-2, and indo-1, and advances in digital imaging and computer technology have made it possible to detect Ca2+ changes in single cells with high temporal and spatial resolution. However, the optical properties of the conventional epifluorescence microscope do not produce a perfect image of the specimen. Instead, the observed image is a spatial low pass filtered version of the object and is contaminated with out of focus information. As a result, the image has reduced contrast and an increased depth of field. This problem is especially important for measurements of localized Ca2+ concentrations. One solution to this problem is to use a scanning confocal microscope which only detects in focus information, but this approach has several disadvantages for low light fluorescence measurements in living cells. An alternative approach is to use digital image processing and a deblurring algorithm to remove the out of focus information by using a knowledge of the point spread function of the microscope. All of these algorithms require a stack of two-dimensional images taken at different focal planes, although the "nearest neighbor deblurring" algorithm only requires one image above and below the image plane. We have used a modification of this scheme to construct a simple inverse filter, which extracts optical sections comparable to those of the nearest neighbors scheme, but without the need for adjacent image sections. We have used this "no neighbors" processing scheme to deblur images of fura-2-loaded mast cells from beige mice and generate high resolution ratiometric Ca2+ images of thin sections through the cell. The shallow depth of field of these images is demonstrated by taking pairs of images at different focal planes, 0.5-microns apart. The secretory granules, which exclude the fura-2, appear in focus in all sections and distinct changes in their size and shape can be seen in adjacent sections. In addition, we show, with the aid of model objects, how the combination of inverse filtering and ratiometric imaging corrects for some of the inherent limitations of using an inverse filter and can be used for quantitative measurements of localized Ca2+ gradients. With this technique, we can observe Ca2+ transients in narrow regions of cytosol between the secretory granules and plasma membrane that can be less than 0.5-microns wide. Moreover, these Ca2+ increases can be seen to coincide with the swelling of the secretory granules that follows exocytotic fusion.

Practical applications of chemical shift imaging.

Abstract: Methods of spectral localization are briefly reviewed and divided into two classes: those using phase encoding and those using frequency selective RF pulses in a constant gradient. A potentially troubling artifact in the latter case is the spatial misregistration of different compounds which causes serious errors in 31P spectra from smaller regions. Chemical shift imaging (CSI) is presented as a typical example of phase encoding techniques. An analytical expression for the relationship of the signal observed to the true signal (the point spread function) is derived. Examples of CSI in one, two, and three dimensions are used to illustrate the principles of this type of localization.

High‐contrast resolution of CT images for bone structure analysis

Abstract: The modulation transfer function (MTF) of an imaging system may be used as a figure of merit to assess its geometrical resolution. As such it is often derived from the point spread function (PSF) through a Fourier transformation, or through a FFT in case of digital images. Using the special features of the convolution-backprojection algorithm and making some simplifying assumptions about the number of rays, it is shown that the desired MTF is also obtainable without a Fourier transformation of the PSF, different shapes and sizes of the beam-profile are then analyzed, and finally it is shown that calculated and measured MTF functions are in good agreement. The effects of aliasing on the cutoff frequency are also discussed.

Resolution enhancement for ultrasonic reflection mode imaging

Abstract: An annular array scanner utilizes a synthetic focusing approach to improve imaging results. Image sharpening methods include corrections for the speed of sound of the image, phased array misregistration and separate view misalignment as well as inverse filtering for the scanning system point spread function.

Annular array imaging with full‐aperture resolution

Abstract: The problem of imaging with an annular array of transducers by employing all pairs of transducer elements around the circumference of the annulus as transmitters and receivers is considered. If θt and θr are, respectively, the angular locations of a pair of transmitting and receiving elements, then weighting the received signal with the positive weight 2‖sin(θt−θr)‖ before coherent summation results in an image point spread function of the form J1(R)/R. This corresponds to the point spread function of a full circular (area) aperture. Moreover, it is shown that the diameter of this synthetic aperture is twice that of the annulus. A more general weighting function is also derived that results in a point spread function of the form Jn(R)/Rn, n=1,2,..., which is shown to correspond to an apodized circular aperture of diameter twice that of the annulus.

