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Article  |   September 2012
Change in visual acuity is highly correlated with change in six image quality metrics independent of wavefront error and/or pupil diameter
Author Affiliations
  • Ayeswarya Ravikumar
    Visual Optics Institute, College of Optometry, University of Houston, Houston, TX, USA
    ayeswarya22@gmail.com
  • Edwin J. Sarver
    Sarver and Associates, Carbondale, IL, USA
    ejsarver@aol.com
  • Raymond A. Applegate
    Visual Optics Institute, College of Optometry, University of Houston, Houston, TX, USA
    RApplegate@optometry.uh.edu
Journal of Vision September 2012, Vol.12, 11. doi:10.1167/12.10.11
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      Ayeswarya Ravikumar, Edwin J. Sarver, Raymond A. Applegate; Change in visual acuity is highly correlated with change in six image quality metrics independent of wavefront error and/or pupil diameter. Journal of Vision 2012;12(10):11. doi: 10.1167/12.10.11.

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Abstract
Abstract
Abstract:

Abstract  It is well known that the wavefront error (WFE) of the eye varies from individual to individual with pupil diameter (PD) and age. Numerous studies have been proposed evaluating the relationship between visual acuity and WFE, but all these studies were performed with either a fixed or natural PD. It is still not clear if metrics of image quality correlate well with visual acuity independent of PD. Here we investigate the correlation between the change in visual acuity and the change in 30 image quality metrics for a range of optical quality typically established in normal eyes that varies both with age and PD. Visual acuity was recorded for 4 normal subjects using simulated blurred logMAR acuity charts generated from the point spread functions of different scaled WFEs for 6 different PDs (2–7 mm in 1 mm steps). Six image quality metrics (log neural sharpness, log visual Strehl [spatial domain], log visual Strehl [MTF method], log pupil fraction [tessellated], log pupil fraction [concentric area], and log root mean square of WFE slope) accounted for over 80% of variance in change in acuity across all WFEs and all PDs. Multiple regression analysis did not significantly increase the R2. Simple metrics derived from WFE could potentially act as an objective surrogate to visual acuity without the need for complex models.

