Test Gratings Research Articles

Grating pitch comparator traceable to the Cr atom transition frequency

Calibration of the grating pitch typically requires metrological instruments or diffraction techniques. The traceability and stability demands for laser wavelength in these techniques present substantial challenges for on-site grating calibration. This paper introduces a novel traceability approach to grating pitch calibration using a grating pitch comparator that utilizes the transition frequency of the chromium. The chromium transition frequency is converted into a chromium grating through atom lithography, establishing a self-traceable length standard dCr = 212.7787 ± 0.0049 nm. Calibration of the test grating’s pitch is achieved by comparing the phase shift caused by the simultaneous movement of the chromium grating and the test grating. By using the dCr, this approach combines the high-accuracy of fundamental physical constants with the environmental stability of grating interferometers, eliminating the need for measuring laser wavelength, air refraction, diffraction angles. It significantly enhances the precision and makes more straightforward and portable, crucial for facilitating traceable on-site grating measurements.

Challenges of reliable AFM-tip shape reconstruction and approximation.

Reliable reconstruction of AFM tip geometry is not an easy task. The shape of the tip can be (partially) reconstructed from the AFM image of a calibration sample using a blind reconstruction method. The result is a range of the tip shapes (from unrealistically sharp to blunt). A criterion for selecting the true shape is proposed. It is based on reconstruction of the calibration relief. Further refining the probe geometry by indenting an elastic polymer is discussed. The choice of the test sample is another problem. In practice, the researcher has a small number of commercially available test gratings. Their limitations are highlighted. An approximation of tip geometry by a body of revolution is required in indentation experiments. A hyperboloid was found to be the closest approximation to the conventional probes. The contact area was obtained for the hyperboloids with different parameters indenting an elastic material. RESEARCH HIGHLIGHTS: Criteria for blind reconstruction algorithm of AFM tip shape. Pros and cons of tip shape calibration samples. Contact area of the elastic indentation by hyperbolic indenter.

Small-angle attraction in the tilt illusion.

The tilt illusion (TI) describes the phenomenon in which a surround inducer grating of a particular orientation influences the perceived orientation of a central test grating. Typically, inducer-test orientation differences of 5 to 40 degrees cause the test orientation to appear shifted away from the inducer orientation (i.e. repulsion). For orientation differences of 60 to 90 degrees, the inducer typically causes the test grating orientation to appear shifted toward the inducer orientation, termed here “large-angle” attraction. Both repulsion and large-angle attraction effects have been observed in contrast-modulated as well as luminance-modulated grating patterns. Here, we show that a secondary, “small-angle” 0 to 10 degrees attraction effect is observed in contrast-modulated and orientation-modulated gratings, as well as in luminance-modulated gratings that are relatively low in spatial frequency, low in contrast, or contain added texture. The observed small-angle attraction, which can exceed in magnitude that of the repulsion and large-angle attraction effects, is dependent on the spatial phase relationship between the inducer and test, being maximal when in-phase. Both small-angle attraction and repulsion effects are reduced when a gap is introduced between the test and inducer. Our findings suggest that small-angle attraction in the TI is a result of assimilation of the inducer pattern into the receptive fields of neurons sensitive to the test.

Characterizing profile tilt of nanoscale deep-etched gratings via x-ray diffraction

