Sinusoidal Gratings Research Articles

InFoRM (Indicate-Follow-Replay-Me): A novel method to measure perceptual multistability dynamics using continuous data tracking and validated estimates of visual introspection

Perceptual multistability, e.g. Binocular Rivalry, has been intensively used as a tool to study visual consciousness. Current methods to assess multistability do not capture all potentially occurring perceptual states, provide no estimate of introspection, and lack continuous, high-temporal resolution to resolve perceptual changes between states and within mixed perceptual states. We introduce InFoRM (Indicate-Follow-Replay-Me), a four-phase method that (1) trains a participant to self-generate estimates of perceptual introspection-maps that are (2) validated during a physical mimic task, (3) gathers perceptual multistability data, and (4) confirms their validity during a physical replay. 28 condition-blinded adults performed InFoRM while experiencing binocular rivalry evoked with orthogonal sinusoidal gratings. A 60 Hz joystick (3600 data samples/minute) was used to indicate continuously changes across six perceptual states within each 1 min trial. A polarized monitor system was used to present the stimuli dichoptically. Three contrast conditions were investigated: low vs low, high vs high, and low vs high. InFoRM replicates standard outcome measures, i.e. alternation rate, mean and relative proportions of perception, and distribution of exclusive percepts that are well fitted with gamma functions. Furthermore, InFoRM generates novel outcomes that deliver new insights in visual cognition via estimates of introspection maps, in ocular dominance via perceptual-state-specific dominance scores, in transitory dynamics between and within perceptual states, via techniques adopted from eye-tracking, and in rivalry-zone-size estimates utilizing InFoRM’s ability to simulate piecemeal perception. The replay phase (physical replay of perceptual rivalry) confirmed good overall agreement (73% ±5 standard deviation). InFoRM can be applied to other multistable paradigms and can be used to study visual consciousness in typical and neuro-atypical populations.

Parameters of Optokinetic Nystagmus Are Influenced by the Nature of a Visual Stimulus

Studies on contrast sensitivity (CS) testing using optokinetic nystagmus (OKN) proposed adjusting the stimulus presentation duration based on its contrast, to increase the time efficiency of such measurement. Furthermore, stimulus-specific limits of the least OKN gain might reduce false negatives in OKN detection procedures. Therefore, we aimed to test the effects of various stimulus characteristics on OKN and to propose the stimulus-specific limits for the OKN gain and stimulus presentation duration. We tested the effect of contrast (C), spatial frequency (SF), and color on selected parameters of robust OKN response, namely its onset and offset time, amplitude, and gain. The right eyes of fifteen emmetropes were tracked with an infrared eye tracker during monocular observations of sinusoidal gratings moving over the horizontal plane with a velocity of (21∘/s). The available contrast levels were C: 0.5%, 2.0%, 8.2%, 16.5%, 33.0%, and 55.5% presented in a random order for ten times in all measurements of SF: 0.12, 0.25, 0.5, and 1.00 cycles per degree and grating type: luminance, red-green, and blue-yellow. This study showed a significant effect of the stimulus characteristics on the OKN onset, offset and gain. The effect of SF was insignificant in OKN amplitude; however, it indicated significance for the C and grating type. Furthermore, the OKN gain and offset limits were proposed as functions of contrast for the luminance and chromatic gratings. This study concludes the characteristics of a visual stimulus have an effect on the OKN gain and onset and offset time, yet do not affect the eye-movement amplitude considerably. Moreover, the proposed limits are expected to improve the time efficiency and eye-movement detection in OKN-based contrast sensitivity measurements.

Weighted summation and contrast normalization account for short-latency disparity vergence responses to white noise stimuli in humans.

Natural images are typically broadband, whereas detectors in early visual processing are selective for narrow ranges of spatial frequency. White noise patterns are widely used in laboratory settings to investigate how responses are derived from Fourier components in the image. Here, we report disparity vergence responses (DVRs) to white noise stimuli in human subjects and compare these with responses to white noise patterns filtered with bandpass filters and notch filters and to sinusoidal gratings. Although the contribution of these short-latency eye movements to the overall vergence response to a given stimulus is generally small, they have proven to be a valuable tool for the study of the early mechanisms that process disparity stimuli in human subjects. Removing lower spatial frequency (SF) components reduced DVR amplitude, whereas removing higher SF components led to an increase in DVR amplitude. For larger disparities, the transition occurred at lower SFs. All of these effects were quantitatively well described by a model that combined two factors: (a) an excitatory drive determined by a weighted sum of stimulus Fourier components, which was scaled by (b) a contrast normalization mechanism.

