Showing papers on "Point spread function published in 1983"

Speckle masking in astronomy: triple correlation theory and applications

Abstract: Due to the turbulent atmosphere the resolution of conventional astrophotography is limited to ∼1 sec of arc. However, the speckle-masking method can yield diffraction-limited resolution, i.e., 0.03 sec of arc with a 3.6-m telescope. Speckle masking yields true images of general astronomical objects. No point source is required in the isoplanatic field of the object. We present the theory of speckle masking; it makes use of triple correlations and their Fourier counterparts, the bispectra. We show algorithms for the recovery of the object from genuine astronomical bispectra data.

The k-trajectory formulation of the NMR imaging process with applications in analysis and synthesis of imaging methods

Abstract: The fundamental operations of nuclear magnetic resonance (NMR) imaging can be formulated, for a large number of methods, as sampling the object distribution in the Fourier spatial-frequency domain, followed by processing the digitized data (often simply by Fourier transformation) to produce a digital image. In these methods, which include reconstruction from projections, Fourier imaging, spin-warp imaging, and echo-planar imaging, controllable gradient fields determine the points in the spatial-frequency domain which are sampled at any given time during the acquisition of data (the free induction decay, or FID). The detailed time dependence of the resulting trajectory of sample points (the k trajectory) determines the relative weight and accuracy with which image information at each spatial frequency is measured, establishing theoretical limitations on image quality achievable with a given imaging method. We demonstrate here that these considerations may be used to compare the theoretical capabilities of NMR imaging methods, and to derive new imaging methods with optimal theoretical imaging properties.

Image processing for extended depth of field

Abstract: Improvement in the depth of field is demonstrated by properly processing a succession of image samples. Due to the limited depth of field each image sample has in-focus as well as out-of-focus segments. By setting criteria for selecting the in-focus segments, an improved composite image is formed. Three algorithms for implementing this construction are discussed.

Digital Processing for Improvement of Ultrasonic Abdominal Images

Abstract: Digital processing that increases resolution by spatial deconvolution and histogram-based amplitude mapping has been used to improve ultrasonic abdominal image quality. The processing was applied to pulse-echo ultrasound data obtained from clinical imaging instrumentation modified to permit digital recording of signals in either RF or video forms for subsequent off-line analysis. Spatial deconvolution was accomplished both along the axis and across the width of the ultrasonic beam. Axial deconvolution was carried out on RF data with a point spread function derived from the echo of a wire target. Lateral deconvolution was performed on the video envelope placed in a matrix by an inverse filter with parameters that adjust themselves to the spatial frequency content of the image being processed. Resultant image amplitudes were mapped into a hyperbolic distribution to increase image contrast for improved demonstration of low amplitudes. The combination of processing produced resolution improvements to show boundaries more sharply and contrast changes to demonstrate more detail in the images.

Light blocking stop for electro-optic line printers

Abstract: The stop for the Schlieren imaging optics which are used in an electro-optic line printer to image a multigate light valve onto a photosensitive recording medium has smoothly tapered sides to reduce crosstalk between the pixels of the image. As a result, the transmittance of the imaging aperture, as viewed along the modulation axis of the printer, rolls off relatively gradually and more or less continuously along the edges of the stop, thereby reducing the high angle diffraction off the stop so that the troublesome sidelobes of the coherent amplitude point spread function of the imaging system are suppressed. The stop preferably is in the shape of a parallelogram selected to substantially attenuate either the zero order or the higher order diffraction components of the phase front modulated light beam exiting from the light valve so that the intensity profile of the remaining or unattenuated light has the required image characteristics. Variations in the basic parallelogram shape wherein the stop sides have specially curved configurations to optimize triangular, cosine, and Gaussian light amplitude transmittance profiles are also disclosed.

Aberrated point-spread functions for rotationally symmetric aberrations.

Abstract: The effect of fourth-, sixth-, and eighth-order balanced spherical aberrations on the incoherent point-spread function of an optical imaging system with a circular pupil is considered. It is shown that the location of the first minimum remains practically unchanged and its value remains close to zero as aberrations are introduced into the system. Thus, the central Airy disk maintains its size and distinction. Moreover, the aberrations reduce the irradiance distribution inside the Airy disk quite uniformly. The central irradiance, i.e., the Strehl ratio, can be determined quite accurately from the phase aberration variance according to S≃exp(−σΦ2). Thus, the aberrated spread functions and encircled energy for a given aberration can be determined very quickly from the aberration-free results by multiplying them with the Strehl ratio. For further simplicity, the spread functions are approximated by a Gaussian function appropriately scaled by the Strehl ratio. The approximation is quite good for points lying within a circle of radius roughly half that of the Airy disk. Defocused but otherwise aberration-free spread functions are also considered. It is shown that results similar to those for spherical aberrations are obtained but over a narrower range of Strehl ratio as well as distance from the center of the spread functions.

