A method to predict refractive errors from wave aberration data

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.

Subjective versus objective refraction in healthy young adults

PURPOSE

To evaluate objective and subjective refraction differences in healthy young adults.

METHODS

Data concerning candidates for the Israeli Air Force Flight Academy, as well as active air force pilots in all stages of service who underwent a routine health checkup between the years 2018 and 2019 were retrospectively analyzed. Objective refraction measured using a single autorefractometer was compared with subjective refraction measured by an experienced military optometrist during the same visit. The results were converted to power vectors (spherical equivalent [SE], J0, and J45). To interpret astigmatism using power vector values, the cylinder power (Cp) was determined.

RESULTS

This study included 1,395 young adult participants. The average age was 22.17 years (range, 17-39, 84.8% males). The average SE was - 0.65 ± 1.19 diopter (D) compared with - 0.71 ± 0.91D in the auto- and subjective refraction, respectively (p = 0.001). Cp was 0.91 ± 0.52D and 0.67 ± 0.40D, respectively (p < 0.001). This difference was more common in older participants (p < 0.001). J0 and J45 value differences were not significant. The absolute SE value of subjective refraction was lower in the myopic (p < 0.001) and hyperopic (p < 0.001) patients.

CONCLUSIONS

Young hyperopic participants tended to prefer "less plus" in subjective refraction compared with autorefraction. Young myopic participants tended to prefer "less minus" in subjective refraction compared with autorefraction. All participants, but mainly older participants, preferred slightly "less Cp" than that measured using autorefraction; The astigmatic axis did not differ significantly between the methods.

Comparison between wavefront-derived refraction and auto-refraction

BACKGROUND

This study aimed to compare objective refractive errors and keratometry measurements obtained using the Nidek OPD-Scan II aberrometer/topographer and Topcon KR 8900 autorefractokeratometer.

METHODS

The right eye medical records of 176 patients aged 18-35 years who were admitted to our clinic as refractive surgery candidates were tested for refractive status and keratometry measurements with a Nidek OPD-Scan II aberrometer/topographer and a standard table-top autorefractokeratometer (Topcon KR 8900) before and after the induction of cycloplegia. Patients who had undergone any eye surgery and had hereditary, ectatic, or acquired corneal pathology were excluded. Refractive data were compared as spheres, cylinders, spherical equivalents, and power vectors before and after the induction of cycloplegia. Flat and steep keratometry (K1-K2) readings were recorded in diopters (D) and axis degrees, respectively, for each eye.

RESULTS

The spherical, cylindrical, spherical equivalence, J0-J45 vector values and K1-K2 readings (D, axis) between the two devices were statistically significant before and after the induction of cycloplegia (p<0.05). Bland-Altman analysis identified mean differences (95%CI of limits of agreement) of 0.77 (-0,57 to 2,11) in sphere, 0.74 (-0,54 to 2,01) in spherical equivalent, -0,07 (-0,41 to 0,26) in J0 vector, 0,06 (-0,31 to 0,43) in J45 vector, -0,16 (-0,66 to 0,33) in K1, -0,23 (-0,79 to 0,33) in K2 values before induction of cycloplegia.

CONCLUSION

The refractive and keratometry results of the Nidek OPD Scan II system and Topcon KR 8900 standard table-top autorefractokeratometer are not interchangeable in healthy adult population before and after induction of cycloplegia.

Refractive Outcomes of Cataract Surgery in Patients With Intrastromal Femtosecond Laser Treatment of Presbyopia (INTRACOR)

PURPOSE

To evaluate the outcomes of cataract surgery with intraocular lens (IOL) implantation in patients who underwent intrastromal femtosecond laser treatment of presbyopia (INTRACOR).

METHODS

This was an interventional case series of 8 patients (10 eyes) who presented for cataract surgery 6.1 ± 3.2 years (mean ± standard deviation [SD]) after INTRACOR (Technolas Perfect Vision GmbH) treatment. A monofocal IOL was implanted in 9 eyes (7 patients) and a small-aperture IOL was implanted in 1 eye. The IOL power was calculated without adjustments using biometry obtained after the INTRACOR treatment. For additional calculations, keratometry obtained before the INTRACOR treatment was used. Postoperative examinations included visual acuity testing, manifest refraction, defocus curve, ocular biometry, corneal tomography, aberrometry, anterior segment optical coherence tomography, and slit-lamp examination.

RESULTS

After the cataract surgery, the mean ± SD uncorrected distance visual acuity was 0.37 ± 0.17 logMAR, the corrected distance visual acuity was 0.10 ± 0.10 logMAR, and the manifest refraction spherical equivalent, adjusted to infinity, was +0.39 ± 0.63 diopters (D). Intermediate and near visual acuity, both uncorrected and distance-corrected, and distance-corrected defocus curves varied considerably among patients. Using biometry performed after INTRACOR, the traditional IOL power calculation formulas produced hyperopic outcomes, with the mean ± SD prediction error ranging from +0.72 ± 0.34 to +0.96 ± 0.41 D. Although the mean ± SD prediction error decreased (range: -0.34 ± 0.56 to -0.15 ± 0.53 D) when using keratometry obtained before INTRACOR, the accuracy remained low due to high variability.

CONCLUSIONS

In patients with cataract who had previous INTRACOR treatment, IOL power calculation could be inaccurate, with a tendency toward hyperopic outcomes. These results require confirmation in more extensive studies. [J Refract Surg. 2023;39(10):676-682.].

Absolute prediction of relative changes in contrast sensitivity with aberrations using a single metric of retinal image quality

Metrics of retinal image quality predict optimal refractive corrections and correlate with visual performance. To date, they do not predict absolutely the relative change in visual performance when aberrations change and therefore need to be a-posteriori rescaled to match relative measurements. Here we demonstrate that a recently proposed metric can be used to predict, in an absolute manner, changes in contrast sensitivity measurements with Sloan letters when aberrations change. Typical aberrations of young and healthy eyes (for a 6 mm pupil diameter) were numerically introduced, and we measured the resulting loss in contrast sensitivity of subjects looking through a 2 mm diameter pupil. Our results suggest that the metric can be used to corroborate measurements of visual performance in clinical practice, thereby potentially improving patient follow-ups.

Impact of temporal fluctuations in optical defocus on visual acuity: Empirical results and modeling outcomes

Optical defocus in human eyes is seldom steady during naturalistic steady-state viewing. It fluctuates by 0.3 to 0.5 diopters (D) from accommodative microfluctuations and by 1.5 to 2.5 D in dysfunctions such as spasm of near reflex, both with ≤2 Hz low-pass frequency spectra. This study observed losses in monocular visual acuity of cyclopleged adults who encountered varying amplitude (0.25-2.0 D) and temporal frequency (0.25-2.0 Hz) combinations of sinusoidal defoci induced using an electrically tunable lens. Visual acuity, recorded for 300-ms flashes of Sloan optotype presentation using the method of constant stimuli, deteriorated with defocus amplitude at a rate steeper for lower than higher temporal frequencies. A template matching model of acuity, incorporating optical and neural low-pass filters, neural noise, and a cross-correlated decision operator, showed the best match with empirical data when acuity was governed by the minimum defocus available during optotype display. This criterion minimized acuity loss for higher temporal frequencies due to the increased probability of zero-defocus encounters within the presentation duration. Other decision criteria such as defocus averaging across the entire or parts of the presentation duration yielded less satisfactory results. These results imply that vision loss in humans encountering broadband time-varying defocus is dictated by the dominant low frequencies, with higher frequencies largely compensated using the least defocus decision strategy.

