Grating Resolution Research Articles

Examining the concordance of retinal ganglion cell counts generated using measures of structure and function.

There are several indirect methods used to estimate retinal ganglion cell (RGC) count in an individual eye, but there is limited information as to the agreement between these methods. In this work, RGC receptive field (RGC-RF) count underlying a spot stimulus (0.43°, Goldmann III) was calculated and compared using three different methods. RGC-RF count was calculated at a retinal eccentricity of 2.32 mm for 44 healthy adult participants (aged 18-58 years, refractive error -9.75 DS to +1.75 DS) using: (i) functional measures of achromatic peripheral grating resolution acuity (PGRA), (ii) structural measures of RGC-layer thickness (OCT-model, based on the method outlined by Raza and Hood) and (iii) scaling published histology density data to simulate a global expansion in myopia (Histology-Balloon). Whilst average RGC-RF counts from the OCT-model (median 105.3, IQR 99.6-111.0) and the Histology-Balloon model (median 107.5, IQR 97.7-114.6) were similar, PGRA estimates were approximately 65% lower (median 37.7, IQR 33.8-46.0). However, there was poor agreement between all three methods (Bland-Altman 95% limits of agreement; PGRA/OCT: 55.4; PGRA/Histology-Balloon 59.3; OCT/Histology-Balloon: 52.4). High intersubject variability in RGC-RF count was evident using all three methods. The lower PGRA RGC-RF counts may be the result of targeting only a specific subset of functional RGCs, as opposed to the coarser approach of the OCT-model and Histology-Balloon, which include all RGCs, and also likely displaced amacrine cells. In the absence of a 'ground truth', direct measure of RGC-RF count, it is not possible to determine which method is most accurate, and each has limitations. However, what is clear is the poor agreement found between the methods prevents direct comparison of RGC-RF counts between studies utilising different methodologies and highlights the need to utilise the same method in longitudinal work.

Switching the Sign of the Topological Charge of Vortex Beams Via Changing the Fork Grating Resolution

Switching the Sign of the Topological Charge of Vortex Beams Via Changing the Fork Grating Resolution

Large-format X-Ray Reflection Grating Operated in an Echelle-like Mounting

Abstract We report on resolving power measurements of an X-ray reflection grating designed for use in an astronomical soft X-ray spectrograph. The grating was patterned via electron-beam lithography (EBL) to have fanned grooves to match the convergence of an illuminating beam. Grating measurements were conducted in an echelle-like mounting, which yields access to high diffraction orders in the soft X-ray bandpass (0.2–2.0 keV). By comparing the zeroth-order line-spread function to the telescope focus, we find evidence for minimal broadening (<1″) introduced by the figure of the grating. In addition, we fit for the spectral resolution (R = λ/Δλ) intrinsic to this grating using a Bayesian Markov Chain Monte Carlo approach. Using an ensemble fitting technique, we find that the grating resolution R exceeds 2200 (3σ lower bound). This current grating resolution meets the performance required for a notional soft X-ray grating spectroscopy mission measuring hot baryonic material in the extended halos of galaxies. Using ray-trace simulations, we identify a geometric aberration resulting from path length differences across the width of the grating as a limiting factor in assessing the resolution of these gratings and discuss methods for placing better constraints on the inherent resolution of X-ray astronomical reflection gratings fabricated using EBL.

Measurement of femtosecond pulses based on transient grating frequency-resolved optical gating