Reflecting Schmidt imaging spectrometers

Abstract: A new wide-angle imaging spectrometer configuration is proposed where an all-reflecting Schmidt camera is used with a prism spectrometer to give a field of view up to 60 deg or more. Four different designs using this approach are presented. These are the Imaging Spectrometer Free Flyer, the Shuttle Imaging Spectrometer A, the Shuttle Imaging Spectrometer B, and the Wide-Field System. These systems are capable of broadband spectral coverage from 0.4 to 2.5 microns, with footprints 20 m on a side or less, and with swath widths hundreds of kilometers; they are capable of spectral resolving powers of 200 or more.

Geometric Deconvolution: A Meta-Algorithm for Limited View Computed Tomography

Abstract: Images reconstructed using a limited number of projections spanning a narrow angular range suffer from a systematic geometric distortion due to the two-dimensional point spread function of the reconstruction process. Applying the projection theorem, we show that the problem of removing this distortion reduces to that of estimating the one-dimensional spread function and deconvolving projections computed for a complementary set of new angles from the initial reconstruction. A second reconstruction is performed using the deconvolved projections along with the original set of projections, thus incorporating wider angular coverage. We present here initial results of such geometric deconvolution performed via inverse filtering using fast Fourier transform techniques. While the results are noisy due to well-known problems associated with inverse filtering, they illustrate the plausibility of the underlying ideas.

A fast recursive algorithm for binary-valued two-dimensional filters

Abstract: An efficient algorithm for computing the response of a linear spatially varying digital image filter to an arbitrary digital input image is described. This response is the superposition summation of the input image with a digital point spread function (PSF). It is assumed here that the PSF is binary valued. The approach to this computation is based on the Principle of Inclusion and Exclusion. This approach leads to a new efficient algorithm. This algorithm is also efficient when the PSF is spatially invariant.

Estimation of a remote sensing system point-spread function from measured imagery

Abstract: A general approach to identifying the point spread function (PSF) of a remotely sensed scene is demonstrated in terms of a step function for an abrupt change in the gray level along the row or column of the image data The estimate of the PSF is made in terms of a finite sum of basis functions, employing a sequence of rectangular pulses covering the spatial extent of the PSF The approximation, if narrow impulses are employed, provides accurate fidelity to the PSF The method becomes practical when the geometrical structure of the scene elements producing the measured response is known The field boundary is obtained through consideration of the differing intensities on each side of the boundary, which is a step discontinuity The mathematical procedure for the technique is provided, together with a sample problem from Landsat-4 Thematic Mapper data Atmospheric blurring and electronic effects on the overall PSF and the cubic convolution resampling effects are noted

Point-spread Function Calculation for Optical Systems with Residual Aberrations and a Non-uniform Transmission Pupil

Abstract: A numerical method for evaluating the intensity at points in the image space of an optical system is developed. This method can be applied to optical systems with any kind of residual aberrations and any pupil transmission function. It is valid for the general case of an axial or extra-axial monochromatic object point. The accuracy of the method is also studied.

Image transmission through a turbulent medium using a point reflector and four-wave mixing. 2: Characteristics of the system.

Abstract: The characteristics of the one-way image transmission system presented in Part 1 are investigated in detail [ Appl. Opt.22, 2192 ( 1983)]. First, a general expression of the expectation of the transmitted image is derived for turbulence that may be typical in image transmission in the horizontal direction. Then, with the help of numerical examples, the image quality is discussed in terms of the point spread function for both thin layer and uniformly distributed turbulence. It is shown that the image transmission system is effective especially where turbulence exists relatively close to the transmission plane.

Imaging of complex NMR spectra.

Abstract: The Point Spread Function (PSF) in NMR imaging is the result of both the line broadening due to magnet field inhomogeneity and the intrinsic spectrum of the nucleus at resonance. In the case of proton imaging, the line broadening dominates the small chemical shifts and the spectral lines are not resolved. This is not generally the case with other nuclei having strong chemical shifts and the PSF then has a complex structure. During imaging, the complex PSF is convolved with the spatial distribution of the nucleus at resonance and this leads to halo artifacts which are dependent on the imaging technique employed. The images due to the ensemble of spectral lines can be separated in principle by deconvolution of the data with the PSF before reconstruction. In the special case where the complex PSF is spatially independent, it can be obtained from the Free Induction Decay (FID) data produced in the absence of a spatially encoding gradient field. This technique has been successfully applied to in-vivo imaging of exogenous perfluorocarbon material.

Fiber-optic image transmission system with high resolution.

Abstract: A system has been designed and built for transmitting images of diffusely reflecting objects through optical fibers and displaying those images at a receiving station. Wavelength coding is used to reduce the number of fibers required for transmission while allowing transmission of >1000 pixels/fiber. The system is an optical/electronic hybrid which operates under computer control. A tunable dye laser is used for a high-brightness light source, and a CRT is used for the output image display. The system and its operation are described, and examples of results are shown.

