Showing papers on "Point spread function published in 1986"

High-Speed Spiral-Scan Echo Planar NMR Imaging-I

Abstract: An improved echo planar high-speed imaging technique using spiral scan is presented and experimental advantages are discussed. This proposed spiral-scan echo planar imaging (SEPI) technique employs two linearly increasing sinusoidal gradient fields, which results in a spiral trajectory in the spatial frequency domain (k-domain) that covers the entire frequency domain uniformly. The advantages of the method are: 1) circularly symmetric T2 weighting, resulting in a circularly symmetric point spread function in the image domain; 2) elimination of discontinuities in gradient waveforms which in turn will reduce initial transient as well as steady-state distortions; and 3) effective rapid spiral-scan from dc to high frequency in a continuous fashion, which ensures multiple pulsing with interlacing for further resolution improvement without T2 decay image degradation. Some preliminary experimental results will be presented and further possible improvements suggested.

An Iterative Image Space Reconstruction Algorthm Suitable for Volume ECT

Abstract: The trend in the design of scanners for positron emission computed tomography has traditionally been to improve the transverse spatial resolution to several millimeters while maintaining relatively coarse axial resolution (1-2 cm). Several scanners are being built with fine sampling in the axial as well as transverse directions, leading to the possibility of the true volume imaging. The number of possible coincidence pairs in these scanners is quite large. The usual methods of image reconstruction cannot handle these data without making approximations. It is computationally most efficient to reduce the size of this large, sparsely populated array by back-projecting the coincidence data prior to reconstruction. While analytic reconstruction techniques exist for back-projected data, an iterative algorithm may be necessary for those cases where the point spread function is spatially variant. A modification of the maximum likelihood algorithm is proposed to reconstruct these back-projected data. The method, the iterative image space reconstruction algorithm (ISRA), is able to reconstruct data from a scanner with a spatially variant point spread function in less time than other proposed algorithms. Results are presented for single-slice data, simulated and actual, from the PENN-PET scanner.

Superresolving filters in confocally scanned imaging systems

Abstract: The limitations of superresolving filters in imaging systems are investigated. The constraints on such filters in the nonscanning imaging mode are discussed. The possible advantages of such filters in confocal scanning imaging are highlighted. It is shown theoretically and verified experimentally that simply designed complex-amplitude filters can be used effectively to double the exit pupil of a confocal imaging system and thus improve resolution. Superresolution can be achieved with acceptable energy losses and manufacturing tolerances.

Suppression of respiratory motion artifacts in magnetic resonance imaging

Abstract: Anatomical structures that are displaced periodically during respiration are repeated as ghosts in magnetic resonance (MR) images These ghosts can be suppressed in many ways: the averaging of multiple sets of data, respiratory gating, deliberate positioning of ghosts, and respiratory ordering of phase encoding Each method has a unique mechanism, which is described in detail A theoretical investigation has been conducted into the effects that the methods have on the point spread function of a moving point Data acquired in Fourier imaging are actually in the spatial frequency domain, so that respiratory motion can be regarded as a function of spatial frequency The four methods above modify this functional dependence in different ways, allowing a unified comparison Motion artifact suppression imposes additional constraints on image acquisition, which can prolong the imaging time A technique has been developed that keeps the imaging time short by using the configuration of the subject to regulate the timing of image acquisition

Characterization of the point spread function and modulation transfer function of scattered radiation using a digital imaging system

Abstract: A digital radiographic system was used to measure the distribution of scattered x radiation from uniform slabs of Lucite at various thicknesses. Using collimation and air gap techniques, [primary + scatter] images and primary images were digitally acquired, and subtracted to obtain scatter images. The scatter distributions measured using small circular apertures were computer fit to an analytical function, representing the circular aperture function convolved with a modified Gaussian point spread function (PSF). On the basis of goodness of fit criterion, the proposed Gaussian function is a very good model for the scatter PSF. The measured scatter PSF's are reported for various Lucite thicknesses. Using the PSF's, the modulation transfer functions are calculated, and this spatial frequency information may have value in analytical scatter removal techniques, grid design, and air gap optimization.