The authors report the development of fast, nondestructive, and high accuracy metrology for the characterization of profile tilt relative to the surface normal in nanoscale gratings using x-ray diffraction. Gratings were illuminated with a collimated x-ray beam (Cu Kα), similar to variable-angle small-angle x-ray scattering, to record changes of diffraction efficiency (DE) as a function of incidence angle. Simulations using scalar diffraction theory and rigorous coupled wave analysis predict extrema (0th order DE minimized, ±1st order DE maximized) when local grating bars are parallel to the incident x-ray beam. The surface normal was measured independently by reflecting a laser beam from the grating surface. The independent measurements using x rays and laser beams were referenced to each other via a slit reference plane to characterize the bar tilt angle relative to the surface normal. The fast x-ray measurement can be repeated at arbitrary points to study the spatial variation of the bar tilt angle across large gratings. Two test gratings etched with different deep reactive-ion etch chambers were prepared to investigate the performance of the proposed method. The authors report a repeatability of <0.01° and an accuracy of ∼0.08° with a fast scan speed (total integration time of 108 s to scan a line across ∼55 mm large grating samples at an interval of ∼2 mm). High spatial resolution (<50 μm) can be easily achieved at the expense of speed by limiting the incident x-ray spot size. This process is applicable to any periodic nanostructure as long as x-ray diffraction is well modeled.

Sensing fabrication errors in diffraction gratings using high dynamic range imaging.

We describe the design of a simple instrument for the identification and characterization of fabrication errors in diffraction gratings. The instrument uses an uncooled charge-coupled device (CCD) camera and a high dynamic range imaging process to detect the light scattered off a grating under test in the focal plane of a lens. We demonstrate that the instrument can achieve a dynamic range around nine orders of magnitude and we show that we are able to clearly identify small, periodic fabrication errors in two test gratings that could not be detected with microscopic techniques.

Amblyopic Suppression: Passive Attenuation, Enhanced Dichoptic Masking by the Fellow Eye or Reduced Dichoptic Masking by the Amblyopic Eye?

To test the amblyopic suppression at mid to low spatial frequencies when compensating for signal attenuation. Eight amblyopes with (n = 5) or without (n = 3) strabismus and 10 normal controls with normal or corrected to normal visual acuity (≥20/20) and normal stereopsis (≤40 arcseconds) participated. Using a quick contrast sensitivity function approach, we measured individuals' monocular contrast sensitivity functions when the untested eye saw a mean luminance background and when the untested eye saw a bandpass filtered noise whose peak spatial frequency was matched to that of the test grating. Interocular suppression was quantified by the difference in thresholds occurring between these two conditions for each eye. The contrast of the noise mask was set at five times the threshold of the untested eye. Selected spatial frequencies (0.67-1.31 cyc/deg) were identified where neither ceiling (five times the mask contrast threshold in the amblyopic eye <100%) nor floor (threshold of the amblyopic eye when there was a noise mask in the fellow eye <100%) effects occurred for all observers. Within this frequency range, we found no interocular suppressive imbalance in normal observers. However, in amblyopes, the amblyopic eye exerted significantly less suppression than the fellow eye, while the suppression from the fellow eye to the amblyopic eye was similar to that found in the normal controls. We conclude that the reduced dichoptic masking by the amblyopic eye, within the context of normally balanced interocular inhibition, produces the amblyopic suppression at mid to low frequencies.

Adaptation to interocular difference.

Patterns in the two eyes' views that are not identical in hue or contrast often elicit an impression of luster, providing a cue for discriminating them from perfectly matched patterns. Here we ask whether the mechanism for detecting interocular differences (IDs) is adaptable. Our stimuli were horizontally oriented multispatial-frequency grating patterns that could be subject to varying degrees of ID through the introduction of interocular phase differences in the grating components. Subjects adapted to patterns that were either correlated, uncorrelated, monocular (one eye only), or anticorrelated. Following adaptation, thresholds for detecting IDs were measured using a staircase procedure. It was found that ID thresholds were elevated following adaptation to uncorrelated, monocular, and anticorrelated but not correlated patterns. Threshold elevation was found to be maximal when the orientations of the adaptor and test gratings were the same, and when their spatial frequencies were similar. The results support the existence of a specialized mechanism for detecting IDs, the most likely candidate being the binocular differencing channel proposed in previous studies.

Absolute, high-accuracy characterization of a variable line spacing grating for the European XFEL soft X-ray monochromator.