Resolution Limits for Deconvolved Images

Abstract: The limits imposed by photon statistics on the resolution attainable by deconvolving seeing-broadened astronomical images are investigated. By analogy with the classical Rayleigh limit for diffraction-limited images, resolution is defined as the separation of the equal component double star that can be just resolved by deconvolution. An approximate analytic theory is given that predicts the dependence of resolution thus defined on the number of detected photons, and this theory is tested by deconvolution experiments on synthetic images

Diffractive multifocal intraocular lens image quality

Abstract: The diffractive multifocal intraocular lens is implanted in the eye to replace a cataractous crystalline lens. Axially separated images from two diffraction orders provide near and distance vision. Overall image quality is affected by both the quality of the in-focus component and the energy distribution between images. Modulation transfer function and energy distribution data are presented. Measurement accuracy is limited by the diameter of the point spread function and by the difficulty in separating the focused and defocused components.

Optical Performance of Large Ground-based Telescopes

Abstract: Images taken with ground-based telescopes are dominated by atmospheric seeing. Analytical expressions of long-exposure optical functions, namely the modulation transfer function, point spread function and encircled energy are established, under the assumption that dome and telescope seeing are brought to negligible values, and that the diameter of the telescope is larger than the atmospheric coherence length. The influence of guiding errors and axisymmetrical telescope aberrations is also assessed, and a definition of optical quality is proposed. The results are generalized and the optical performance of a ground-based telescope is expressed in terms of effective diameter and signal-to-noise ratio.

Optical spatial filter

Abstract: An optical filter 10 for filtering spatial frequencies from an output of an optical imaging system comprises a substantially transparent, or reflective, optical element 12 having a plurality of light refracting, or reflecting, segments 18 arranged on a surface thereof. Each of the plurality of segments 18 is provided with a predetermined angle of refraction, or reflection, distinct from adjacently located segments 18, wherein the different angles of refraction, or reflection, and the arrangement of the segments 18 on the optical element 12, are determined based on a desired spatial frequency transfer function for the filter 10. The optical spatial filter 10 reduces errors in optically formed images by accurately confining a broadened Point Spread Function (PSF) to a desired spot size.

Effect of detector weighting functions on the point spread function of high-resolution PET tomographs: a simulation study

Abstract: The point spread function (PSF) of a ring PET tomograph is known to be spatially variant and difficult to obtain because it must be reconstructed from projections A mathematical model was developed to simulate the data acquisition from a point source and to reconstruct the PSF, taking into account weighting functions to describe the detector response functions In order to investigate the effect of the detector weighting function on the PSF, the reconstruction, based on the filtered backprojection algorithm, was implemented with three classes of weighting functions of decreasing complexity: exact, locally invariant, and constant Significant differences are observed to result from the three hypotheses, and this is shown to lead to distorted PSFs and to erroneous estimates of the intrinsic resolution off the center of the tomograph >

A tilting device for three-dimensional microscopy: application to in situ imaging of interphase cell nuclei.

Abstract: The resolution of an optical microscope is considerably less in the direction of the optical axis (z) than in the focal plane (x-y plane). This is true of conventional as well as confocal microscopes. For quantitative microscopy, for instance studies of the three-dimensional (3-D) organization of chromosomes in human interphase cell nuclei, the 3-D image must be reconstructed by a point spread function or an optical transfer function with careful consideration of the properties of the imaging system. To alleviate the reconstruction problem, a tilting device was developed so that several data sets of the same cell nucleus under different views could be registered. The 3-D information was obtained from a series of optical sections with a Zeiss transmission light microscope Axiomat using a stage with a computer-controlled stepping motor for movement in the z-axis. The tilting device on the Axiomat stage could turn a cell nucleus through any desired angle and also provide movement in the x-y direction. The technique was applied to 3-D imaging of human lymphocyte cell nuclei, which were labelled by in situ hybridization with the DNA probe pUC 1.77 (mainly specific for chromosome 1). For each nucleus, 3-D data sets were registered at viewing angles of 0 degrees, 90 degrees and 180 degrees; the volumes and positions of the labelled regions (spots) were calculated. The results also confirm that, in principle, any angle of a 2 pi geometry can be fixed for data acquisition with a high reproducibility. This indicates the feasibility of axiotomographical microscopy of cell nuclei.