Introduction
Before the advent of viable ocular wavefront sensing and adaptive optics, the relationship between wavefront error (WFE) and acuity was studied by manipulating defocus or astigmatism in terms of equivalent diopters (Atchison, Smith, & Efron, 1979; Bedell, Patel, & Chung, 1999; Herse & Bedell, 1989; Prince & Fry, 1957; Smith, 1991; Smith, Jacobs, & Chan, 1989; Swaine, 1925; Thorn & Schwartz, 1990; Tucker & Charman, 1975). Only a few of these early studies included the important role of pupil diameter (PD) as an experimental parameter (Atchison et al., 1979; Smith, 1991; Smith et al., 1989; Swaine, 1925; Tucker & Charman, 1975). Swaine (1925), albeit less formally than Smith (1991), explained the correlation between acuity and defocus in terms of the fundamental principles of geometric optics using blur circle diameters. Smith (1991) defined the angular blur disc diameter (X) in terms of PD in meters and defocus in diopters. In Smith's formulation the blur circle diameter was calculated as detailed in Equation 1: where X = angular blur disc diameter (in radians), D = diameter of entrace pupil (in meters), and ΔL = defocus (in diopters). Smith and his colleagues (Smith, 1991; Smith et al., 1989) reported a linear relationship between acuity and defocus that holds over a wide range of defocus errors (0–10 D) accounting for 98% of the variance in acuity. The relationship began to fail for low dioptric values, and the authors suggested this may be due to the increasing influence of the high order aberrations of their subjects. In these studies all 5 subjects were young (19–23 yrs old) with refractive errors for the 1.9 m test distance of 0–0.75 D with best-corrected acuities of 6/4.5 (20/15) or better. Higher order aberrations of the subjects were not reported. 
After the advent of viable time efficient ocular wavefront sensors (Liang, Grimm, Goelz, & Bille, 1994) several studies revealed that the WFE of the eye varies considerably from individual to individual (Castejon-Mochon, Lopez-Gil, Benito, & Artal, 2002; Porter, Guirao, Cox, & Williams, 2001; Salmon & van de Pol, 2006; Thibos, Hong, Bradley, & Cheng, 2002; Wang & Koch, 2003), as a function of PD (Campbell & Gubisch, 1966; Charman, Jennings, & Whitefoot, 1978; Wang, Zhao, Jin, Niu, & Zuo, 2003) and as a function of age (Applegate, Donnelly, Marsack, Koenig, & Pesudovs, 2007; Artal, Berrio, Guirao, & Piers, 2002; Artal, Ferro, Miranda, & Navarro, 1993; Guirao et al., 1999; Guirao, Redondo, & Artal, 2000; McLellan, Marcos, & Burns, 2001). Other studies revealed the impact of an individual or a combination of monochromatic aberration on visual acuity (Applegate, Ballentine, Gross, Sarver, & Sarver, 2003; Applegate, Sarver, & Khemsara, 2002; McLellan, Prieto, Marcos, & Burns, 2006; Rocha, Vabre, Harms, Chateau, & Krueger, 2007) and on subjective image quality (Chen, Singer, Guirao, Porter, & Williams, 2005). These studies demonstrated that all aberrations are not equal in their impact on visual acuity and/or subjective image quality as defined by root mean squared (RMS) WFE (RMS WFE), and individual aberrations increase or decrease visual performance for any given level of RMS WFE. The earlier of these studies prompted a search for optical quality metrics that were more highly correlated with acuity than RMS WFE, which led to the development of numerous different metrics based on measured WFE (Thibos, Hong, Bradley, & Applegate, 2004; Williams, 2003; Williams, Applegate, & Thibos, 2004). 
Over the last decade there have been several studies exploring the use of metrics of optical quality calculated from WFE for several different purposes. These include the prediction of a sphero-cylindrical refraction (Guirao & Williams, 2003; Martin, Vasudevan, Himebaugh, Bradley, & Thibos, 2011; Navarro, 2010; Thibos et al., 2004); the correlation of visual acuity to metrics of optical quality (Cheng, Bradley, Ravikumar, & Thibos, 2010; Cheng, Bradley, & Thibos, 2004; Legras & Rouger, 2008; Marsack, Thibos, & Applegate, 2004); predicting visual acuity via modeling (Dalimier & Dainty, 2008; Dalimier, Pailos, Rivera, & Navarro, 2009; Nestares, Navarro, & Antona, 2003; Rouger, Benard, & Legras, 2010; Watson & Ahumada, 2008); estimating subjective image quality (Chen et al., 2005); predicting subjective quality of vision after refractive surgeries (Buhren et al., 2009); and predicting accommodative responses/depth of focus from wave aberration (Buehren & Collins, 2006; Collins, Buehren, & Iskander, 2006; Tarrant, Roorda, & Wildsoet, 2010; Yi, Iskander, & Collins, 2010). More recently studies have been conducted to evaluate the relationship between the visual acuity and metrics in highly aberrated eyes (Buhren et al., 2009; Shi, Wei, Ravikumar, & Applegate, 2011; Yoon, 2008). 
It is well known that optical quality varies with PD (Artal & Navarro, 1994; Campbell & Gregory, 1960; Campbell & Gubisch, 1966; Charman et al., 1978; Walsh & Charman, 1988) and that PD varies with ambient light level and age (Birren, Casperson, & Botwinick, 1950; Winn, Whitaker, Elliott, & Phillips, 1994). Studies to date using letter acuity as the outcome measure have typically used individual or a combination of aberrations (Cheng et al., 2010; Cheng et al., 2004; Legras & Rouger, 2008; Marsack et al., 2004; Rouger et al., 2010; Watson & Ahumada, 2008) or natural aberration structures for a fixed PD (Nestares et al., 2003) and natural PD for young adult eyes, which have a limited range of PD, (Dalimier & Dainty, 2008) and scaled WFEs from normal eyes for a fixed PD (Ravikumar, Applegate, Shi, & Bedell, 2011). 
Here we wish to examine whether the correlation between acuity and single value metrics of optical quality hold over the range of optical quality typically observed in a normal population between the ages of 20 and 80 and pupil diameters 3-7 mm (see Range of optical quality in normal eyes in the Methods section). 
Methods
Protection of human subjects
The study followed the tenets of the Declaration of Helsinki and was approved by the Institutional Review Board of the University of Houston. Each subject signed an informed consent form. 
Subjects
Four healthy, normal subjects (24–27 yrs old) free of systemic and ocular pathology with best corrected distance visual acuity better than 20/20 served as subjects (Table 1). Three out of four subjects were naive to the psychophysical experiments and the design of the experiment. One subject was familiar with the approach from a previous study (Ravikumar et al., 2011). 
Table 1
 