X-ray imaging of extended objects using nonoverlapping redundant array

Abstract: A common problem associated with X-ray imaging using coded apertures is the reconstruction of low-intensity extended objects. In the decoding of such objects, the overlapping images from the multiple pinholes give rise to noise cross talk and, in many cases, also to signal cross talk. In this paper, an alternate approach is proposed based on the principle used in an earlier (Yin et al., 1980) laboratory device for the real-time viewing of X-ray objects. It is shown that with this approach, the nonoverlapping redundant array, the sidelobes in the point spread function are not eliminated but merely displaced through a suitable choice of geometry. In this manner, the sidelobes no longer contribute to the background in the vicinity of a reconstructed image, and both signal and noise cross talks are completely eliminated. It may now be possible to reconstruct extended X-ray objects in 3-D by simple optical correlation and tomographically by a computer.

Design And Testing Of Lenses For Optical Disk Technology

Abstract: Optical disk technology today finds widespread application in laser vision, compact disk, and data storage equipment. The required specifications of lenses which meet these requirements are discussed. Their image quality is given by rms of wave aberration, by point spread function, by encircled energy, or by modulation transfer function (MTF). Due to the automatic servo focusing technique, a certain amount of field curvature can be tolerated. Measured results of image quality are compared with theoretical values.

Image compensation in the presence of thermal blooming.

Abstract: The effect of image compensation in viewing extended targets through thermal blooming is discussed. A wave-optics propagation code simulating multiple point sources and a low-bandwidth return-wave adaptive optics system is used to determine the steady-state thermally induced phase distortions and wave-front correction through various Zernike modes. Incoherent point spread functions for the isoplanatic regions are generated and convolved with the appropriate object field to reconstruct the extended target image. Image distortion, degradation in peak irradiance, and adaptive optics loop stability are discussed with respect to degree of correction and wavelength sensitivity.

Optics and Accommodation in Owls and Flying Foxes

Abstract: Photorefraction is a method for determining the plane of focus of vertebrate eyes (Howland and Howland 1963), which is based on a measurement of the point spread function (Smith 1966). It is well known that defocus of an optical system increases the width of the point spread function; consequently measurement of the double pass point spread function of the eye yields a measure of the defocus of the eye relative to the plane of the illuminated object point. The first practical realization of the photorefractive method was accomplished with an attachment to a 35-mm camera (Howland and Howland 1973). In this method the eye to be studied is illuminated from a fiber optic light guide centered in an array of four cylinder lenses in front of a f#/1.2 camera lens. The cylinder lens segments gather the returned light into a cross-pattern at the film plane. In this manner, the length of the cross-arms is a direct measure of the degree of defocus of the refracted eye (Fig. 1).

Dependence Of Resolution And Detector SNR On Detector Design, Optical Performance, And Flight Dynamics

Abstract: Design constraints for optimal resolution of pushbroom scanned linear arrays are studied Resolution and detector signal-to-noise ratio (SNR) trade-offs are analyzed with respect to detector geometry, quantum integration timing, flight dynamics, and optical point spread function The point spread function model includes the effects of optical aberrations, diffraction limiting effects and platform vibration Optimal resolution in the scan direction is defined for discretely sampled point sources The system model maximizes detector responsive area in time delay and integrate (TDI) arrays under an optimal resolution constraint

Minimum Variance Estimation Of Wavefront Aberration

Abstract: An image-based indirect wavefront aberration estimation which is noise optimal is presented. The minimum variance estimation is obtained by linearizing the focal plane intensity distribution in terms of the aberration parameters and a known set of derivatives of the point spread function. The technique was also made to work successfully for unknown extended sources by Fourier transforming the image to the frequency space. The results obtained from a computer simulation show excellent noise rejection. With a signal-to-noise ratio of 5, the wavefront correction is achieved down to 0.1 λ. In some cases, this method worked when the initial signal-to-noise ratio was less than one. Since the estimation is performed with a linear approximation, the dynamic range of operation was found to be limited to 0.35 RMS λ.© (1983) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Two-Dimensional White-Light Space-Variant Processing

Abstract: An optical system is designed to perform two-dimensional space-variant processing for the case of a separable point spread function. The design makes use of the wavelength dimension of light by color-encoding the input to provide the necessary third dimension required in performing the operation. An analysis of the system provides theoretical results which are compared with the results obtained in an experiment using real, positive functions for the input and point spread function. Finally, the inherent limitations of the system are discussed, noting both the advantages and disadvantages of the technique.© (1983) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Point Spread Function For A Segmented Mirror System

Abstract: A procedure was developed to generate point spread functions for a segmented mirror system for a deployable reflector for submillimeter astronomy. These point spread functions were generated using ACCOS V and special purpose software. This procedure allows tilt and piston sensitivities to be evaluated. Point spread functions with tilt and piston errors are discussed.