Showing papers on "Point spread function published in 1978"
TL;DR: A Type-2 scanning microscope is found to have a much reduced depth of field according to these criteria, which makes it useful for studying thick biological slices, which does not contradict the claim thatDepth of field may be much increased in such a microscope by using lenses with annular pupil functions.
Abstract: Various definitions of depth of field in the microscope are discussed. The variation in the integrated intensity in the image of a point object outside the focal plane shows how the microscope discriminates against such objects. The power diffusely scattered by a translucent object is also considered. A Type-2 scanning microscope is found to have a much reduced depth of field according to these criteria, which makes it useful for studying thick biological slices. These results do not contradict the claim that depth of field may be much increased in such a microscope by using lenses with annular pupil functions.
201 citations
TL;DR: It is shown that at a large optical distance where the total coherent intensity is negligibly small compared with the total incoherent intensity, it is still possible to form the Airy disk due to the coherent intensity.
Abstract: In underwater photography, it was reported that clear photographs were obtained through water with large (10–15) optical distances even though the MTF rolls off at a few cycles per mrad. This paper presents an explanation of this apparent contradiction by showing that at a large optical distance where the total coherent intensity is negligibly small compared with the total incoherent intensity, it is still possible to form the Airy disk due to the coherent intensity. We present the condition under which this can take place and applied the results to an imaging system in still water and in water with particulate matter.
82 citations
TL;DR: The tedious numerical computations associated with the calculation of partially coherent imagery are alleviated by a method which uses dimensionless coordinates and takes advantage of the properties of the Fourier transform.
Abstract: The tedious numerical computations associated with the calculation of partially coherent imagery are alleviated by a method which uses dimensionless coordinates and takes advantage of the properties of the Fourier transform. A 1-D periodic object function can model many objects of practical interest, including nonperiodic objects. The properties of a given optical system are described in terms of the transmission cross coefficient. For aberration-free systems with circular pupils, including annular sources (dark-field illumination), the cross coefficient can be calculated analytically. For aberrated or apodized systems, a 1-D approximation can be used. The effect of a convolving slit in the image plane of a scanning microscope can also be included.
79 citations
TL;DR: The restoration of images degraded by film-grain noise is considered in the context of estimation theory and a discrete Wiener filer is developed which explicitly allows for the signal dependence of the noise.
Abstract: Film-grain noise describes the intrinsic noise produced by a photographic emulsion during the process of image recording and reproduction. In this paper we consider the restoration of images degraded by film-grain noise. First a detailed model for the over-all photographic imaging system is presented. The model includes linear blurring effects and the signal-dependent effect of film-grain noise. The accuracy of this model is tested by simulating images according to it and comparing the results to images of similar targets that were actually recorded on film. The restoration of images degraded by film-grain noise is then considered in the context of estimation theory. A discrete Wiener filer is developed which explicitly allows for the signal dependence of the noise. The filter adaptively alters its characteristics based on the nonstationary first order statistics of an image and is shown to have advantages over the conventional Wiener filter. Experimental results for modeling and the adaptive estimation filter are presented.
58 citations
TL;DR: In this article, a maximum entropy (ME) restoring formalism was derived under the assumption of zero background and additive noise in the image, which is not consistent with the maximum likelihood and Poisson hypotheses: where the background is high and consequently contributes much noise to the observed image, a restored star is broader and smoother than where the foreground is low.
Abstract: The maximum entropy (ME) restoring formalism has previously been derived under the assumptions of (i) zero background and (ii) additive noise in the image. However, the noise in the signals from many modern image detectors is actually Poisson, i.e., dominated by single-photon statistics. Hence, the noise is no longer additive. Particularly in astronomy, it is often accurate to model the image as being composed of two fundamental Poisson features: (i) a component due to a smoothly varying background image, such as caused by interstellar dust, plus (ii) a superimposed component due to an unknown array of point and line sources (stars, galactic arms, etc.). The latter is termed the “foreground image” since it contains the principal object information sought by the viewer. We include in the background all physical backgrounds, such as the night sky, as well as the mathematical background formed by lower-frequency components of the principal image structure. The role played by the background, which may be separately and easily estimated since it is smooth, is to pointwise modify the known noise statistics in the foreground image according to how strong the background is. Given the estimated background, a maximum-likelihood restoring formula was derived for the foreground image. We applied this approach to some one-dimensional simulations and to some real astronomical imagery. Results are consistent with the maximum-likelihood and Poisson hypotheses: i.e., where the background is high and consequently contributes much noise to the observed image, a restored star is broader and smoother than where the background is low. This nonisoplanatic behavior is desirable since it permits extra resolution only where the noise is sufficiently low to reliably permit it.
56 citations
TL;DR: It is shown that partially coherent illumination has advantages over coherent or incoherent illumination in this system and experimental results are shown which indicate that the system can be used to perform a simple type of texture-to-color conversion.
Abstract: An optical spatial filtering system is described which color encodes the local spatial frequency content of an image It is shown that partially coherent illumination has advantages over coherent or incoherent illumination in this system Experimental results are shown which indicate that the system can be used to perform a simple type of texture-to-color conversion The system could be used to enhance textural differences for a human observer or as a preprocessor which provides texture related information to a second image processing device
41 citations
TL;DR: A technique is described which allows the removal of seeing distortions from a single frame of speckle-type imagery, provided that this frame is obtained using an aperture consisting of a nonredundant array of subapertures, each smaller than the seeing correlation length.
