Spatial Transfer Function Research Articles

Cross-correlation antenna systems with modified principal solution spatial frequency transfer functions

The principal solution type of spatial frequency transfer function (SFTF) for a linear antenna system, e.g., line source or linear array, is constant (flat) over its entire spatial frequency (SF) passband and drops abruptly to zero at the edges of the band. Such a SFTF is obtainable with cross-correlation (multiplicative) techniques. The associated power pattern, of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sin (Lu)/Lu</tex> type, has high sidelobes diminishing asymptotically as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u^{-1}</tex> . Moreover, the weighting distribution for the line source has an inverse taper with end point singularities. A modified principal solution SFTF, flat over most of the SF passband but with a smoothly varying transition function of the quadratic-linear-quadratic type at the edges of the passband is introduced. This engenders a power pattern whose sidelobes diminish asymptotically as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u^{-3}</tex> instead of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u^{-1}</tex> . The line source weighting distributions, moreover, are continuous and free of singularities, making physical realizability no longer a problem.

Adaptation of spatial modulation transfer functions via nonlinear lateral inhibition.

Adaptation, or change of shape of spatial modulation transfer functions (MTFs) on change of mean luminance level, occurs in visual interneurone and human psychophysical observations. Generally the bandwidth decreases and relative low frequency attenuation decreases as mean luminance decreases. Here it is shown how these changes in MTFs can be accounted for by nonlinear lateral inhibition based on spatial distributions of efficacy of voltage controlled synaptic conductance variation.

Vision in the presence of known natural retinal image motion.

Previously we reported that failures of compensatory eye movements led to appreciable binocular retinal image motion during head rotation. Subjectively, the visual world appeared clear, fused, and stable under these conditions. The present experiments examined these impressions psychophysically. The spatial modulation transfer function of subjects with known retinal image motion was measured during head rotation. We found that contrast sensitivity was reduced for gratings over 6 cycles/degree and was increased for lower spatial frequencies. Our results, when compared with Kelly's [J. Opt. Soc. Am. 69, 1340-1349 (1979)] measurements made with artificially moving stabilized gratings, show that natural retinal image motion is less harmful to contrast sensitivity at high spatial frequencies and more beneficial at low spatial frequencies. Furthermore, we had previously found that natural retinal image motion was different in each eye during head movement but no diplopia was noticed. We confirmed this subjective impression by measuring forced-choice stereoacuity thresholds concurrent with binocular head and eye recordings. Stereoacuity was not disturbed by large fixation disparities or high vergence velocities. Recordings also were made while a fused Julesz stereogram was viewed during attempts to break fusion with violent head movements. Fusion could not be broken. Stereograms turned on during violent head movement fused rapidly. We conclude that vision is better with natural retinal image motion than expected from experiments done with stabilized heads.

Frequency Domain Description Of Interferogram Analysis

Interferogram analysis is discussed as a sampling problem using the concepts of Fourier analysis. The relative merits of random, raster, and uniform sampling of a wavefront are examined. A relationship between a global least squares fit and interpolation in the spatial domain and transfer functions in the frequency domain is described.

Spatial and temporal properties of luminosity horizontal cells in the turtle retina.

Luminosity horizontal cells in the turtle retina respond approximately linearly to visual stimuli with contrast levels spanning a large part of the physiological range. We characterized the response properties of these cells under conditions of low photopic background illumination by measuring their spatial and temporal frequency transfer functions. Our experimental results indicate in two ways that, under these conditions, feedback from luminosity horizontal cells to cones does not play a major role in the mechanisms underlying the spatial and temporal tuning of horizontal cell responses. First, the shape of the spatial transfer function depended only weakly on the temporal frequency with which it was measured. Second, the shape of the temporal transfer function depended only weakly on the spatial frequency with which it was measured.