Best refractive correction and the best-corrected logMAR visual acuity of all four subjects.
Table 1
 
Best refractive correction and the best-corrected logMAR visual acuity of all four subjects.
Subject ID Best corrected spectacle correction Best corrected visual acuity (BCVA)
Subject 1 Plano −0.12 logMAR
Subject 2 Plano/–4.5 DC × 170 −0.1 logMAR
Subject 3 −0.50 DS/0.75 DC × 160 −0.1 logMAR
Subject 4 +0.75 DS/–0.25 DC × 175 −0.14 logMAR
Measurement of subject's WFE
For each subject, the eye with better acuity was dilated with 1% cyclopentolate hydrochloride to minimize accommodation. Prior to WFE measurement, the subject was trial frame refracted through a 3 mm artificial pupil for the 3.7 feet testing distance while viewing a logMAR acuity chart. 
The artificial pupil was removed and each subject's WFE was measured 10 times using a Shack-Hartmann wavefront sensor (COAS-HD, AMO Wavefront Science, Albuquerque, NM) while wearing their best 3 mm cycloplegic spectacle correction. To minimize the reflections from the trial frame, the subjects tipped their heads slightly and/or the pantoscopic tilt of the glasses was altered slightly. Each measured WFE was fit with a normalized Zernike expansion (ANSI-28–2004) through the tenth radial order over a 3 mm pupil and averaged coefficient by coefficient. The average of the 10 measurements for each subject was taken as the best estimate of the test eye's WFE and used for the precompensation procedure described below. 
Range of optical quality for normal eyes
To estimate the extent by which pupil size and age can influence optical quality, Figure 1 displays log visual Strehl calculated from the higher order aberrations of 148 eyes from 148 subjects as a function of age and PD from the Applegate et al (2007) study. Figure 1 reveals that for any given PD, optical quality gets worse with age and with increasing PD. For example, the difference in mean log visual Strehl for the average 6 mm eye of persons in their 70s (a 70-yr-old eye rarely physiologically dilates to PD greater than 6 mm) and the average 3 mm pupil of someone in their 20s induces a change in log visual Strehl of approximately −0.9 log units with a range of −1.2 log units. However, this change does not include improvements in image quality that may be achieved wearing a best sphero-cylindrical correction. Performing a similar analysis on the Thibos et al. (2002) 200 eye data set (both eyes of 100 normal young adult subjects in their 20s to early 30s), where WFE was measured with a best-corrected cycloplegic refraction, the mean difference in log visual Strehl between a 3 mm pupil and a 6 mm pupil was −0.4 log units, and the range was −1.8 log units. Given the analysis of these two data sets, we elected to allow the aberration structures to vary −1.8 log units. 
Figure 1
 
logVSX as a function of age and PD for the 148 eye data set reported by Applegate et al. (2007).
Figure 1
 
logVSX as a function of age and PD for the 148 eye data set reported by Applegate et al. (2007).
Selection of the normal WFEs of interest
Three normal WFEs over a 7.5 mm pupil were selected randomly from the best-corrected 100-eye normal WFE data set published by Thibos et al. (2002). The wave aberration maps and the point spread functions of the 3 WFEs are presented in Figure 2
Figure 2
 
Panel A, B, and C display the three wave aberration maps from the Thibos et al (2002) data set used in this study. Panels D, E, and F display their corresponding point spread functions.
Figure 2
 