Femtosecond pulse measurement of ultrafast spectrum is one of the important research directions in the ultrafast laser field. The conventional femtosecond pulse autocorrelation method is implemented by measuring the autocorrelated frequency-doubling signal, and the frequency-doubling signal has wavelength selectivity, so the femtosecond pulse measurement for the case of different central wavelengths needs to replace different frequency-doubling crystals, which is very inconvenient. This paper reports a kind of modified transient grating frequency resolution optical gating for measuring the femtosecond pulses. The method combines frequency-resolved optical gating (FROG) method with four-wave mixing. Its basic process is to divide the pulse to be measured into three beams. Two of the pulses can reach spatiotemporal coincidence on optical medium through precise delay control and focus. The other pulse interacts with the transient grating, and serves as the detection light to produce signal light. The spectrum and delay time of the signal light are measured by a spectrometer, and the spectrum and electric field information of the femtosecond pulse to be measured are obtained through the inversion iterative algorithm. Because this method only needs the power density of the measured light to reach the third-order nonlinear effect, it can be applied to the femtosecond pulse measurement of any central wavelength. We use this method to measure the femtosecond pulses with the central wavelengths of 800 nm and 400 nm respectively, and the ultra-wide spectrum femtosecond pulses with the period magnitude of sub-10 fs, and compare the measurement results with the results obtained with the conventional interferometric autocorrelation instrument. They are basically consistent. The experimental results show that our frequency-resolved optical switching method based on transient grating is very effective for measuring the femtosecond pulses with different central wavelengths and pulse widths.

Relationship between Psychophysical Measures of Retinal Ganglion Cell Density and In Vivo Measures of Cone Density in Glaucoma

Considerable between-individual variation in retinal ganglion cell (RGC) density exists in healthy individuals, making identification of change from normal to glaucoma difficult. In ascertaining local cone-to-RGC density ratios in healthy individuals, we wished to investigate the usefulness of objective cone density estimates as a surrogate of baseline RGC density in glaucoma patients, and thus a more efficient way of identifying early changes. Exploratory cohort study. Twenty glaucoma patients (60% women) with a median age of 54 years and mean deviation (MD) in the visual field of -5 dB and 20 healthy controls (70% women) with a median age of 57 years and a mean MD of 0 dB were included. Glaucoma patients and healthy participants underwent invivo cone imaging at 4 locations of 8.8° eccentricity with a modified Heidelberg Retina Angiograph HRA2 (scan angle, 3°). Cones were counted using an automated program. Retinal ganglion cell density was estimated at the same test locations from peripheral grating resolution acuity thresholds. Retinal cone density, estimated RGC density, and cone-to-RGC ratios in glaucoma patients and healthy controls. Median cone-to-RGC density was 3.51:1 (interquartile range [IQR], 2.59:1-6.81:1) in glaucoma patients compared with 2.35:1 (IQR, 1.83:1-2.82:1) in healthy participants. Retinal ganglion cell density was 33% lower in glaucoma patients than in healthy participants; however, cone density was very similar in glaucoma patients (7248 cells/mm2) and healthy controls (7242 cells/mm2). The area under the receiver operator characteristic curve was 0.79 (95% confidence interval [CI], 0.71-0.86) for both RGC density and cone-to-RGC ratio and 0.49 (95% CI, 0.39-0.58) for cone density. Local measurements of cone density do not differ significantly from normal in glaucoma patients despite large differences in RGC density. There was no statistically significant association between RGC density and cone density in the normal participants, and the range of cone-to-RGC density ratios was relatively large in healthy controls. These findings suggest that estimates of baseline RGC density from cone density are unlikely to be precise and offer little advantage over determination of RGC alone in the identification of early glaucomatous change.

The Effect of Age on the Area of Complete Spatial Summation for Chromatic and Achromatic Stimuli

Previously, an association between the area of complete spatial summation (Ricco's area) and age under scotopic conditions had been found. The authors sought to determine whether Ricco's area is similarly associated with age under photopic achromatic and selective S-cone conditions in peripheral vision and whether any association relates to a loss of ganglion cell density as determined by measurements of peripheral grating resolution acuity. Achromatic spatial summation functions were plotted for 68 healthy subjects (aged 20-77 years) in four oblique meridians on a gray background field of 10 cd/m(2). Similar functions were generated for the S-cone pathway (isolated using Stiles' two-color threshold method) for the same locations. Ricco's area was determined using two-phase regression analysis. Achromatic peripheral grating resolution acuity was measured at the same locations using high-contrast Gabor stimuli, as an estimate of localized functional ganglion cell density. There was a notable decrease in overall contrast sensitivity with age for all stimulus sizes. However, there was no evidence of age-related change in Ricco's area for either achromatic (superior field, r(2) = 0.05; inferior field, r(2) = 0.0007; all P > 0.05) or chromatic (superior field, r(2) = 0.01; inferior field, r(2) = 0.006; all P > 0.05) stimuli, despite a significant decrease in peripheral grating resolution acuity with age (superior field, r(2) = 0.15; inferior field, r(2) = 0.17; both P < 0.05). An age-related decline in functional ganglion cell density is not accompanied by a significant change in Ricco's area for achromatic or chromatic stimuli.