The European XFEL is a free-electron laser (FEL) with a superconducting linear accelerator and three beamlines (SASE1, SASE2, and SASE3) covering the energy range from 250 eV to 24 keV. The SASE3 beamline is dedicated to the soft x-ray range (0.25-3 keV) and is designed to operate in both monochromatic and non-monochromatic mode. A variable line spacing - plane grating (VLS-PG) monochromator is placed along the beam transport system for the monochromatic mode. The VLS parameters of the grating profile are challenging from a manufacturing and measuring perspective, especially at the desired length of 530 mm. A shorter grating of 150 mm has been procured to allow early operation of the facility. We describe the characterization method that was used to assess the VLS parameters of the grating using Fizeau interferometry. The method is intrinsically absolute and limited only by the quality of the test grating and the noise level. Further measurements using a white-light-interferometry profilometer are also reported. We discuss the possibility of extending the method to the future 530 mm long grating.

Spatial Frequency Shifts From Counterphase Flicker and From Simultaneous Contrast.

In simultaneous contrast of spatial frequency (SF), a test grating surrounded by a coarser inducing grating looks apparently finer. We combined this effect with another visual illusion; the fact that flickering the inducing grating raises its apparent SF. We found that the inducer’s apparent, not physical spatial frequency, drove the simultaneous contrast that it induced into a test grating. Thus, when the inducer was made to flicker, its SF appeared to be higher and consequently, the test’s SF appeared lower than before. This suggests that simultaneous contrast of spatial frequency exists further downstream than the flicker-induced increase in perceived SF.

Brief presentation enhances various simultaneous contrast effects

Kaneko & Murakami (2012) showed that simultaneous contrast for brightness and for color (saturation-shift type) are both enhanced by briefly presenting the stimulus. Simultaneous contrast is a universal phenomenon seen across many visual features. So how universal is the inverse relationship between the strength of simultaneous contrast and the stimulus duration? In the first study, we examined the relationship between the simultaneous tilt contrast (a.k.a. tilt illusion) and stimulus duration. A vertical test grating (2 cpd sinusoidal) and a tilted surrounding grating (inducer) appeared repeatedly and subjects adjusted the orientation of the comparison grating to make it parallel to the test. Test and inducer appeared simultaneously and their duration was either 10 ms or 500 ms. When the inducer was tilted 15 deg away from the test, the tilt contrast effect was more than doubled for 10 ms condition compared with 500 ms condition. When the inducer was tilted 3 deg, neither duration gave any effect. For tilts greater than 9 deg, the 10 ms condition always yielded greater effect than the 500 ms condition. However, tilts of less than 9 deg gave no significant difference between durations. In the second study, we looked for similar effects of duration in hue-shift type simultaneous color contrast (cf. Klauke & Wachtler, 2015). We chose all our colors from the equiluminant cone-contrast space whose origin was the equal-energy white (20 cd/m2). Results from experiments using unique yellow as a target hue suggest that the unique-yellow shift was strongly enhanced by briefly flashing the stimulus. Results suggest the existence of universal mechanisms that enhance the difference across visual features between neighboring regions, which work only for briefly presented targets. Meeting abstract presented at VSS 2016

Myopes experience greater contrast adaptation during reading

In this study, we investigated whether reading influences contrast adaptation differently in young adult emmetropic and myopic participants at the spatial frequencies created by text rows and character strokes. Pre-adaptation contrast sensitivity was measured for test gratings with spatial frequencies of 1cdeg−1 and 4cdeg−1, presented horizontally and vertically. Participants then adapted to reading text corresponding to the horizontal “row frequency” of text (1cdeg−1), and vertical “stroke frequency” of the characters (4cdeg−1) for 180s. Following this, post-adaptation contrast sensitivity was measured. Twenty young adults (10 myopes, 10 emmetropes) optimally corrected for the viewing distance participated. There was a significant reduction in logCS post-text adaptation (relative to pre-adaptation logCS) at the row frequency (1cdeg−1 horizontal) but not at the stroke frequency (4cdeg−1 vertical). logCS changes due to adaptation at 1cdeg−1 horizontal were significant in both emmetropes and myopes. Comparing the two refractive groups, myopic participants showed significantly greater adaptation compared to emmetropic participants. Reading text on a screen induces contrast adaptation in young adult observers. Myopic participants were found to exhibit greater contrast adaptation than emmetropes at the spatial frequency corresponding to the text row frequency. No contrast adaptation was observed at the text stroke frequency in either participant group. The greater contrast adaptation experienced by myopes after reading warrants further investigation to better understand the relationship between near work and myopia development.