Rotational aperture synthesis for x rays

Abstract: Aperture synthesis for the x-ray region can be accomplished with an array of rotation modulation collimators. A Hermitianizing recipe extracts sine and cosine components from a pair of collimators for each fringe spacing, and Fourier synthesis then reconstructs the images. The point-spread function has low sidelobes and is applicable with extended sources. A Monte Carlo simulation is used to illustrate and evaluate the statistical effects of quantum noise. Even better images may be expected from positively constrained reconstruction. The effects of axial misalignment on the point-spread function are illustrated. The conclusion is a favorable appraisal of the array as an astronomical telescope for hard x rays.

Low-light-level charge-coupled device imaging in astronomy

Abstract: Charge-coupled devices (CCD’s) on both large and small telescopes are revolutionizing astronomy, permitting studies to be made of objects up to 10 times fainter than possible by using photographic and video camera techniques. This is due both to the high quantum efficiency and to the photometric stability of the CCD. Chopping techniques, taking advantage of this stability, permit cancellation of low-level systematics. Faint galaxies and stars of 27-V magnitude are detected in 2-h integration on a 4-m telescope, corresponding to 0.02 (photons/sec)/pixel. Automated image preprocessing and pattern recognition at high data rates permit statistical studies to be made of multispectral CCD data. In the future the efficiency of large telescopes for survey studies will be improved by the use of CCD mosaics covering the entire usable focal plane.

Quantitative contrast measurements in B-mode images comparison between experiment and theory.

Abstract: Quantitative measurements of image contrast were carried out for B-mode images of anechoic spheres (cysts) embedded in a random scattering medium. Four transducer geometries were used: (a) f 5.7 spherical transducer in pulse echo mode, (b) f 2.4 spherical transducer in pulse echo mode, (c) f 2.4 , 30° cone (hybrid transducer), (d) f 5.7 , 30° cone (hybrid transducer). The image contrast was also calculated via two methods; (i) a three-dimensional computer simulation and (ii) a relatively simple numerical convolution which relates the image of a small point-like scatterer [point spread function (PSF)] to image contrast. Generally, good agreement was found between the experimental measurements and the values calculated via both theoretical methods. The results indicate that image contrast is not determined solely by the full width at half maximum (FWHM) of the PSF. In particular, the results demonstrate the importance of far off-axis contributions of the ultrasound beam to the significant degradation of contrast in images obtained with high resolution (low f-number) axicons.

Astronomical imaging by filtered weighted-shift-and-add technique

Abstract: The weighted-shift-and-add speckle imaging technique is analyzed using simple assumptions. The end product is shown to be a convolution of the object with a typical point-spread function (psf) that is similar in shape to the telescope psf and depends marginally on the speckle psf. A filter can be applied to each data frame before locating the maxima, either to identify the speckle locations (matched filter) or to estimate the instantaneous atmospheric psf (Wiener filter). Preliminary results show the power of the technique when applied to photon-limited data and to extended objects.

Generalization of some incoherent spatial filtering techniques.

Abstract: A two-channel incoherent spatial filtering system is generalized by considering two object transparencies, one in each of the two channels. Various special cases result, including two that have previously been described and others not previously given. The system can be either linear in irradiance (the basic incoherent case) or linear in field (the basic coherent case) even though the illumination is incoherent in either case. In particular, we show spatial filtering with the object in one channel and the spatial filter in the other channel.

Measurement of 1-μm diam beams

Abstract: Measurements of beams of ~1 μm in diameter are presented. Three approaches, one using a Ronchi ruling, the other two based on knife-edge scan techniques are compared experimentally. Effects of Ronchi ruling accuracy and nonconstant scan velocity are discussed. Included are results of theoretical studies on the effect of imperfect scanning edges and non-Gaussian beam profiles on measurement results.

A Parametric Study Of Various Synthetic Aperture Telescope Configurations For Coherent Imaging Applications

Abstract: The comparative advantages of synthetic aperture telescopes (SATs) of segmented primary mirror and common secondary mirror type, on the one hand, and on the other those employing an array of independent telescopes, are discussed. The diffraction-limited optical performance of both redundant and nonredundant subaperture configurations are compared in terms of point spread function characteristics and encircled energy plots. Coherent imaging with afocal telescope SATs involves a pupil-mapping operation followed by a Fourier transform one. A quantitative analysis of the off-axis optical performance degradation due to pupil-mapping errors is presented, together with the field-dependent effects of residual design aberrations of independent telescopes.

