Spatial Frequency Bandwidth Research Articles

Cross-talk noise reduction in volume holographic storage with an extended recording reference

We propose and analyze a novel method of reducing cross-talk noise in angle-multiplexed volume holographic optical storage. The method records each hologram by using a reference beam that extends uniformly within a narrow spatial frequency bandwidth but reads the memory by using a plane wave. Our result shows that the signal-to-noise ratio obtained by the proposed method can be 20 dB higher than that obtained by the conventional method with planar reference waves. In addition, the extended reference method has a larger tolerance for angle misalignment during readout than the conventional method. Results of numerical simulation are presented and discussed.

Spatial-frequency bandwidth in the photolithographic transfer of submicron gratings

The principle of the photolithographic mask transfer of high-spatial-frequency gratings under the Littrow angle is shown to be so tolerant that a broad spatial-frequency spectrum can be transferred under the same exposure conditions.

Imaging through the atmosphere: practical instrumentation-based theory and verification of aerosol modulation transfer function: reply to comment

New exact numerical calculations as well as exact calculations in J. Opt. Soc. Am. A10, 172 ( 1993) indicate that the approximations in the Comment in J. Opt. Soc. Am. A11, 1175 ( 1994) are based on faulty perceptions of basic scattering phenomena and on a misreading of our paper. The Comment does not sufficiently consider effects of instrumentation. Whereas our model refers to the aerosol modulation transfer function (MTF) in the image plane, the values of maximum angles for scattered (θS) and unscattered (θ0) light used in the Comment refer to the optics plane. The Comment does not consider the fact that dynamic range limits (θS) in the image, whereas limited spatial-frequency bandwidth broadens θ0 in the image, each by orders of magnitude. Therefore the Comment’s conclusion contradicts experimental results obtained by numerous researchers. The Comment’s conclusion that aerosol MTF is insignificant is based on that author’s own experiments, in which clear weather and haze atmospheric MTF (composed of turbulence and aerosol MTF’s) could not be measured, the reason being insufficient equipment resolution, rather than insignificant turbulence or aerosol MTF. Furthermore, the claim in our original paper that aerosol MTF is extremely significant has since been supported by many different types of experiments that included short and long exposures, thermal imaging, and image restoration based on atmospheric MTF, including a highly significant practical, uniquely shaped, aerosol MTF.

Three-dimensional Image Formation in Confocal Microscopy Under Ultra-short-laser-pulse Illumination

Reported in this paper is, to our knowledge, the first theoretical investigation of three-dimensional (3D) imaging properties in a confocal microscope under ultra-short-pulse illumination. Time-resolved, time-averaged and interferometric imaging modes in reflection and transmission systems are considered. The concept of the 3D transfer function is used to understand the imaging performance of the system. In the case of a 10fs pulse, the spatial frequency bandwidth in the axial direction is twice that for a system under continuous-wave (CW) illumination, while the spatial frequency bandwidth in the transverse direction is increased by only 10%. As a result, axial resolution can be improved by approximately 30%, compared with the limiting value under CW laser illumination of the same wavelength as the pulsed beam.

Linear and non-linear filtering in stereopsis

To better understand the spatial filtering operations underlying stereopsis, and their relationship to those underlying monocular localization of the same stimuli, we examined the dependence of stereoacuity on carrier and envelope size of Gabor patches. For stimuli of broad spatial bandwidth, stereoacuity depends on the carrier spatial frequency whereas for stimuli of narrow bandwidth, stereoacuity depends on the modulation frequency. The dependence of stereoacuity on the separation of the reference elements differs for stimuli of broad and narrow spatial frequency bandwidths. These relationships suggests that stereopsis has access to two different types of information from the early filters which we term, linear and non-linear. This distinction is important not only for understanding the relationship between monocular and stereoscopic localization, but also for understanding the different filter operations underlying stereopsis.

Simultaneous discrimination of the spatial frequency and contrast of periodic stimuli

Discrimination thresholds for spatial frequency and contrast were measured as a function of (1) the spatial-frequency bandwidth of the stimuli, (2) the reference contrast of the stimuli, and (3) whether the observer knew on which dimension, spatial frequency or contrast, the stimuli would differ. Relative bandwidth was manipulated by a one-dimensional Gaussian window and varied from 0.25 to 2.0 octaves. The results of two different tasks were compared. In a single-judgment task the observer knew on which dimension the stimuli would differ, and discrimination thresholds were measured in a standard two-interval forced-choice staircase procedure. In a dual-judgment task the dimension on which the stimuli differed varied from trial to trial. In this task the observer made two judgments on each trial in a modified two-interval forced-choice procedure: (1) on which dimension the stimuli differed and (2) in which interval the stimulus with the higher spatial frequency or contrast appeared. Thresholds were measured by five interleaved staircases for five reference contrast levels that varied from 0.02 to 0.32. Thresholds for both spatial frequency and contrast increased with increasing stimulus bandwidth and decreased with increasing stimulus contrast. Thresholds were, on average, 1.8 times higher in the dual-judgment task than in the single-judgment task, independent of the stimulus contrast and the bandwidth. A stimulus-uncertainty model is described that accounts for the difference between thresholds in the single- and the dual-judgment tasks.