On-axis conoscopic holography without a conjugate image.

Abstract: We present a method for removing the conjugate image in an incoherent-light holographic technique, namely, on-axis conoscopic holography. The point-spread function that we obtain is that of a complex Gabor zone pattern, which thus should allow good-quality reconstructions of objects. Experimental results are also presented, which confirm the validity of this method.

Coarray synthesis with circular and elliptical boundary arrays

Abstract: An elliptical boundary aperture is a collection of points lying on an ellipse from which energy is transmitted and/or received. An important special case is the circular boundary aperture. When these apertures are used with beamforming to produce a narrowband image of a far-field source, the corresponding point spread function (PSF) is characterized by high sidelobes. The concept of the coarray of an imaging system is used here to develop techniques which synthesize the effect of a more desirable PSF with an elliptical boundary aperture. Techniques are given for use in active imaging of spatially coherent sources, as well as passive imaging of spatially incoherent sources. Discrete arrays and continuous apertures are considered separately. The approach shows that the PSF synthesis problem can be solved in many more ways than previously recognized, and this fact is exploited to develop procedures which have a least-squares optimality property. >

Effects of defocus and primary spherical aberration on three-dimensional coherent transfer functions in confocal microscopes.

Abstract: For both reflection- and transmission-mode confocal scanning microscope systems, three-dimensional coherent transfer functions are investigated by considering the effects of defocus and primary spherical aberration. We numerically calculate the three-dimensional coherent transfer functions for various amounts of aberration and show that three-dimensional confocal imaging is strongly degraded if the amount of aberration is larger than a quarter wavelength. The compensation of the primary spherical aberration by introducing defocus is also discussed.

Definition, resolution, and contrast in photothermal imaging

Abstract: Photothermal imaging can be described quantitatively by means of a point spread function (PSF), which represents the image of a buried thermal point defect. From this PSF conclusions can be drawn about amplitude and phase contrast, half‐width, and resolution of photothermal imaging. The theoretical findings are stated by measurements from an appropriately designed model sample.

Non-iterative compensation for the distance-dependent detector response and photon attenuation in SPECT imaging

Abstract: A filtering approach is described which accurately compensates for the 2-D distance-dependent detector response, as well as for photon attenuation in a uniform attenuating medium. The filtering method is based on the energy distance principle (EDP), which states that points in the object at a specific source-to-detector distance provide the most significant contribution to specified frequency regions in the discrete Fourier transform (DFT) of the sinogram. By modeling the detector point spread function as a 2-D Gaussian function whose width is dependent on the source-to-detector distance, a spatially variant inverse filter can be computed and applied to the 3-D DFT of the set of all sinogram slices. To minimize noise amplification the inverse filter is rolled off at high frequencies by using a previously published Wiener filter strategy. Attenuation compensation is performed with Bellini's method. It was observed that the tomographic point response, after distance-dependent filtering with the EDP, was approximately isotropic and varied substantially less with position than that obtained with other correction methods. >

Image restoration in computed tomography: estimation of the spatially variant point spread function

Abstract: An indirect method for determining the point-spread-function (PSF) in computed tomography (CT) is described. Unlike experimental techniques in which a resolution phantom is scanned to obtain the system PSF, the approach estimates the parameters of a model which describes the two-dimensional X-ray beam profile at each point as a convolution of the appropriately scaled focal spot intensity and detector sensitivity distributions. The model was validated by experimental measurement of the focal spot intensity distribution. Using known X-ray beam profiles, the PSF of a CT scanner can be derived by simulating the data collection process and applying conventional image reconstruction techniques. Visual comparison of directly measured and computed PSFs reveals an asymmetry resulting from misregistration of the phantom wires and the image grid. >

Determination of the wave-front aberration function from measured values of the point-spread function: a two-dimensional phase retrieval problem

Abstract: We outline a method for the determination of the unknown wave-front aberration function of an optical system from noisy measurements of the corresponding point-spread function. The problem is cast as a nonlinear unconstrained minimization problem, and trust region techniques are employed for its solution in conjunction with analytic evaluations of the Jacobian and Hessian matrices governing slope and curvature information. Some illustrative numerical results are presented and discussed.