Method and apparatus for sidelobe suppression in scanning imaging systems

Abstract: The paraxial, c.w. focal zone resolution of a focussed scanning imaging system is improved by choosing the ratio of the size of the apertures which are used to transmit and receive energy from the scene such that the first and second sidelobes of the system point spread function have equal amplitudes.

A signal processing model of diagnostic x-ray scatter.

Abstract: A model of scatter is developed from a signal processing approach. The scattering process is viewed as a nonlinear filter (NLF), which transforms a two‐dimensional signal representing phantom thickness into a two‐dimensional signal of scattered radiation. The NLF point spread function (PSF) is derived from a single scattering model, using the principles of Compton scattering and x‐ray attenuation. The PSF is characterized by three approximations: a constant geometric shape, a volume that depends on the phantom thickness, and a width that depends on the phantom‐to‐detector distance. This leads to a closed form expression for the scatter‐to‐primary ratio as a function of phantom thickness, field size,photon energy, source‐to‐phantom distance, and phantom‐to‐detector distance. The NLF model is compared with previously reported measurements using constant thickness phantoms, and discrepancies are discussed. The good agreement found between the NLF model and measured data shows that the functional dependence of scatter on the above parameters, previously only explained in terms of empirical models or Monte Carlo simulations, can be incorporated into a signal processing model.

Transform based proximity corrections: Experimental results and comparisons

Abstract: This paper presents a comparison between the transform based proximity correction method and the GHOST background equalization method. Both methods are presented and evaluated in general as well as for a specific test structure. Emphasis is placed upon the frequency domain characteristics of each approach. It is shown that the GHOST method, by itself, while successfully equalizing the background exposure without the use of extensive computation, lacks good high frequency characteristics. This limits the fidelity of the corrections for features in the range of 0.50–0.20 μm. The transform or Fourier precompensation method can handle such features but it requires some degree of computation and data compaction. Experimental results are presented along with corresponding computer generated simulations. It is found that a very accurate measurement of the e‐beam point spread function is essential to make the transform method perform properly. A technique is presented to achieve such a measurement.

Rotational and boiling motion of speckles in a two-lens imaging system

Abstract: The motion of speckles produced by a rotating diffuse object with a spatial velocity distribution was investigated. It was shown that speckle motion in a two-lens imaging system depends on the Doppler-shift frequency distribution that is due to the spatial velocity distribution of the diffuse object within the point spread of the optical system used. By measuring the time correlation of speckle intensity fluctuations, the predicted properties of the speckle motion that exhibit a good agreement with the experimental results are presented.

Restoration of images distorted by systems of random time-varying impulse response

Abstract: The problem of restoring a constant image distorted by a system of random time-varying impulse response is investigated. The restoration is based on the observed time-varying distorted image during a finite period of time. Three methods are considered. Restorations based on the average image and on the averaged spatial correlation of the image are discussed briefly. Restoration based on a finite number of image frames is examined in detail. We use an iterative method based on the minimum-variance unbiased estimation. A transformation that decorrelates the frames is used to reduce the computations.

Reduction of aliasing in modulation transfer function measurements

Abstract: The images formed by many radiological systems are difficult to sample at spatial intervals small enough to avoid aliasing in the calculation of the system's modulation transfer function. However, if a system's response can be assumed to be symmetrical, this assumption can be used to effectively double the sampling density and to double the frequency limit before aliasing occurs. To accomplish this, a more complex algorithm is required. In this work, the formula for the calculation of the modulation transfer function from a symmetrical, one-dimensional line spread function is derived and a similar result for a symmetrical, two-dimensional point spread function is presented. The effect of noisy data and errors in the estimation of the offset of the center of the line spread function from a sampling point are investigated by simulation studies. For low noise (relative standard deviation of 1%) and an offset error of no more than 2% or 3% of a sampling interval, reasonable precision is obtained. These conditions appear to be achievable, especially when the noise is Poisson distributed.

Passive synthetic aperture imaging using an achromatic grating interferometer.

Abstract: Synthetic aperture imaging with active systems is relatively well developed. The implementation of passive systems, on the other hand, is being hindered by a low SNR and the difficulty in achieving 2-D aperture fill. The achromaticity of the grating interferometer permits the use of a wider instantaneous spectral bandwidth to produce better SNR, and it provides a simple means to synthesize a 2-D aperture. A passive synthetic aperture imaging approach implemented with an achromatic grating interferometer is described, and laboratory experimental results are presented to demonstrate the proposed concept.

