Showing papers on "Point spread function published in 1988"

Autocorrelation and regularization in digital images. I. Basic theory

Abstract: Spatial structure occurs in remotely sensed images when the imaged scenes contain discrete objects that are identifiable in that their spectral properties are more homogeneous within than between them and other scene elements. The spatial structure introduced is manifest in statistical measures such as the autocovariance function and variogram associated with the scene, and it is possible to formulate these measures explicitly for scenes composed of simple objects of regular shapes. Digital images result from sensing scenes by an instrument with an associated point spread function (PSF). Since there is averaging over the PSF, the effect, termed regularization, induced in the image data by the instrument will influence the observable autocovariance and variogram functions of the image data. It is shown how the autocovariance or variogram of an image is a composition of the underlying scene covariance convolved with an overlap function, which is itself a convolution of the PSF. The functional form of this relationship provides an analytic basis for scene inference and eventual inversion of scene model parameters from image data. >

X-ray scatter removal by deconvolution.

Abstract: The distribution of scattered x rays detected in a two-dimensional projection radiograph at diagnostic x-ray energies is measured as a function of field size and object thickness at a fixed x-ray potential and air gap. An image intensifier-TV based imaging system is used for image acquisition, manipulation, and analysis. A scatter point spread function (PSF) with an assumed linear, spatially invariant response is modeled as a modified Gaussian distribution, and is characterized by two parameters describing the width of the distribution and the fraction of scattered events detected. The PSF parameters are determined from analysis of images obtained with radio-opaque lead disks centrally placed on the source side of a homogeneous phantom. Analytical methods are used to convert the PSF into the frequency domain. Numerical inversion provides an inverse filter that operates on frequency transformed, scatter degraded images. Resultant inverse transformed images demonstrate the nonarbitrary removal of scatter, increased radiographic contrast, and improved quantitative accuracy. The use of the deconvolution method appears to be clinically applicable to a variety of digital projection images.

Maximum-likelihood image restoration adapted for noncoherent optical imaging

Abstract: Noncoherent optical-imaging systems are identified as potential applications for the maximum-likelihood image-restoration methods that are currently being studied for various modalities of nuclear-medicine imaging. An analogy between the quantum-photon measurements of such an optical system and that of a gamma camera allow for this new application. Results of a computer simulation are presented that support its feasibility. One important property revealed by this simulation is that the maximum-likelihood method demonstrates the ability to extrapolate the Fourier spectrum of a band-limited signal. This ability can be partially understood in that this algorithm, similar to some of the other spectral-extrapolation algorithms, constrains the solution to nonnegative values. This observation has implications on the potential of superresolution, the restoration of images from a defocused optical system, and three-dimensional imaging with a microscope.

An analytical model of the scattered radiation distribution in diagnostic radiology.

Abstract: A simple scatter model is used to analytically derive the point spread function (PSF) for scattered radiation in diagnostic radiology. The resulting equation is a function of four physical parameters; object thickness, object-to-detector distance (air gap), and the linear attenuation coefficients for both primary and scatter radiation. Though the model is based upon single scattering, it is shown that by reducing the scatter attenuation coefficient the analytic model compares well to the multiple scattering PSF determined using Monte Carlo analysis.

Reconstruction by weighted correlation for MRI with time-varying gradients

Abstract: A general reconstruction algorithm for magnetic resonance imaging (MRI) with gradients having arbitrary time dependence is presented. This method estimates spin density by calculating the weighted correlation of the observed free induction decay signal and the phase modulation function at each point. A theorem which states that this method can be derived from the conditions of linearity and shift invariance is presented. Since these conditions are general, most of the MRI reconstruction algorithms proposed so far are equivalent to the weighted correlation method. An explicit representation of the point spread function (PSF) in the weighted correlation method is given. By using this representation, a method to control the PSF and the static field inhomogeneity effects is studied. A correction method for the inhomogeneity is proposed, and a limitation is clarified. Some simulation results are presented. >

Monte Carlo simulation of the scattered radiation distribution in diagnostic radiology

Abstract: Monte Carlo techniques were employed to evaluate the point spread function (PSF) of scattered radiation in diagnostic radiology. The Monte Carlo procedure is described and shown to compare well with Monte Carlo scatter analysis of other authors. The intensity and distribution of the PSF are described independently. The effects of object thickness, air gap, and beam spectra are examined. An analytic derivation of the scatter PSF is presented in a companion article, and the Monte Carlo results discussed herein are used for comparison.

