Modeling acuity for optotypes varying in complexity

Defining metrics of visual acuity from theoretical models of observers

Many experimental studies show that metrics of visual image quality can predict changes in visual acuity due to optical aberrations. Here we use statistical decision theory and Fourier optics formalism to demonstrate that two metrics known in the field of vision sciences are approximations of two different theoretical models of linear observers. The theory defines metrics of visual acuity to potentially predict changes in visual acuity due to optical aberrations, without needing a posteriori scale or offset. We illustrate our approach with experiments, using combinations of defocus and spherical aberration, and pure coma.

Optical modelling of an accommodative light field display system and prediction of human eye responses

The spatio-angular resolution of a light field (LF) display is a crucial factor for delivering adequate spatial image quality and eliciting an accommodation response. Previous studies have modelled retinal image formation with an LF display and evaluated whether accommodation would be evoked correctly. The models were mostly based on ray-tracing and a schematic eye model, which pose computational complexity and inaccurately represent the human eye population's behaviour. We propose an efficient wave-optics-based framework to model the human eye and a general LF display. With the model, we simulated the retinal point spread function (PSF) of a point rendered by an LF display at various depths to characterise the retinal image quality. Additionally, accommodation responses to the rendered point were estimated by computing the visual Strehl ratio based on the optical transfer function (VSOTF) from the PSFs. We assumed an ideal LF display that had an infinite spatial resolution and was free from optical aberrations in the simulation. We tested points rendered at 0-4 dioptres of depths having angular resolutions of up to 4x4 viewpoints within a pupil. The simulation predicted small and constant accommodation errors, which contradict the findings of previous studies. An evaluation of the optical resolution on the retina suggested a trade-off between the maximum achievable resolution and the depth range of a rendered point where in-focus resolution is kept high. The proposed framework can be used to evaluate the upper bound of the optical performance of an LF display for realistically aberrated eyes, which may help to find an optimal spatio-angular resolution required to render a high quality 3D scene.

Correlation between Contrast Sensitivity and Modulation Transfer Functions

SIGNIFICANCE

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.

PURPOSE

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).

METHODS

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.

RESULTS

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.

CONCLUSIONS

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.

Simulation of visual acuity by personalizable neuro-physiological model of the human eye

We present a model of the whole visual train to estimate an individual's visual acuity based on their eye's physical properties. Our simulation takes into account the optics of the eye, neural transmission and noise, as well as the recognition process. Personalized input data are represented by the ocular wavefront aberration and pupil diameter, both either coming from in vivo measurements of a subject or being produced by optical design software using a schematic eye. This flexibility opens the door to a broad range of potential applications, such as objective visual acuity measurements and intraocular lens design. Our algorithm contains only two adjustable neural parameters: additive noise σ, and discrimination range δρ, with their values being experimentally calibrated by fitting the results of simulations to the outcome of real acuity tests performed on healthy young subjects with normal vision (visual acuity: 0…-0.3 logMAR range). It was established that by using fixed values of σ = 0.10 and δρ = 0.0025 for each person examined, the residual of the acuity simulations averaged over the calibration group reached its minimum at 0.045 logMAR.

Application of Correlation-Based Scoring Scheme for Visual Acuity Measurements in the Clinical Practice

Purpose

Visual acuity tests are generally performed by showing eye charts to the subjects and registering their correct/incorrect identifications for the presented optotypes. We recently developed a correlation-based scoring method that significantly reduces the statistical error associated with relative letter legibility. In this paper, our purpose was to demonstrate the advantages and clinical utility of our scoring scheme compared to standard methods.

Methods

We developed a new computer-controlled measurement setup aligned with the ophthalmological standard. With this system, we presented the application of our correlation-based scoring in conventional clinical environment for 25 subjects and estimated the systematic error of the obtained acuity values. A separate experiment was performed by 14 additional subjects to reveal the test-retest variability of the new scoring method.

Results

The average systematic error relative to standard probability-based scoring is 0.01 logMAR over the examined subject group. Application of the correlation-based scheme when used in clinical environment with five letters per size decreases the repeatability error by ∼20% and increases diagnosis time by ∼10%.

Conclusions

The new scoring scheme is directly applicable in clinical practice providing unbiased results with improved repeatability compared to standard visual acuity measurements. It reduces test-retest variability by the same amount as if the number of letters was doubled in traditional tests.

Translational Relevance

Our new method is a promising alternative to conventional acuity tests in cases when high-precision measurements are required, for example evaluating implanted intraocular lenses, testing subjects with retinal diseases or cataract, and refractive surgery candidates.

Pupil size stability of the cubic phase mask solution for presbyopia

Presbyopia correction involves different types of studies such as lens design, clinical study, and the development of objective metrics, such as the visual Strehl ratio. Different contact lens designs have been proposed for presbyopia correction, but performance depends on pupil diameter. We will analyze the potential use of a nonsymmetrical element, a cubic phase mask (CPM) solution, to develop a contact or intraocular lens whose performance is nearly insensitive to changes in pupil diameter. We will show the through focus optical transfer function of the proposed element for different pupil diameters ranging from 3 to 7 mm. Additionally, we will show the images obtained through computation and experiment for a group of eye charts with different visual acuities. Our results show that a CPM shaped as 7.07  μm*(Z33-Z3-3)-0.9  μmZ20 is a good solution for a range of clear vision with a visual acuity of at least 0.1 logMar from 0.4 to 6 m for pupil diameters in the 3- to 7-mm range. Our results appear to be a good starting point for further development and study of this kind of CPM solution for presbyopia.