FIAT: A Device for Objective, Optical Measures of Accommodation in Phakic and Pseudophakic Eyes

Purpose

To present FIAT, a novel optical instrument and analysis package that is designed to elicit and optically record accommodation in human eyes.

Methods

FIAT employs a Shack-Hartmann wavefront sensor and a retro-illumination pupil camera that records from a single eye at video rates. It is effective at eliciting accommodation by offering the subject a full-field binocular view of an alternating distant target and a near-eye display. FIAT analysis software computes wave aberrations for each video frame over full- or subpupil sizes and computes accommodative dynamics and accommodative range.

Results

The system is validated by showing accurate refraction measurements in model eyes and human eyes with trial lenses. Robust accommodative responses are shown for young eyes, and a lack of accommodative response is shown for a known presbyopes. Accommodative stimulus-response curves from five phakic subjects over a range of ages show expected results. Results from two individuals with monofocal intraocular lenses are shown.

Conclusions

FIAT is an effective instrument for making accurate, objective measures of accommodation in phakic and pseudophakic eyes.

Translational Relevance

We present a device that can play an important role in the development and testing of accommodating intraocular lenses.

Predicting the effects of defocus blur on contrast sensitivity with a model-based metric of retinal image quality

We measure the effect of defocus blur on contrast sensitivity with Sloan letters in the 0.75-2.00 arc min range of letter gaps. We compare our results with the prediction of the Dalimier and Dainty model [J. Opt. Soc. Am. A25, 2078 (2008)JOAOD60740-323210.1364/JOSAA.25.002078] and propose a new metric of retinal image quality that we define as the model limit for very small letters. The contrast sensitivity is measured for computationally blurred Sloan letters (0, 0.25, and 0.50 diopters for a 3 mm pupil) of different sizes (20/40 to 20/15 visual acuity), and subjects look through a small (2 mm) diaphragm to limit the impact of their own aberration on measurements. Measurements and model predictions, which are normalized by the blur-free condition, weakly depend on letter size and are in good agreement with our metric of retinal image quality. Our metric relates two approaches of modeling visual performance: complete modeling of the optotype classification task and calculation of retinal image quality with a descriptive metric.

Accommodation lags are higher in myopia than in emmetropia: Measurement methods and metrics matter

Purpose

To determine whether accommodative errors in emmetropes and myopes are systematically different, and the effect of using different instruments and metrics.

Methods

Seventy‐six adults aged 18–27 years comprising 24 emmetropes (spherical equivalent refraction of the dominant eye +0.04 ± 0.03 D) and 52 myopes (−2.73 ± 0.22 D) were included. Accommodation responses were measured with a Grand Seiko WAM‐5500 and a Hartmann–Shack Complete Ophthalmic Analysis System aberrometer, using pupil plane (Zernike and Seidel refraction) and retinal image plane (neural sharpness—NS; and visual Strehl ratio for modulation transfer function—VSMTF) metrics at 40, 33 and 25 cm. Accommodation stimuli were presented to the corrected dominant eye, and responses, referenced to the corneal plane, were determined in the fellow eye. Linear mixed‐effects models were used to determine influence of the refractive group, the measurement method, accommodation stimulus, age, race, parental myopia, gender and binocular measures of heterophoria, accommodative convergence/accommodation and convergence accommodation/convergence ratios.

Results

Lags of accommodation were affected significantly by the measurement method (p < 0.001), the refractive group (p = 0.003), near heterophoria (p = 0.002) and accommodative stimulus (p < 0.05), with significant interactions between some of these variables. Overall, emmetropes had smaller lags of accommodation than myopes with respective means ± standard errors of 0.31 ± 0.08 D and 0.61 ± 0.06 D (p = 0.003). Lags were largest for the Grand Seiko and Zernike defocus, intermediate for NS and VSMTF, and least for Seidel defocus.

Conclusions

The mean lag of accommodation in emmetropes is approximately equal to the previously reported depth of focus. Myopes had larger (double) lags than emmetropes. Differences between methods and instruments could be as great as 0.50 D, and this must be considered when comparing studies and outcomes. Accommodative lag increased with the accommodation stimulus, but only for methods using a fixed small pupil diameter.

Effect of decentration, tilt and rotation on the optical quality of various toric intraocular lens designs: a numerical and experimental study

Toric intraocular lenses (T-IOLs) may lose their optical quality if they are not correctly positioned inside the capsular bag once implanted. In this work, T-IOLs with cylinder powers of +1.50, +4.50 and +7.50 D and differing degrees of spherical aberration have been designed, manufactured and tested in vitro using a commercial optical bench that complies with the requirements of standard ISO 11979-2. Moreover, the effect of tilt and rotation on optical quality was assessed by means of numerical ray tracing on an astigmatic eye model, while the effect of decentration was evaluated numerically and experimentally.

Understanding In Vivo Chromatic Aberrations in Pseudophakic Eyes Using on Bench and Computational Approaches

Diffractive multifocal intraocular lenses (IOLs) modulate chromatic aberration and reduce it at certain distances due to interactions between the refractive and diffractive chromatic components. However, the extent to which computer modeling and on bench measurements of IOL chromatic aberration translate to chromatic aberration in patients implanted with these multifocal IOLs (MIOLs) is not yet fully understood. In this study, we compare the chromatic difference of focus and longitudinal chromatic aberrations in pseudophakic patients implanted with different IOL designs (monofocal and trifocal IOLs) and materials (hydrophobic and hydrophilic), and compared them with predictions from computer eye models and on bench measurements with the same IOLs. Patient data consisted of results from 63 pseudophakic eyes reported in four different studies and obtained psychophysically in the visual testing channel of a custom-developed polychromatic adaptive optics system. Computational predictions were obtained using ray tracing on computer eye models, and modulation transfer function (MTF) on bench measurements on physical eye models. We found that LCA (in vivo/simulated) for far vision was 1.37 ± 0.08 D/1.19 D for monofocal hydrophobic, 1.21 ± 0.08 D/0.88 D for monofocal hydrophilic, 0.99 ± 0.06 D/1.19 D for MIOL hydrophobic, and 0.82 ± 0.05 D/0.88 D for MIOL hydrophilic. For intermediate and near vision, LCA (in vivo/simulated) was 0.67 ± 0.10 D/0.75 D and 0.23 ± 0.08 D/0.19 D for MIOL hydrophobic and 0.27 ± 0.15 D/0.38 D and 0.15 ± 0.15 D/−0.13 D for MIOL hydrophilic, respectively. In conclusion, computational ray tracing and on bench measurements allowed for evaluating in vivo chromatic aberration with different materials and designs for multifocal diffractive intraocular lenses.

Predicting subjective refraction with dynamic retinal image quality analysis

The aim of this work is to evaluate the performance of a novel algorithm that combines dynamic wavefront aberrometry data and descriptors of the retinal image quality from objective autorefractor measurements to predict subjective refraction. We conducted a retrospective study of the prediction accuracy and precision of the novel algorithm compared to standard search-based retinal image quality optimization algorithms. Dynamic measurements from 34 adult patients were taken with a handheld wavefront autorefractor and static data was obtained with a high-end desktop wavefront aberrometer. The search-based algorithms did not significantly improve the results of the desktop system, while the dynamic approach was able to simultaneously reduce the standard deviation (up to a 15% for reduction of spherical equivalent power) and the mean bias error of the predictions (up to 80% reduction of spherical equivalent power) for the handheld aberrometer. These results suggest that dynamic retinal image analysis can substantially improve the accuracy and precision of the portable wavefront autorefractor relative to subjective refraction.