Panel A, B, and C display the three wave aberration maps from the Thibos et al (2002) data set used in this study. Panels D, E, and F display their corresponding point spread functions.
WFE scaling and calculation of image quality metrics
The three normal WFEs of interest were rescaled to six different PDs ranging from 2–7 mm in 1-mm steps (Schwiegerling, 2002). The Zernike coefficients of each of these 18 WFEs (3 WFEs × 6 PDs) were in turn linearly scaled up and down by multiplying the coefficients of each WFE by some constant to yield seven levels of visual Strehl ratio ranging from 0 (no aberration) to −1.8 log units in steps of approximately −0.3 log units. The WFE for each was in turn used to calculate 30 IQ metrics as previously described (Thibos et al., 2004). 
Generation of precompensated blurred logMAR acuity charts
Using an experimental approach that places the blur resulting from WFE in the target as opposed to the optics (Applegate, Marsack, Ramos, & Sarver, 2003; Applegate & Sarver, 1999; Applegate et al., 2002; Burton & Haig, 1984; Cheng et al., 2010; Cheng et al., 2004; Doshi, Sarver, & Applegate, 2001; Marsack et al., 2004; Sarver & Applegate, 2000), acuity was measured for each subject using computationally blurred random letter configurations of logMAR acuity charts for each of the 126 different WFEs precompensated for the residual WFE of each subject. 
The residual aberration of each subject was precompensated by pre-emphasizing (Burton & Haig, 1984; Cheng et al., 2010) the optical transfer function (OTF) of each scaled WFE with each subject's best-corrected OTF over a 3 mm pupil as defined in Equation 2. where OTF(scaled WFE) = the OTF calculated for each scaled WFE. OTF(3 mm) = the OTF over a 3 mm pupil with best cycloplegic spectacle correction of the viewing subject calculated from the subject's average WFE over a 3 mm pupil. 
Eleven line logMAR acuity charts (0.7 to −0.3 logMAR) of 30% contrast were generated using Visual Optics Laboratory Professional software (version 6.89, Sarver & Associates, Inc., Carbondale, IL). The software uses an equally identifiable Bailey Lovie letter set (Bailey & Lovie, 1976) to generate the letters on each logMAR chart randomly such that no letter is repeated in a given line. The logMAR acuity charts were scaled to be viewed at 3.7 meters feet testing distance. For each of the 126 test conditions (3 WFE × 6 PD × 7 scaled levels of WFE), three unique acuity charts were simulated after precompensating for the aberrations of each subject over 3 mm pupil, yielding 378 unique logMAR chart simulations for each subject. 
Measurement of acuity
The logMAR acuity charts were displayed on a gamma-corrected monochromatic, high resolution LCD monitor (Totoku M253i2, Totoku Electric Co., Ltd., Tokyo, Japan; 1200 × 1600 pixels). Each of the 378 charts (3 WFE × 6 PD × 7 scaled levels of WFE × 3 unique charts) was displayed randomly through a custom Matlab program (The MathWorks, Inc., Natick, MA) using psychtoolbox (Brainard, 1997). Subjects viewed the charts through a 3 mm pupil placed in the back cell of the trial frame along with their best sphero-cylindrical corrections placed in the remaining cells of the trial frame. 
First the entire chart containing 11 lines was displayed. Testing started by requesting the subject to read the lowest line they could read without error. If they missed a letter, the subject was asked to read the line above. Once the subject read a line without error, one line at a time was displayed in the center of the screen with the rest of the screen blank white. We used a strict endpoint criterion where each subject read each chart until they missed five letters. At the point the subject missed the fifth letter there was a 15 s pause with a uniform white screen containing only the last line where the fifth missed letter occurred while the program loaded the next randomly selected 11 line chart. We used a logMAR letter-by-letter scoring, where credit was given for each letter read correctly (0.02 logMAR). This procedure was chosen as it provides optimized test retest reliability (Carkeet, 2001). Subjects were given credit for all letters read correctly up to the fifth missed letter on each chart, and the number of letters read correctly converted to logMAR acuity. 
Normalization of acuity data
To compare data across subjects, the data for each subject was normalized to the subject's mean logMAR acuity as measured on an unaberrated logMAR acuity chart as detailed in Equation 3. where L = logMAR acuity gained or lost, LA = logMAR acuity on an aberrated chart, and LB = average logMAR acuity on an unaberrated precompensated chart. As such, positive changes in acuity values indicate a change to poorer acuity, and negative values indicate a change to better acuity. 
Data analysis
To determine the percentage of the variance in change in acuity that is accounted for by change in image quality, the coefficient of determination (R2) was calculated by linearly regressing the change in logMAR acuity against change in each IQ metric. 
  1.  
    Linear regression analysis: Change in logMAR acuity was regressed against change in each of the 30 retinal image quality metrics for the combined data of all four subjects, three WFEs, and six PDs. The goal was to find metrics with an R2 value greater than 0.80. The image quality metrics with the highest R2value were taken to be the best metrics.
  2.  
    Multiple linear regression: Multiple linear regression was performed to determine if a combination of metrics would significantly increase R2 compared to a single metric regression model.
Results
Linear regression of change in logMAR acuity against change in each of 30 image quality metrics revealed six statistically equivalent image quality metrics accounting for greater than 80% of the variance in change in acuity, regardless of PD and the underlying WFE (Figure 3). Three of the image quality metrics were calculated in the image plane and included neural filters: logNS (Figure 3A), logVSX (Figure 3B), and logVSMTF (Figure 3C), and three others were calculated in the pupil plane: logRMSs (Figure 3D), logPFSt (Figure 3E), and logPFSc (Figure 3F). LogNS, logVSX, and logVSMTF are largely equivalent metrics that employ slightly different calculation strategies. 
Figure 3
 