新複合レチクルによる光学式座標標定方式

The optical target-coordinator is the important element in automatic infrared tracking systems for moving target. In this paper, we propose a method for optical-coordinator which is possible to determine the coordinates of the target with its surrounding background noise. This system has two kinds of optical modulating discs aligned with cascade on co-optical-axis and rotated in one direction with different velocity.One of them is an involute reticle reported previouslly by the authors, which has excellent characteristics for suppression of background noise. And the other is used for determination of the target location, named “coordinate reticle” here.Usually, the problem in such a double reticle system is a false signal causd by projection from the front reticle to the rear ond. This is, however, avoidable by means of separating each main path-band of spatial transfer function of two reticles. Validity of this approch is proved theoretically and experimentally. And effectiveness for the coordinator is confirmed through some experimental results.

Resolution of Optoacoustic Transducers

An optoacoustic transducer (OAT) is a multilayer planar device which produces a focused acoustic field distribution by trans- forming a focus-inducing optical pattern into a corresponding acoustic pattern. One measure of the effectiveness of such a device is its in- herent resolving ability, which is determined by the sharpness of its focal-plane distribution. me resolving ability of the OAT has been studied by analyzing its spatial transfer function. This transfer func- tion, called the optoacoustic spatial transfer function (OASTF), has been shown to be the product of two factors: an aberration-limited transfer function and a diffraction-limited transfer function. The aberration-limited transfer function, derived in an eariier paper, has been modified to include the effect of a photoconductive backing layer. By comparing the aberration and diffraction-limited transfer functions, optimum OAT size has been determined. Simulated images produced by an optimum-sized OAT have been obtained using the OASTF, and maximum resolution has been calculated.

Arden grating test in evaluating "early" posterior subcapsular cataracts.

Patients with "early" posterior subcapsular (PSC) cataracts often complain of severe visual impairment, despite maintenance of relatively good Snellen acuity. The Arden grating test of contrast sensitivity provides a simple method of evaluating visual function in a manner more nearly approximating the real visual world. This test often reveals profound loss of contrast sensitivity in patients with early PSC cataracts who maintain relatively good acuity (20/40 or better) on Snellen's test. Examination of 122 such eyes revealed wide variations in contrast sensitivity, with Arden scores showing better correlation with subjective complaints than with Snellen acuity levels. While Snellen's test measures only one end of the spatial modulation transfer function (MTF), the Arden test plates provide an overall picture of MTF and help us to better understand the effect of PSC cataracts on visual function.

Visual form perception and the spatial phase transfer function.

The quality of many imaging devices can be characterized, within certain constraints, by means of the modulation transfer function (MTF) and the phase transfer function (PTF). In many cases, it is possible to estimate, qualitatively, the effect of the MTF on the appearance of objects, and much progress has been made in making quantitative predictions of the detectability of objects and features within objects. This is not the case, however, for the PTF, and its influence is often neglected, even though nonideal PTF's obviously may degrade image quality. Experiments are described that attempt to assess the significance of the PTF for human visual performance. The effects of various PTF's were simulated by means of a technique that maintained the modulation of the spatial-frequency components closely constant. The visual detectability of such phase changes was measured by a discrimination method, and phase threshold levels were evaluated. Simple linear patterns provided the targets for all measurements, although some images are shown that illustrate qualitatively the phase-shift results on real two-dimensional targets. The work enables an assessment to be made of the effects of phase changes produced by various imaging systems.

Spatial response of arbitrarily electroded piezoelectric plates by plane-wave decomposition

The spatial response of resonant piezoelectric plates used in various acoustic imaging systems is of significant practical interest and is closely related to the resolving ability of these systems. In a certain class of applications, in order to achieve the desired transducing action, the faces of the plate are only partially electroded. There, it is advantageous to be able to predict and control the spatial distribution of the acoustic output from the knowledge of the spatial distribution of the electrodes. A new technique is presented for determining the spatial distribution of the acoustic output of an arbitrarily electroded piezo-electric plate. This technique regards the transduced as a linear spatial system, with the electrode pattern considered as the input and the resulting acoustic particle displacement pattern immediately in front of the transducer in the propagation medium as the output. Once the spatial transfer function or the spatial impulse response of the system is known, the output for any electrode configuration can be found using Fourier techniques. Experimental measurements of the output of several piezoelectric plates due to different electrode patterns compare closely with calculations based on the above theory.

Spatial response of arbitrarily electroded piezoelectric plates by plane-wave decomposition.