Neural correlates of lateral modulation and perceptual filling-in in center-surround radial sinusoidal gratings: an fMRI study

We investigated lateral modulation effects with functional magnetic resonance imaging. We presented radial sinusoidal gratings in random sequence: a scotoma grating with two arc-shaped blank regions (scotomata) in the periphery, one in the left and one in the right visual field, a center grating containing pattern only in the scotoma regions, and a full-field grating where the pattern occupied the whole screen. On each trial, one of the three gratings flickered in counterphase for 10 s, followed by a blank period. Observers were instructed to perform a fixation task and report whether filling-in was experienced during the scotoma condition. The results showed that the blood-oxygen-level-dependent signal was reduced in areas corresponding to the scotoma regions in the full-field compared to the center condition in V1 to V3 areas, indicating a lateral inhibition effect when the surround was added to the center pattern. The univariate analysis results showed no difference between the filling-in and no-filling-in trials. However, multivariate pattern analysis results showed that classifiers trained on activation pattern in V1 to V3 could differentiate between filling-in and no-filling-in trials, suggesting that the neural activation pattern in visual cortex correlated with the subjective percept.

Optical Fourier Volumes: A Revisiting of Holographic Photopolymers and Photoaddressable Polymers

AbstractTo avoid mixing of the undesired frequencies in a free‐space, the point sources of gratings, defined by a spatially varying refractive index, should be sinusoidally rather than binarily arranged. This long‐lasting but gold standard lesson attainable from a classical Fourier optics, however, is underutilized in the practical materialization of gratings, mainly because most of the fabrication methods, developed thus far, are intrinsically compatible with a binary rather than sinusoidal grating. Recently, such design concept of optical Fourier elements has been implemented into the real surface gratings (referred to as optical Fourier surfaces) by taking advantage of advanced nanofabrication, whereas their volumetric equivalents (optical Fourier volumes, OFVs) have yet to be conceptually and experimentally elucidated. In this work, the key characteristics of OFVs and their structural requirements are systematically exploited with the assistance of analytical and numerical calculations. Especially, the dynamic range and thickness of volume gratings, required for OFVs, are newly defined. Given these theoretical blueprints, both the holographic photopolymers and photoaddressable polymers are then revisited and they are experimentally validated as easy‐to‐craft mediums of OFVs. The landscape of volume gratings is extended by providing an integrative pipeline of OFVs across their theoretical design and practical materialization.

Dual-path inscription of plasmonic nano-Ag moiré fringes.

Construction of moiré surface patterns has attracted considerable attention due to the fascinating function of photoelectric manipulation. Holographic inscription offers superposition of two or more sinusoidal gratings to form moiré structures. However, the current material platforms primarily depend on a single process of photoinduced physical property change to build up multicomponent gratings. Herein, we demonstrate a strategy of bidirectional photochemical reaction on mesoporous TiO2 matrices to form plasmonic nano-Ag moiré fringes. This consists of a photoreduction grating from in situ growth of Ag nanoparticles (NPs) and a photooxidation grating utilizing the Schottky interface of Ag/TiO2. The pattern obtained under the superposition of double spatial frequencies exhibits non-equidistant moiré fringes. This Letter provides a pathway for implementing complex surface structures.

Saccade suppression of displacements, but not of contrast, depends on context.