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.

Digital ocular swept source optical coherence aberrometry

Ocular aberrometry is an essential technique in vision science and ophthalmology. We demonstrate how a phase-sensitive single mode fiber-based swept source optical coherence tomography (SS-OCT) setup can be employed for quantitative ocular aberrometry with digital adaptive optics (DAO). The system records the volumetric point spread function at the retina in a de-scanning geometry using a guide star pencil beam. Succeeding test-retest repeatability assessment with defocus and astigmatism analysis on a model eye within ± 3 D dynamic range, the feasibility of technique is demonstrated in-vivo at a B-scan rate of >1 kHz in comparison with a commercially available aberrometer.

Analyses on the distribution and influence of higher-order aberrations both clinically and experimentally among varied refractive errors

PURPOSE:

The aim of this work is to determine and compare the distribution and influence of higher-order aberrations (HOAs) both clinically and experimentally between different refractive errors.

METHODS:

Commercially available Shack–Hartmann aberrometer was employed to measure the HOA clinically in human eyes. Experimentally, HOA was measured in a model eye by simulating various refractive errors by constructing an aberrometer based on the same Shack Hartmann principle. One-way analyses of variance and simple regression were employed to analyze the distribution and influence of HOA among various refractive errors.

RESULTS:

A total of 100 eyes were clinically measured for aberrations, of which 35, 50, and 15 eyes were emmetropes, myopes, and hyperopes, respectively. Out of the total root mean square (RMS) value, the HOAs found in the human eyes were 23%, 7%, and 26% and in the model eye, it was 20%, 8%, and 10% between emmetropes, myopes, and hyperopes, respectively. The mean higher-order RMS was almost similar between the groups and among various refractive errors. There was no statistical significance between the individual Zernikes except for the coma in both human and model eyes.

CONCLUSION:

The mean HOA is similar amidst the different refractive errors. The presence of 23% HOA in emmetropes signifies that larger part of the human eye is capable of complying with HOA without compromising the image quality. This work signifies that HOA does not play an important role in image clarity for human eyes with regular refractive surface unlike irregular refractive surfaces.

Visual image quality after small-incision lenticule extraction compared with that of spectacles and contact lenses

PURPOSE

To assess the influence of small-incision lenticule extraction (SMILE) for high myopia on the visual image quality assessed by the logarithm of the visual Strehl ratio (logVSX) and put this into a clinical context by pairwise comparing the logVSX of postoperative eyes with those of myopic controls wearing spectacles and/or contact lenses.

SETTING

University hospital.

DESIGN

Prospective and cross-sectional clinical study.

METHODS

Patients with a myopic spherical equivalent of at least 6.00 diopters treated with SMILE aimed at emmetropia and correspondingly myopic controls corrected with spectacles and/or contact lenses were included. The logVSX calculation was divided into habitual logVSX based on the wavefront aberration measurement directly and optimal logVSX calculated in a theoretical through-focus experiment to obtain the best-achievable logVSX.

RESULTS

A total of 117 eyes of 61 patients and 64 eyes of 34 myopic controls were included. SMILE did not affect the habitual logVSX but worsened the optimal logVSX (P < .001). The postoperative habitual logVSX was statistically significantly worse compared with contact lenses (P = .002). The postoperative optimal logVSX was significantly worse compared with both spectacles (P < .01) and contact lenses (P = .003). There was no statistically significant difference in habitual or optimal logVSX between spectacles and contact lenses.

CONCLUSIONS

SMILE for high myopia does not affect the habitual logVSX but decreases the optimal logVSX slightly. The postoperative habitual logVSX is worse than for contact lenses but not spectacles, and the postoperative optimal logVSX is worse than for both contact lenses and spectacles. There is no statistically significant difference in either habitual or optimal logVSX between spectacles and contact lenses.

Agreement and variability of subjective refraction, autorefraction, and wavefront aberrometry in pseudophakic patients

PURPOSE

To evaluate the comparability and variability of subjective refraction (SR), autorefraction (AR), and wavefront aberrometry (WA) in pseudophakic patients.

SETTING

Hanusch Hospital, Vienna, Austria.

DESIGN

Prospective study.

METHODS

Subjective refraction was performed by 2 independent examiners at 2 study visits. Furthermore, 5 measurements of AR and WA were performed in each patient at both visits. Agreement between the 3 refraction methods for spherical equivalent (M) and cylindrical vectors (J0, J45) was analyzed using Friedman multiple comparison and Bland-Altman plots. Predictability of spherical equivalent determined by SR from AR and WA measurements was tested with partial least squares regression and random forest regression.

RESULTS

Ninety eyes of 90 pseudophakic patients were measured. The mean absolute error and arithmetic mean difference of SR measurements of M, J0, and J45 were comparable between both examiners. A small mean difference was found for SR between both visits. Spherical equivalent was more negative when measured by AR [-0.87 diopters (D)] and WA (-0.90 D) compared with SR (-0.60 D), whereas astigmatic vectors agreed well. Good test-retest reliability was found between all 3 refraction methods for M, J0, and J45. Partial least squares regression and random forest regression showed moderate predictive power for M measured by objective refraction and SR.

CONCLUSIONS

Reproducibility and reliability of SR measurements in pseudophakic patients showed good agreement. AR and WA measured the spherical equivalent more myopic than SR, whereas astigmatic vectors were comparable between the 3 methods after uneventful cataract surgery.

Comparison of Low Degree/High Degree and Zernike Expansions for Evaluating Simulation Outcomes After Customized Aspheric Laser Corrections

Purpose

The purpose of this study was to compare the low degree/high degree (LD/HD) and Zernike Expansion simulation outcomes evaluating the corneal wavefront changes after theoretical conventional and customized aspheric photorefractive ablations.

Methods

Initial anterior corneal surface profiles were modeled as conic sections with pre-operative apical curvature, R0, and asphericity, Q0. Postoperative apical curvature, R1, was computed from intended defocus correction, D, diameter zone, S, and target postoperative asphericity, Q1. Coefficients of both Zernike and LD/HD polynomial expansions of the rotationally symmetrical corneal profile were computed using scalar products. We modeled different values of D, R0, Q0, S, and ΔQ = Q1 to Q0. The corresponding postoperative changes in defocus (Δz20 vs. Δg20), fourth order (Δz40 vs. Δg40) and sixth order (Δz60 vs. Δg60) Zernike and LD/HD spherical aberrations (SAs) were compared. In addition, retrospective clinical data and wavefront measurements were obtained from two examples of two patient eyes before and after corneal laser photoablation.

Results

The z20, varied with both R0 and Q0, whereas the LD/HD defocus coefficient, g20, was relatively robust to changes in asphericity. Variations of apical curvature better correlated with defocus and ΔQ with SA coefficients in the LD/HD classification. The impact of ΔQ was null on g20 but induced significant linear variations in z20 and fourth order SA coefficients. LD/HD coefficients provided a good correlation with the visual performances of the operated eyes.

Conclusions

Simulated variations in postoperative corneal profile and wavefront expansion using the LD/HD approach showed good correlations between defocus and asphericity variations with variations in corneal curvature and SA coefficients, respectively.

Translational Relevance

The relevance of this study was to provide a clinically relevant alternative to Zernike polynomials for the interpretation of wavefront changes after customized aspheric corrections.