Panels A through F plot change in acuity as a function of change in six image quality metrics. The central black line represents the best-fitting regression line, red dashed lines represent the 95% CI for the regression, blue lines represent the 95% CI from the regression line for clinically significant change in acuity as defined by Arditi and Cagenello (1993), and the black dotted line represents the 95% CI defined by the data.
Figure 3
 
Panels A through F plot change in acuity as a function of change in six image quality metrics. The central black line represents the best-fitting regression line, red dashed lines represent the 95% CI for the regression, blue lines represent the 95% CI from the regression line for clinically significant change in acuity as defined by Arditi and Cagenello (1993), and the black dotted line represents the 95% CI defined by the data.
Multiple linear regression analysis did not significantly increase the R2value, implying the optical quality metrics are highly correlated to each other, as can be visualized in Figure 4
Figure 4
 
Correlation matrix between each IQ metric.
Figure 4
 
Correlation matrix between each IQ metric.
Table 2 shows for each of the top six metrics, the percentage of change in acuity measurements falling within ±0.14 logMAR of the regression line (95% confidence interval [CI]) as specified by Arditi and Cagenello (1993). The table also shows the percentage of measurements falling within ±0.10 logMAR, which is the average 95% CI from six different studies (Arditi & Cagenello, 1993; Bailey, Bullimore, Raasch, & Taylor, 1991; Bailey & Lovie, 1976; Elliott & Sheridan, 1988; Raasch, Bailey, & Bullimore, 1998; Vanden Bosch & Wall, 1997). 
Table 2
 
Percent of all data for all subjects within the 95% CI for clinical significance (±0.14 logMAR) for test–retest measurement of acuity as defined by Arditi and Cagenello (1993) and the percentage of data within ±0.1 logMAR of the regression line (the average 95% CI of six different studies [Arditi & Cagenello, 1993; Bailey et al., 1991; Bailey & Lovie, 1976; Elliott & Sheridan, 1988; Vanden Bosch & Wall, 1997]).
Table 2
 