Iterative noncoherent angular superresolution (radar)

Abstract: In noncoherent scanning or imaging sensors, the angular resolution, theta , is limited by the aperture size, D, to the value theta infinity lambda /D, where lambda is the wavelength. A method is proposed for improving the effective angular resolution by three to eight times by postdetection processing of the aperture-limited signal. The technique derives from modeling the detected signal as the desired high-resolution equivalent signal degraded by convolution with the antenna pattern or point-spread function of the physical sensor. The resolution is therefore increased by deconvolving the real-aperture data. This deconvolution, or inverse filtering, approach is inherently numerically unstable. A constrained iterative deconvolution algorithm was adapted to obtain well-behaved results exhibiting true superresolution, and a fast algorithm was developed to overcome the computational burden of the iterative approach. Examples using both simulated and real millimeter-wave radar data is shown. >

Ambiguity function as a design tool for high focal depth

Abstract: The optical transfer functions for variable focus error are contained as a single picture representation in the ambiguity function that is associated with the pupil function. This picture representation is shown to be useful for designing pupil functions that increase the depth of focus. We specify a criterion for an optical transfer function with low sensitivity defocus in terms of a nonlinear differential equation for the point spread function. Based on this approach, we design and compare five new spatial filters for achieving high focal depth.

Transfer function characterization of grazing incidence optical systems.

Abstract: By using Fourier techniques and linear systems theory we have derived an analytic expression for a generalized transfer function for grazing incidence optical systems operating at ultraviolet and x-ray wavelengths that includes the effects of optical fabrication errors over the entire range of relevant spatial frequencies. The Fourier transform of this transfer function yields the image distribution (or point spread function) from which encircled energy characteristics or other image quality criteria can be obtained. This transfer function characterization of grazing incidence optical systems allows parametric trade studies and sensitivity analyses to be performed as well as the derivation of fabrication tolerances necessary to satisfy a given image quality requirement.

Retrieval of wave aberration of human eyes from actual point-spread-function data.

Abstract: The wave aberration of human eyes is retrieved from actual point-spread-function (PSF) data and the modulus of the pupil function. The PSF had been obtained previously by application of a hybrid optical–digital method developed recently. The retrieval is done by using a bidimensional Gerchberg–Saxton phase-retrieval algorithm joined to an iterative phase-unwrapping algorithm. To obtain an adequate convergence, the initial wave aberration for starting the retrieval–unwrapping algorithm is estimated with a nonlinear least-squares algorithm. The resulting wave aberrations for several subjects show irregular aberrations superimposed upon the regular wave-aberration components, with astigmatism being the most important asymmetric aberration.

Aberrations in high aperture conventional and confocal imaging systems.

Abstract: An appropriate form for the expansion of an aberration function for an optical system of high numerical aperture is considered. The effects on the defocus signal of a confocal imaging system of aberrations, high aperture, finite Fresnel number, system configuration, and surface tilt are discussed.

Fast point spread function computation from aperture functions in high-resolution positron emission tomography

Abstract: The problem of extracting point spread functions from detector aperture functions in high-resolution PET is addressed. In the limit of very small size detectors relative to the ring dimensions, assumptions are made that lead to a fast and simple computation model yielding point spread functions with negligible errors due to the reconstruction algorithm. The methods allows one to assess accurately the intrinsic performance of a PET tomograph, and it appears to be adequate to relate the imaging capabilities in every point of the camera reconstruction field to the geometric and physical characteristics of the detection system. The method was developed as an investigation tool to help design the next generation of very-high-resolution PET tomographs. >

Method and system for wavefront reconstruction

Abstract: Method and system for wavefront reconstruction from an image plane intensity distribution profile. An imaging device may be an agent for producing the image plane intensity distribution profile, for example, a point spread function. In one embodiment, the method and system include defining a feature vector from the point spread function, and employing an adaptive computational architecture for associating the feature vector with at least one identifying characteristic of the imaging device, e.g., such as an amount of astigmatism.

Measurement of the Landsat Thematic Mapper modulation transfer function using an array of point sources

Abstract: This paper presents a method for measuring the Thematic Mapper (TM) imaging system point spread function (PSF) using TM imagery or a specially constructed target consisting of a two-dimensional array of approximate point sources of known dimensions and radiometric qualities. The target allows 16 separate point sources to be imaged simultaneously by the TM. The point sources were carefully placed on the ground so that their relative positions were known. Owing to sample-scene phasing, each imaged point source exhibits a different amount of blur in the digital image. The target pixels may then be recombined according to their known relative positions to form a single, sampled, nonaliased imaging system PSF. The modulation transfer function is then obtained as the modulus of the discrete Fourier transform of the PSF.

Wavefront correcting properties of corner-cube arrays.

