A Review of Changes in High-Order Ocular Aberrations as a Function of Pupil Size and Age

If there were such a thing as an optically ideal, emmetropic human eye, then light from a distant point source would form a sharp point image limited only by diffraction (the interaction of peripheral light rays with the pupil margin). The human eye, however, is a complex and imperfect optical system with multiple refractive surfaces and a pupil serving as a limiting aperture. Irregularities of any of the refractive surfaces or misalignments of their optical centers relative to each other or to the pupil can lead to image-degrading optical aberrations.

Ophthalmic aberrometers have allowed for the study of the characteristics of and changes in optical aberrations of human eyes under varying conditions, including aberrations in the general population,^1-3 changes in aberrations as a function of age,^4-8 and changes as a function of pupil size.^4,9 Because pupil size is an important factor when considering, for example, the correction of presbyopia with multifocal soft contact lenses, one might wonder how aberrations of the eye change as a function of pupil size. Furthermore, pupil size has itself been shown to change with age,¹⁰ and the relationship between ocular aberrations and age is also meaningful. This article reviews changes in aberrations of the human eye as a function of pupil size and age.

Figure 1. Illustration of light rays reflecting off the retina (far right) and propagating leftward through the lens (middle) and cornea (left). Rays exiting the eye to the left form an aberrated wavefront (red), which can be fit with the set of Zernike polynomials and compared to an ideal, plane wavefront (blue).

Optical Aberrations and the Eye

A helpful way to think about total ocular aberrations (corneal and internal) might be from the point of view of measuring them. A common type of aberrometer, the Hartmann-Shack wavefront sensor, uses the retinal reflection of a point of light from a superluminescent diode to determine the characteristics of the wavefront exiting the eye. The reflected light passes back through the crystalline lens and cornea, and it is the exiting wavefront that is analyzed. The shape of this exiting wavefront is determined by the aberrations of the eye. For an emmetropic eye without aberrations, the exiting wavefront should be a flat, or plane, wavefront. Considered in reverse, this fact suggests that a distant point object should be perfectly conjugate with and cleanly imaged on the retina, each ray from the point focusing on the same point in the image. The conditions under which this expectation is not met can be divided into low-order (defocus and astigmatism) and high-order (coma, spherical aberration, etc.) type aberrations. It is the high-order aberrations that are the focus of this article.

With the exception of some highly aberrated eyes, ocular wavefront aberrations are well described by a set of Zernike polynomials,^11,12 and standards have been developed for their use in ophthalmic reporting.¹³ Zernike polynomials fit and describe aberrated wavefronts relative to radial and circular changes in the wavefront within the circular pupil. That is, wavefront errors are described from the center of the pupil outward and in circles at all radii concentric with the pupil center. The magnitude of all deviations from a perfectly plane wavefront can be calculated as the root mean square wavefront error (RMS WFE). Comparing the ideal wavefront to the aberrated ocular wavefront, based on the fit of the Zernike polynomials, RMS WFE can be thought of as the standard deviation of the wavefront error over the area of the pupil. RMS WFE can be calculated for specific Zernike terms, eg, defocus and spherical aberration, or for broader sets of low- and/or high-order Zernike terms. We examine here how high-order RMS WFE changes with both pupil size and age.

Figure 2. Exponential fit to change in high-order root mean square wavefront error (RMS WFE) as a function of pupil size for 6 different age groups (adapted from Applegate et al, Table 24). High-order RMS WFE is shown to increase at least 4 to 5 fold for each doubling of the pupil diameter.

High-order Aberrations, Pupil Size, and Age

If aberrations were random and not systematic, then the standard deviation of those aberrations, as measured over a circular pupil, would not be expected to change systematically with the size of the pupil. Being well fit by Zernike polynomials, ocular aberrations do vary systemically within the pupil, and RMS WFE has been found to depend on pupil diameter. Applegate et al⁴ and Wang et al⁹both found an increase in wavefront error with increasing pupil diameter. More specifically, with an exponential fit to their data, wavefront error can be shown to increase just greater than the square of the pupil diameter, ie, high-order RMS WFE increases 4 to 5 times for every doubling of the pupil diameter. This outcome suggests potentially large changes in vision with increasing pupil diameter. However, vision may not be impacted as much as expected with larger pupil diameters due to potential interactions between various Zernike components¹⁴ and/or the Stiles-Crawford effect^15,16 (the angular orientation of photoreceptors toward and greater sensitivity to light from the center of the pupil). This exponential change in high-order RMS WFE can be seen in Figure 2 for 3-mm to 7-mm pupil diameters for 6 age groups (adapted from Applegate et al, Table 2⁴).