Fourier-plane filtering by a thick grating: a space - bandwidth analysis.

Abstract: The space–bandwidth requirements of thick gratings in the Fourier plane of a coherent optical image processor are analyzed. Based on Kogelnik’s relationship for the diffraction efficiency, relations for the space–bandwidth products of the input image and the point-spread function are obtained in terms of grating parameters. It is concluded that thick gratings, such as photorefractive crystals, are not well suited for implementing shift-invariant operations through Fourier-plane filtering.

Point spread function of the general cone‐beam x‐ray reconstruction formula

Abstract: In this paper, the spatially varying point spread function (PSF) of the general cone-beam x-ray reconstruction formula is derived. It is proved that the vertical integral of the PSF is a two-dimensional δ function. Therefore, although the general cone-beam formula is not exact in nature, the vertical integral of the reconstructed three-dimensional image is equal to that of the actual image. The band-limited version of the PSF is also derived. The PSF of the general cone-beam formula is simulated, based on which the reconstruction resolution can be approximately inferred.

Edge-setting criterion in confocal microscopy.

Abstract: The intensity that locates the image of an edge in a confocal microscope is calculated as a function of detector size. Both pinhole and slit detectors are considered. Knowledge of this edge-setting criterion permits accurate determination of the edge position, as is necessary for confocal metrology.

Blind deconvolution of 2-D and 3-D fluorescent micrographs

Abstract: This paper presents recent results of our reconstructions of 3-D data from Drosophila chromosomes as well as our simulations with a refined version of the algorithm used in the former. It is well known that the calibration of the point spread function (PSF) of a fluorescence microscope is a tedious process and involves esoteric techniques in most cases. This problem is further compounded in the case of confocal microscopy where the measured intensities are usually low. A number of techniques have been developed to solve this problem, all of which are methods in blind deconvolution. These are so called because the measured PSF is not required in the deconvolution of degraded images from any optical system. Our own efforts in this area involved the maximum likelihood (ML) method, the numerical solution to which is obtained by the expectation maximization (EM) algorithm. Based on the reasonable early results obtained during our simulations with 2-D phantoms, we carried out experiments with real 3-D data. We found that the blind deconvolution method using the ML approach gave reasonable reconstructions. Next we tried to perform the reconstructions using some 2-D data, but we found that the results were not encouraging. We surmised that the poor reconstructions were primarily due to the large values of dark current in the input data. This, coupled with the fact that we are likely to have similar data with considerable dark current from a confocal microscope prompted us to look into ways of constraining the solution of the PSF. We observed that in the 2-D case, the reconstructed PSF has a tendency to retain values larger than those of the theoretical PSF in regions away from the center (outside of those we considered to be its region of support). This observation motivated us to apply an upper bound constraint on the PSF in these regions. Furthermore, we constrain the solution of the PSF to be a bandlimited function, as in the case in the true situation. We have derived two separate approaches for implementing the constraint. One approach involves the mathematical rigors of Lagrange multipliers. This approach is discussed in another paper. The second approach involves an adaptation of the Gershberg Saxton algorithm, which ensures bandlimitedness and non-negativity of the PSF. Although the latter approach is mathematically less rigorous than the former, we currently favor it because it has a simpler implementation on a computer and has smaller memory requirements. The next section describes briefly the theory and derivation of these constraint equations using Lagrange multipliers.

Fluorescent image formation in the fibre-optical confocal scanning microscope

Abstract: Reported in this paper are theoretical studies on two-dimensional and three-dimensional image formation with fluorescent objects in a fibre-optical confocal scanning microscope. An effective point spread function is introduced to derive the two- and three-dimensional optical transfer functions. It is found that, unlike confocal fluorescence microscopes with a finite circular detector, there is no missing cone of spatial frequencies, and no negative tail in the transfer function. The effect of the system parameters on the optical sectioning property is also investigated.