Percent of all data for all subjects within the 95% CI for clinical significance (±0.14 logMAR) for test–retest measurement of acuity as defined by Arditi and Cagenello (1993) and the percentage of data within ±0.1 logMAR of the regression line (the average 95% CI of six different studies [Arditi & Cagenello, 1993; Bailey et al., 1991; Bailey & Lovie, 1976; Elliott & Sheridan, 1988; Vanden Bosch & Wall, 1997]).
Metric R2 (%) % of data % of data
within ±0.14 logMAR within ±0.1 logMAR
logNS 90 93.1 80.6
logVSX 87 87.5 73.8
logVSMTF 86 89.4 76.9
logPFSt 86 88.0 73.6
logPFSc 84 90.0 78.9
logRMSs 82 84.5 70.6
Average 88.7 75.7
Discussion
Change in logMAR acuity is highly correlated with change in six different image quality metrics: logNS, logVSX, and logVSMTF (image plane metrics with neural filters; see Figure 3A through C) and logRMSs, logPFSt, and logPFSt (pupil plane metrics without neural filters; Figure 3 D through F) for three different underlying WFEs and six PDs. These 6 metrics provided statistically equivalent correlations and on average accounted for 86% of the variance in the measured change in logMAR acuity. 
For image quality metrics logNS, logVSX, and logVSMTF, the metric value under diffraction limited conditions is 1 (resulting in a log value of 0). If change in acuity varies directly with change in image quality, it would be expected that the intercept of the best fitting linear regressions to pass through zero. However, for these three metrics the intercept of the best-fitting line has a significantly better acuity (p < 0.05). This observation can be explained by the fact that image quality can change small amounts before a change in optical quality of the image (blur) can be detected. Image quality has to change even more before a change in acuity is detected. More specifically, Ravikumar et al. (2011) demonstrated that there are on average six just noticeable differences in blur for every five letter change of logMAR acuity (one line). This “dead zone” shifts the linear regressions to the right, and as a consequence, shifts the intercept of the best-fitting linear regression to a slightly better acuity. 
The story for the pupil plane metrics is slightly different. In the aberration-free condition for PFSt and PFSc, the log metric value is also 0. The log metric value at low levels of aberration will remain 0 until a criterion is reached. The criterion for PFSt is met when any subaperture within the pupil area satisfies the criterion that both the horizontal and vertical ray slopes are less than a defined criterion, here 1 arcmin. The total area of all good subapertures within the pupil is then divided by the total area of the pupil to define the PFSt ratio. Likewise, PFSc has a similar criterion. Here the criterion for the critical pupil diameter is defined as the maximum concentric area for which root mean squared slopes of the rays contained within the area are less than 1 arcmin. The diameter of this concentric area meeting the criterion is then divided by the diameter of the pupil. The resulting quotient is squared to yield PFSc. As a consequence, small amounts of aberration will fail to reach the set criterion, and the change in log metric value will remain 0 when in fact there is aberration within the system. The criterion effect is most easily seen in Figure 3F for the metric PFSc where several data points plot at zero. Likewise in Figure 3E, for the metric PFSt, several values plot very near to zero. The result of these two metrics having a criterion level of aberration before a change in metric value shifts the intercept in a positive direction and suggests that the criterion should be adjusted to increase sensitivity to smaller aberration changes. 
The pupil plane metric logRMSs in the unaberrated state equals 0. The log of 0 is undefined; hence we set it to 0, thus allowing the change to go negative when values of RMSs were >0 and <1. Here, like the three image plane metrics, the negative intercept can be explained by having small changes in aberration that do not induce a change in acuity. 
Is the change in measured acuity as a function of change in metric value within the test–retests limits for the measurement of acuity?
Arditi & Cagenello (1993) reported the 95% CI for detecting a clinically significant change in logMAR acuity spans ±0.14 log units (±7 letters). These limits are illustrated in Figure 3 for each of the six best image quality metrics by the two blue lines. On average, 89% of the acuity measurements fall within ±0.14 log units of the best-fitting regression line (Table 2). The average of six different studies (Arditi & Cagenello, 1993; Bailey et al., 1991; Bailey & Lovie, 1976; Elliott & Sheridan, 1988; Raasch et al., 1998; Vanden Bosch & Wall, 1997) reveals a 95% CI of five letters (±0.10 logMAR) reducing the average number of acuity measurements falling within the interval to 75% (Table 2). 
To illustrate the near visual equivalency of charts generated with different WFEs but having the same optical quality metric value, Figure 5 displays six different simulated logMAR acuity charts for six different pupil diameters with 3 different underlying WFEs; in each case the underlying WFE yielded a log visual Strehl of −0.6 log units. Small differences in the image quality can be seen; nonetheless, the average change in visual acuity for these 6 charts was 0.16 with a standard deviation ±0.06 logMAR, which is right at the test re-test reliability for the measurement of acuity. 
Figure 5
 
