Fundamental Spatial Frequency Research Articles

Modeling of Current-Driven End-Effect Force Ripple in Air-Cored Linear Synchronous Motor With Multiple Modular Stators

This paper presents a segmented layer model (SLM) for the air-cored linear permanent-magnet synchronous motors (LPMSMs) with multiple modular stators. In the LPMSM with modular stators, the significant current-driven ripples (CDRs) are observed as the PM mover moves across the stator modules, due to the magnetic end effects. Such CDRs become more severe as the current excitation level increases. In order to correctly model the overall motor forces in the LPMSM, the analytic motor model needs to be able to capture the magnetic end effects from both the stator and mover, and also include the current-driven effects. The SLM method presented in this paper divides the analytical region into several segmented layers to be able to accurately capture both the geometric-saliency- and current-driven force ripples by using layers with different fundamental spatial frequencies. The fidelity of the proposed SLM is validated both by the finite element method (FEM) and the experiments. The SLM achieves an accuracy of more than 97 % and 87 % compared to the FEM and experimental results, respectively, while reducing the computation time by two orders of magnitude as compared to the FEM.

Mechanisms of speed encoding in the human middle temporal cortex measured by 7T fMRI.

Perception of dynamic scenes in our environment results from the evaluation of visual features such as the fundamental spatial and temporal frequency components of a moving object. The ratio between these two components represents the object's speed of motion. The human middle temporal cortex hMT+ has a crucial biological role in the direct encoding of object speed. However, the link between hMT+ speed encoding and the spatiotemporal frequency components of a moving object is still under explored. Here, we recorded high resolution 7T blood oxygen level-dependent BOLD responses to different visual motion stimuli as a function of their fundamental spatial and temporal frequency components. We fitted each hMT+ BOLD response with a 2D Gaussian model allowing for two different speed encoding mechanisms: (1) distinct and independent selectivity for the spatial and temporal frequencies of the visual motion stimuli; (2) pure tuning for the speed of motion. We show that both mechanisms occur but in different neuronal groups within hMT+, with the largest subregion of the complex showing separable tuning for the spatial and temporal frequency of the visual stimuli. Both mechanisms were highly reproducible within participants, reconciling single cell recordings from MT in animals that have showed both encoding mechanisms. Our findings confirm that a more complex process is involved in the perception of speed than initially thought and suggest that hMT+ plays a primary role in the evaluation of the spatial features of the moving visual input.

The Clinical Application of Polarization Pattern Perception.

PurposeDetermine the repeatability of and optimum stimulus parameters for testing polarization pattern perception in a real-world clinical population, and assess the ability of polarization perception to distinguish normal from abnormal eyes.MethodsPolarization perception was evaluated in staff and patients attending ophthalmology clinics at Warwick Hospital, UK. A series of visual stimuli were presented in pseudorandom order using a liquid-crystal-display–based polarization pattern generator. Stimuli included geometric patterns, gratings, checkerboards, and optotypes. Participants had one or both eyes diagnosed as normal or abnormal following ophthalmic examination, optical coherence tomography, and measures of visual acuity. Measurement scores were assigned to the eye(s) of each participant depending on the total number of stimuli perceived or identified.ResultsStimuli covered the range of spatial scales resolvable within polarization perception by normal and abnormal eyes. Different stimuli had different saliencies. For each stimulus type, polarization perception in the abnormal group was significantly reduced compared with normal eyes (P < 0.001). Relative stimulus salience was broadly similar for normal-eye and abnormal-eye viewing groups, being greatest for radially symmetric patterns and least for optotypes. Checkerboard pattern salience had an inverse logarithmic relationship with check fundamental spatial frequency. A devised metric covering the dynamic range of polarization perception was repeatable, and the score derived from the metric was reduced in the abnormal group compared with the normal group (P < 0.001).ConclusionsClinically useful metrics of polarization perception distinguish between normal and abnormal eyes.Translational RelevancePerception of spatial patterns formed of non-uniform polarization fields has potential as a quantitative clinical diagnostic measurement.