Restoration for sampled imaging systems.

Abstract: Digital image restoration requires some knowledge of the degradation phenomena in order to attempt an inversion of that degradation Typically, degradations which are included in the restoration process are those resulting from the optics and electronics of the imaging device Occasionally, blurring caused by an intervening atmosphere, uniform motion or defocused optics is also included Recently it has been shown that sampling, the conversion of the continuous output of an imaging system to a discrete array, further degrades or blurs the image Thus, incorporating sampling effects into the restoration should improve the quality of the restored image The system transfer function (the Fourier transform of the point spread function), was derived for the Landsat Multi-Spectral Scanner (MSS) and Thematic Mapper (TM) systems Sampling effects were included, along with the relevant optical, instantaneous-field-of-view and electronic filter data, in the system analysis Using the system transfer function, a least-squares (Wiener) filter was derived A Wiener filter requires the ratio of the power spectra of the scene and noise, which is often, for simplicity, assumed to be a constant over frequency Our restoration includes models for the power spectra which are based on the study of several different types of Landsat scenes The Wiener filter is then inverse Fourier transformed to find a restoration filter which is spatially windowed to suppress ringing Visual evaluations are made of the restored imagery

Study of the direct Fourier method for the three-dimensional reconstruction of objects in the case of a missing angular data range

Abstract: SUMMARY Some practical and theoretical considerations on the three-dimensional reconstruction of an object from its two-dimensional projections by the direct Fourier method have been obtained using computer generated images. The procedure applied has been designed to study the specific problems derived from the collection of images in transmission electron microscopes (TEM), making special emphasis on images of biological objects. The study of the calculated point spread function (PSF) of the experimental system and the mean and variance profiles of the reconstructions have provided useful criteria to assess the quality and the interpretability of three-dimensional reconstructions of real data.

Synthetic Focused Image Reconstruction in the Presence of a Finite Delay Noise

Abstract: It, is shown that a finite random delay (or phase) noise leads to spurious imaging sidelobes in the point-spread-function of a synthetic focused ultrasonic imaging system. In medical ultrasound, this delay noise can, for example, arise from spatial variation of tissue velocity. It is further shown that the magnitude and structure of these sidelobes are a function of both delay noise level and i ts s patial variation across the aperture. The magnitude and significance of these sidelobes are studied in this paper. Results indicate that in order to realize a focus with an acceptable sidelobe level the peak-te peak delay noise must be much smaller than half a period of the imaging signal. We calculate the point spread function of a synthetic focused system at 2 MHz, using broadband excitation and a perture apodization, to achieve a -60 dB sidelobe level at 10 cm depth with zero delay noise. Under these conditions but with a finite delay noise, results show, to retain the sidelobes below 40 dB, the peak-to-peak delay noise must be smaller than 0.1 of a period.

Three-Dimensional Ultrasound C-Scan Imaging Using Holographic Reconstruction

Abstract: A three-dimensional ultrasound C-scan imaging method based on holographic reconstruction has been developed. Using wide angle coherent illumination of the object and holographic principles, high lateral resolution is achieved throughout the imaging space. For this method the object is insonified by monochromatic ultrasound bursts, and the wavefronts reflected from the different object levels are recorded into a stack of holograms, each of which corresponds to a different object level. After recording each plane of the three-dimen- sional hologram is first Fourier transformed. Then each plane wave spectrum is transferred to the object space by a transfer function, and the wavefront of the object plane is calculated using an inverse Fourier transform. Finally all the object planes are combined to form a three- dimensional image, which is displayed as front, side, and top projec- tions and as a stereopair. Both simulated and real measurements of test objects that contained point-like features were accomplished. An ultrasonic frequency of 4 MHz was used in all measurements. The sim- ulated measurements showed that the resolution of the three-dimen- sional imaging method is better than 2 mm in all three directions. Using effective coding methods and fast Fourier transform algorithms, the imaging time of a 64 X 64 X 32-point image could be reduced to 2 h with an ordinary 256-kword minicomputer.