Retinal image simulations of 6 logMAR acuity charts (without precompensation). Each chart was generated for a different PD (2–7 mm in 1 mm steps). All WFEs had a log visual Strehl of −0.6.
Figure 5
 
Retinal image simulations of 6 logMAR acuity charts (without precompensation). Each chart was generated for a different PD (2–7 mm in 1 mm steps). All WFEs had a log visual Strehl of −0.6.
Why normalize by plotting change in logMAR acuity vs. change in metric values as opposed to using actual values?
Across subjects, for any given retinal image quality metric value, there is a wide range of logMAR acuities (Applegate, Marsack, & Thibos, 2006; Villegas, Alcon, & Artal, 2008). This is not surprising given high contrast letters contain a lot of redundant information and it is to the individual's advantage to learn to extract content using all available information. As a consequence, to minimize the long term adaptation effects to one's own aberrations, we elected to normalize by studying change. However, normalizing in this manner does not eliminate the shorter term neural adaptation effects of complex blur (Artal et al., 2004; Chen, Artal, Gutierrez, & Williams, 2007) and to symmetric blur (Webster, Georgeson, & Webster, 2002). 
Correlation between the metrics
The results presented in Figure 4 reveal that different metrics are highly correlated to each other in either a positive or negative manner. As a consequence, combining metrics does not lead to a significant increase in the amount of variance accounted for. The result reported here is similar to the results obtained by Thibos, Hong, Bradley, and Applegate (2004), where they show similar correlations between metrics for the objective determination of refraction. 
Are the acuity vs. optical quality metric correlations predictive?
Preliminary studies (Rouger et al., 2010) and unpublished data reported at the Wavefront Congress (Shi, 2012) reveal that image quality metrics are predictive of acuity.If future studies continue to confirm these results, the clinical and research communities will have an objective surrogate for predicting likely changes in visual acuity due to an optically-induced change in image quality without the need to employ a more complex model for spatial vision (Dalimier & Dainty, 2008; Dalimier et al., 2009; Nestares et al., 2003; Watson & Ahumada, 2008). Having a simple objective surrogate for acuity allows the impact of noise at various levels of a corrective procedure (WFE measurement, implementation of the correction, registration of the correction, etc.) to be modeled in terms of acuity using Monte Carlo simulations. 
Moving forward we plan to: (1) Verify more stringently the results of the current study by taking only actual WFEs measured in normal eyes and highly aberrated eyes for various PDs where the underlying WFE is different for each condition; (2) Investigate whether the highly correlated metrics are predictive of acuity in both normal and highly aberrated eyes; and (3) Probe more carefully small optical quality changes to determine the predictive limits of the correlational model at low levels of WFE. 
Conclusion
Change in acuity is highly correlated with change in six image quality metrics independent of PD and underlying WFE (log neural sharpness [logNS], log visual Strehl calculated in spatial domain [logVSX], log visual Strehl calculated by MTF method [logVSMTF], log root mean square of WFE slope [logRMSs], log pupil fraction tessellated [logPFSt], and log pupil fraction as concentric area [logPFSc]). The findings suggest that these six image quality metrics can be used to model the likely distribution of acuity change for customized refractive corrections (e.g., various corneal refractive surgeries, intraocular lens designs, and contact lenses for the highly aberrated eye) and to objectively evaluate their success or outcome. 
Acknowledgments
The work is supported by NIH/NEI R01 EY08520 (RAA), NIH/NEI R01 EY019105 (RAA), NIH/NEI P30 EY 07551 (Core Grant), Navy contract N0025910 P1354 (RAA), Borish Endowment (RAA). In addition, the authors wish to thank Dr. Larry N. Thibos for the MATLAB code to calculate image quality metrics and sharing their normal best corrected WFE data set, Hope Queener and her team of programmers for developing the GUI for metric calculations, and Dr. Scott B. Stevenson for helping in gamma correction of our monitor and other programming for image display and Darren Koenig for generating Figure 1 from archival lab data. The authors thank the reviewers for their helpful comments. A portion of these findings were presented at the American Academy of Optometry in Boston, MA in October 13, 2011. 
Commercial relationships: The University of Houston has patent interest in retinal image quality metrics on which Raymond A. Applegate is listed as a co-inventor. No other author has a proprietary interest in any material or method mentioned. 
Corresponding author: Ayeswarya Ravikumar. 
Email: ayeswarya22@gmail.com 
Address: Visual Optics Institute, College of Optometry, University of Houston, Houston, TX, USA 
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Figure 1
 