Demonstrated resolution enhancement capability of a stripmap holographic aperture ladar system

Holographic aperture ladar (HAL) is a variant of synthetic aperture ladar (SAL). The two processes are related in that they both seek to increase cross-range (i.e., the direction of the receiver translation) image resolution through the synthesis of a large effective aperture. This is in turn achieved via the translation of a receiver aperture and the subsequent coherent phasing and correlation of multiple received signals. However, while SAL imaging incorporates a translating point detector, HAL takes advantage of a two-dimensional translating sensor array. For the research presented in this article, a side-looking stripmap HAL geometry was used to sequentially image a set of Ronchi ruling targets. Prior to this, theoretical calculations were performed to determine the baseline, single subaperture resolution of our experimental, laboratory-based system. Theoretical calculations were also performed to determine the ideal modulation transfer function (MTF) and expected cross-range HAL image sharpening ratio corresponding to the geometry of our apparatus. To verify our expectations, we first sequentially captured an oversampled collection of pupil plane field segments for each Ronchi ruling. A HAL processing algorithm incorporating a high-precision speckle field registration process was then employed to phase-correct and reposition the field segments. Relative interframe piston phase errors were also removed prior to final synthetic image formation. By then taking the Fourier transform of the synthetic image intensity and examining the fundamental spatial frequency content, we were able to produce experimental modulation transfer function curves, which we then compared with our theoretical expectations. Our results show that we are able to achieve nearly diffraction-limited results for image sharpening ratios as high as 6.43.

Measurement of grating acuity in guinea pigs by a customized automated optomotor device

The guinea pig becomes an important model for studies on myopia, but little is known about its visual performance. In this study, grating acuity was measured using a custom-built automated device to track optomotor responses. To record head nystagmus, guinea pigs were individually placed in the center of a rotating drum of 130 cm diameter. The drum was covered inside with square wave gratings of adjustable fundamental spatial frequencies and contrast. The turning movements of the head were tracked using custom-written video software that detected two little white spots painted on a small black piece of cardboard that was attached to the guinea pig's head. Angular head speed was determined from the positions of the two white spots with respect to each other over time, and the ratio of angular head speed to drum speed was determined (the "gain"). In 11 guinea pigs of the same age, but with different refractive states (+9.7 to -15.0 D), responses to spatial frequencies of 0.6 and 2.4 cyc/deg were tested. Furthermore, 17 guinea pigs were tested which had similar refractive states but were different in age (1 to 3 months old). Finally, the effects of different grating contrasts were studied (25%, 50% and 100% contrast respectively) and the effects of different stripe luminances (10, 30, and 350 cd/m(2) respectively). The optomotor response could be used to measure vision in one eye only even if both eyes opened. The optomotor gain was affected by refractive error. Younger animals (one month old) had lower optomotor gain than older ones (0.61 ± 0.2 in one-month, 0.77 ± 0.13 in two-month and 0.80 ± 0.11 in three-month old). For a spatial frequency of 0.6 cyc/deg, the effects of stripe contrast were tested in two months old guinea pigs. At an average stripe luminance of 30 cd/m(2), the optomotor gain dropped from 0.95 ± 0.20 at maximal contrast, to 0.94 ± 0.16 at 50% contrast, and 0.70 ± 0.10 at 25% contrast. At three different luminances, gains were 0.81 ± 0.25 (10 cd/m(2)), 0.95 ± 0.20 (30 cd/m(2)), and 0.80 ± 0.09 (350 cd/m(2)), measured with gratings of 100% contrast, respectively. Myopic guinea pigs have reduced grating acuity compared to hyperopic ones. The optomotor gain increases with age. For a given grating contrast, the highest optomotor gains are obtained at the highest luminance of 30 cd/m(2). In summary, spatial vision in guinea pig declines with the magnitude of myopia, and increases with luminance and age.

Quantitative and functional influence of surround luminance on the letter contrast sensitivity function

To determine the influence of surround luminance on the letter contrast sensitivity function. The binocular contrast sensitivities of 31 young and ocularly healthy individuals were measured with letters of sizes calculated to obtain the targeted fundamental frequencies of 3, 10, 20, and 30 c deg(-1), respectively; with surround luminances from 1 to 1000 cd m(-2), always with a test chart background luminance of 200 cd m(-2). The letter contrast sensitivity increased with surround luminance up to 100 cd m(-2) and decreased when surround luminance increased from 100 to 1000 cd m(-2). These increments are larger for higher fundamental spatial frequencies, while decrements are similar for all frequencies. To analyse pupil size influence, results were compared with theoretical predictions obtained by combining different ocular MTFs with a typical neural function, where pupil size decrease leads to letter contrast sensitivity increments and veiling luminance causes the observed decrements. Other possible optical or neural factors that influence these values have also been considered. Letter contrast sensitivity function depends on surround luminance and this influence should be considered in future standardized directives.

Classical conditioning of autonomic fear responses is independent of contingency awareness.