Quantitative Aspects of Image Intensifier- Television-Based Digital X-Ray Imaging

Abstract: The utilization of video systems in diagnostic X-ray imaging has been around for quite some time. In addition to the visual diagnostic value of images obtained by such systems, the X-ray video systems also offer the potential for extracting quantitative information from the images. In this chapter we will not deal with quantitative determinations based on distance measurements. Even though the quantitation potential has been under investigation for the past decade,(1–3) it was not until the introduction of digital subtraction angiography (DSA)(4) that it received a concentrated effort. DSA makes it possible to visualize a small amount of radiopaque contrast agent within the vessels by means of various digital image enhancement methods which are discussed elsewhere in this book (Chapters 3, 7). Image processing takes place after the digitization of the video signal. Many users may assume that since the output is digital format, it must be as accurate as the data in computed tomography (CT) systems. Unfortunately, this is not true, and the reason is the existence of some basic differences between the CT and image intensifier—television (IT—TV)-based digital X-ray imaging systems. In digital fluoroscopy (or radiography), one usually uses large-area detectors such as an X-ray II. Due to poor detection geometry, the scattered photons within the patient seriously degrade the information obtained by a digital fluoroscopic system.

Statistical Aspects of Image Handling in Low-Dose Electron Microscopy of Biological Material

Abstract: Publisher Summary In low-dose circumstances the image intensity distribution recorded on the micrograph is a realization of a stochastic process. This noise process that is directly related to the way in which images are recorded has been investigated in this chapter. The stochastic nature of the recorded image has a consequence that the results of image processing also become stochastic quantities, for example, the results obtained with an algorithm for phase retrieval. The chapter discusses the properties of the various methods and algorithms that are proposed in the literature for solving the phase problem when they are applied to low-dose imaging conditions. It mentions the basic integral equation that relates the object wave function to a recorded intensity distribution in the image plane. In order to keep the equations as simple as possible, one lateral dimension of the images only is treated in the chapter. For electron microscopes with square diaphragms (if there are any), the extension to two lateral dimensions is straightforward. The chapter discusses the contrast between imaging of the substructure of biological specimens by means of an electron microscope and low-dose imaging. The imaging of the substructure of biological specimens by means of an electron microscope is greatly limited by the radiation sensitivity of these objects. In low-dose imaging, however, the contrast is very noisy. Because of this poor signal-to-noise ratio, the evaluation in particular of nonperiodic object structures is very cumbersome.

Spatial filters for replicating images

Abstract: The conditions for self-imaging, longitudinal periodicity are relaxed to demand image replication only along the optical axis. Lateral periodicity in the square of the radius, in the spatial-frequency domain, is necessary and sufficient for image replication along the optical axis. This formulation allows one to employ any zone plate as a spatial filter that creates self-replicating images of a given object, under either coherent or incoherent illumination.

Source of light with spatially periodic coherence and its uses in image addition or subtraction

Abstract: We describe image-synthesis processing (ie, image addition or subtraction) using novel illumination obtained from mutually incoherent point sources The illumination exhibits periodic coherence whose degree of coherence can take the limiting values of 1 and −1 necessary for processing By using two point sources satisfying the coherence condition Δa = λf/2b (Δa and 2b are, respectively, the separations between the sources and between the inputs), image subtraction is demonstrated experimentally in an imaging system that uses a diffraction grating The coherence conditions for performing image synthesis are also given in the case of multiple point sources

Spatial frequency filtering in an optical imaging system with an extended incoherent light source.

Abstract: A single-lens imaging system is described that provides spatial frequency filtering to an extended incoherent light source. Two ways to calculate the modified image are considered: First, the image is derived from the filtered diffraction pattern by Fourier synthesis. Second, the convolution of the object function with a Fourier transform of the filter function has to be evaluated with regard to a phase function that corresponds to the light source position.

Aberration-variance-based formula for calculating point-spread functions: rotationally symmetric aberrations

Abstract: By using exponential evaluations of the Strehl ratio and appropriate Dini-sampling formulas in concert, an approximate formula is derived for fast calculation of intensity distributions in the central bright core of rotationally symmetric aberrational diffraction patterns. Since the formula involves no special functions, it is convenient both for numerical and analytical purposes. Numerical examples show that for moderate amounts of rotationally symmetric aberrations, the formula gives excellent results inside the unity disk (compared with a radius of 1.22 for the Airy disk) at the image plane. In the case of balanced (Zernike) spherical aberrations, our formula reduces to the perfect Airy pattern multiplied by corresponding Strehl ratio. A useful tool for the optical system designer, it can easily be implemented using any desk-top calculator for evaluating parameters as encircled energy, truncated radius of gyration, or to compute the central part of polychromatic diffraction patterns.