Imaging through the atmosphere: practical instrumentation-based theory and verification of aerosol modulation transfer function

Recent experimental measurements of overall atmospheric modulation transfer function (MTF) indicate a significant difference between overall atmospheric and turbulence MTF’s except often at midday, when turbulence is strong. We suggest a physical explanation for these results that essentially relates to a practical instrumentation-based atmospheric aerosol MTF that is a modification of the classical aerosol MTF theory. Based on radiative transfer theory, this practical approach takes into account the effect of finite field of view, finite dynamic sensitivity, and finite spatial bandwidth of every existing imaging system. These generally limit the scattering angles of received light to values far less than the diffraction limit for aerosols, thereby decreasing blur radius and increasing spatial frequency bandwidth. This can explain the broadening of the aerosol MTF from that theoretically expected. We discuss the asymptote value that the measured aerosol MTF approaches at high spatial frequencies, which is significantly higher than the theoretical prediction of turbid medium transmittance. An important conclusion that we derive is that the aerosol MTF is often the dominant part in the actual overall atmospheric MTF. In addition, there seems to be an inescapable trade-off between image resolution and image irradiance. The system designer must choose between imaging of faint and bright objects at the expense of image quality or imaging of either faint or bright objects with improved image quality. The concepts here are basic to all long-range imaging through the atmosphere.

Theoretical analysis of electrode raster performance in reliefographic spatial light modulators with signal recording at the substrate side

The results are presented of the theoretical analysis of spatial light modulators (SLM) with a deformable viscoelastic layer, builtin electrode raster, and change recording at the substrate side. Using a new effective calculation technique, the influence of electrode raster parameters on SLM's characteristics is investigated. The enhancing role of the deformable layer conductive cover is found out for electric deforming forces of latent image. The influence of viscoelastic features of deformable layer (with Voight rheology as example) on SLM's efficiency is investigated too. The SLM's optical scattering rate is considered as a function of transfered signal spatial frequency. The conclusion is made about advantages in transfered spatial frequency bandwidth for SLM with a conductive cover.

Microstructure characterization by angle-resolved scatter and comparison to measurements made by other techniques

The theory and measurement of angle-resolved scatter are described. Values of rms roughness that were obtained by using this technique to characterize four different materials are compared with values that were obtained by using a total integrated scatter measuring instrument, an optical profiler, and a mechanical profiler. The spatial frequency bandwidths and modulation transfer functions of the four instruments are different, and results are described in light of these differences.

Apparent duration and spatial structure.

In three experiments, we investigated the relative perceived duration of a full bandwidth image and a set of high- and lowpass filtered images of a scene, briefly presented on a visual display unit. In Experiment 1, the various images were compared with each other, using a paired comparison method. All images were presented for 40 msec, and observers were asked to judge which of each pair of images had the longest duration. The results showed that images containing a wide spatial frequency bandwidth were judged to be of longer duration than were images of a narrower bandwidth, regardless of whether the latter were high- or lowpass filtered. In Experiment 2, a 40-msec presentation of each of the images was compared with a presentation of a probe that was 20, 40, 60, or 80 msec in duration. Observers again judged which of each pair of images had the longest duration. The results were very similar to those of Experiment 1, with wide bandwidth images being judged to be of longer duration than were narrow bandwidth images. In Experiment 3, instead of comparing the various filtered versions of the image with each other, we attempted to obtain a direct measure of perceived duration by comparing a flashing LED to a 40-msec flash of a subset of the images used in the previous experiments. The observers' task was to adjust the duration of the LED flash to match the perceived duration of each image.(ABSTRACT TRUNCATED AT 250 WORDS)

Spatial frequency discrimination of band-limited periodic targets: Effects of stimulus contrast, bandwidth and retinal eccentricity