The role of contingency awareness in classical conditioning experiments using human subjects is currently under debate. This study took a novel approach to manipulating contingency awareness in a differential Pavlovian conditioning paradigm. Complex sine wave gratings were used as visual conditional stimuli (CS). By manipulating the fundamental spatial frequency of the displays, we were able to construct pairs of stimuli that varied in discriminability. One group of subjects was given an "easy" discrimination, and another was exposed to a "difficult" CS+ and CS-. A 3rd group was exposed to a stimulus that was paired with the unconditional stimulus (UCS) 50% of the time and served as a control. Skin conductance response (SCR) and continuous UCS expectancy data were measured concurrently throughout the experiment. Differential UCS expectancy was found only in the easy discrimination group. Differential SCRs were found in the easy discrimination group as well as in the difficult discrimination group, but not in the 50% contingency control. The difficult discrimination group did not exhibit differential UCS expectancy but did show clear differential SCR. These observations support a dual process interpretation of classical conditioning whereby conditioning on an implicit level can occur without explicit knowledge about the contingencies. The role of contingency awareness in classical conditioning experiments using human subjects is currently under debate. This study took a novel approach to manipulating contingency awareness in a differential Pavlovian conditioning paradigm. Complex sine wave gratings were used as visual conditional stimuli (CS). By manipulating the fundamental spatial frequency of the displays, we were able to construct pairs of stimuli that varied in discriminability. One group of subjects was given an "easy" discrimination, and another was exposed to a "difficult" CS+ and CS-. A 3rd group was exposed to a stimulus that was paired with the unconditional stimulus (UCS) 50% of the time and served as a control. Skin conductance response (SCR) and continuous UCS expectancy data were measured concurrently throughout the experiment. Differential UCS expectancy was found only in the easy discrimination group. Differential SCRs were found in the easy discrimination group as well as in the difficult discrimination group, but not in the 50% contingency control. The difficult discrimination group did not exhibit differential UCS expectancy but did show clear differential SCR. These observations support a dual process interpretation of classical conditioning whereby conditioning on an implicit level can occur without explicit knowledge about the contingencies.

Perceiving motion transparency in the absence of component direction differences

The simultaneous perception of multiple motion components within the same region in the visual field is a difficult processing task, which can be solved by human observers for a range of transparently moving stimuli. We use transparently moving gratings to study this phenomenon psychophysically, focussing on configurations in which individual components move in the same direction and can only be discriminated by speed differences. We first demonstrate that the stimuli are perceived as transparent and then proceed to quantify how the strength of motion transparency changes while component grating parameters such as fundamental spatial frequency, speed and luminance are varied. The results were consistent with perception resolving a signal detection task of separating two superimposed global motion signals corresponding to each of the components. We also identify the importance of broadband stimuli containing edges, both for perceiving transparency with the same direction stimulus configuration, and for static transparency. The local density of edges has a direct influence on the strength of perceived transparency, suggesting that local motion detection at the edges of the stimuli, which is sensitive to speed differences, may be critical to solve the task. The work suggests that there may be a simultaneous retinotopic representation of the two speeds of motion analogous to that accomplished by the motion direction tuned neurons found across regions of visual cortex.

Reflectivity and optical surface height requirements in a broadband coronagraph 1Contrast floor due to controllable spatial frequencies

We derive the broadband contrast floor in a coronagraphic telescope having nonideal optical surfaces. We consider only fundamental spatial frequencies within the control bandwidth of the coronagraph's deformable mirror. Cross terms arising from the beating of spatial frequencies beyond the deformable mirror control bandwidth will be considered in a second paper. Two wavefront control systems are analyzed:a zero-path difference Michelson interferometer with two deformable mirrors at a pupil image, and a sequential pair of deformable mirrors with one placed at a pupil image. We derive requirements on optical surface figure and reflectivity uniformity for both cases.

Measurement of Wavefront Aberration of Human Eye Using Talbot Image of Two-Dimensional Grating

The measurement of human ocular aberration is now frequently performed because of the increase in refractive surgery on the human cornea. The Hartmann-Shack (H-S) wavefront sensor is considered to be the most useful wavefront sensor, and a calculation method for wavefront aberration has been established. New methods of measuring wavefront aberrations of human eyes, using the Talbot image of a two-dimensional grating as a wavefront sensor and local shift of the Talbot image to calculate tilt of the wavefront are shown. The shift of the Talbot image was determined by comparing the phases of fundamental spatial frequency between the grating and the local patch of the Talbot image by Fourier transformation. The actual experiment was performed using a modified commercially available wavefront analyzer. Using these methods, Talbot images were obtained from model eyes and a human eye, and wavefront shapes were successfully reconstructed. Wavefront aberrations can be measured even when the obtained image is degraded by defocusing or scattering.