Changes in human short-wavelength-sensitive and achromatic resolution acuity with retinal eccentricity and meridian

Psychophysical measurements using achromatic grating resolution acuity in peripheral vision show a prominent retinal asymmetry in acuity which is consistent with predicted values based on available estimates of midget ganglion cell density. Recent studies have shown that peripheral grating resolution acuity values for short-wavelength-sensitive (SWS) isolating gratings in normal observers are closely related to predicted values based on the underlying small bistratified ganglion cell density. By measuring SWS resolution acuity at different locations across the visual field, we wished to see if any significant acuity asymmetry exists for the short-wavelength system. In addition to this, we wanted to compare SWS and achromatic resolution acuity at different retinal locations of equal eccentricity. SWS and achromatic grating resolution acuity was measured in two observers at a number of different retinal meridians of 10- and 25-deg eccentricity from the fovea, and out to 35-deg eccentricity along the horizontal meridian. Achromatic resolution acuity was higher than SWS resolution acuity at all locations. At 10-deg eccentricity there was slight radial asymmetry in SWS and achromatic acuity, both displaying highest acuity along the horizontal meridian. At 25-deg eccentricity, SWS and achromatic acuity showed significant asymmetry with acuity being higher in the nasal retina compared to the temporal retina and with higher acuity in the superior retina compared to the inferior retina. At 35-deg eccentricity, the acuity asymmetry along the horizontal meridian was maintained with acuity for both significantly higher in the nasal retina. The SWS acuity changes with eccentricity and meridian were qualitatively similar to that found for achromatic acuity at the majority of retinal locations. Like achromatic acuity, SWS acuity shows significant asymmetry at different retinal locations of equal eccentricity. This suggests that both the midget and small bistratified ganglion cell population density changes significantly with retinal location and eccentricity. SWS acuity appears to change in parallel with achromatic acuity for the majority of retinal locations measured, although the amount of nasotemporal asymmetry appears to be slightly less for the SWS system at 25- and 35-deg eccentricity.

Peripheral resolution using stationary and flickering gratings: the effects of age

PURPOSE. Currently, little or no psychophysical data exist on the decline in retinal ganglion cell density, with age or on the nature of any selective age-related loss of one cell type over another. The authors wished to determine the nature of any decline in ganglion cell density with age using measurements of peripheral grating resolution, which is directly related to ganglion cell sampling density. METHODS. We measured grating resolution at 4 different retinal locations in a group of 97 normal subjects ranging in age from eight to eighty-one years. Stimuli were either stationary or employed counterphase flicker at 30 Hz in order to selectively stimulate a greater proportion of either P or M ganglion cells. RESULTS. Mean resolution was significantly higher for stationary gratings than flickering gratings. Loss of peripheral resolution was approximately 5%/decade for stationary gratings and 6%/decade for flickering gratings. The ratio of resolution for flickering/non-flickering stimuli showed a small but insignificant decline with age. CONCLUSIONS. There is a general decline in peripheral resolution with age, indicating a corresponding loss of retinal ganglion-cell density. This age-related loss does not appear to be very selective in terms of cells that are sensitive to either stationary or flickering gratings. These results increase the diagnostic power of clinical tests that employ measures of peripheral resolution in subjects of different ages to detect diseases which cause loss of ganglion cells.