Abstract: The performance of corner-cube arrays as pseudophase-conjugation wavefront correctors is investigated theoretically and experimentally. Hollow electroformed arrays and solid plastic arrays of corner-cube retroreflectors have been optically characterized and studied in a pseudophase-conjugate imaging system. The use of a collimating lens is found to improve dramatically the image quality.

Holographic image of a point source in the presence of misalignment

Abstract: The imaging of a point source by high numerical aperture holograms was studied theoretically and experimentally in the presence of aberrations caused by inaccurate adjustment of the plane reference and plane reconstructing waves or by inaccurate positioning of the hologram. The accuracy requirement is defined by the angular resolution allowed by an aperture equal to the hologram size. Any deviation from this limit leads to deformation of the point transfer function defined by the unavoidable diffraction. For coarse mismatch (>10(-3) rad for the actual case), clearly demonstrable geometrical-type aberrations occur; for smaller angles, appreciable broadening of the diffraction pattern and rapid fall of the Strehl ratio diminish the applicability of the holographic method. The calculations and the photographic and photometric measurements are in good agreement.

Computed point spread functions for light in tissue using a measured volume scattering function.

Abstract: Optical techniques are increasingly being used in the field of medicine in areas as diverse as surgery (for cutting and coagulation), cancer treatment (through photoradiation therapy) and blood flow monitoring (by laser doppler measurements). At University College, we are using the technique of near infrared spectroscopy (nirs) to monitor changes in cerebral blood and tissue oxygenation in newborn infants (1), and are investigating methods of optical imaging across the head (2). In all these applications, a detailed knowledge of light transport in tissue is required. For spectroscopy studies, in order to quantitate data, one needs to know the effective photon pathlength through the tissue, and a knowledge of the path also allows one to calculate the volume of tissue from which results are being obtained. In the case of imaging through tissue, data is required on the point spread function (PSF) for the tissue, both for the prediction of the image quality that could be obtained using various imaging schemes, and for use in image enhancement and reconstruction computations.

Signal-to-noise limitations in white light holography

Abstract: A simple derivation is given for the signal-to-noise ratio (SNR) in images reconstructed from incoherent holograms. Dependence is shown to be on the hologram SNR, object complexity, and the number of pixels in the detector. Reconstruction of involved objects becomes possible with high dynamic range detectors such as charge-coupled devices. We have produced such white light holograms by means of a rotational shear interferometer combined with a chromatic corrector. A digital inverse transform recreated the object.

A characterization of the scatter point-spread-function in terms of air gaps

Abstract: Characterizing the scatter point-spread-function (PSF) yields a model for predicting the behavior of the scatter and a PSF for deconvolution techniques that correct for scatter. Assuming the X-ray scatter is isotropic, the authors present a model for the scatter point-spread-function parameterized only by air gap. This model suggests that small increases in air gap significantly attenuate the higher-frequency structure of the scatter distribution. To evaluate this model, the authors examined the behavior of the spatial frequency distributions of experimental scatter images as a function of air gap. Using film as the detector, they imaged a 20-cm uniformly thick water phantom with aperture diameters of 8, 12, 16, 20, and 24 mm at air gaps of 0-24 cm. >

Frequency-response characteristics of a perfect lens masked by polarizing devices

Abstract: The imaging characteristics of a perfect lens partially masked by a linear polarizer can be varied continuously either by rotating an analyzer placed at the output side or by changing the state of polarization of the input beam. In this paper we study the frequency-response characteristics and the point-spread function of such a system. It is also shown that the proposed system can be adapted either for apodization or for superresolution simply by rotating the analyzer. The fact that the unpredictable phase introduced by the mask has no harmful effect on the performance of the system makes it convenient for several applications. Expressions are obtained for the optical transfer function and the point-spread function of such a system. Some specific cases are illustrated graphically, and some probable applications are discussed.

Quantitative simulation of image correction for astronomy with a segmented active mirror

Abstract: Correction by active mirror systems of image distortion due to atmospheric turbulence promises to improve the quality of ground-based astronomical observations. Although the ideal of fully correcting average-to-poor seeing to the diffraction limit of a large telescope cannot be easily realized with current technology, it has been demonstrated that partial correction of severe seeing disturbances can significantly improve image resolution. This paper describes a computer simulation of partial seeing correction by the Lockheed Active Mirror. Quantitative evaluation of the effects of partial correction on simulated wavefronts indicates that, even with a modest number of mirror actuators, one can achieve a diffraction-limited image superimposed on a background of scattered light.

Three-dimensional imaging in microscopy as an extension of the theory of two-dimensional imaging

Abstract: A straightforward and intuitive method is desired for the derivation of the transfer theory developed recently by Streibl [ J. Opt. Soc. Am. A2, 121 ( 1985)] for three-dimensional image formation of optically weak objects by transmission microscopy. The derivation described here establishes the relationship between three-dimensional imaging and the well-known theory of two-dimensional image formation.