Saccades let the visual scene sweep with high speed across the retina, thus producing a massive motion stimulus. Yet, in natural vision, we never perceive motion that is produced by saccades. The absence of perisaccadic motion perception might be caused by a transient reduction of visual sensitivity at the time of saccade initiation, so-called saccadic suppression. Saccade suppression occurs for contrast, displacement, and motion stimuli. Saccade suppression of displacements has been shown to be context sensitive. After performing saccades in sessions without perisaccadic stimulation, saccade suppression magnitude is drastically decreased (Zimmermann, 2020). Here, we aimed to test whether saccade suppression of contrast is similarly modulated by context. To this end, we projected stimuli on a homogeneously white wall such that we could establish a ganzfeld-like environment that, depending on the experimental session, did or did not contain any visible contrast stimuli. We first successfully replicated the context sensitivity of saccade suppression of displacements. Then, we tested context sensitivity of contrast suppression by asking subjects to perform several saccades either across the uniform white wall or across a background consisting of a sinusoidal grating. In contrast to perisaccadic context sensitivity for displacement suppression, we did not find context sensitivity for suppression of contrast.

Probing doors to visual awareness: Choice set, visibility, and confidence

ABSTRACT Visibility and confidence are two subtly (sensation-based and intuition-based) different ways to assess our visual experiences. We investigated how different choice sets affect the ability of confidence and visibility judgments to retrieve conscious information from perceptual decision-making processes. Six participants made introspective judgments on sinusoidal gratings at close to chance signal-to-noise values. We used signal detection theory and mixed regression models to analyze choices and pupilometric recordings. The results suggest that allowing null responses (e.g., “I saw nothing”) asymmetrically affects the signal distribution variances associated with null and non-null responses; confidence is more effective than visibility in accessing unconscious information; and bias-free methods hinder accurate introspective judgment by forbidding free decision criteria. Our findings underscore the importance of the context afforded by choice and stimulus sets, which determines the extent to which elicited introspective judgments are based on the actual information from the past events they are intended to measure.

Activity in the Fronto-Parietal and Visual Cortex Is Modulated by Feature-Based Attentional Weighting.

In day-to-day dynamic activities where sensory input is abundant, stimulus representations in the visual cortex are modulated based on their attentional priority. Several studies have established the top-down role of a fronto-parietal dorsal attention network in selective attention. In the current study, we aimed to investigate whether activity of subregions of this network and the visual cortex is modulated by feature-based attentional weighting, and if so, whether their timecourses of activity are correlated. To this end, we analyzed fMRI data of 28 healthy subjects, who performed a feature-based go/no-go task. Participants had to attend to one or two colored streams of sinusoidal gratings and respond to each grating in the task-relevant stream(s) except to a single non-target grating. Univariate and multivariate fMRI results indicated that activity in bilateral fronto-parietal (frontal eye fields, intraparietal sulcus and superior parietal lobe) and visual (V1–V4, lateral occipital cortex and fusiform gyrus) regions was modulated by selecting one instead of attending to two gratings. Functional connectivity was not significantly different between fronto-parietal and visual regions when attending to one as opposed to two gratings. Our study demonstrates that activity in subregions of both the fronto-parietal and visual cortex is modified by feature-based attentional weighting.

Single-shot N-step phase measurement profilometry

A single-shot N-step phase measurement profilometry (single-shot N-PMP) is proposed. In the traditional N-step PMP, N (N > 2) frames of phase-shifting sinusoidal gratings are needed to be projected onto the measured object. The corresponding N frames of phase-shifting deformed patterns modulated by the object are needed to be captured. And the larger the N is, the higher the measuring accuracy will be. In the proposed method, only one sinusoidal grating is needed to be projected and only one corresponding deformed pattern is captured. The proposed method can efficiently avoid direct filtering in the spectrum of the deformed pattern because of the secondary modulation in computer. The proposed method is an innovative single-shot, three-dimensional (3D) measurement with the highest accuracy among the single-shot 3D measurements so far for inheriting of the traditional optional N-step PMP. And the optional larger N can result in higher accuracy while the single-shot feature can be always guaranteed both the static and real-time 3D measurements. Furthermore, the mathematical model of the proposed method is more concise compared with the traditional PMP for the phase just modulated by the measured object itself can be directly solved without two phase resolutions and two phase unwrappings for both the reference plane and the measured object. The simulations and experimental results show the feasibility and validity of the proposed method.

Vision tests on spectacle lenses and contact lenses for optical myopia correction: a pilot study

ObjectiveVisual performance and short-term tolerability of different designs of myopia correcting options, including therapeutically relevant bifocal contact lenses (CL) and spectacle lenses with ‘defocus incorporated multiple segments (DIMS)’ technology were...

