Normal Wavefront Error as a Function of Age and Pupil Size

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Normal Wavefront Error as a Function of Age and Pupil Size Raymond A. Applegate, OD, PhD Borish Chair of Optometry Director of the Visual Optics Institute College of Optometry University of Houston

In the interest of full disclosure: My research is funded by NIH/NEI R01 grant 08520. I consult for: Sarver and Associates, Inc Steve Shallhorn s group at the Naval Refractive Surgery Center I have proprietary interests in variety of image quality metrics.

0.2 20/32 6/9.5 20/15 is normal vision 0.1 20/25 6/7.5 LogMAR visual acuity 0.0-0.1-0.2 20/15 20/20 6/6 20/16 6/4.8 20/13 6/3.8-0.3 < 60 20/10 6/3-0.4 15 25 35 45 55 65 75 85 20/8 6/2.4 Age in years Modified from Elliot et al Optometry and Vision Science, 1995

Texas Investigation of Normal and Cataract Optics (TINCO Study) Photopic High Contrast logmar P HC Acuity.4.3.2.1 0 -.1 -.2 < 60 20/17 -.3 20 30 40 50 60 70 80 90 Age 20/32 20/25 20/20 20/16 20/13 20/10

Can we attribute the loss of acuity in older individuals to an increase in HO WFE?

I will address the question of normal WFE in this context: Discuss the uncertainty S/H centroid location Edge effects Poorly formed spots WFE vs. dioptric error WFE and pupil diameter WFE and age TINCO Study HO RMS WFE as a function of pupil diameter and age HO RMS WFE as a function of physiologic pupil diameter and age Log Area OTF as a function of physiologic pupil diameter and age Implications for vision and aging

U H In a S/H wavefront sensor, the S/H image is the raw information from which all calculations are subsequently made.

Typically but not always the S/H image is captured with the pupil dilated.

Once captured the centroid of each spot is determined by using an instrument-specific proprietary algorithm. Centroid location of a well defined S/H spot Centroid location of an ill defined S/H spot

Further complicating proper centroiding are pupil edge effects. The pupil border allows only partial filling of some lenslets. The S/H image formed by these lenslets are incomplete leading to centroiding errors.

It is important to understand how your machine minimizes both types of centroiding errors in representing the WFE.

Once the centroids are located, the change in centroid location of each lenslet image from the calibrated position is used calculate the WFE.

In normal eyes, the resulting WFE is well fit with the normalized Zernike expansion (ANSI Z80 standard), or by a Fourier fit.

By well fit, it is meant that the fitted function can be used to re-calculate the centroid locations with little error.

If the fundamental data (centroid locations) have some error, do we really want the fitting function to perfectly represent the data?

To minimize potential errors from edge effects it is typical to either ignore centroid data defining the edge of the pupil or follow the Dan Neil rule of thumb and fit the WFE with two more Zernike radial orders than being reported.

Example of the Dan Neil n-2 rule of thumb: To minimize edge effects for Zernike modes through the 6 th radial order, fit through the 8 th and report through the 6 th.

The centroiding errors away from the pupil edge have to be dealt with differently. Centroid location of an ill defined S/H spot

When such errors exist (as they do in any real data), it is typical to fit the raw data with a function to better estimate the actual form of the of the WFE as opposed to fitting the data exactly.

Dependent variab Dependent Variable 12 10 8 6 4 2 0 y = 1.0048x + 0.0133 R 2 = 0.9973 0 2 4 6 8 10 12 Independent variable

In order for the fitting function to better represent the WFE of the eye s optics (as opposed to accurately representing the centroid locations) the fitting function should reflect fundamental aspects of the behavior of the WFE.

Many modes (certainly not all) of the Zernike expansion contain key aberrations known to exist in the eye. Spherical WFE Astigmatic WFE Coma WFE Spherical aberration WFE Trefoil WFE

So what does all this have to do with aging, physiologic pupil diameters and HO WFE? Details matter in WFE calculations Care was taken to minimize centroiding artifacts and the introduction of noise

To address this question: Discuss the uncertainty S/H centroid location Edge effects Poorly formed spots WFE vs. dioptric error WFE and pupil diameter WFE and age TINCO Study HO RMS WFE as a function of pupil diameter and age HO RMS WFE as a function of physiologic pupil diameter and age Log Area OTF as a function of physiologic pupil diameter and age Implications for vision and aging

WFE increases as the eye s pupil diameter increases. This fact gives WFE and other measures of optical quality a distinct advantage over the traditional diopter.