The spatial response of resonant piezoelectric plates used in various acoustic imaging systems is of significant practical interest and is closely related to the resolving ability of these systems. In a certain class of applications, in order to achieve the desired transducing action, the faces of the plate are only partially electroded. There, it is advantageous to be able to predict and control the spatial distribution of the acoustic output from the knowledge of the spatial distribution of the electrodes. A new technique is presented for determining the spatial distribution of the acoustic output of an arbitrarily electroded piezoelectric plate. This technique regards the transducer as a linear spatial system, with the electrode pattern considered as the input and the resulting acoustic particle displacement pattern immediately in front of the transducer in the propagation medium as the output. Once the spatial transfer function or the spatial impulse response of the system is known, the output for any electrode configuration can be found using Fourier techniques. Experimental measurements of the output of several piezoelectric plates due to different electrode patterns compare closely with calculations based on the above theory.

A four mechanism model for threshold spatial vision

Data on the threshold visibility of spatially localized, aperiodic patterns are used to derive the properties of a general model for threshold spatial vision. The model consists of four different size-tuned mechanisms centered at each eccentricity, each with a center-surround sensitivity profile described by the difference of two Gaussian functions. The two smaller mechanisms show relatively sustained temporal characteristics, while the larger two exhibit transient properties. All four mechanisms increase linearly in size with eccentricity. Mechanism responses are combined through spatial probability summation to predict visual thresholds. The model quantitatively predicts the spatial modulation transfer function (cosine grating thresholds) under both sustained and transient conditions with no free parameters.

Laterally induced impedance effects in vision

A linear integral equation for a system of mutually impeding points is developed and solved explicitly. Particular solutions are shown to be subharmonic functions for a large class of stimuli. Specialized forms of the general equation presented in this paper occur within a number of mathematical models of Mach bands. In addition to these known spatial properties, our results also show that the time course of this basic equation may be useful in developing models of transient neural activity as well as of temporal psychophysical phenomena, such as the Broca-Sulzer effect. Further, a spatial transfer function much like the low-frequency cutoff of empirically derived modulation transfer functions follows directly from our basic integral equation if the additional assumption of spatial homogeneity is imposed.

A spatio-temporal model of cat's retinal cells.

This paper presents a model of the spatiotemporal processes of simple ganglion cells of cat's retina. The model is based on the existence of two anatomical paths in the retina: a direct path, responsible for central excitatory effects, and a transversal path, responsible for peripherical inhibitory effects. Plausible spatial weighting functions and temporal transfer functions for photoreceptors, horizontal, bipolar and ganglion cell are introduced by prudent application of comparative neurophysiology.

Temporal response of microdensitometers.

Microdensitometers have both spatial and temporal finite responses which may lead to degradation in images being analyzed. These responses may be quantitated in terms of spatial and temporal modulation transfer functions (MTFs). The temporal response of microdensitometers is studied here. Specifically, the technique of differentiating temporal step-function responses to determine the temporal MTF is presented. Experimental results illustrating the theory are described using a Baird Atomic microdensitometer.

Angle estimation and binaural processing in animal echolocation.

Physical structures separate the ears of many mammals, and the ears themselves have complex transfer functions that depend upon the direction of a sound source. Neither of these observations is usually incorporated into standard array analysis. The conventional array problem generally assumes that individual elements are omnidirectional, and there are no physical structures between elements to provide partial isolation. This investigation of binaural angle estimation specifically incorporates the effects of partial isolation and directivity patterns that vary with angle and frequency. Cramér–Rao bounds for the variance of maximum likelihood angle estimates are derived. These bounds, along with a generalized ambiguity function, are used to evaluate the significance of isolation between the ears, angle-dependent magnitude, and phase variations in the spatial transfer functions of the ears, the use of wide-band and narrow-band signals in animal echolocation, symmetry of aural directivity patterns, the transmitted beam patterns that are employed by certain bats, and the angle-dependent signal variations that have been observed in cetacean echolocation. Only two broadband hydrophones are sufficient for accurate, unambiguous azimuth measurement if the width of the signal autocorrelation function is small relative to the distance between hydrophones. The analysis indicates that many past measurements of transmitted beam patterns and aural transfer functions in animals are incomplete, since they do not consider direction-dependent phase variations. It may also be necessary to reinterpret the meaning of time difference and pressure difference cues for localization. These insights can be used not only for better correlation of behavioral and physiological measurements, but also for better design of man-made systems for communication, radar, sonar, and ultrasonic medical diagnosis.