Mapping spatial frequency preferences across human primary visual cortex.

Neurons in primate visual cortex (area V1) are tuned for spatial frequency, in a manner that depends on their position in the visual field. Several studies have examined this dependency using functional magnetic resonance imaging (fMRI), reporting preferred spatial frequencies (tuning curve peaks) of V1 voxels as a function of eccentricity, but their results differ by as much as two octaves, presumably owing to differences in stimuli, measurements, and analysis methodology. Here, we characterize spatial frequency tuning at a millimeter resolution within the human primary visual cortex, across stimulus orientation and visual field locations. We measured fMRI responses to a novel set of stimuli, constructed as sinusoidal gratings in log-polar coordinates, which include circular, radial, and spiral geometries. For each individual stimulus, the local spatial frequency varies inversely with eccentricity, and for any given location in the visual field, the full set of stimuli span a broad range of spatial frequencies and orientations. Over the measured range of eccentricities, the preferred spatial frequency is well-fit by a function that varies as the inverse of the eccentricity plus a small constant. We also find small but systematic effects of local stimulus orientation, defined in both absolute coordinates and relative to visual field location. Specifically, peak spatial frequency is higher for pinwheel than annular stimuli and for horizontal than vertical stimuli.

Does Oblique Effect Affect SSVEP-Based Visual Acuity Assessment?

This study aimed to explore whether there was an effect on steady-state visual evoked potential (SSVEP) visual acuity assessment from the oblique effect or the stimulus orientation. SSVEPs were induced by seven visual stimuli, e.g., the reversal sinusoidal gratings with horizontal, two oblique, and vertical orientations, reversal checkerboards with vertical and oblique orientations, and oscillating expansion-contraction concentric-rings, at six spatial frequency steps. Ten subjects participated in the experiment. Subsequently, a threshold estimation criterion was used to determine the objective SSVEP visual acuity corresponding to each visual stimulus. Taking the SSVEP amplitude and signal-to-noise-ratio (SNR) of the fundamental reversal frequency as signal characteristics, both the SSVEP amplitude and SNR induced by the reversal sinusoidal gratings at 3.0 cpd among four stimulus orientations had no significant difference, and the same finding was also shown in the checkerboards between vertical and oblique orientation. In addition, the SSVEP visual acuity obtained by the threshold estimation criterion for all seven visual stimuli showed no significant difference. This study demonstrated that the SSVEPs induced by all these seven visual stimuli had a similarly good performance in evaluating visual acuity, and the oblique effect or the stimulus orientation had little effect on SSVEP response as well as the SSVEP visual acuity.

Structural and oxide-based colours on laser textured copper

Laser texturing to create colours has recently attracted significant interest due to the rapid and non-contact nature of the technique. The complex optical response of femtosecond laser-textured copper surfaces, producing a palette of perceived colours with varying amounts of angle dependence, is presented. The colours depend on the line spacing used in the laser raster-scanning process. Grazing angle Fourier transform Infrared spectroscopy (FTIR) and Raman microscopy show increased oxide content with larger total accumulated fluence and increased pulse overlap. The increased oxide content coincides with a greater angle independence of the colours compared to colours obtained at larger line spacings. All samples have a similar sinusoidal periodic microstructure, with amplitudes ranging from 400 nm for the smallest line spacings (∼1 µm) to 100 nm for the largest line spacings (∼20 µm), and are decorated with nanoparticles. The angle dependence of the colours is quantified using reflectance measurements, which show a shift in reflectance peak with observation angle. The overall complex colour of the surfaces is attributed to a combination of copper oxides and structural colours driven by underlying nanoparticles, be they metal or metal-oxide, and sinusoidal gratings with a pitch of approximately 1 µm.