Objective Measures of Retinal Image Degradation Due to Refractive Corrections

SIGNIFICANCE

There is a need for a measure, as simple and yet as informative as possible, to describe objectively the retinal image quality when a patient views targets at various distances through spectacle, contact, or intraocular corrections with optics more elaborate than single vision.

PURPOSE

The purposes of this study are to examine the current status of quantitative descriptions of retinal image blur and find optimal characterization of image degradation.

METHODS

A variety of indexes of image degradation are computed for a typical eye and polychromatic light, in and out of focus, and as exemplars of sophisticated wave shaping, when the pupil transmission has been modified to a truncated Bessel amplitude function and to a "fractal" phase function.

RESULTS

Figures are shown for the optical transfer, point- and edge-spread functions, and Koenig bar and optotype letter blur for the various imaging and defocus conditions, and the relative values of several blur indexes are compared graphically and in a correlation table.

CONCLUSIONS

No single index captures the many ways in which the image can deviate from the diffraction-limited ideal. Among the incomplete descriptors of image degradation, the light distribution at a sharp edge stands out as optimally informative and economical, and, when condensed to just two values, one representing central image sharpness and the other outlying light spread, allows for a quick survey of the imaging deficit.

Recent advances in representation of monochromatic aberrations of human eyes

The field of aberrations of the human eye is moving rapidly, being driven by the desire to monitor and optimise vision following refractive surgery. In this paper, I discuss the different ways of representing aberrations of the human eye, the terminology used, how wave aberrations are used to determine refractions, the influence of pupil size on aberrations, how to compare right and left eye aberrations, how aberrations can be manipulated into different forms, how to make corrections for changes in wavelength, the appropriate ocular axis, and corneal and lenticular components of the aberrations.

Particle swarm optimization for wavefront correction in ophthalmic applications

Many optical systems require the correction of the cumulative wavefront error of the system for performance optimization. In ophthalmology the wavefront error of the eye corresponds to the visual defect and can be measured up to high-order aberrations today. Lower orders of the wavefront error are usually corrected with spectacles, contact lenses or refractive surgery. In this paper we apply an optimization method called particle swarm optimization to calculate the optimal correction for visual defects based on measured high-order wavefront results. It is shown that an optimized conventional correction and in particular an extended wavefront correction including higher orders yields a better result for the visual Strehl ratio, as compared to a simple conjugate correction scheme.

Advancing Digital Workflows for Refractive Error Measurements

Advancements in clinical measurement of refractive errors should lead to faster and more reliable measurements of such errors. The study investigated different aspects of advancements and the agreement of the spherocylindrical prescriptions obtained with an objective method of measurement ("Aberrometry" (AR)) and two methods of subjective refinements ("Wavefront Refraction" (WR) and "Standard Refraction" (StdR)). One hundred adults aged 20-78 years participated in the course of the study. Bland-Altman analysis of the right eye measurement of the spherocylindrical refractive error (M) identified mean differences (±95% limits of agreement) between the different types of measurements of +0.36 D (±0.76 D) for WR vs. AR (t-test: p < 0.001), +0.35 D (± 0.84 D) for StdR vs. AR (t-test: p < 0.001), and 0.0 D (± 0.65 D) for StdR vs. WR (t-test: p < 0.001). Monocular visual acuity was 0.0 logMAR in 96% of the tested eyes, when refractive errors were corrected with measurements from AR, indicating that only small differences between the different types of prescriptions are present.

Accuracy of the Hand-held Wavefront Aberrometer in Measurement of Refractive Error

Purpose

To compare refractive error measured by hand-held wavefront aberrometers with postcycloplegic autorefraction (AR) and cycloplegic refraction (CR).

Methods

The medical records of patients who received refractive measurements using the wavefront aberrometer, postcycloplegic AR, and CR between January 2014 and January 2016 were retrospectively analyzed. The mean differences, 95% confidence intervals, and limits of agreement (LOA) were calculated for the refractive vector components (M, J₀, and J₄₅).

Results

Fifty-one patients (9.0 ± 5.5 years, male 41.2%) were enrolled in this study, and only the right eye of each was included. Refractive errors ranged from −9.25 to +7.25 diopters (D) for spherical equivalent (median, 0.75 D). The M component was not significantly different among the three methods (p = 0.080). However, the J₀ vector component was significantly different (p < 0.001). After post hoc analysis, the wavefront aberrometer obtained more positive values for J₀ compared to the other methods. The J₄₅ component was not significantly different among the three methods (p = 0.143). The mean difference between the wavefront aberrometer and postcycloplegic AR was −0.115 D (LOA, −1.578 to 1.348 D) for M, 0.239 D (LOA, −0.371 to 0.850 D) for J₀, and −0.015 D (LOA, −0.768 to 0.738 D) for J₄₅. The mean difference between the wavefront aberrometer and CR was −0.220 D (LOA, −1.790 to 1.350 D) for M, 0.300 D (LOA, −0.526 to 1.127 D) for J₀, and −0.079 D (−0.662 to 0.504 D) for J₄₅.

Conclusions

The wavefront aberrometer showed good agreement with postcycloplegic AR and CR in spherical equivalents, but tended to produce slightly myopic results. The wavefront aberrometer also overestimated with-the-rule astigmatism. Therefore, we recommend that the device be used for estimations of refractive error, which may be useful for patients who have postural difficulties, live in undeveloped countries, or are bedridden.

Using Artificial Intelligence and Novel Polynomials to Predict Subjective Refraction

This work aimed to use artificial intelligence to predict subjective refraction from wavefront aberrometry data processed with a novel polynomial decomposition basis. Subjective refraction was converted to power vectors (M, J0, J45). Three gradient boosted trees (XGBoost) algorithms were trained to predict each power vector using data from 3729 eyes. The model was validated by predicting subjective refraction power vectors of 350 other eyes, unknown to the model. The machine learning models were significantly better than the paraxial matching method for producing a spectacle correction, resulting in a mean absolute error of 0.301 ± 0.252 Diopters (D) for the M vector, 0.120 ± 0.094 D for the J0 vector and 0.094 ± 0.084 D for the J45 vector. Our results suggest that subjective refraction can be accurately and precisely predicted from novel polynomial wavefront data using machine learning algorithms. We anticipate that the combination of machine learning and aberrometry based on this novel wavefront decomposition basis will aid the development of refined algorithms which could become a new gold standard to predict refraction objectively.

Relating wavefront error to visual acuity in pre- and post-LASIK eyes: a comparison of methods

Contrast threshold and visual Strehl ratio methods are used to predict visual acuity from wavefront error for a sample population of pre- and post-LASIK patients. Relative error (in logMAR) between predicted and measured visual acuity values are computed for each method and compared using paired t-tests. Differences in aberration data between pre- and post-LASIK eyes are then evaluated. The visual acuity prediction using visual Strehl proved to be more accurate for pre-LASIK patients than contrast threshold. However, both methods are comparable for post-LASIK patients.

Image Quality Metric Derived Refractions Predicted to Improve Visual Acuity Beyond Habitual Refraction for Patients With Down Syndrome

Purpose

To determine which optimized image quality metric (IQM) refractions provide the best predicted visual acuity (VA).

Methods

Autorefraction (AR), habitual refraction (spectacles, n = 23; unaided, n = 7), and dilated wavefront error (WFE) were obtained from 30 subjects with Down syndrome (DS; mean age, 30 years; range, 18–50). For each eye, the resultant metric value for 16 IQMs was calculated after >25000 sphero-cylindrical combinations of refraction were added to the measured WFE to generate residual WFE. The single refraction corresponding to each of the 16 optimized IQMs per eye was selected and used to generate acuity charts. Charts also were created for AR, habitual refraction, and a theoretical zeroing of all lower-order aberrations, and grouped into 10 sets with a clear chart in each set. Dilated controls (five observers per set) read each chart until five letters were missed on a high contrast monitor through a unit magnification telescope with a 3 mm pupil aperture. Average letters lost for the five observers for each chart was used to rank the IQMs for each DS eye.

Results

Average acuity for the best performing refraction for all DS eyes was within five letters (0.11 ± 0.05 logMAR) of the clear chart acuity. Optimized IQM refractions had ∼3.5 lines mean improvement from the habitual refraction (0.37 ± 0.22 logMAR, P < 0.001). Three metrics (Visual Strehl Ratio [VSX], VSX computed in frequency domain [VSMTF], and standard deviation of intensity values [STD]) identified refractions that were ranked first, or within 0.09 logMAR of first, in >98% of the eyes.

Conclusions

Optimized IQM refraction is predicted to improve VA in DS eyes based on control observers reading simulated charts.

Translational Relevance

Refractions identified through optimization of IQM may bypass some of the challenges of current refraction techniques for patients with DS. The optimized refractions are predicted to provide better VA compared to their habitual correction.

Polynomial decomposition method for ocular wavefront analysis

Zernike circle polynomials are in widespread use for wavefront analysis because of their orthogonality over a circular pupil and their representation of balanced classical aberrations. However, some of the higher-order modes contain linear and quadratic terms. A new aberration series is proposed to better separate the low- versus higher-order aberration components. Because its higher-order modes are devoid of linear and quadratic terms, our new basis can be used to better fit the low- and higher-order components of the wavefront. This new basis may quantify the aberrations more accurately and provide clinicians with coefficient magnitudes which better underline the impact of clinically significant aberration modes.

Variant myopia: A new presentation?

Purpose:

Variant myopia (VM) presents as a discrepancy of >1 diopter (D) between subjective and objective refraction, without the presence of any accommodative dysfunction. The purpose of this study is to create a clinical profile of VM.

Methods:

Fourteen eyes of 12 VM patients who had a discrepancy of >1D between retinoscopy and subjective acceptance under both cycloplegic and noncycloplegic conditions were included in the study. Fourteen eyes of 14 age- and refractive error-matched participants served as controls. Potential participants underwent a comprehensive orthoptic examination followed by retinoscopy (Ret), closed-field autorefractor (CA), subjective acceptance (SA), choroidal and retinal thickness, ocular biometry, and higher order spherical aberrations measurements.

Results:

In the VM eyes, a statistically and clinically significant difference was noted between the Ret and CA and Ret and SA under both cycloplegic and noncycloplegic conditions (multivariate repeated measures analysis of variance, P < 0.0001). A statistically significant difference was observed between the VM eyes, non-VM eyes, and controls for choroidal thickness in all the quadrants (Univariate ANOVA P < 0.05). The VM eyes had thinner choroids (197.21 ± 13.04 μ) compared to the non-VM eyes (249.25 ± 53.70 μ) and refractive error-matched controls (264.62 ± 12.53 μ). No statistically significant differences between groups in root mean square of total higher order aberrations and spherical aberration were observed.

Conclusion:

Accommodative etiology does not play a role in the refractive discrepancy seen in individuals with the variant myopic presentation. These individuals have thinner choroids in the eye with variant myopic presentation compared to the fellow eyes and controls. Hypotheses and clinical implications of variant myopia are discussed.

Normative best-corrected values of the visual image quality metric VSX as a function of age and pupil size

The visual image quality metric the visual Strehl ratio (VSX) combines a comprehensive description of the optics of an eye (wavefront error) with an estimate of the photopic neural processing of the visual system, and has been shown to be predictive of subjective best focus and well correlated with change in visual performance. Best-corrected visual image quality was determined for 146 eyes, and the quantitative relation of VSX, age, and pupil size is presented, including 95% confidence interval norms for age groups between 20 and 80 years and pupil diameters from 3 to 7 mm. These norms were validated using an independently collected population of wavefront error measurements. The best visual image quality was found in young eyes at smaller pupil sizes. Increasing pupil size caused a more rapid decrease in VSX than increasing age. These objectively determined benchmarks represent the best theoretical levels of visual image quality achievable with a sphere, cylinder, and axis correction in normal eyes and can be used to evaluate both traditional and wavefront-guided optical corrections provided by refractive surgery, contact lenses, and spectacles.

Predicted accommodative response from image quality in young eyes fitted with different dual-focus designs

PURPOSE

To investigate the separated and combined influences of inner zone (IZ) diameter and effective add power of dual-focus contact lenses (CL) in the image quality at distance and near viewing, in a functional accommodating model eye.

METHODS

Computational wave-optics methods were used to define zonal bifocal pupil functions, representing the optic zones of nine dual-focus centre-distance CLs. The dual-focus pupil functions were defined having IZ diameters of 2.10 mm, 3.36 mm and 4.00 mm, with add powers of 1.5 D, 2.0 D and 2.5 D (dioptres), for each design, that resulted in a ratio of 64%/36% between the distance and treatment zone areas, bounded by a 6 mm entrance pupil. A through-focus routine was implemented in MATLAB to simulate the changes in image quality, calculated from the Visual Strehl ratio, as the eye with the dual-focus accommodates, from 0 to -3.00 D target vergences. Accommodative responses were defined as the changes in the defocus coefficient, combined with a change in fourth and sixth order spherical aberration, which produced a peak in image quality at each target vergence.

RESULTS

Distance viewing image quality was marginally affected by IZ diameter but not by add power. Near image quality obtained when focussing the image formed by the near optics was only higher by a small amount compared to the other two IZ diameters. The mean ± standard deviation values obtained with the three adds were 0.28 ± 0.02, 0.23 ± 0.02 and 0.22 ± 0.02, for the small, medium and larger IZ diameters, respectively. On the other hand, near image quality predicted by focussing the image formed by the distance optics was considerably lower relatively to the other two IZ diameters. The mean ± standard deviation values obtained with the three adds were 0.15 ± 0.01, 0.38 ± 0.00 and 0.54 ± 0.01, for the small, medium and larger IZ diameters, respectively.

CONCLUSIONS

During near viewing through dual-focus CLs, image quality depends on the diameter of the most inner zone of the CL, while add power only affects the range of clear focus when focussing the image formed by the CL near optics. When only image quality gain is taken into consideration, medium and large IZ diameters designs are most likely to promote normal accommodative responses driven by the CL distance optics, while a smaller IZ diameter design is most likely to promote a reduced accommodative response driven by the dual-focus CL near optics.

Symmetric visual response to positive and negative induced spherical defocus under monochromatic light conditions

The purpose of the study was to investigate the sign-dependent response to real and simulated spherical defocus on the visual acuity under monochromatic light conditions. The investigation included 15 myopic participants with a mean spherical equivalent error of -2.98 ± 2.17 D. Visual acuity (VA) was tested with and without spherical defocus using the source method (simulated defocus) and the observer method (lens-induced defocus) in a range of ±3.0 D in 1.0 D steps. VA was assessed using Landolt C's, while the threshold was determined with an adaptive staircase procedure. Monochromatic light conditions were achieved using band pass filters with a wavelength of 450 ± 2 nm, 530 ± 2 nm and 630 ± 2 nm. Results showed that the reduction of VA was significantly different under blue lighting conditions, when compared to the green and red light conditions. No significant difference in the reduction of the VA was found between the positive and the negative sign of defocus for all lighting conditions. The agreement for the VA between the source and observer method was significantly dependent on the wavelength as well as on the level of defocus. To conclude, under monochromatic light conditions, myopes show a symmetric sign-dependency regarding the influence of spherical defocus on visual acuity. The observed results indicate that the human visual system is capable of integrating the chromatic differences in refraction to distinguish between the signs of defocus.

New Objective Refraction Metric Based on Sphere Fitting to the Wavefront

Purpose

To develop an objective refraction formula based on the ocular wavefront error (WFE) expressed in terms of Zernike coefficients and pupil radius, which would be an accurate predictor of subjective spherical equivalent (SE) for different pupil sizes.

Methods

A sphere is fitted to the ocular wavefront at the center and at a variable distance, t. The optimal fitting distance, t_opt, is obtained empirically from a dataset of 308 eyes as a function of objective refraction pupil radius, r₀, and used to define the formula of a new wavefront refraction metric (MTR). The metric is tested in another, independent dataset of 200 eyes.

Results

For pupil radii r₀ ≤ 2 mm, the new metric predicts the equivalent sphere with similar accuracy (<0.1D), however, for r₀ > 2 mm, the mean error of traditional metrics can increase beyond 0.25D, and the MTR remains accurate. The proposed metric allows clinicians to obtain an accurate clinical spherical equivalent value without rescaling/refitting of the wavefront coefficients. It has the potential to be developed into a metric which will be able to predict full spherocylindrical refraction for the desired illumination conditions and corresponding pupil size.

Axis-free correction of astigmatism using bifocal soft contact lenses

PURPOSE

Pilot study to investigate the feasibility of an axis-free correction approach of regular astigmatism using soft, bifocal contact lenses (CL).

METHODS

The investigation covers an optical simulation and a pilot study for the assessment of visual performance (over refraction OR, monocular visual acuity VA). The power of the two zones was adjusted according to the power of the astigmatic meridians, individually. Subjective performance was assessed in 30 participants with a mean horizontal cylindrical component of J₀=- 0.65±1.29 D (cylinder from -0.75 to -4.00 DC). OR and VA were measured directly after fitting the CL, after one hour and after 5days (3FUP).

RESULTS

Evaluating the modulation transfer function, CL increased the Strehl ratio by 10% and the transferred spatial frequency was improved from 6.6 cpd to 21.3 cpd. Analysis of Sturm's interval revealed a residual astigmatism of D_Ast=0.73 D. OR revealed a statistically significant reduction of spherical error between baseline and all follow up (ΔM=-2.14 D, p<0.001) and between the J₀ from baseline to 3FUP (ΔJ₀=-0.46 D, p=0.04). Wearing the CL for 5days did not result in a significant difference of VA (ΔVA_3FUP=+0.01 logMAR, p=0.99).

CONCLUSION

Axis-free correction of astigmatism using bifocal CL resulted in reasonable performance based on computer simulation. Participants showed no clinically reduced visual acuity or contrast sensitivity. Further clinical studies are needed to show if this approach provides a good alternative to conventional astigmatic correction.

Effect of Pupil Size on Wavefront Refraction during Orthokeratology

PURPOSE

It has been hypothesized that central and peripheral refraction, in eyes treated with myopic overnight orthokeratology, might vary with changes in pupil diameter. The aim of this work was to evaluate the axial and peripheral refraction and optical quality after orthokeratology, using ray tracing software for different pupil sizes.

METHODS

Zemax-EE was used to generate a series of 29 semi-customized model eyes based on the corneal topography changes from 29 patients who had undergone myopic orthokeratology. Wavefront refraction in the central 80 degrees of the visual field was calculated using three different quality metrics criteria: Paraxial curvature matching, minimum root mean square error (minRMS), and the Through Focus Visual Strehl of the Modulation Transfer Function (VSMTF), for 3- and 6-mm pupil diameters.

RESULTS

The three metrics predicted significantly different values for foveal and peripheral refractions. Compared with the Paraxial criteria, the other two metrics predicted more myopic refractions on- and off-axis. Interestingly, the VSMTF predicts only a marginal myopic shift in the axial refraction as the pupil changes from 3 to 6 mm. For peripheral refraction, minRMS and VSMTF metric criteria predicted a higher exposure to peripheral defocus as the pupil increases from 3 to 6 mm.

CONCLUSIONS

The results suggest that the supposed effect of myopic control produced by ortho-k treatments might be dependent on pupil size. Although the foveal refractive error does not seem to change appreciably with the increase in pupil diameter (VSMTF criteria), the high levels of positive spherical aberration will lead to a degradation of lower spatial frequencies, that is more significant under low illumination levels.

Is an objective refraction optimised using the visual Strehl ratio better than a subjective refraction?

PURPOSE

To prospectively examine whether using the visual image quality metric, visual Strehl (VSX), to optimise objective refraction from wavefront error measurements can provide equivalent or better visual performance than subjective refraction and which refraction is preferred in free viewing.

METHODS

Subjective refractions and wavefront aberrations were measured on 40 visually-normal eyes of 20 subjects, through natural and dilated pupils. For each eye a sphere, cylinder, and axis prescription was also objectively determined that optimised visual image quality (VSX) for the measured wavefront error. High contrast (HC) and low contrast (LC) logMAR visual acuity (VA) and short-term monocular distance vision preference were recorded and compared between the VSX-objective and subjective prescriptions both undilated and dilated.

RESULTS

For 36 myopic eyes, clinically equivalent (and not statistically different) HC VA was provided with both the objective and subjective refractions (undilated mean ± S.D. was -0.06 ± 0.04 with both refractions; dilated was -0.05 ± 0.04 with the objective, and -0.05 ± 0.05 with the subjective refraction). LC logMAR VA provided by the objective refraction was also clinically equivalent and not statistically different to that provided by the subjective refraction through both natural and dilated pupils for myopic eyes. In free viewing the objective prescription was preferred over the subjective by 72% of myopic eyes when not dilated. For four habitually undercorrected high hyperopic eyes, the VSX-objective refraction was more positive in spherical power and VA poorer than with the subjective refraction.

CONCLUSIONS

A method of simultaneously optimising sphere, cylinder, and axis from wavefront error measurements, using the visual image quality metric VSX, is described. In myopic subjects, visual performance, as measured by HC and LC VA, with this VSX-objective refraction was found equivalent to that provided by subjective refraction, and was typically preferred over subjective refraction. Subjective refraction was preferred by habitually undercorrected hyperopic eyes.

Usefulness of refractive measurement of wavefront autorefraction in patients with difficult retinoscopy

PURPOSE

To assess the ability of the WaveScan WaveFront System (VISX Inc, Santa Clara, CA) to measure refractive errors in patients with difficult retinoscopy and to compare results to standard cycloplegic retinoscopy.

METHODS

The medical records of patients with an ocular condition that could contribute to difficult or unreliable retinoscopy who underwent nondilated, noncycloplegic evaluation with the WaveScan WaveFront System were reviewed retrospectively. Results were compared to a standard cycloplegic retinoscopy.

RESULTS

A total of 60 eyes of 31 patients were included. Wavefront sphere, cylinder, and spherical equivalent measurements were strongly correlated with retinoscopy results; however, the wavefront measured more myopia and more cylinder compared to standard retinoscopy.

CONCLUSIONS

Wavefront can be used to augment and enhance cycloplegic streak retinoscopy.

Morphology, topography, and optics of the orthokeratology cornea

The goal of this work was to objectively characterize the external morphology, topography, and optics of the cornea after orthokeratology (ortho-k). A number of 24 patients between the ages of 17 and 30 years (median=24  years) were fitted with Corneal Refractive Therapy® contact lenses to correct myopia between −2.00 and −5.00 diopters (D) (median=−3.41  D). A classification algorithm was applied to conduct an automatic segmentation based on the mean local curvature. As a result, three zones (optical zone, transition zone, and peripheral zone) were delimited. Topographical analysis was provided through global and zonal fit to a general ellipsoid. Ray trace on partially customized eye models provided wave aberrations and retinal image quality. Monozone topographic description of the ortho-k cornea loses accuracy when compared with zonal description. Primary (C40) and secondary (C60) spherical aberration (SA) coefficients for a 5-mm pupil increased 3.68 and 19 times, respectively, after the treatments. The OZ area showed a strong correlation with C40 (r=−0.49, p<0.05) and a very strong correlation with C60 (r=0.78, p<0.01). The OZ, as well as the TZ, areas did not correlate with baseline refraction. The increase in the eye’s positive SA after ortho-k is the major factor responsible for the decreased retinal optical quality of the unaccommodated eye.

Evaluation of the SVOne: A Handheld, Smartphone-Based Autorefractor

Purpose

The SVOne is a portable Hartmann-Shack wavefront aberrometer that can be attached to a smartphone to determine the refractive error of the eye objectively. The aim of the present study was to compare the findings of the SVOne with retinoscopy, subjective refraction, and two commercially available autorefractors (Topcon KR-1W and Righton Retinomax-3).

Methods

Refractive error was assessed both with and without cycloplegia in 50 visually normal, young adults using the five techniques described above. Further, to assess repeatability of the instruments, the entire procedure was repeated in a subgroup of 10 subjects. All data were analyzed in terms of power vectors (M, J₀, and J₄₅).

Results

No significant difference was observed between the mean values of M (spherical equivalent) for the different techniques. However, a significantly higher mean value of precyclopegic J₀ was recorded for the SVOne, which also had the highest limits of agreement for both the J₀ and J₄₅ astigmatic components. Retinoscopy and subjective refraction showed the best repeatability (in terms of M values) for precycloplegic and postcycloplegic measurements, respectively. High and significant linear correlations were observed between the subjective findings and the other four techniques.

Conclusions

The results indicate that the SVOne handheld aberrometer provides measurements of refractive error in normal, young individuals that are not significantly different from other subjective and objective procedures. This instrument is valuable for vision screenings, as well as examinations taking place outside the clinical office. It may also serve as an adjunct in the standard optometric examination.

Retinal Image Simulation of Subjective Refraction Techniques

Refraction techniques make it possible to determine the most appropriate sphero-cylindrical lens prescription to achieve the best possible visual quality. Among these techniques, subjective refraction (i.e., patient's response-guided refraction) is the most commonly used approach. In this context, this paper's main goal is to present a simulation software that implements in a virtual manner various subjective-refraction techniques--including Jackson's Cross-Cylinder test (JCC)--relying all on the observation of computer-generated retinal images. This software has also been used to evaluate visual quality when the JCC test is performed in multifocal-contact-lens wearers. The results reveal this software's usefulness to simulate the retinal image quality that a particular visual compensation provides. Moreover, it can help to gain a deeper insight and to improve existing refraction techniques and it can be used for simulated training.

Modelling the effects of secondary spherical aberration on refractive error, image quality and depth of focus

PURPOSE

To examine the role of Zernike secondary spherical aberration and its component terms on refraction, image quality and depth of focus.

METHODS

Computational methods were used to define wavefronts with controlled levels of r(6) , r(4) and r(2) terms, and image quality associated with these terms for a range of target vergences. Target vergences that generated maximum image quality were used as an objective measures of refractive error.

RESULTS

Unlike primary Zernike spherical aberration, which generates peak image quality with a near paraxial focus, in the absence of other higher order aberrations, peak image quality with secondary spherical aberration is achieved with a near marginal focus. When alone, positive primary and secondary spherical aberration induce small hyperopic shifts in refraction, but in the presence of other higher order aberrations, secondary spherical aberration can induce significant myopic shifts in refractive error, as predicted by the combined lower order r(4) & r(2) component of Z60. The predicted expansion in depth of focus associated with increased primary or secondary spherical aberration is mostly absent if a strict image quality criterion is applied. The expansion of depth of focus observed with a low image quality criterion when opposite sign Z40 and Z60 are combined is primarily due to the elevated r(4) term.

CONCLUSIONS

Secondary Zernike spherical aberration can have a significant impact on refractive error, image quality and depth of focus, but mostly due to the lower order components within this polynomial. Our analysis shows that the r(6) term that defines secondary spherical aberration actually narrows rather than expands depth of focus, when in the presence of the r(4) term within Z60. Therefore, a multifocal lens generated with exclusively primary spherical aberration is likely to be more effective than one that includes opposite sign of primary and secondary spherical aberration.

Cycloplegic autorefraction versus subjective refraction: the Tehran Eye Study

AIM

To compare cycloplegic autorefraction with non-cycloplegic subjective refraction across all age and refractive error groups.

METHODS

In a cross-sectional study with random stratified cluster sampling, 160 clusters were chosen from various districts proportionate to the population of each district in Tehran. Following retinoscopy and autorefraction with the 0.25 D bracketing (Topcon KR-8000, Topcon, Tokyo, Japan), all participants had a subjective refraction. Then all participants underwent cycloplegic autorefraction.

RESULTS

The final analysis was performed on 3482 participants with a mean age of 31.7 years (range 5-92 years). Based on cycloplegic and subjective refraction, mean spherical equivalent (SE) was +0.31±1.80 and -0.32±1.61 D, respectively (p<0.001). The 95% limits of agreement (LoA) between these two types of refraction were from -0.40 to 1.70 D. The largest difference between these two types of refraction was seen in the age group of 5-10 years (1.11±0.60 D), and the smallest difference was in the age group of >70 years (0.34±0.45 D). The 95% LoA was -0.52 to 0.89 D in patients with myopia and -0.12 to 2.04 D in patients with hyperopia. We found that female gender (coefficients=0.048), older age (coefficients=-0.247), higher education (coefficients=-0.043) and cycloplegic SE (coefficients=-0.472) significantly correlated with lower intermethod differences.

CONCLUSIONS

The cycloplegic refraction is more sensitive than the subjective one to measure refractive error at all age groups especially in children and young adults. The cyclorefraction technique is highly recommended to exactly measure the refractive error in momentous conditions such as refractive surgery, epidemiological researches and amblyopia therapy, especially in hypermetropic eyes and paediatric cases.

Polychromatic refractive error from monochromatic wavefront aberrometry

PURPOSE

To determine if measurement of monochromatic wavefront aberrations in near-infrared light can accurately and precisely predict subjective refractive error for polychromatic light. Our approach requires knowledge of the monochromatic wavelength-in-focus (WiF) when polychromatic light is well focused, for which new empirical measurements are reported.

METHODS

With accommodation paralyzed, subjective refractive error was measured as a function of wavelength using a Badal optometer by optimally focusing a letter chart illuminated with monochromatic or white light (color temperature, 4575 K). Wavelength-in-focus was determined by interpolation as that wavelength for which monochromatic refractive error matches white light refractive error. The population-based mean value of WiF, used in conjunction with the Indiana Eye model of chromatic aberration, corrected for monochromatic (842 nm) estimates of refractive error obtained from wavefront aberration measurements, predicts the absolute refractive error of individual eye for polychromatic light for comparison with empirical measurements.

RESULTS

Average WiF for eight subjects was 569 nm (SE = 3.6 nm) for a 3-mm pupil and 575 nm (SE = 3.0 nm) for an 8-mm pupil. For small (3 mm) pupils, the mean (±SD) error in predicting refractive error for white light was 0.20 (±0.05) diopters (D) (range, +0.70 to -0.46 D), and for large (>8 mm) pupils, the mean (±SD) prediction error was 0.004 (±0.12) D (range, +0.56 to -0.52 D). The population mean of prediction errors was statistically not different from zero for large pupils but was slightly hyperopic for small pupils.

CONCLUSIONS

Subjective refractive error for white light can be accurately and precisely predicted objectively from monochromatic wavefront aberrations obtained for near-infrared light, but intersubject variability limits accuracy for individual subjects.

First demonstration of ocular refractive change using blue-IRIS in live cats

PURPOSE

To determine the efficacy of intratissue refractive index shaping (IRIS) using 400-nm femtosecond laser pulses (blue light) for writing refractive structures directly into live cat corneas in vivo, and to assess the longevity of these structures in the eyes of living cats.

METHODS

Four eyes from two adult cats underwent Blue-IRIS. Light at 400 nm with 100-femtosecond (fs) pulses were tightly focused into the corneal stroma of each eye at an 80-MHz repetition rate. These pulses locally increased the refractive index of the corneal stroma via an endogenous, two-photon absorption process and were used to inscribe three-layered, gradient index patterns into the cat corneas. The optical effects of the patterns were then tracked using optical coherence tomography (OCT) and Shack-Hartmann wavefront sensing.

RESULTS

Blue-IRIS patterns locally changed ocular cylinder by -1.4 ± 0.3 diopters (D), defocus by -2.0 ± 0.5 D, and higher-order root mean square (HORMS) by 0.31 ± 0.04 μm at 1 month post-IRIS, without significant changes in corneal thickness or curvature. Refractive changes were maintained for the duration they were tracked, 12 months post-IRIS in one eye, and just more than 3 months in the remaining three eyes.

CONCLUSIONS

Blue-IRIS can be used to inscribe refractive structures into live cat cornea in vivo that are stable for at least 12 months, and are not associated with significant alterations in corneal thicknesses or radii of curvature. This result is a critical step toward establishing Blue-IRIS as a promising technique for noninvasive vision correction.

Factors accounting for the 4-year change in acuity in patients between 50 and 80 years

PURPOSE

It is well known that acuity slowly decreases in the later decades of life. We wish to determine the extent by which 4-year longitudinal acuity changes can be accounted for by changes in optical quality, or combination of optical quality metrics and of age between 50 and 80 years.

METHODS

High-contrast logMAR acuity, 35 image quality metrics, 4 intraocular scatter metrics, and 4 Lens Opacification Classification System III metrics and entry age were measured on one eye of each of the 148 subjects. Acuity change between baseline and the last visit was regressed against change in each metric for all eyes and a faster changing subset of 50 eyes with a gain or loss of four or more letters.

RESULTS

Average change across 148 subjects was a 1.6 ± 4 letter loss (t148 = 4.31, p < 0.001) and loss for the faster changing subset was 3.4 ± 6.1 letters (t50 = 2.73, p = 0.008). The multiple-regression model for faster changing eyes included change in point spread function entropy, posterior subcapsular cataract, and trefoil and baseline age (sequential r adjusted values of 0.19, 0.27, 0.32, and 0.34, respectively; p = 1.48 × 10 for the full four-factor model). The same variables entered the multiple-regression model for the full 148 data set where most of the acuity measurements were within test-retest error and accounted for less of the variance (r adjusted = 0.15, p = 2.37 × 10).

CONCLUSIONS

Despite being near noise levels for the measurement of acuity, change in optical quality metrics was the most important factor in eyes that lost or gained four or more letters of acuity. These findings should be generalizable given that our 4-year acuity change is essentially identical to other studies and indicate that these optical quality markers can be used to help identify those on a faster track to an acuity change.

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.

Impact of primary spherical aberration, spatial frequency and Stiles Crawford apodization on wavefront determined refractive error: a computational study

PURPOSE

We tested the hypothesis that pupil apodization is the basis for central pupil bias of spherical refractions in eyes with spherical aberration.

METHODS

We employed Fourier computational optics in which we vary spherical aberration levels, pupil size, and pupil apodization (Stiles Crawford Effect) within the pupil function, from which point spread functions and optical transfer functions were computed. Through-focus analysis determined the refractive correction that optimized retinal image quality.

RESULTS

For a large pupil (7 mm), as spherical aberration levels increase, refractions that optimize the visual Strehl ratio mirror refractions that maximize high spatial frequency modulation in the image and both focus a near paraxial region of the pupil. These refractions are not affected by Stiles Crawford Effect apodization. Refractions that optimize low spatial frequency modulation come close to minimizing wavefront RMS, and vary with level of spherical aberration and Stiles Crawford Effect. In the presence of significant levels of spherical aberration (e.g. C(4)(0) = 0.4 μm, 7 mm pupil), low spatial frequency refractions can induce -0.7 D myopic shift compared to high SF refraction, and refractions that maximize image contrast of a three cycle per degree square-wave grating can cause -0.75 D myopic drift relative to refractions that maximize image sharpness.

DISCUSSION

Because of small depth of focus associated with high spatial frequency stimuli, the large change in dioptric power across the pupil caused by spherical aberration limits the effective aperture contributing to the image of high spatial frequencies. Thus, when imaging high spatial frequencies, spherical aberration effectively induces an annular aperture defining that portion of the pupil contributing to a well-focused image. As spherical focus is manipulated during the refraction procedure, the dimensions of the annular aperture change. Image quality is maximized when the inner radius of the induced annulus falls to zero, thus defining a circular near paraxial region of the pupil that determines refraction outcome.

Age-related changes in accommodation measured with a double-pass system

PURPOSE

To measure the accommodative response in a wide age range population using the retinal image quality assessments provided by a double-pass system.

METHODS

The accommodative response was measured using a custom-built double-pass setup in 84 patients from 15 to 55 years of age. Patients were classified in four groups (A: 15-25 year old; B: 26-35; C: 36-45; D: 46-55). Accommodation was stimulated from 0 to 5 dioptres (D) with the push up method using an open field fixation test. The total accommodative response in the stimulated range, the accommodative stimulus-response curve, the slope and the progression of optical quality with accommodation were measured.

RESULTS

The total accommodation obtained in groups A and B was high, with a mean value of 4 D or higher, whereas values in older individuals were significantly lower. The accommodative stimulus-response curve and the slope were also high with a sudden decrease in patients over 35 years of age. The optical quality of the eye during accommodation did not change significantly.

CONCLUSIONS

Participants aged 15-35 years showed a good accommodative response. Thereafter, a significant decrease of the response in the total accommodation, stimulus response curve and slope was observed. The younger groups showed a larger accommodative response than previously published.