Comparing the minimum spatial-frequency content for recognizing Chinese and alphabet characters

Visual blur is a common problem that causes difficulty in pattern recognition for normally sighted people under degraded viewing conditions (e.g., near the acuity limit, when defocused, or in fog) and also for people with impaired vision. For reliable identification, the spatial frequency content of an object needs to extend up to or exceed a minimum value in units of cycles per object, referred to as the critical spatial frequency. In this study, we investigated the critical spatial frequency for alphabet and Chinese characters, and examined the effect of pattern complexity. The stimuli were divided into seven categories based on their perimetric complexity, including the lowercase and uppercase alphabet letters, and five groups of Chinese characters. We found that the critical spatial frequency significantly increased with complexity, from 1.01 cycles per character for the simplest group to 2.00 cycles per character for the most complex group of Chinese characters. A second goal of the study was to test a space-bandwidth invariance hypothesis that would represent a tradeoff between the critical spatial frequency and the number of adjacent patterns that can be recognized at one time. We tested this hypothesis by comparing the critical spatial frequencies in cycles per character from the current study and visual-span sizes in number of characters (measured by Wang, He, & Legge, 2014) for sets of characters with different complexities. For the character size (1.2°) we used in the study, we found an invariant product of approximately 10 cycles, which may represent a capacity limitation on visual pattern recognition.

Correlation-based evaluation of visual performance to reduce the statistical error of visual acuity

Ophthalmologists evaluate visual acuity tests by the number of correctly recognized optotypes (usually letters) in the different lines of an eye chart. This probability-based scoring results in significant statistical error that can only be decreased by the time-consuming analysis of a larger number of optotypes. In this paper, we present a new, more precise correlation-based scoring method that takes the degree of misidentification into consideration too, rather than the mere fact of it. According to our experimental results, this new method decreases the uncertainty error by 28% if using the same number of optotypes at a given letter size or requires half the optotype number to produce the same error as that of probability-based scoring.

A New Font, Specifically Designed for Peripheral Vision, Improves Peripheral Letter and Word Recognition, but Not Eye-Mediated Reading Performance

Reading speed is dramatically reduced when readers cannot use their central vision. This is because low visual acuity and crowding negatively impact letter recognition in the periphery. In this study, we designed a new font (referred to as the Eido font) in order to reduce inter-letter similarity and consequently to increase peripheral letter recognition performance. We tested this font by running five experiments that compared the Eido font with the standard Courier font. Letter spacing and x-height were identical for the two monospaced fonts. Six normally-sighted subjects used exclusively their peripheral vision to run two aloud reading tasks (with eye movements), a letter recognition task (without eye movements), a word recognition task (without eye movements) and a lexical decision task. Results show that reading speed was not significantly different between the Eido and the Courier font when subjects had to read single sentences with a round simulated gaze-contingent central scotoma (10° diameter). In contrast, Eido significantly decreased perceptual errors in peripheral crowded letter recognition (-30% errors on average for letters briefly presented at 6° eccentricity) and in peripheral word recognition (-32% errors on average for words briefly presented at 6° eccentricity).

Comparing the visual spans for faces and letters

The visual span-the number of adjacent text letters that can be reliably recognized on one fixation-has been proposed as a sensory bottleneck that limits reading speed (Legge, Mansfield, & Chung, 2001). Like reading, searching for a face is an important daily task that involves pattern recognition. Is there a similar limitation on the number of faces that can be recognized in a single fixation? Here we report on a study in which we measured and compared the visual-span profiles for letter and face recognition. A serial two-stage model for pattern recognition was developed to interpret the data. The first stage is characterized by factors limiting recognition of isolated letters or faces, and the second stage represents the interfering effect of nearby stimuli on recognition. Our findings show that the visual span for faces is smaller than that for letters. Surprisingly, however, when differences in first-stage processing for letters and faces are accounted for, the two visual spans become nearly identical. These results suggest that the concept of visual span may describe a common sensory bottleneck that underlies different types of pattern recognition.