Two experiments were conducted to explore the ability of human observers to discriminate the spatial frequency of briefly-presented, Gaussian-truncated sinewave gratings. In the first experiment, the influence of stimulus contrast and stimulus bandwidth on discrimination thresholds was measured after removing any position cues by randomizing the spatial phase of the gratings for each presentation. In a second experiment, the influence of retinal eccentricity on discrimination thresholds was explored for Gaussian-truncated gratings of constant spatial frequency bandwidth (0.5 octave) and suprathreshold contrast value (5 × detection threshold). The spatial frequency of the reference gratings varied from 1 to 8c/deg. The gratings were positioned centered at the fixation point or 1–20 deg eccentric of the point of fixation along the horizontal meridian. Two observers responded in a two-interval forced-choice paradigm, which of two gratings had a higher spatial frequency. A difference frequency was randomly added to or subtracted from the spatial frequency of either the first or second grating. Using a maximum-likelihood algorithm, the spatial-frequency discrimination threshold was computed from 40 trials, at which the observer responded with 75% accuracy. The results indicate that discrimination thresholds increase with (1) decreasing stimulus contrast, (2) increasing stimulus bandwidth, and (3) increasing retinal eccentricity. It is shown that spatial-frequency discrimination thresholds are only independent of contrast for narrow bandwidth stimuli having a contrast > 0.02. The eccentricity-dependent increase in discrimination thresholds varies with reference spatial frequency: with increasing retinal eccentricityΔf/f increases gradually for low spatial frequencies but rapidly for high spatial frequencies.

Image resolution limits resulting from mechanical vibrations. Part III:numerical calculation of modulation transfer function

Low-frequency mechanical vibrations are a significant problem in robotics, machine vision, and practical reconnaissance where primary image vibrations involve random process blur radii. They cannot be described by an analytical MTF. A method of numerical calculation of MTF, relevant in principle to any type of image motion, is presented. It is demonstrated here for linear, high, and low vibration frequencies. The method yields the expected closed form solutions for linear and high-frequency motion. The low-vibration-frequency situation involves random process blur radii and MTFs that can only be handled statistically since no closed form solution is possible. This is illustrated here. Comparisons are made to a closed form approximate MTF solution suggested previously for low-frequency motion. Agreement between that analytical approximation and exact MTF calculated numerically is generally good, especially for relatively large and linear motion blur radius situations. For nonlinear short exposure motion, MTF levels off at relatively high nonzero values and never approaches zero. Such situations yield a two-fold benefit: (1) larger spatial frequency bandwidth and (2) higher MTF values at all spatial frequencies since MTF does not approach zero.

Contrast adaptation and contrast masking in human vision

After a preliminary study of visual evoked potentials (VEPS) to a test grating seen in the presence of masks at different orientations, psychophysical data are presented showing the effects of adaptation and of masking on thresholds for detecting the same test grating. The test is a vertical grating of spatial frequency 2 cycles per degree; adapting and masking gratings differ from the test either in orientation or in spatial frequency. The effects of adaptation and masking are explained by a single mechanism model that assumes: (i) adaptation and masking both alter the contrast response (or transducer) function of the mechanism that detects the test; (ii) masks, but not adaptors, stimulate the mechanism that detects the test; and (iii) a test is detectable when it raises response level by a constant amount. The model incorporates two distinct tuning functions, a broad adaptive contrast function and a narrow effective contrast function. It accounts adequately for all the data, including the location and size of the facilitative dip found in some masking functions, the constant slopes of the threshold elevation segments of adaptation functions and the varying slopes of masking functions. It also predicts the sometimes surprising joint effects of adaptation followed by masking and of two masks operating simultaneously.

Data compression and depth shape reproduction of stereoscopic images

AbstractThree‐dimensional visual communications, realized with stereoscopic images, can achieve total display realism. To create a three‐dimensional (3‐D) transmission and display system, the large amount of information typically contained in natural images must be reduced and coded by an efficient technique appropriate for stereoscopic images.As the initial step in realizing such a coding scheme, statistical characteristics of stereoscopic images and image characteristics viewed from the aspect of human stereopsis are presented.First, the possibility of data compression that exploits the cross correlation between right and left images is shown. Based on this, a method that shifts one image horizontally and subtracts it from the corresponding area of the other is proposed and evaluated. Next, it is shown that complete depth amplitude reproduction of stereoscopic images through the use of existing CRT display systems is difficult. This is due to the poor horizontal resolution of the forementioned systems even though the depth spatial frequency bandwidth of stereoscopic images can be reduced without deteriorating depth shape reproduction accuracy. Finally, a method for overcoming discontinuous depth reproduction is proposed and its effectiveness is confirmed.

4812762 Fast method and device for determining an NMR distribution in a region of a body

Two visually evoked brain responses were elicited simultaneously by stimulating the eye with two superimposed sinewave grating patterns that were temporally modulated at slightly different rates. The VEP to one grating was comparatively little affected by the presence of the other grating when the two spatial frequencies were very different, but mutual attenuation grew stronger and stronger as the spatial frequencies of the two gratings were progressively brought together. The attenuation rose to a sharp maximum when the two spatial frequencies were equal. This held at each of the five spatial frequencies tested. This finding can be explained if the spatially-selective mechanisms responsible for grating VEPs contain multiple subunits of narrower spatial frequency bandwidth. The two-grating technique was also used to search for evidence of multiple subunits that are most sensitive at the same spatial frequency, but are tuned to different temporal frequencies. Findings were quite different for temporal and for spatial tuning. Attenuation of one grating VEP was greatest when the temporal frequency of the other grating fell within a broad frequency range of about 3–30 reversals sec−1: maximum attenuation could occur when the gratings had quite different temporal frequencies. This finding denies that for every given temporal frequency there is a subunit maximally sensitive to that frequency.