The papers by Applegate et al and Wang et al are similar in their investigations of RMS WFE as a function of pupil size, but they differ in their subjects’ ages and refractive statuses. The former included 146 eyes of 146 subjects (using only the preferred eye) ranging between 20 and 80 years of age, and the latter included 102 eyes of 51 myopic subjects (using right and left eyes of all subjects) ranging between 18 and 35 years of age. Subjects’ refractive status was not stated in the investigation by Applegate et al. The former also measured RMS WFE for pupil sizes ranging from 3 mm to 7 mm (in 1-mm steps), and the latter measured RMS WFE for pupil sizes ranging from 4 mm to 6 mm (in 1-mm steps). Aside from reporting only combined high-order aberrations, Applegate et al also reported changes in pupil size for coma, trefoil, and spherical aberrations. The results can be compared for these 3 Zernike components for similar age groups between the 2 papers after fitting the values reported in Tables 2 and 3 of Wang et al with similar functions. For the smaller range of pupils,⁹coma and spherical aberrations increased more than trefoil, but for the larger range of pupils,⁴ spherical aberration had a greater increase than coma and trefoil aberrations. There appeared to be no strong trend among these 3 Zernike components except that trefoil consistently increased less than spherical aberration across both ranges of pupil sizes.

The decrease in pupil size that has been shown to occur with age may help to mitigate the impact of increasing high-order RMS WFE by reducing the magnitude of the aberrations with pupil size and by increasing the depth of focus.

Finally, several studies have reported an increase in high-order RMS WFE with age.^4-8 Figure 3 shows an exponential increase in high-order RMS WFE with age for 3-mm, 4-mm, 5-mm, 6-mm, and 7-mm pupil diameters (adapted from Applegate et al, Table 6⁴). With roughly doubling of age between mean ages of 25.2 and 55.4 and between ages of 35 and 72.9, there is an average 1.57-fold and 1.79-fold increase in aberrations, respectively. When comparing internal and corneal aberrations across age for the same populations, studies have shown that corneal aberrations remain relatively stable, while internal aberrations (attributed to the crystalline lens) contribute more.^5-7 The decrease in pupil size that has been shown to occur with age¹⁴ may help to mitigate the impact of increasing high-order RMS WFE by reducing the magnitude of the aberrations with pupil size and by increasing the depth of focus.^15,16

Figure 3. Exponential function fit to changes in ocular high-order RMS WFE as a function of age for 5 pupil diameters (adapted from Applegate et al, Table 64).Roughly doubling ages, between ages 25.2 and 55.4, high-order RMS WFE increases about 1.59 fold for all pupil diameters, and between ages 35 and 72.9, high-order RMS WFE increases about 1.77 fold for all pupil diameters.

Summary

• High-order RMS WFE increases with pupil diameter, increasing 4 to 5 fold for each doubling of the pupil.^4,9 However, the impact on vision at larger pupil diameters may be mitigated by the interaction of different Zernike WFE components¹⁷ and/or the greater directional sensitivity of the photoreceptors to rays from the central pupil.¹⁰

• High-order RMS WFE also increases exponentially with age.⁴However, the impact on vision quality for older individuals may be mitigated somewhat by the decrease in average pupil diameter with age.¹⁴ Previous studies have suggested that the increase in high-order RMS WFE with age is due more to changes in the internal optics of the eye with age (ie, the crystalline lens), as the high-order RMS WFE attributed to the cornea remains relatively stable.^5-7

Darren E. Koenig Dr. Koenig teaches Geometric and Theoretical Optics at the Illinois College of Optometry. He also coordinates a clinical skills lab and is an attending in the Illinois Eye Institute. His interests include vision quality and visual optics, and OCT-A evaluation of the human eye.

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