A bias-free measure of the tilt illusion.

The perceived orientation of a central test grating is influenced by the orientation structure of the surrounding image. Measurement of this "tilt illusion" traditionally requires subjects to report the orientation of the test relative to a cardinal reference (e.g., clockwise or anticlockwise of vertical). Given that the test is presented within a surround that is itself oriented clockwise or anticlockwise from vertical, there is obvious potential for the orientation of the surround to bias the subject's response irrespective of any perceptual effects. To avoid this bias, we ran a two temporal interval forced-choice experiment. The two intervals contained opposite surround orientations (±15°), and we manipulated the orientation of the center gratings. Participants were asked to judge which of the test gratings was closer to vertical. We found no significant difference between measurements of the tilt illusion using the traditional and two-interval procedures. We then examined interindividual differences in a larger sample and found a significant correlation between the magnitudes of the tilt illusion measured using the two procedures. Our experiments demonstrate a method free from response bias in measuring the tilt illusion although our results indicate that response biases were unlikely to factor significantly in prior tilt illusion experiments.

Hydraulic interception efficiency of gully gratings on steep roads

The hydraulic interception efficiency of a gully grating decreases with the steepness of the road on which it is installed. This can lead to a higher potential for flooding at the downstream area of a steep road. In this study, the hydraulic inception efficiency of several types of gully gratings on steep roads, including a new grating with angled bars on a parallelogram cross-section was investigated experimentally. The experimental results for all test gratings show that the hydraulic interception efficiency varies linearly with a non-dimensional parameter expressed as a product of the Froude number, water depth to grating length ratio and flow width to grating width ratio. The empirical relationship can be easily included in numerical models for the detailed study and design of storm water drainage systems. The hydraulic performance of the grating with longitudinal bars and the new grating with angled bars on a parallelogram cross-section was better than that of the existing grating. The relative incre...

Flicker adaptation or superimposition raises the apparent spatial frequency of coarse test gratings

Independent channels respond to both the spatial and temporal characteristics of visual stimuli. Gratings <3cycles per degree (cpd) are sensed by transient channels that prefer intermittent stimulation, while gratings >3cpd are sensed by sustained channels that prefer steady stimulation. From this we predict that adaptation to a spatially uniform flickering field will selectively adapt the transient channels and raise the apparent spatial frequency of coarse sinusoidal gratings. Observers adapted to a spatially uniform field whose upper or lower half was steady and whose other half was flickering. They then adjusted the spatial frequency of a stationary test (matching) grating on the previously unmodulated half field until it matched the apparent spatial frequency of a grating falling on the previously flickering half field. The adapting field flickered at 8Hz and the spatial frequency of the gratings was varied in octave steps from 0.25 to 16cpd. As predicted, adapting to flicker raised the apparent spatial frequency of the test gratings. The aftereffect reached a peak of 11% between 0.5 and 1cpd and disappeared above 4cpd. We also observed that superimposed 10Hz luminance flicker raised the apparent spatial frequency of 0.5cpd test gratings. The effect was not seen with slower flicker or finer test gratings. Altogether, our study suggests that apparent spatial frequency is determined by the balance between transient and sustained channels and that an imbalance between the channels caused by flicker can alter spatial frequency perception.