Modulation transfer function of photographic emulsion: the small-angle approximation in radiative transfer theory

The modulation transfer function (MTF) of photographic emulsion can be conveniently represented by an expression derived from the theory of radiative transfer. Small-angle scattering is assumed to simplify the transfer equation and a Gaussian model is used to represent the forward lobe of the scattering phase function. The MTF depends on such variables as emulsion thickness, crystal size and concentration, relative refractive index, and the wavelength of incident light. The experimental results show that the Gaussian model adequately represents the phase function and also that useful MTF predictions are possible in the spatial frequency bandwidth 0-40 cycles/mm for AgBr crystals in a gelatin matrix.

Visual masking at different polar angles in the two-dimensional Fourier plane

Human contrast thresholds were measured at 86 points in the two-dimensional Fourier plane with and without masks. The test stimuli were sinusoidal gratings in a 2.55-deg circular field. The superimposed masks were sinusoidal gratings having a polar spatial frequency of 8 cycles/deg, a contrast of 0.31, and one of five polar angles: 90, 105, 120, 135, and 180 deg. The test grating contrast for 75.5% correct detection in a three-alternative, forced-choice paradigm was determined by a maximum-likelihood adaptive psychophysical procedure. Three other observers were tested on subsets of these conditions. The threshold elevation surfaces produced by the masks lead to the following conclusions: spatial-frequency bandwidth is independent of mask orientation and has a value of approximately 2 octaves, orientation bandwidth is wider for oblique masks than for horizontal and vertical masks, the principle of spectral polar separability is violated, and two-dimensional Gabor functions in the frequency domain account for the masking effects. Individual differences were found among the observers.

A Taylor synthesis for principal solution patterns of multiplicative antenna systems

A multiplicative (cross-correlation) receiving antenna system with a linear aperture can have a power pattern P/sub 0/(u) (the so-called principal-solution power pattern) whose spatial frequency transfer function (SFTF) is uniform over the entire spatial frequency (SF) bandwidth. A modified principal solution system which retains the uniform SFTF except for smooth transitions at the ends of the SF passband is described. The transitions are due to a change in the original pattern P/sub 0/(u), which suffers from high sidelobes, to a Taylor (1955) synthesis pattern P/sub T/(u) which involves a slowly varying envelope pattern. All of the slowly varying envelope sidelobes of P/sub T/(u) are set at the same appropriate low level, e.g. -30 dB. The aperture weighting distributions are free of singularities, unlike those for P/sub 0/(u), and can be sampled to provide the current weightings for a linear multiplicative array.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Spatial-frequency discrimination of drifting gratings

Spatial-frequency discrimination thresholds were measured for briefly (300 msec) presented sinewave gratings having a contrast one logarithmic unit above detection threshold. The gratings were drifted at rates varying from 1.1 to 40 Hz. In a two-interval forced-choice paradigm thresholds were determined for vertically and obliquely oriented gratings. Three reference spatial frequencies (1, 4, 12 c/deg) were tested. For the 1 c/deg reference spatial frequency, spatial-frequency discrimination thresholds were constant over the wide range of drift rates used. For 4 and 12 c/deg reference gratings, discrimination thresholds were constant for drift frequencies up to 14 Hz. For drift frequencies beyond 14 Hz, spatial-frequency discrimination thresholds increased abruptly, rising from approx. 6% at 14 Hz to 25% at 40 Hz drift rate. Measurements with obliquely oriented gratings yielded comparable results. The increase in the spatial-frequency discrimination threshold for medium-high spatial frequencies and high temporal frequencies might reflect an increase in the spatial frequency bandwidth of the mechanisms sensitive to these stimulus frequencies.

Note on interpolational basis functions in the method of moments (EM scattering)

Efficient basis sets for the method of moments may be obtained using quasi-localized bandlimited interpolational functions that, broadly speaking, are defined relative to a mean sampling rate that is adjusted to curvature and proximity to edges, thus reflecting the local spatial-frequency bandwidth. Computed scattering data in a number of structures, including perfectly conducting circular and elliptical two-dimensional cylinders as well as a flat infinite strip, indicate that reasonable accuracy can be obtained with an average rate of between 2.5 and 3 basis functions per wavelength. Average sampling rates need not correspond strictly to the bandwidth of the basis functions, and there is considerable latitude with respect to random variation of sampling intervals. Although each basis function typically extends over several sample points, required integrals can be obtained speedily by the use of standard sampling-theoretical methods. >