Hyperacuity for spatial localization of contrast-modulated patterns

The acuity for localizing the position of a grating and other first order patterns which are defined directly by the luminance distribution, is much higher than the resolution for such gratings. This well-described phenomenon usually is referred to as hyperacuity, and is regarded as a cortical function which is not limited by the optics and the sampling properties of the eye. Second order patterns which can be defined by the distribution of local contrast gained some interest because they require more complex processing mechanisms than first order patterns. We investigated how well gratings and bars which are exclusively defined by the variation of the local contrast of static random dot patterns can be localized in space. In this case localization acuity does not reach the precision which is known for first order patterns. However, the localization of contrast-modulated patterns can be almost one order of magnitude better than second order grating resolution, and therefore reaches into the hyperacuity range. In combination with findings for motion-defined or stereo-defined patterns it is concluded that the brain mechanisms responsible for the localization of features in the visual scene have not only access to first order information which is available immediately from the retinal image, but in addition, to second order information which has to be extracted from the retinal intensity distribution by some sort of nonlinear processing.

The influence of aluminum concentration on photoelectrochemical etching of first order gratings in GaAs/AlGaAs

We present a set of experiments which systematically clarifies the enhancement of photoelectrochemical (PEC) etching due to the mole fraction of aluminum in AlxGa1−xAs. The spatial resolution of gratings etched in Al0.3Ga0.7As is as much as three times greater than the spatial resolution of gratings etched in GaAs, so that the smallest practical grating period is about 0.3 μm, as compared with about 0.7 μm using previous techniques. This technique enabled PEC fabrication of first order gratings for waveguide outcouplers. The lower hole mobility of AlxGa1−xAs is proposed as a possible explanation for this grating resolution improvement.

Effect of temporal frequency and contrast on peripheral grating resolution.

We measured resolution at 10 degrees in the inferior temporal retina using horizontal and vertical gratings of different contrasts which modulated in time at temporal frequencies from 0 to 40 Hz. Since peripheral grating resolution is directly related to the sampling density of retinal ganglion cells this allowed us to observe changes in responding ganglion cell density as the stimulus properties changed to selectively stimulate magnocellular pathway cells (M cells) instead of parvocellular pathway cells (P cells). At all contrasts there was no decline in resolution performance up to 10 Hz, after which resolution deteriorated significantly, this effect being greater at lower contrasts. The predicted psychophysical resolution limit for M cells calculated from the anatomical data of Dacey indicates that resolution for high temporal frequency (30 Hz) or low contrast (5%) stimuli is too good to be mediated by M cells alone and there is still significant P cell stimulation by these stimuli.

The development of vernier acuity in human infants

Vernier acuity, i.e. the detection of a small misalignment between lines, is about one order of magnitude finer than the resolution of periodic gratings in adult humans. This hyperacuity is generally attributed to cortical mechanisms, and the time-course of its development seems to differ from the development of grating resolution that probably is limited by retinal factors. We investigated 271 human infants and children between 2 months and 8 yr of age with essentially identical stimuli and experimental procedures. Vernier thresholds for Vernier targets were compared to grating resolution. The preferential looking experiments led to the following results: (i) Vernier acuity starts below grating resolution. (ii) Like grating resolution, Vernier acuity develops gradually, but more rapidly and longer; at the age of 5 yr performance becomes comparable to that of adults. (iii) Flanking borders without offset, added to the Vernier targets at various distances, did not affect thresholds consistently across distances and age groups.

The Limitations of Currently Used Methods for Evaluating the Resolution of Diffraction Gratings

The concept of resolving power is found to be an unsatisfactory way of specifying the resolution properties of imperfect diffraction gratings. Three methods of measuring the resolution are considered in detail, the direct scan of a spectral line using a single frequency stabilized helium-neon laser as the light source, the knife edge test, and interferometry of the grating wavefront. Each method has its own particular merits and limitations, It is suggested that any one of the methods in isolation is of limited usefulness and that the results of more than one method are required to characterize completely grating resolution for practical purposes.

Infrared Spectrum of Diboron Tetrafluoride in the Gaseous and Solid States

Infrared spectra of B2F4 are reported over the range 2.5 to 50 μ at small grating resolution for both the gaseous and polycrystalline states. Examination of band envelopes for the gas and of differences between gas and solid spectra indicates that a structural difference exists between gaseous and solid B2F4. It is suggested that the alteration is analogous to that observed for B2Cl4 with the Vd or staggered configuration applying in gas and the Vh or planar configuration applying in the solid. Rough estimates are made for some of the principal potential constants.