Real-time deflection and friction force imaging by bimorph-based resonance-type high-speed scanning force microscopy in the contact mode.

We report herein an alternative high-speed scanning force microscopy method in the contact mode based on a resonance-type piezoelectric bimorph scanner. The experimental setup, the modified optical beam deflection scheme suitable for smaller cantilevers, and a high-speed control program for simultaneous data capture are described in detail. The feature of the method is that the deflection and friction force images of the sample surface can be obtained simultaneously in real time. Images of various samples (e.g., a test grating, a thin gold film, and fluorine-doped tin oxide-coated glass slides) are acquired successfully. The imaging rate is 25 frames per second, and the average scan speed reaches a value of approximately 2.5 cm/s. The method combines the advantages of both observing the dynamic processes of the sample surface and monitoring the frictional properties on the nanometer scale.PACS07.79.Lh; 07.79.Sp; 68.37.Ps

Brightness induction and suprathreshold vision: effects of age and visual field.

A variety of visual capacities show significant age-related alterations. We assessed suprathreshold contrast and brightness perception across the lifespan in a large sample of healthy participants (N=155; 142) ranging in age from 16 to 80 years. Experiment 1 used a quadrature-phase motion cancelation technique (Blakeslee & McCourt, 2008) to measure canceling contrast (in central vision) for induced gratings at two temporal frequencies (1 Hz and 4 Hz) at two test field heights (0.5° or 2°×38.7°; 0.052 c/d). There was a significant age-related reduction in canceling contrast at 4 Hz, but not at 1 Hz. We find no age-related change in induction magnitude in the 1 Hz condition. We interpret the age-related decline in grating induction magnitude at 4 Hz to reflect a diminished capacity for inhibitory processing at higher temporal frequencies. In Experiment 2 participants adjusted the contrast of a matching grating (0.5° or 2°×38.7°; 0.052 c/d) to equal that of both real (30% contrast, 0.052 c/d) and induced (McCourt, 1982) standard gratings (100% inducing grating contrast; 0.052 c/d). Matching gratings appeared in the upper visual field (UVF) and test gratings appeared in the lower visual field (LVF), and vice versa, at eccentricities of ±7.5°. Average induction magnitude was invariant with age for both test field heights. There was a significant age-related reduction in perceived contrast of stimuli in the LVF versus UVF for both real and induced gratings.

Influence of Collimation on Alignment Accuracy in Proximity Lithography

The alignment method based on moiré imaging has been wildly used for its high accuracy of physical measurement, which utilized the phase of moiré fringe to measure the relative linear displacement between the mask and the wafer. However, this method is only theoretically accurate due to the affection of certain parameters, such as the optical beam collimation. In this paper, the influence of collimation on the alignment accuracy is thoroughly analyzed. The theoretical analyses and simulation results indicate that the alignment accuracy, which was observed just behind the test grating, is sensitive to the divergence or convergence angle of incident light. On this basis, the method for the error correction is proposed and confirmed.

Fast Translational Motion, but not Radial, Circular or Biological Motion, Causes Spatially Selective Adaptation of Event Duration