Linking Diffractive and Geometrical Optics Surface Scattering at a Fundamental Level

Optical surface scattering analyses based on diffractive optics (DO) are typically applied to one surface; however, there is a need for simulating surface scattering losses for devices having many surface interactions such as light pipes. Light pipes are often simulated with geometric optics (GO) using ray tracing, where surface scattering is driven by the surface slope distribution. In the DO case, surface scattering analyses depend on the spatial frequency distribution and amplitude as well as wavelength, with the sinusoidal grating as a fundamental basis. A better understanding of the link, or transition, between DO and GO scattering domains would be helpful for efficiently incorporating scattering loss analyses into ray trace simulations. A formula for the root-mean-square (rms) scattered angle width of a sinusoidal reflection grating that depends only on the surface rms slope is derived from the nonparaxial scalar diffraction theory, thereby linking it to GO. The scatter angle’s mean and rms width are evaluated over a range of grating amplitudes and periods using scalar theory and full vector simulations from the COMSOL® wave optic module for a sinusoidal reflection grating. The conditions under which the diffraction-based solution closely approximates the GO solution, as predicted by the rms slope, are identified. Close agreement is shown between the DO and GO solutions for the same surface rms slope scattering loss due to angular filtering near the critical angle of a total internal reflection (TIR) glass-to-air interface.

The impact of LSP–SPP coupling on the electric field enhancement of a composite SERS substrate consisting of an Au 2D sinusoidal grating and Ag colloidal nanoparticles

In this study, a composite Surface-Enhanced Raman Scattering (SERS) substrate, consisting of an Au 2D sinusoidal grating and Ag colloidal nanoparticles (AgNPs-Au2DSG), was designed. The impact of the coupling of surface plasmon polariton (SPP) and localized surface plasmon (LSP) on electric field enhancement of the composite substrate, insensitive to the polarization of incident light, is thoroughly discussed and studied. FDTD simulations showed that the maximum enhancement factor (EF) of the substrate appeared at the LSP–SPP coupling resonance frequencies. For the incident light of TM at 785 nm, the substrate had a larger hot spot area and EF when the AgNP radius was 50∼60 nm. By adapting the size of the AgNPs, the SPP–LSP coupling can be optimized to offer greater electric enhancement at the wavelengths of interest, contributing to the practical improvement of SERS detection.

Photoablative lithography of cellulose acetate at 172 nm: Subtractive 3D printing of biodegradable optical microstructures and molds for polydimethylsiloxane patterning

Cellulose is a glucose polymer and the most abundant biological material on earth. Because it is biodegradable and yet water insoluble, cellulose has been pursued in the past as a scaffold or base structural material for medical applications, sensors, and optical devices. Patterning of two cellulose polymers, cellulose acetate and cellulose acetate butyrate, by photoablative lithography at 172 nm has been demonstrated and is reported here. This 3D subtractive process yields complex micro- and nanostructures and optical components, including sinusoidal gratings and waveguides. Having a depth precision of 15 nm and requiring no photoresist or solvents, vacuum-ultraviolet photoetching of cellulose polymer films proceeds at a constant rate of ∼0.8 μm/h for depths of up to and beyond 25 μm when the intensity of the flat lamp is 10 mW cm−2. A polydimethylsiloxane (PDMS) microimprinting process, in which photoetched cellulose serves as a negative master mold for PDMS, provides feature sizes as small as 0.5 μm and allows for optical structures such as gratings to be integrated with microfluidic devices while eliminating the existing necessity of fabricating Si molds in a cleanroom environment.

Correlation between Contrast Sensitivity and Modulation Transfer Functions.

Previous studies found no correlation between visual acuity and optical quality in a population of young subjects with good vision. Using sinusoidal gratings, we systematically investigate the correlation between contrast sensitivity and optical quality as a function of spatial frequency. This study describes the correlation between the contrast sensitivity function (CSF) and the modulation transfer function (MTF) in a sample of young and informed subjects. Our results are compared with prior studies on the correlation between visual acuity and metrics of image quality. We also compare our results with previous studies that compare the CSF, the MTF, and the neural contrast sensitivity function (NCSF). The CSF of 28 informed subjects is measured in photopic conditions. The polychromatic MTF is computed from the measurements of monochromatic aberrations. The (CSF, MTF) correlation is estimated as the Pearson correlation coefficient, at each spatial frequency. The NCSF of each subject is estimated as the ratio of CSF to MTF. We obtain high correlation coefficients (0.8) in the range of spatial frequencies of 3 to 6 cycles per degree, which also corresponds to high NCSF. Correlation decreases with increasing spatial frequency in the range of 6 to 18 cycles per degree (down to 0.0 at 18 cycles per degree). In that range, optical and neural contrast sensitivities are both approximately reduced by factor 4. In our sample of young subjects with good vision, the CSF with sinusoidal gratings better differentiates eyes of good optical quality at intermediate spatial frequencies (3 to 6 cycles per degree) than at higher spatial frequencies (12 to 18 cycles per degree). At the highest tested spatial frequency of sinusoidal gratings (18 cycles per degree), there is no significant correlation between optical quality and contrast sensitivity.