Effective Values of Variable Components of the Refractive Index upon Nonlinear Recording of Phase Holograms

The diffraction of a plane wave incident on a thick hologram at the first and second Bragg angles in the process of nonlinear recording is analyzed using the coupled-wave equations. It is shown that, in this case, the two-wave approximation with the use of effective modulation amplitudes of the refractive index, n1ef and n2ef, can be applied. Analytical dependences of n1ef and n2ef on the modulation amplitudes of the refractive index n1 and n2 at the fundamental and doubled spatial frequencies are obtained and the criteria of their applicability are determined. The dependences found are used to calculate the parameters of gratings recorded in a photopolymeric material.

Monocular and dichoptic masking effects on the frequency doubling illusion

The purpose of this paper was to investigate the effects of both monocular and dichoptic masking on the frequency doubling (FD) illusion, using both temporal and spatial masks. Monocular spatial tuning effects occurred around the fundamental FD spatial frequency of 0.25 cycles per degree (c/deg), whereas dichoptic spatial frequency tuning effects occurred at the doubled spatial frequency of 0.50 c/deg. Temporal tuning effects were observed at the FD temporal frequency of 25 Hz, in both monocular and dichoptic paradigms. These results suggest that the FD illusion is cortical in origin and is dominated by a flicker component.

Spatial frequency tuning of the Ouchi illusion and its dependence on stimulus size

This study investigated the effects of the stimulus size on the spatial frequency tuning of the Ouchi illusion, which is an illusory sliding motion perceived in a checkerboard pattern of rectangular elements that is surrounded by a checkerboard pattern of orthogonally oriented elements. Two experiments were conducted to measure the perceived strength of illusion. The optimal size of the inner pattern increased proportionally with check size. In contrast, the optimal check size increased with the size of the inner pattern but not proportionally, and the range of increase was relatively small. The optimal fundamental spatial frequency was lower for a larger stimulus both for checkerboard patterns and simpler sinusoidal grating patterns, but there were differences in the tuning curves for the two types of stimuli. These results support the idea that two processes underlie the Ouchi illusion; one computes the local motion direction, and the other integrates motion signals across space for surface segmentation. For the checkerboard and grating stimuli, the former process may be different while the latter can be shared.

Motion of contrast envelopes: peace and noise.

We examined the effect of changing the composition of the carrier on the perception of motion in a drifting contrast envelope. Human observers were required to discriminate the direction of motion of contrast modulations of an underlying carrier as a function of temporal frequency and scaled (carrier) contrast. The carriers were modulations of both color and luminance, defined within a cardinal color space. Random-noise carriers had either binary luminance profiles or flat (gray-scale-white) or 1/f (pink) spectral power functions. Independent variables investigated were the envelope spatial frequency and temporal-drift frequency and the fundamental spatial frequency, color, and temporal-update frequency of the carrier. The results show that observers were able to discriminate correctly the direction of envelope motion for binary-noise carriers at both high (16 Hz) and low (2 Hz) temporal-drift frequencies. Changing the carrier format from binary noise to a flat (gray-scale) or 1/f amplitude profile reduced discrimination performance slightly but only in the high-temporal-frequency condition. Manipulation of the fundamental frequency of the carrier elicited no change in performance at the low temporal frequencies but produced ambiguous or reversed motion at the higher temporal frequencies as soon as the fundamental frequency was higher than the envelope modulation frequency. We found that envelope motion detection was sensitive to the structure of the carrier.

Spatial Property of Formed Patterns Depending on Focus Condition in a Two-Dimensional Optoelectronic Feedback System

The spatial properties of a pattern generated in an optoelectronic system composed of an electronically addressable spatial light modulator, a detector array, and two-dimensional optical feedback are experimentally investigated. The square-root dependence of the fundamental spatial frequency on the positive and negative deviations from the in-focus condition of the optical feedback is demonstrated under conditions of the inversion property of the spatial light modulator. The optoelectronic system has a serial process, but its spatial properties are almost equivalent to the spatial properties of an all-optical system based on an optically addressed spatial light modulator. Patterns generated by variation of the frame rate of the optoelectronic system are also demonstrated.

Binocular interaction in normal vision studied by pattern-reversal visual evoked potential (PR-VEPS).