Slide 28 Defocus = 0.25D RMS wave aberration = 0.58 µm 2001 By Default! 20/40 20/20 20/12 Pupil Diameter = 8.00mm A Free sample background from www.pptbackgrounds.fsnet.co.uk RAA

Slide 29 Defocus = 0.25D RMS wave aberration = 0.14 µm 2001 By Default! Pupil Diameter = 4.00mm 20/40 20/20 20/12 A Free sample background from www.pptbackgrounds.fsnet.co.uk RAA

Slide 30 Defocus = 0.25D RMS wave aberration = 0.036 µm 2001 By Default! Pupil Diameter = 2.00mm 20/40 20/20 20/12 A Free sample background from www.pptbackgrounds.fsnet.co.uk RAA

Slide 31 2001 By Default! In this case, wavefront error tells us that the image is getting better or worse, dioptric error does not. 0.58µm WFE 0.036µm WFE 8.0mm pupil 0.25D Myope 2.0mm pupil A Free sample background from www.pptbackgrounds.fsnet.co.uk RAA

High order (HO) WFE is typically defined as WFE not correctable with a spherocylindrical correction.

n m 0-4 -3-2 -1 0 1 2 3 4 1 Z m n 2 3 4 Zernike Expansion modes in the 3 rd order and higher are collectively called the higher order aberrations.

Like WFE due to simple defocus, HO RMS-WFE increases with pupil diameter.

As an individual ages HO WFE increases for any given pupil diameter of interest.

Articles that show aberrations increase with pupil diameter include: W. N. Charman, "Wavefront aberration of the eye: a review," Optom Vis Sci 68, 574-83 (1991). F. W. Campbell and D. G. Green, "Optical and retinal factors affecting visual resolution," J Physiol 181, 576-93 (1965). P. Artal and R. Navarro, "Monochromatic modulation transfer function of the human eye for different pupil diameters: an analytical expression," J Opt Soc Am A Opt Image Sci Vis 11, 246-9 (1994). K. Venkateswaran, A. Roorda, and F. Romero-Borja, "Theoretical modeling and evaluation of the axial resolution of the adaptive optics scanning laser ophthalmoscope," J Biomed Opt 9, 132-8 (2004). C. E. Martinez, R. A. Applegate, S. D. Klyce, M. B. McDonald, J. P. Medina, and H. C. Howland, "Effect of pupillary dilation on corneal optical aberrations after photorefractive keratectomy," Arch Ophthalmol 116, 1053-62 (1998). Y. Wang, K. Zhao, Y. Jin, Y. Niu, and T. Zuo, "Changes of higher order aberration with various pupil sizes in the myopic eye," J Refract Surg 19, S270-4 (2003). W. N. Charman, J. A. Jennings, and H. Whitefoot, "The refraction of the eye in the relation to spherical aberration and pupil size," Br J Physiol Opt 32, 78-93 (1978).

Articles that show aberrations increase with age include: A. Guirao, C. Gonzalez, M. Redondo, E. Geraghty, S. Norrby, and P. Artal, "Average optical performance of the human eye as a function of age in a normal population," Invest Ophthalmol Vis Sci 40, 203-13 (1999). J. S. McLellan, S. Marcos, and S. A. Burns, "Age-related changes in monochromatic wave aberrations of the human eye," Invest Ophthalmol Vis Sci 42, 1390-5 (2001). A. Guirao, M. Redondo, and P. Artal, "Optical aberrations of the human cornea as a function of age," J Opt Soc Am A Opt Image Sci Vis 17, 1697-702 (2000). P. Artal, E. Berrio, A. Guirao, and P. Piers, "Contribution of the cornea and internal surfaces to the change of ocular aberrations with age," J Opt Soc Am A Opt Image Sci Vis 19, 137-43 (2002). R. I. Calver, M. J. Cox, and D. B. Elliott, "Effect of aging on the monochromatic aberrations of the human eye," J Opt Soc Am A Opt Image Sci Vis 16, 2069-78 (1999).

We confirm these observations reported by others in the Texas Investigation of Normal and Cataract Optics (TINCO) and extend the observation to show the 3 dimensional relationship between HO RMS WFE, age and pupil diameter.

146 TINCO subjects by decade Label Age in years Count Mean age in years, SD Minimum age in years Maximum age in years 20s 20-29 20 25.2, ±2.3 21.6 29.8 30s 30-39 18 35.0, ±2.4 30.1 38.7 40s 40-49 32 45.2, ±2.8 40.5 49.9 50s 50-59 32 54.4, ±2.9 50.5 58.7 60s 60-69 21 62.9, ±1.9 60.3 67.4 70s 70-79 23 72.9, ±2.4 70 78.4 Applegate, RA, Donnelly, WJ III, Marsack, JD, Pesudovs, K, The 3-D relationship between high order RMS wavefront error, pupil diameter, and aging, J Opt Soc Am-A, 24:578-587, 2007.

In the TINCO study, WFE was measured using a S/H wavefront sensor through dilated pupils. WFE pupil diameters 3, 4, 5, 6, 7 were calculated using the method of rescaling. J. Schwiegerling, "Scaling Zernike expansion coefficients to different pupil sizes," J Opt Soc Am A Opt Image Sci Vis 19, 1937-45 (2002).

Average HO RMS WFE was then plotted for each age group and pupil to illustrate the typical 3 dimensional relationship between age, pupil diameter and HO RMS WFE.