The origin and characterization of the primary signal, noise, and interference sources in the high frequency electrocardiogram

An analysis technique was developed that enabled accurate measurement of the spectral and spatial characteristics of the predominant signal, noise, and interference components in high frequency electrocardiograms. A selective sampling technique, utilizing the isoelectric interval during the T-P segments, enabled the charactetistics of the internally generated noise and external interference to be obtained independently of the heart signal. Using this sampling technique, it was found that the electrical activity of skeletal muscles was the major source of noise in the high frequency electrocardiogram. The amounts of skdetal muscle noise present in the high frequency electrocardiograms of resting patients were measured quantitatively through the use of anesthetics and muscle relaxant drugs. In the normal resting state, the electrical activity of skeletal muscles contributed up to 15 dB of random noise to the spectra of waveforms generated by the electrical activity of the heart. Moderate, voluntary contraction of small groups of skeletal muscles increased their electrical output by 15 to 20 dB. Spectral analysis of high frequency electrocardiograms indicated that a dynamic range of approximately 66 dB is requized to adequately measure the signal and noise components present. Power spectra of high frequency electrocardiograms indicated that the 60-Hz power lines were the major source of interference Harmonics of the 60-Hz power line added significant interference components at frequencies as high as 1 kHz. The magnitude-squared coherence function between pairs of electrocardiographic leads, in conjunction with segment sampling and analysis techniques, was used to measure the spatial coherence of waveforms from electrical source associated with heart and skeletal muscle activity. The high values of spatial coherence of heart signal waveforms indicated that the body spatial transfer functions for electrical sources associated with heart activity acted as linear, noiseless transmission channels. The low spatial coherence of the waveforms generated by the electrical activity of skeletal muscles indicated that the body spatial transfer functions for electrical sources associated with skeletal muscle activity acted as noisy (nondeterministic) transmission channels. The spatial coherence of isoelectric interval waveforms was inversely proportional to both the distance between measurement sites and the amount of skeletal muscle activity.

Gradient detection and contrast transfer by the human eye

Threshold measurements were performed with stimulus patterns involving gradual changes in luminance. The results of these measurements indicate that threshold data obtained using linear luminance gradients permit quantitative prediction of the dependence of the threshold modulation on the spatial frequency as well as on the number of cycles of sinusoidal gratings. It appears that for detection purposes, a sinusoidal grating can be considered as one linear gradient with the same width. This makes it possible to predict the spatial modulation transfer function of the eye from measurements with spatial luminance gradients.

Full diffraction theory numerical simulation of sound propagation in the ocean in the presence of sound-velocity variations

We describe a numerical technique which uses a fast Fourier transform to make a plane-wave decomposition of the transmitter field. Spatial propagation is realized by multiplying the transmitter spectra with a spatial transfer function. An inverse FFT is performed on the resulting spectra to determine the field down range. Sound velocity variations, such as velocity gradients and those associated with turbulence which exist between the transmitter and receiver, are modeled. The distance between transmitter and receiver is broken up into slabs. The slab thickness is chosen to be the Rayleigh length of the smallest significant size in the problem. The velocity variations within a slab are modeled as a phase mask at the front of the slab. The remainder of the slab is assumed to be free of velocity variations. Since diffraction effects are not important over the Rayleigh length, the slab decomposition used represents a good model of the actual problem. We present results of simulations of direct path propagation in the presence of velocity gradients and turbulence.

Dynamics of Thin-Film Thermal Detectors in Infrared Imaging Systems 2: Imaging of Fixed and Moving Objects

In a previous paper we derived the basic equations and the spatial and temporal modulation transfer functions (MTF) for a three-dimensional model of thin-film thermal imaging systems. Here we discuss the imaging of fixed and moving objects.