Abstract: A technique is described which allows the removal of seeing distortions from a single frame of speckle-type imagery, provided that this frame is obtained using an aperture consisting of a nonredundant array of subapertures, each smaller than the seeing correlation length. Although performed a posteriori, the method is related to those already proposed for use with active optical systems. Computer simulations are decribed which verify the basic features of this technique. The simulations indicate that reconstructed images of diffraction-limited quality should be obtainable for starlike objects as dim as eighth magnitude. For more extended objects, the limiting magnitude depends somewhat on the object structure. The technique described is immediately applicable to any large telescope, and because the processing is done after the fact, a frame containing many isoplanatic patches may be processed piecewise, allowing the reconstruction of large areas.
22 citations
TL;DR: The capabilities of optical computers are extended to perform the class of bilinear transformations on 1-D signals and this technique is applied to the study of partially coherent optical systems and to systems in which coherent optical processing is followed by postdetection linear spatial filtering.
Abstract: The capabilities of optical computers are extended to perform the class of bilinear transformations (of nonzero spread) on 1-D signals. Use is made of the additional degree of freedom in 2-D linear processing. The technique is applied to the study of partially coherent optical systems and to systems in which coherent optical processing is followed by postdetection linear spatial filtering.
18 citations
TL;DR: A new coded-aperture configuration for gamma-ray imaging that measures a single Fourier component of the object distribution at a time and does not require a position-sensitive detector.
Abstract: A new coded-aperture configuration for gamma-ray imaging is described. It measures a single Fourier component of the object distribution at a time and does not require a position-sensitive detector. If, however, a position-sensitive detector is used, three-dimensional information about the source can be obtained.
15 citations
TL;DR: In this article, the signal-to-noise (S/N) ratio of a 180 deg rotationally shearing interferometer for image recovery at the diffraction limit of a large telescope is computed.
Abstract: The signal-to-noise (S/N) ratio to be expected when a 180 deg rotationally shearing interferometer is used for image recovery at the diffraction limit of a large telescope is computed. The variance and covariance of the irradiance fluctuations at the detector array are shown to yield measures of the high-frequency spatial spectrum of the source. Four fundamental sources of noise are considered: temporal fluctuations of the source, space-time fluctuations of the atmosphere, shot noise in the detected photocurrents, and the effects of finite sampling. S/N is found to be directly proportional to the angular resolution of the telescope, the single-frame integration time, the square root of the number of frames, the cube of the operating wavelength, the quantum efficiency of the detector, and the average spectral irradiance from the source on the pupil. It is inversely proportional to the cube of the field angle subtended by the source (or part thereof) under study.
15 citations
TL;DR: In this paper, the point spread function, encircled energy, and optical transfer function for non-centrally obscured circular pupils were derived for a system with linear obscuration ratios of 0.25, 0.50, and 0.75.
Abstract: Imaging systems with noncentrally obscured circular pupils are considered, and expressions for the point-spread function, encircled energy, and the optical transfer function are obtained. It is shown that at image points which lie within the Airy circle, a noncentral obscuration yields higher or equal irradiance compared to a central obscuration, and consequently a higher concentration of energy near the image center. In general, a noncentral obscuration, compared to a central one, increases the transfer function at low intermediate spatial frequencies and decreases it at high intermediate frequencies; at very low and very high frequencies the transfer function is the same in both cases. Numerical results for pupils with linear obscuration ratios of 0.25, 0.50, and 0.75 are presented.
TL;DR: An image degraded by linear smear is restored in a spatial filtering setup by using a sinusoidal distribution of amplitude transmittance in the frequency plane using a Wollaston prism and two linear polarizers to provide redundancy in the image formation process.
Abstract: An image degraded by linear smear is restored in a spatial filtering setup by using a sinusoidal distribution of amplitude transmittance in the frequency plane. The sinusoidal amplitude distribution is generated with the help of a Wollaston prism and two linear polarizers. The experimental arrangement permits the use of an extended incoherent source (angular width of the order of 2°). This provides redundancy in the image formation process and, consequently, eliminates the disturbing diffraction effects which are always present when highly directed light is used. The retrieved image is significantly improved if the degraded amplitude image is transformed by bleaching into a pure phase image, and the filtering is carried out subsequently. Some restored images are shown.
TL;DR: In this paper, the performance of optical systems in the presence of linear coma was evaluated and the applicability of this balance to imaging of extended objects was examined and the results for the point spread function in presence of optimum balanced linear coma were also included.
Abstract: Disk spread functions are evaluated to study the performance of optical systems in the presence of linear coma. Optimum balance among various coma terms based on Strehl intensity criterion is used and the applicability of this balance to imaging of extended objects is examined. Graphical results of intensity distribution in the paraxial receiving plane for the diffraction images of extended circular targets for various sizes and azimuths are presented. Results for the point spread function in presence of optimum balanced linear coma come out as a special case and are also included.