Applegate, RA, Donnelly, WJ III, Marsack, JD, Pesudovs, K, The 3-D relationship between high order RMS wavefront error, pupil diameter, and aging, J Opt Soc Am-A, 24:578-587, 2007. Figure 3A.

Notice that with increasing age and with increasing pupil diameter WFE is increasing exponentially.

This fact suggests that plotting log RMS WFE as a function of pupil diameter and age may be well defined as a plane.

Applegate, RA, Donnelly, WJ III, Marsack, JD, Pesudovs, K, The 3-D relationship between high order RMS wavefront error, pupil diameter, and aging, J Opt Soc Am-A, 24:578-587, 2007. Figure 5. U H

These findings on the surface suggest that some of the decrease in acuity with age may be due to increase WFE with age.

It is also known that the physiologic pupil diameter: 1) Decreases as luminance increases; and 2) For any given individual and luminance level, pupil diameter decreases with age.

This raises the interesting question as to whether the natural decrease in pupil diameter with age offsets the increase in HO RMS-WFE with age?

To answer this question, we first turned to the literature to determine how the physiologic pupil diameter varied as a function of age and luminance.

Winn et al measured physiologic pupil diameters for 5 luminance levels (9, 44, 220, 1100, and 4400 cd/m2) of 91 individuals ranging in age from 17 to 83 years of age. B. Winn, D. Whitaker, D. B. Elliott, and N. J. Phillips, "Factors affecting light-adapted pupil size in normal human subjects," Invest Ophthalmol Vis Sci 35, 1132-7 (1994).

They found: 1) The physiologic pupil diameter decreases linearly with increasing age for any given light level. 2) The effect of age on physiologic pupil diameter is considerably less than the effect of luminance level. 3) As luminance increases the rate of change in physiological pupil diameter as a function of age decreases.

Derived from data of B. Winn, D. Whitaker, D. B. Elliott, and N. J. Phillips, "Factors affecting light-adapted pupil size in normal human subjects," Invest Ophthalmol Vis Sci 35, 1132-7 (1994). Applegate, RA, Donnelly, WJ III, Marsack, JD, Pesudovs, K, The 3-D relationship between high order RMS wavefront error, pupil diameter, and aging, J Opt Soc Am-A, 24:578-587, 2007. Figure 1. U H e anc n i m Lu h Hig Lu w Lo ce n a min

cd/m 2 Slope Intercept R 2 9-0.043 8.046 0.557 44-0.04 7.413 0.486 220-0.032 6.275 0.377 1100-0.02 4.854 0.226 4400-0.015 4.07 0.214 As luminance increases the rate of change in physiological pupil diameter as a function of age decreases. B. Winn, D. Whitaker, D. B. Elliott, and N. J. Phillips, "Factors affecting light-adapted pupil size in normal human subjects," Invest Ophthalmol Vis Sci 35, 1132-7 (1994).

Although the typical physiologic pupil diameters as defined by these linear regressions are age and luminance level dependent the variability in pupil diameters at any one age is very large and on the order of 2 mm.

We calculated the HO RMS WFE using the Winn et al data to define typical physiological pupil diameters and the TINCO data set to define how HO RMS WFE varies as a function these physiological pupil diameters and age.

Applegate, RA, Donnelly, WJ III, Marsack, JD, Pesudovs, K, The 3-D relationship between high order RMS wavefront error, pupil diameter, and aging, J Opt Soc Am-A, 24:578-587, 2007. Better Optics Poorer Optics Smaller pupil Larger pupil

Since HO RMS WFE is a metric of retinal image quality, it can be argued that the loss in acuity in older eyes cannot be accounted for by an increase in HO RMS WFE.

Other metrics of retinal image quality are better than RMS wavefront at predicting visual acuity. Applegate, RA, Marsack, JD, Thibos, LN, Metrics of retinal image quality predict visual performance in eyes with 20/17 or better visual acuity, Opt Vis Sci, in press.

The area under the Optical Transfer Function (OTF) is a better predictor of visual acuity performance. Applegate, RA, Marsack, JD, Thibos, LN, Metrics of retinal image quality predict visual performance in eyes with 20/17 or better visual acuity, Opt Vis Sci, in press.

So we calculated a similar function using the Area OTF as the metric of retinal image quality.

log luminance cd/m^2 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 70 60 50 40 30 1.0 2.5 2.0 1.5 3.5 3.0 Larger pupil Smaller pupil Better Optics Poorer Optics Age in years Area OTF UH

It is therefore difficult to attribute decreasing acuity with increasing age to an increase in aberration when acuities are measured under physiologic pupil conditions.

These findings suggest that the acuity loss with age under physiological conditions is most likely due to neural changes combined with other optical effects including scatter and decreased light transmission and not the increase in WFE.

Applegate, RA, Donnelly, WJ III, Marsack, JD, Pesudovs, K, The 3-D relationship between high order RMS wavefront error, pupil diameter, and aging, J Opt Soc Am-A, 24:578-587, 2007.

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