Contrast sensitivity is formed by visual experience and task demands

The contrast sensitivity function (CSF) is a fundamental signature of the visual system and has been measured extensively in numerous species. It is defined by measurements of the visibility threshold for sinusoidal gratings at all spatial frequencies. Here, we measured the CSF in artificial visual systems, namely deep neural networks (DNNs), using the same contrast discrimination paradigm as used in human psychophysical experiments. During training, networks are exclusively exposed to natural images, and the task is to identify which one of two input images has higher contrast. The contrast discriminator networks learn a linear classifier over frozen features of pretrained DNNs. At the testing stage, we measured the network's CSF by presenting sinusoidal gratings of different orientations and spatial frequencies. Our results demonstrate that the pretrained DNNs show the band-limited, inverted U-shaped CSF, that is characteristic of the human CSF. The exact shape of the DNNs' CSF appears to be task-dependent. The human CSF is better captured by scene segmentation DNNs than image classification ones (tested under identical settings such as the architecture and computational complexity). When the network was trained to discriminate the contrast in natural images from scratch (i.e., with no previous training task), a relatively flat CSF emerged, dissimilar to the human CSF. The environment of pretrained DNNs proved influential as well. Those with a diet of natural images, similar to human experience (e.g. objects or faces), obtain more human-like CSF. Pretrained DNNs with aerial pictures, such as a bird flying in the sky would see, obtain a shifted CSF towards higher spatial frequencies, similar to that of an eagle. In conclusion, the CSFs derived from the DNNs are the result of efficient processing of the natural world around us. Different visual environments have succinct effects on the shape of the CSFs.

Distinguishing signal strength and spatial structure in fMRI pattern analyses of human primary visual cortex

Multivariate pattern analyses are widely used in neuroimaging studies. But it is unclear what these analyses reveal about neural coding. Such approaches often obfuscate the link between neural measurements and the stimulus, greatly limiting their utility. Linear classification, a highly-popular approach, exploits the Euclidean distance among pattern vectors. Our recent theoretical work suggests that information regarding tuning properties is best captured by angular distances, not Euclidean distances. The goal of this experiment was to relate specific aspects of multivariate measurements to parametrically defined dimensions of visual stimuli. We used primary visual cortex as a model system to test the following predictions: (i) Euclidean distances conflate information regarding response amplitude and selectivity, (ii) angular distances best reflect information about selectivity, and (iii) data demeaning—a common preprocessing procedure—invalidates inferences regarding selectivity because it changes angular relationships among pattern vectors. fMRI BOLD activity was measured from 5 participants (7T, 32-channel coil, 1.2x1.2x1.2 mm resolution). Stimuli consisted of Cartesian sinusoidal gratings multiplied by flower-shaped apertures. The orientation of the “petals” was controlled by the phase of the radial frequency (RF) used to generate the aperture. In a fully crossed experimental design, the compound stimulus varied along three dimensions: grating orientation, contrast, and RF-phase, resulting in a total of 96 unique conditions. We found that the Euclidean metric was sensitive to stimulus contrast and relatively insensitive to grating orientation and aperture phase. Angular distances proved sensitive to grating orientation and aperture phase, and robust to changes in stimulus contrast. As predicted, data demeaning led to mischaracterizations of neural tuning. Finally, we used a biologically-inspired image-computable model to provide a theoretic account of these observations. Our results have fundamental implications for the interpretation of MVPA, and inform the development of data analysis strategies that are more readily interpretable in terms of the underlying neurophysiology.