Monocular and binocular visual evoked potentials (VEPs) in response to different check size (15-21-38-84 minutes or arc) were studied in 14 subjects with normal visual acuity and stereopsis. The binocular VEP amplitude is slightly higher than the VEP amplitude on stimulation of the "better eye" and significantly higher than the VEP amplitude on stimulation of the "worse eye"; this effect is observed using small checks and almost exclusively involved N75-P100. Both the N75 and P100 peaks occur earlier after binocular than monocular stimulation. The shortening of the N75 mean latency is significantly greater than that of the P100 mean latency when larger check sizes are used. The mean latency of the N145 potential is not significantly different in monocular and binocular stimulus conditions. The slight summation effect and latency shortening in the binocular VEPs are not consistent with the hypothesis that it is the sum of separate monocular signals originating from the visual cortex that gives rise to the response. The early components of both monocular and binocular VEPs are thought to be of post-synaptic origin (outside layer 4c of area 17), where the inputs become mixed so that most cells receive information from both eyes. The amplitude enhancement of binocular VEPs, which mainly occurs when using small checks, may be related to the increase in the total amount of cortical activity representing the macular region; this may account for binocular superiority in fine spatial resolution. The latency shortening in binocular conditions can be explained by considering that the critical determinant of the latency is the fundamental spatial frequency of the pattern. When coarse patterns are used, their effectiveness in parafoveal stimulation may affect the VEPs, with a significant contribution coming from the more peripheral retina. The enlargement of the visual field when the eyes see simultaneously may therefore further reduce the latency of the response when using the larger checks suitable for eccentric stimulation.

Reading with magnifiers.

The design of low vision aids for partially sighted people, such as magnifiers, is evaluated theoretically in order to identify meaningful directions of research for improving these aids. Both reading with and without a magnifier involves alternating sequences of locating and recognizing textual information. Little is known, however, about these processes in magnifier reading. On the basis of an extensive review of the literature, two topics are identified that stand out as being in need of experimental investigation: (1) the relationship between the (typo)graphical characteristics of printed text and the location and recognition of textual information, and (2) the interplay of location and recognition processes in magnifier reading, including the role of non-visual factors, such as movements of the hand, trunk, head and eyes in this interplay. With regard to the first topic, it is expected that the visibility and, hence, the recognition of textual information by partially sighted people can be improved by matching the fundamental spatial frequencies of graphical structures with the spatial contrast sensitivity of partially sighted people. With regard to the second topic, it is argued that persistent problems in the design of the magnifiers, such as the optimal window size, can only be resolved by studying reading with a magnifier as a (multimodal) perceptual-motor activity.

Visual processing of motion boundaries

Psychometric functions for motion detection were measured for various spatial velocity profiles made of independently moving lines of random dots. In the first experiment, sensitivity was greater for square-wave velocity profiles than for sine waves of the same fundamental spatial frequency. Sensitivity for square waves depended on the phase of the waveform with respect to the fixation point, which precludes a characterization of the processes underlying the detection of shearing motion as a translation-invariant system. The second experiment, using velocity fields created by spatial superposition of sine waves, showed that motion boundaries facilitate detection of motion due to the steepness of the velocity gradient, and not simply because of added power at higher harmonics. In the third experiment, fluted velocity waveforms were created by subtracting the fundamental sinusoidal component from square waves, retaining sharp motion boundaries between opposing directions but removing the regions of uniform motion. Subtracting the fundamental from low-frequency square waves did not lower sensitivity to motion, indicating that sensitivity was largely determined by the presence of motion boundaries. In the final section of this article, a model is presented that can account for the data by using linear center-surround velocity mechanisms whose sizes increase with eccentricity while their sensitivity for shearing motion decreases.

Rectification property of photoconductive crystal under spatially asymmetric illumination

Generation of direct current flow through a photoconductive crystal with applied ac electric field under illumination by two intensity patterns with fundamental and doubled spatial frequencies is theoretically investigated. Analysis is restricted to the case of large temporal frequency of external ac field.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Texture segmentation as a function of eccentricity, spatial frequency and target size.

Two experiments examined the role of fundamental spatial frequency, target area and retinal eccentricity in texture segmentation. In Experiment 1, a backward-masked target comprising lines oriented orthogonally to the surround was briefly presented at the fovea, and at eccentricities ranging from 2.55 to 7.63 deg. Reaction time and accuracy were better when targets were presented at non-foveal locations. In Experiment 2, eccentricity effects were examined when both spatial frequency and target area were varied. Accuracy was highest and RT fastest at near-peripheral, not foveal locations. The eccentricity corresponding to optimal performance was related inversely to spatial frequency. Results suggest that the near periphery is more adept than the fovea at the early processing which underlies rapid texture segmentation.