It has been recently shown that adaptation to gratings oscillating at high-frequency compress perceived duration of subsequent, slower, stimuli displayed in the same location. These temporal distortions are spatially selective (Johnston et al., 2006), coded in spatiotopic coordinates (Burr et al., 2007, 2011), and do not result from changes in perceived speed of the adapted stimulus. These findings are important as they support the idea of a distributed framework of multiple mechanisms processing event time across the visual field. However, time distortions induced by motion adaptation have been tested only with simple translational motion, rather than more complex motions. Here we used a similar technique to Burr and coll. (2007) to measure time compression induced by adaptation to four kinds of motion stimuli: a) translating gratings, b) expanding concentric gratings, c) rotating radial gratings, and d) biological motion. We first measured changes in perceived speed caused by the motion adaptation (20Hz for the gratings). We found that perceived speed of the 10Hz test stimuli was dramatically reduced by around 40-50% in all conditions. Subsequently, we used these data to adjust the speed to compensate for the adaptation effects, and measure distortions in perceived duration with equated speed of test and probe gratings. In line with previous reports, perceived duration for translating patterns (displayed for 500ms) was found to be reduced up to 30-40%, even after speed compensation. However, duration estimates for radial and circular moving gratings (500ms) were always veridical. We used two versions of circular motion: with tangential speed constant across the visual patch (non-rigid-motion), and with rigid rotation, but neither caused temporal compression. Similarly, adaptation to a “runner” in biological motion reduced considerably the apparent speed of a briefly presented walker, but when matched for apparent speed, duration estimations were completely unaffected by adaptation. Taken together these results suggest that different mechanisms underlie time processing for simple and complex motion profiles. Why should only translational motion cause changes in temporal duration? fMRI evidence (Morrone et al., 2000) suggests that translational motion stimulates different brain regions from those responding to radial and circular motion, and this could be the basis for the selective effects on duration. Interestingly, however, the duration effects (after matching for apparent speed) are almost entirely spatiotopic, suggesting that they are not occurring at early, retinotopic brain areas. On the other hand it makes sense that the adaption should occur in space-based rather than retinal-based coordinates, if the purpose is related to temporal calibration of objects (in the real world). Why translational motion, but not other more complex forms of motion, should calibrate event duration is far from clear.

Cross-orientation masking in human color vision: Application of a two-stage model to assess dichoptic and monocular sources of suppression

Cross-orientation masking (XOM) occurs when the detection of a test grating is masked by a superimposed grating at an orthogonal orientation, and is thought to reveal the suppressive effects mediating contrast normalization. Medina and Mullen (2009) reported that XOM was greater for chromatic than achromatic stimuli at equivalent spatial and temporal frequencies. Here we address whether the greater suppression found in binocular color vision originates from a monocular or interocular site, or both. We measure monocular and dichoptic masking functions for red-green color contrast and achromatic contrast at three different spatial frequencies (0.375, 0.75, and 1.5 cpd, 2 Hz). We fit these functions with a modified two-stage masking model (Meese & Baker, 2009) to extract the monocular and interocular weights of suppression. We find that the weight of monocular suppression is significantly higher for color than achromatic contrast, whereas dichoptic suppression is similar for both. These effects are invariant across spatial frequency. We then apply the model to the binocular masking data using the measured values of the monocular and interocular sources of suppression and show that these are sufficient to account for color binocular masking. We conclude that the greater strength of chromatic XOM has a monocular origin that transfers through to the binocular site.

Discrimination of real and virtual surfaces with sinusoidal and triangular gratings using the fingertip and stylus.

Two-interval two-alternative forced-choice discrimination experiments were conducted separately for sinusoidal and triangular textured surface gratings from which amplitude (i.e., height) discrimination thresholds were estimated. Participants (group sizes: n = 4 to 7) explored one of these texture types either by fingertip on real gratings (Finger real), by stylus on real gratings (Stylus real), or by stylus on virtual gratings (Stylus virtual). The real gratings were fabricated from stainless steel by an electrical discharge machining process while the virtual gratings were rendered via a programmable force-feedback device. All gratings had a 2.5-mm spatial period. On each trial, participants compared test gratings with 55, 60, 65, or 70 μm amplitudes against a 50-μm reference. The results indicate that discrimination thresholds did not differ significantly between sinusoidal and triangular gratings. With sinusoidal and triangular data combined, the average (mean + standard error) for the Stylus-real threshold (2.5 ± 0.2 μm) was significantly smaller (p <; 0.01) than that for the Stylus-virtual condition (4.9 ± 0.2 μm). Differences between the Finger-real threshold (3.8 ± 0.2 μm) and those from the other two conditions were not statistically significant. Further studies are needed to better understand the differences in perceptual cues resulting from interactions with real and virtual gratings.