Year: 2024
Type: letter
Abstract: We read with interest the recent correspondence by Holladay et al., which aims to provide theoretical explanations and graphical illustrations for the findings reported by Kozhaya et al.1,2 Their study found that the induction of positive spherical aberrations (SAs) adds no benefit in terms of depth of focus. The study by Kozhaya et al. evaluated the effect of adding positive or negative SA in vivo on pseudophakic eyes implanted with different types of intraocular lenses using an adaptive optics (AO) system (VAO, Voptica S.L.). The study assessed corrected distance visual acuity, distance-corrected intermediate visual acuity, and distance-corrected near visual acuity under both high- and low-contrast conditions. We believe that the graphs provided by Holladay et al. do not adequately explain the findings by Kozhaya et al. and that there may be experimental issues in the study protocol that could account for the unexpected and counterintuitive result that positive SA did not improve the depth of focus in the study. As highlighted by Kozhaya et al. in the limitations of their study, “modulation of SA might induce a shift in spherical refraction, which can affect the depth of focus.” We suggest that this may explain the counterintuitive difference observed between positive and negative SA induction in this study. The induction of fourth-order SA was performed using a Zernike SA polynomial representation. Fourth-order SAs are commonly described as a progressively rotationally symmetrical phase error along the radial coordinate in r4 toward the periphery, consistent with a Seidel-like r4 wavefront description. However, the Zernike SA polynomial Z40, expressed analytically as 5(6r4−6r2+1), includes not only a positive r4 term but also a negative r2 term indicating defocus of the opposite sign to maintain orthogonality with the Zernike defocus (Z20) mode.3 The amount of myopic or hyperopic defocus is 4 times greater than the fourth-order SA component in the Zernike SA mode Z40 (Figure 1, a).Figure 1.: a: The decomposition of the Zernike fourth-order SA Z40 mode with a coefficient of 1 micron is shown, breaking it down into an r4 component and an r2 component. This is equivalent to approximately 4 microns of Zernike defocus Z20. b: In a system without SAs, the focal plane of the marginal rays and the paraxial focal plane align with the retina in an emmetropic eye. c: With induction of positive Zernike SA, the focal plane of the marginal rays is anterior to the retina, and the paraxial focal plane is posterior. d: With induction of positive Seidel SA, the paraxial focal plane is on the retina, and the focal plane of the marginal rays is anterior to the retina. SA = spherical aberrationThe presence of the negative r2 term in the Z40 polynomial significantly alters the phase profile, introducing a central convexity that would not occur if only the higher-order r4 term were present. This alteration results in the sombrero-like shape of the Z40 mode. The r2 term not only shapes the phase profile but also affects subjective ocular refraction by influencing the perceived focus and clarity of the image, making it a critical factor in vision correction and optical system design. Counterintuitively, inducing positive Zernike SA with an AO introduces a hyperopic defocus in the center of the pupil, whereas inducing negative Zernike SA results in a myopic shift. Conversely, inducing positive Seidel-like SA (which gradually affects the wavefront toward the periphery) leads to an overall myopic shift (Figure 1, b–d). By contrast, negative Seidel-like SA induces a hyperopic shift. In the study by Kozhaya et al., Zernike SA was induced using AO without adjusting the refraction for distance vision. The central hyperopic shift caused by positive Zernike SA led to a degradation in intermediate and near visual acuity, whereas the myopic shift caused by negative Zernike SA resulted in an improvement in intermediate and near visual acuity. This created the misleading impression that only negative SA enhances depth of focus. The study protocol further amplifies the significance of central defocus induced by the Zernike SA polynomial compared with optical bench studies, as it accounted for the Stiles-Crawford effect using real eyes and assessing subjective visual acuity. As a reminder, the Stiles-Crawford effect arises from the geometrical preference of cone photoreceptors for central rays over peripheral rays, highlighting the crucial role of central rays in human vision. This paradoxical induction of defocus by Zernike SA is well described in the study by Rocha et al. using a similar AO protocol. Their study shows a shift of the best focal plane (referred to in their study as the center of focus) in the through-focus curve “in the direction of the sign of the induced SA.”4 Regarding the graphs presented by Holladay et al., we believe they do not support the claim that positive SA fails to enhance depth of focus. Instead, the graphs illustrate that in an optical system with positive Seidel-like SA, peripheral rays undergo myopic defocus compared with central rays. By contrast, a system without SA exhibits no differential defocus between peripheral and central rays. Conversely, a system with negative Seidel-like SA results in peripheral rays experiencing hyperopic defocus. Contrary to the assessment by Holladay et al., the proximity between the best focal plane (behind the retina) and the focalization plane achieved during near vision in an emmetropic patient (also behind the retina) does not indicate good vision. