Kingston, Amanda C.*; Cox, Ian G.†
The unique ocular aberrations and biometry of an individual’s eye play a large role in defining its retinal image quality.1–5 Large strides have been made in ocular measurement systems that are enabling the optical industry to create newer and better ways to predict an individual eye’s subjective image quality. The ultimate goal is to find a single-value metric that is highly correlated with visual quality over a broad range of aberrations and object distances.6 With a suitable single-value metric, a person’s aberrations could be measured and the most appropriate corrective lens selected using these individual modeled results. This could significantly improve the overall visual outcomes of individuals as well as the general efficiency of clinical studies through optimization of the design process.
Computer eye models have been utilized for decades to represent properties of the human eye in terms of ocular aberrations, corneal curvature, anterior chamber depth (ACD), and crystalline lens characteristics.7–10 These eye models are typically based on average anatomic data and rely on certain simplifications such as spherical lens surfaces or a crystalline lens with a single index of refraction.11 Also, current eye models only take into account rotationally symmetric aberrations such as spherical aberration and utilize average population values which are known to vary by age as well as have high individual variation.11 There are only a few models which also incorporate the role of accommodation, and they assume that paraxial best focus is maintained at the retinal plane while a person accommodates.12–15 Given the diversity in people’s accommodative amplitude, depth of focus, and change in aberrations and pupil diameter as a function of object distance, the current models fail to predict the true accommodative response. Individually modeling eyes allows one to predict what the image quality would be for the specific person. This not only helps to understand how a given diverse population would benefit from a certain lens design but it also allows for a better understanding of which aberrations most influence through-focus visual acuity and would be most beneficially corrected.
Equally important to creating individual eye models is to have a metric that can determine predicted retinal image quality. A number of optical metrics have been presented previously to develop a relationship between wavefront aberrations and predicted subjective image quality.16–22 These metrics have primarily been used to correlate with best subjective refraction or clinical acuity at distance.23–25 Very few studies have looked at the correlation of clinical measurements, such as visual acuity, with predicted image quality at multiple object distances and over a large range of natural aberrations and pupil diameters.20,26 Despite the proliferation of wavefront sensors to fully characterize the optical quality of individual eyes at distance and as a function of accommodation, there is not yet a single-value metric that is highly correlated with an individual’s through-focus clinical acuity. There is still uncertainty about how aberrations interact with one another as well as their impact on through-focus retinal image quality.27–29
In general, metrics of optical quality can be divided into two standard approaches: pupil plane metrics and image plane metrics. Pupil plane metrics are defined by the quality of the shape of the wave aberrations in the pupil plane, whereas image plane metrics utilize the point spread function (PFS) or optical transfer function. Work done by Marsack et al in 2004 looked at the change in measured visual acuity and its correlation with 31 image quality metrics proposed in 2004 by Thibos et al.22,24 It was found that visual Strehl optical transfer function was highly correlated with the amount of letters lost in visual acuity at distance (R2 = 0.81). Cheng et al (2004) looked at the same 31 image quality metrics and showed only 3 gave an R2 value ≥0.70 (PFSt, VSMTF, and NS) when looking at the through-focus correlation in the presence of higher-order monochromatic aberrations.25 Both studies used computationally aberrated visual acuity charts and artificial pupil diameters when assessing clinical acuity.
The study presented by Legras et al, which also dealt with the prediction of through-focus visual acuity, showed a reasonable correlation with metrics based on rMTF (R2 between 0.57 and 0.67), whereas optical transfer function-based metrics were less predictive of changes in through-focus acuity (R2 ≤ 0.42).26 A more recent study completed by Ravikumar et al found high correlation to distance visual acuity when taking the log of image quality metrics presented by Thibos et al; specifically logNS, logVSX, logVSMTF, and logPFSt gave R2 ≥0.86.19,20,24
These previous studies show good correlation to distance visual acuity but still present a need for a through-focus image quality metric that takes into account the eye’s natural aberrations, pupil diameter, and residual accommodative amplitude. The goal of this work was to develop a new image quality metric that is highly correlated with through-focus visual acuity and can be easily related to clinical measurements. The image quality metric, in conjunction with individual computer eye models, will provide a more efficient and predictive tool for determining through-focus performance of ophthalmic lens designs.
Clinical Study Design for Baseline Eye Models
The study followed the tenets of the Declaration of Helsinki and was approved by the Southwest Independent Institutional Review Board (Fort Worth, TX). Each subject signed an informed consent form following an explicit description of the study.
In order to create individual eye models and develop a retinal image quality metric, 90 subjects (180 eyes; age range, 24–63 years of age) were enrolled in a non-randomized, bilateral, unmasked evaluation of ocular aberrations, pupil diameter, visual acuity, and accommodative response. For the purpose of this paper, a subset of 64 eyes was used to correlate predicted logarithm of the minimum angle of resolution (logMAR) with measured through-focus visual acuity. These subjects were identified as mature presbyopes based on their measured through-focus visual acuity results (>0.30 logMAR at 2.5 D [40 cm] through 4.0 D [25 cm]) and were chosen because one of the most impactful applications of this design process is around multifocal correction for presbyopic eyes.
To be eligible for entry into the study, all subjects needed to have no greater than 0.75 D of refractive cylinder, a physiologically normal anterior segment, no active ocular disease, and not be using any topical ocular medications. The cylinder requirement was imposed in order to ensure accurate measurement of through-focus wavefront aberrations using the Complete Ophthalmic Analysis System (COAS HD VR; AMO WaveFront Sciences, Albuquerque, NM).30 A best distance spherical equivalent refraction was performed using trial spectacle lenses in a trial frame. To minimize the reflections from the trial lens, subjects were instructed to tip their heads slightly.20 Head tilt with a cylindrical lens would induce unwanted off-axis aberrations; therefore, only subjects with little to no refractive cylinder were included. The anterior and posterior corneal radius, corneal aberrations, and corneal thickness of each eye were measured using the Bausch + Lomb Orbscan IIz corneal topographer (Rochester, NY). ACD and axial length were measured using the Carl Zeiss Meditec IOL Master (Oberkochen, Germany).
High-contrast visual acuity was assessed under conditions of typical room illumination (360 lumens) at 6 m, 2 m, 1 m, 67 cm, 50 cm, 40 cm, 33 cm, 28 cm, and 25 cm using an ETDRS eye chart designed for 40 cm presentation (Precision Vision, LaSalle, IL). All visual acuity results were corrected to account for the non-standard test distances used in this study. While the subject fixated on the lowest readable line, three separate measurements of total ocular aberrations and pupil diameter were performed using the COAS HD VR aberrometer for each object distance.
The COAS is an open-field-of-view Shack-Hartmann wavefront sensor that provides a real-time display of the pupil image. The COAS utilizes an 840 nm wavelength super-luminescent diode as the light source and an array of 33 × 44 square lenslets with each lenslet having a width of 144 μm. The wavefront data generated from the lenslet array images was output as a set of OSA format Zernike coefficients (up to sixth order) that quantify the type and magnitude of aberrations present.31 All measurements were performed with natural pupils under a room illumination of 360 lumens. Each eye was tested monocularly, with the fellow eye occluded.
Designing Individual Computer Eye Models
Commercially available optical design software (Zemax) was used to develop the individual computer eye models. The anterior and posterior corneal radius and corneal thickness were set to the measured values from the Orbscan IIz corneal topographer. Each corneal topography elevation map was fit with Zernike coefficients and imported onto the anterior and posterior corneal surfaces in Zemax. The ACD and axial length were assigned the biometry values measured on the IOL Master, and all indices of refraction were defined by the baseline Arizona eye model (Table 1).32
In order to match the appropriate measured total ocular aberrations for a particular eye for each testing distance, a Zernike surface was overlaid on the crystalline lens within the model, the pupil diameter was matched to the measured value, and the eye was optimized accordingly. The pupil was centered relative to the optical axis and located in front of the crystalline lens anterior surface. During the optimization process, the Zernike surface was allowed to vary until the total ocular aberrations of the Zemax file were equal to the measured values from the COAS HD VR aberrometer. The addition of the Zernike surface circumvents the fact that technology does not currently exist to measure the wavefront aberration contribution of the crystalline lens directly. Use of a Zernike surface on the crystalline lens anterior surface allowed the indirect deduction of the lenticular contribution to the total aberrations of the eye.33 This process was repeated for all nine measured object distances resulting in an individual eye model representing each eye’s wavefront aberration and pupil size through the full measured focus range.
Predicted logMAR Image Quality Metric
The predicted logMAR image quality metric consists of a template created using a perfect letter (binary, 1’s and 0’s) of the same magnification as each eye’s optical system. Then, rays are geometrically traced through the individual eye in Zemax and the corresponding convolved evaluation letter is compared with the template using cross-correlation. A score is given from 0 to 1000 on how closely the evaluation letter matches the perfect letter (1000 being an exact match).21,34,35 Fig. 1 shows an example of a perfect E and geometrically convolved evaluation E.
To account for any contrast changes in an image and to better predict the image quality that a person would perceive at the retina, the cross-correlation score is multiplied by the ratio of the contrast between the evaluation and perfect image. This is necessary since cross-correlation takes into account resolution differences between the template and convolved image, but is insensitive to contrast changes. In practice, calculation of this metric for letters of sizes representing optotype sizes on a logMAR acuity chart (1.0 logMAR to −0.30 logMAR in 0.10 logMAR steps) is completed, and then by comparing the metric score to a predetermined cutoff score, the just discernable image size for each individual eye model at each of the calculated object distances is determined. This modeling process emulates the clinical test of a patient reading down the lines of a logMAR chart to the lowest, resolvable line of acuity.21,35
Clinical Study Design for Validation of Model Predictability
The study followed the tenets of the Declaration of Helsinki and was approved by the Southwest Independent Institutional Review Board (Fort Worth, TX). Each subject signed an informed consent form following an explicit description of the study.
In order to validate the design process using individual eye models in conjunction with the predicted logMAR image quality metric, 24 subjects were enrolled in a randomized, single-eye, single-masked, repeated-measures insertion study. To be eligible for entry into the study, all subjects needed to have at least +1.50 D spectacle addition (at 40 cm), no greater than 2.50 D refractive cylinder, a physiologically normal anterior segment, no active ocular disease, and not be using any topical ocular medications.
To minimize fatigue in subjects, a total of seven object distances were used (6 m, 2 m, 1 m, 67 cm, 50 cm, 40 cm, and 25 cm) to measure monocular high-contrast logMAR acuities. All test lenses had a back vertex power of −3.00 D. Subjects were over-refracted with the best spherocylinderical correction for distance (6 m chart position) prior to acuity measurement. Normalized logMAR was calculated for each contact lens relative to the subject’s best distance spectacle baseline. This gives a value of how visual acuity changed compared to distance correction but with no add power. The goal of the validation study was to determine if the through-focus predicted logMAR from the 64 mature presbyopic eye models could predict visual performance of each contact lens when tested on a typical presbyopic clinical population.
Baseline Predicted logMAR Versus Clinical Acuity
Predicted logMAR was calculated for each of the 64 mature presbyopic eyes at all nine object distances, corresponding with the actual clinical measures. These calculated values were compared to the measured visual acuity scores for each subject. Regression of errors as well as residual differences between predicted logMAR and measured acuity were used to determine which model gave the highest correlation. “Cutoff” scores from 200 to 500 were analyzed to determine how correlation was impacted by the chosen threshold score. Empirical analysis demonstrated that using a quadratic weighting factor along with a “cutoff” score of 400 (range of possible scores is 0 to 1000) to find the individual model’s just discernable letter size gave the highest correlation to measured clinical through-focus visual acuity. The quadratic relationship between clinical acuity and predicted logMAR stems from the dependence of the visual system on spatial frequency components within the clinical acuity assessment. As shown previously, there is a scale invariance in visual acuity measurements with standard broadband optotypes that gives a non-linear relationship between spatial frequency and measured acuity.36
Fig. 2 shows the relationship between predicted logMAR from the Zemax eye models and the actual measured visual acuity from the clinical study. The solid black line represents the 1:1 trend line, whereas the dashed line represents the best-fit trend line for this data set. Linear regression analysis demonstrated a correlation of R2 = 0.85 between through-focus clinical visual acuity and predicted logMAR for the combined 64-eye population.
In order to better visualize the two datasets as a function of object distance, the 64 eyes were averaged to determine the mean through-focus logMAR for clinically measured and predicted populations. Fig. 3 shows the average results along with the standard deviation at each object distance. Because this is a mature presbyopic population, there is an obvious loss of visual acuity as a function of object distance.
Validation of the Model’s Predictive Capability
To be a useful design tool, a computer-based model needs to be able to predict the optical performance of new designs when tested on a clinical population. Validation of the modeling process and image quality metric presented here was achieved by using the 64 mature presbyopic computer models to predict the average clinical logMAR acuity performance of five different multifocal contact lens designs. A description of the optical designs is presented in Table 2 and the optical power profile for each design (lens only) is shown in Fig. 4, as calculated from Zemax.
During the modeling process in Zemax, a spectacle trial lens was added to the baseline lens model to replicate the over-refraction process for each contact lens design on each model. The spectacle trial lens was placed 14 mm away from the apex of the cornea to represent the average vertex distance of a spectacle correction. Defocus was minimized and the closest 0.25 D lens (in the plus power direction) was used to peak image quality for an object at distance. The modeling process described previously was applied to determine the just discernable letter size at each of the seven object distances that were utilized in the validation clinical with each multifocal contact lens in place.
Predicted logMAR with the contact lens on the eye was normalized to the predicted baseline logMAR value, which represents the individual eye’s acuity with a best-corrected distance spectacle correction. This was done to match the primary outcome measure of normalized clinical acuity from the validation study. Mean normalized clinically measured logMAR visual acuities were compared with the mean normalized predicted logMAR acuity results from the 64-eye database. Fig. 5 shows the correlation in through-focus acuity between the mean clinical and predicted acuity measures for each of the five lens designs. The solid black line represents the best-fit trend line for each data set. The Zemax models with predicted logMAR had high correlation with mean through-focus visual acuity from the clinic (R2 ≥ 0.90 for all lenses).
Computer-based predictive optical modeling is a powerful tool when designing relatively complex optical surfaces, such as multifocal contact lenses. However, to be useful and relevant, these models must be predictive using metrics that are easily compared to clinical measures that are typically used to define the optical performance of a multifocal contact lens in situ, such as high-contrast visual acuity. Previously presented computer-based eye models have used retinal image quality metrics that are derived from classical optical design measures such as MTF, Strehl ratio, or point spread functions.16–22 While these metrics are suitable for providing relative comparisons between contact lens designs (typically on a scale from 0 to 1), the lack of direct correlation to traditional clinical metrics means that the magnitude of differences in performance cannot be easily estimated in terms of clinical impact (i.e., logMAR acuity). There are currently very few image quality metrics that can be easily translated to clinical outcome measures.21,34
The model outlined in this study uses an outcome metric based on logMAR acuity, a measurement familiar to all clinicians and contact lens designers, and one where the relative impact of changes caused by a lens design can be easily interpreted. Moreover, the analysis is performed using a number of Zemax-based eye models, each designed to replicate the biometry of an individual human eye, providing mean results from a multitude of individual analyses, rather than a single analysis of a model built to represent the mean biometry of a population. The modeling process described here showed high correlation with through-focus visual acuity for the predicted logMAR baseline models (R2 = 0.85). Accounting for patient’s natural aberrations, pupil diameter changes, and residual accommodation appears to improve the correlation with clinical visual acuity. The addition of complex optical elements, such as multifocal contact lens designs, to the baseline individual computer eye models and the use of normalized predicted logMAR to determine the performance of the lens designs clinically maintained equally high correlations (R2 ≥ 0.90 was found between the predicted computer results and mean clinical results with five multifocal contact lens designs).
The benefits of a highly predictive model for an optical designer are numerous. Traditionally, theoretical modeling and metrology assessment results cannot easily transfer to those found clinically because of the individual differences in subject pupil size, accommodative response, and higher-order wavefront aberrations. Hence, designers are limited to an empirical approach to designing new multifocal lenses, making actual lens prototypes and testing them clinically. Time and cost invariably limit the number of design options and iterations that can be studied, resulting in a less-than-optimum final design. Incorporation of individual subject variations in biometry in concert with an output metric that has a high predictive correlation with through-focus clinical measurements frees the designer to test significantly more design options prior to any clinical testing, significantly expanding the design space that is investigated and increasing the probability that the optimal design solution will be tested and incorporated into the final lens design. Just as importantly, the final design will have been optimized for clinical robustness, meaning that the design will provide the best performance across a wide range of eyes, rather than being successful only on those eyes whose biometry closely matches those of the population mean.
The design approach described here is not limited to contact lens design; it can easily be adapted to intraocular lens designs, and the benefits may even be greater because the invasive nature of the clinical procedure used for implantation of the surgical lens in a clinical study tends to lead to a conservative design philosophy when designing multifocal optics. Although this study focuses on lens designs for mature presbyopic eyes, the modeling methodology is the same for both early presbyopic and non-presbyopic populations, as any impact of accommodation for intermediate and near targets on pupil size, defocus, astigmatism, and higher-order wavefront aberrations are accounted for from the base clinical data adapted to the individual eye models. This expands the many design opportunities that would benefit from this improved retinal image quality metric and optical design process.
Amanda C. Kingston
Bausch and Lomb
1400 N. Goodman Street
Rochester, NY 14609
Received: February 18, 2013; accepted June 23, 2013.
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