logVSX as a function of age and PD for the 148 eye data set reported by Applegate et al. (2007).
Figure 1
 
logVSX as a function of age and PD for the 148 eye data set reported by Applegate et al. (2007).
Figure 2
 
Panel A, B, and C display the three wave aberration maps from the Thibos et al (2002) data set used in this study. Panels D, E, and F display their corresponding point spread functions.
Figure 2
 
Panel A, B, and C display the three wave aberration maps from the Thibos et al (2002) data set used in this study. Panels D, E, and F display their corresponding point spread functions.
Figure 3
 
Panels A through F plot change in acuity as a function of change in six image quality metrics. The central black line represents the best-fitting regression line, red dashed lines represent the 95% CI for the regression, blue lines represent the 95% CI from the regression line for clinically significant change in acuity as defined by Arditi and Cagenello (1993), and the black dotted line represents the 95% CI defined by the data.
Figure 3
 
Panels A through F plot change in acuity as a function of change in six image quality metrics. The central black line represents the best-fitting regression line, red dashed lines represent the 95% CI for the regression, blue lines represent the 95% CI from the regression line for clinically significant change in acuity as defined by Arditi and Cagenello (1993), and the black dotted line represents the 95% CI defined by the data.
Figure 4
 
Correlation matrix between each IQ metric.
Figure 4
 
Correlation matrix between each IQ metric.
Figure 5
 
Retinal image simulations of 6 logMAR acuity charts (without precompensation). Each chart was generated for a different PD (2–7 mm in 1 mm steps). All WFEs had a log visual Strehl of −0.6.
Figure 5
 
Retinal image simulations of 6 logMAR acuity charts (without precompensation). Each chart was generated for a different PD (2–7 mm in 1 mm steps). All WFEs had a log visual Strehl of −0.6.
Table 1
 
Best refractive correction and the best-corrected logMAR visual acuity of all four subjects.
Table 1
 
Best refractive correction and the best-corrected logMAR visual acuity of all four subjects.
Subject ID Best corrected spectacle correction Best corrected visual acuity (BCVA)
Subject 1 Plano −0.12 logMAR
Subject 2 Plano/–4.5 DC × 170 −0.1 logMAR
Subject 3 −0.50 DS/0.75 DC × 160 −0.1 logMAR
Subject 4 +0.75 DS/–0.25 DC × 175 −0.14 logMAR
Table 2
 
Percent of all data for all subjects within the 95% CI for clinical significance (±0.14 logMAR) for test–retest measurement of acuity as defined by Arditi and Cagenello (1993) and the percentage of data within ±0.1 logMAR of the regression line (the average 95% CI of six different studies [Arditi & Cagenello, 1993; Bailey et al., 1991; Bailey & Lovie, 1976; Elliott & Sheridan, 1988; Vanden Bosch & Wall, 1997]).
Table 2
 
Percent of all data for all subjects within the 95% CI for clinical significance (±0.14 logMAR) for test–retest measurement of acuity as defined by Arditi and Cagenello (1993) and the percentage of data within ±0.1 logMAR of the regression line (the average 95% CI of six different studies [Arditi & Cagenello, 1993; Bailey et al., 1991; Bailey & Lovie, 1976; Elliott & Sheridan, 1988; Vanden Bosch & Wall, 1997]).
Metric R2 (%) % of data % of data
within ±0.14 logMAR within ±0.1 logMAR
logNS 90 93.1 80.6
logVSX 87 87.5 73.8
logVSMTF 86 89.4 76.9
logPFSt 86 88.0 73.6
logPFSc 84 90.0 78.9
logRMSs 82 84.5 70.6
Average 88.7 75.7
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