Critical band masking reveals the effects of optical distortions on the channel mediating letter identification

There is evidence that letter identification is mediated by only a narrow band of spatial frequencies and that the center frequency of the neural channel thought to underlie this selectivity is related to the size of the letters. When letters are spatially filtered (at a fixed size) the channel tuning characteristics change according to the properties of the spatial filter (Majaj et al., 2002). Optical aberrations in the eye act to spatially filter the image formed on the retina-their effect is generally to attenuate high frequencies more than low frequencies but often in a non-monotonic way. We might expect the change in the spatial frequency spectrum caused by the aberration to predict the shift in channel tuning observed for aberrated letters. We show that this is not the case. We used critical-band masking to estimate channel-tuning in the presence of three types of aberration-defocus, coma and secondary astigmatism. We found that the maximum masking was shifted to lower frequencies in the presence of an aberration and that this result was not simply predicted by the spatial-frequency-dependent degradation in image quality, assessed via metrics that have previously been shown to correlate well with performance loss in the presence of an aberration. We show that if image quality effects are taken into account (using visual Strehl metrics), the neural channel required to model the data is shifted to lower frequencies compared to the control (no-aberration) condition. Additionally, we show that when spurious resolution (caused by π phase shifts in the optical transfer function) in the image is masked, the channel tuning properties for aberrated letters are affected, suggesting that there may be interference between visual channels. Even in the presence of simulated aberrations, whose properties change from trial-to-trial, observers exhibit flexibility in selecting the spatial frequencies that support letter identification.

Effect of pattern complexity on the visual span for Chinese and alphabet characters

The visual span for reading is the number of letters that can be recognized without moving the eyes and is hypothesized to impose a sensory limitation on reading speed. Factors affecting the size of the visual span have been studied using alphabet letters. There may be common constraints applying to recognition of other scripts. The aim of this study was to extend the concept of the visual span to Chinese characters and to examine the effect of the greater complexity of these characters. We measured visual spans for Chinese characters and alphabet letters in the central vision of bilingual subjects. Perimetric complexity was used as a metric to quantify the pattern complexity of binary character images. The visual span tests were conducted with four sets of stimuli differing in complexity--lowercase alphabet letters and three groups of Chinese characters. We found that the size of visual spans decreased with increasing complexity, ranging from 10.5 characters for alphabet letters to 4.5 characters for the most complex Chinese characters studied. A decomposition analysis revealed that crowding was the dominant factor limiting the size of the visual span, and the amount of crowding increased with complexity. Errors in the spatial arrangement of characters (mislocations) had a secondary effect. We conclude that pattern complexity has a major effect on the size of the visual span, mediated in large part by crowding. Measuring the visual span for Chinese characters is likely to have high relevance to understanding visual constraints on Chinese reading performance.

Accounting for the phase, spatial frequency and orientation demands of the task improves metrics based on the visual Strehl ratio

Advances in ophthalmic instrumentation have allowed high order aberrations to be measured in vivo. These measurements describe the distortions to a plane wavefront entering the eye, but not the effect they have on visual performance. One metric for predicting visual performance from a wavefront measurement uses the visual Strehl ratio, calculated in the optical transfer function (OTF) domain (VSOTF) (Thibos et al., 2004). We considered how well such a metric captures empirical measurements of the effects of defocus, coma and secondary astigmatism on letter identification and on reading. We show that predictions using the visual Strehl ratio can be significantly improved by weighting the OTF by the spatial frequency band that mediates letter identification and further improved by considering the orientation of phase and contrast changes imposed by the aberration. We additionally showed that these altered metrics compare well to a cross-correlation-based metric. We suggest a version of the visual Strehl ratio, VScombined, that incorporates primarily those phase disruptions and contrast changes that have been shown independently to affect object recognition processes. This metric compared well to VSOTF for letter identification and was the best predictor of reading performance, having a higher correlation with the data than either the VSOTF or cross-correlation-based metric.

Predicting through-focus visual acuity with the eye's natural aberrations

PURPOSE

To develop a predictive optical modeling process that utilizes individual computer eye models along with a novel through-focus image quality metric.

METHODS

Individual eye models were implemented in optical design software (Zemax, Bellevue, WA) based on evaluation of ocular aberrations, pupil diameter, visual acuity, and accommodative response of 90 subjects (180 eyes; 24-63 years of age). Monocular high-contrast minimum angle of resolution (logMAR) acuity was assessed at 6 m, 2 m, 1 m, 67 cm, 50 cm, 40 cm, 33 cm, 28 cm, and 25 cm. While the subject fixated on the lowest readable line of acuity, total ocular aberrations and pupil diameter were measured three times each using the Complete Ophthalmic Analysis System (COAS HD VR) at each distance. A subset of 64 mature presbyopic eyes was used to predict the clinical logMAR acuity performance of five novel multifocal contact lens designs. To validate predictability of the design process, designs were manufactured and tested clinically on a population of 24 mature presbyopes (having at least +1.50 D spectacle add at 40 cm). Seven object distances were used in the validation study (6 m, 2 m, 1 m, 67 cm, 50 cm, 40 cm, and 25 cm) to measure monocular high-contrast logMAR acuity.

RESULTS

Baseline clinical through-focus logMAR was shown to correlate highly (R² = 0.85) with predicted logMAR from individual eye models. At all object distances, each of the five multifocal lenses showed less than one line difference, on average, between predicted and clinical normalized logMAR acuity. Correlation showed R² between 0.90 and 0.97 for all multifocal designs.

CONCLUSIONS

Computer-based models that account for patient's aberrations, pupil diameter changes, and accommodative amplitude can be used to predict the performance of contact lens designs. With this high correlation (R² ≥ 0.90) and high level of predictability, more design options can be explored in the computer to optimize performance before a lens is manufactured and tested clinically.