Effect of detector displacement in confocal imaging systems.

Abstract: Confocal imaging systems rely on the use of an accurately positioned axial point detector. We discuss in this paper the effects on the various imaging modes of using a misaligned pinhole. We pay particular attention to the form of the transfer function and the depth discrimination property. A simple model of a thick edge type object is introduced, and it is found that in certain cases a degree of detector offset may be used to advantage in determining the position of the edge.

Performance of Echographic Equipment and Potentials for Tissue Characterization

Abstract: The imaging performance of echographic equipment is greatly depenlent on the characteristics of the ultrasound transducer. The paper is confined to single element focussed transducers which are still widely employed in modern equipment. Extrapolation of the results to array transducers maybe made to a certain extent. The performance is specified by the 2 dimensional point spread function (PSF) in the focal zone of the transmitted sound field. This PS? is fixed by the bandwidth of the transducer when the axial (depth) direction is considered, and by the central frequency and the relative aperture in the lateral direction. The PSF concept applies to the imaging of specular reflections and the PSF is estimated by scanning a single reflector. In case of scattering by small inhomogeneities within parenchymal tissues the concept of “speckle” formation has to be introduced. The speckle is due to interference phenomena at reception. It can be shown that the average speckle size in the focus is proportional to the PSF above defined for specular reflections. The dependencies of the speckle size on the distance of the tissue to the transducer (beam diffraction effects) and on the density of the scatterers were explored. It is concluded that with the necessary corrections tissue characterization by statistical analysis of the image texture can be meaningful.

Fundamentals of the Radon Transform

Abstract: The Radon transform is the mathematical basis of computed tomography and finds application in many other medical imaging modalities as well. In this chapter we present the fundamental mathematics of this transform and its inverse, with emphasis on the central-slice theorem.

Overcoming Polarization Aberrations In Microscopy

Abstract: A long-standing problem in polarized light microscopy has been the inability, due to polarization aberrations, to achieve simultaneously high spatial resolution and high contrast. The rotation of the plane of polarization at oblique interfaces between crossed polars causes the pupil function to resemble a dark cross rather than being uniformly dark. Likewise, the point spread function has the visual appearance of a four-leaf clover rather than the ideal Airy disk, and is also space-variant. Images formed with these systems are severely degraded. In this paper the theory of polarization aberrations is applied to the analysis of three solutions to this problem: Reducing the system aperture to block troublesome high-aperture rays; the AVEC-POL method, in which high bias compensation introduces counterbalancing aberrations; and the polarization rectifier, an optical element designed to introduce equal and opposite rotations of the electric vector.

Noise propagation in electronically collimated single photon imaging

Abstract: Cone-beam views of an object are produced from counts acquired with an electronically collimated system for SPECT (single-photon-emission computed tomography) using a deconvolution procedure. The propagation of noise through this procedure has been investigated using four approaches: a theoretical analysis using an approximate description of the point spread function in the form of an annulus; inverse filtering of a simulated disk source containing hot and cold regions; application of ART (algebraic reconstruction technique) using an accurate point spread function; and experimental reconstruction of a Cs-137 disk source. >

A Theoretically-Correct Algorithm to Compensate for a Three-Dimensional Spatially-Variant Point Spread Function in Spect Imaging

Abstract: Three factors which degrade positional information and the quantitative potential of single photon emission computed tomography (SPECT) are finite detector size, Compton scatter, and the detector point spread function (PSF). We focus here on the PSF, which is modelled as a gaussian whose standard deviation depends on the perpendicular distance between the detector and the point being imaged. Thus the PSF is spatially-variant (SVPSF). The PSF is spatially-invariant, of course, within the plane of the detector for a fixed image point-detector distance.

CCD Star Images: On the Determination of Moffat's PSF Shape Parameters

Abstract: Among the variety of empirical models of optical Point Spread Function used in the astronomical environment, only the Moffat’s (1969) one is able to describe by means of two parameters (in the circular case) both the inner and the outer star image regions. In view of this very important feature, the problem of the simultaneous estimates of Moffat’s PSF shape parameters, off-centring, and the background level in CCD star images has been investigated. The problem does not seem to be rigorously resolvable, but an approximate way to calculate all the parameters except off-centring is shown. It must be stressed that, the Moffat’s PSF model being a softened power law belonging to the family of modified King and Hubble models, the present discussion can be of aid in many other research fields. Also, the integral equation enabling us to convolve a spherical source with Moffat’s PSF is given and applied for comparison to Multi-Gaussian convolution.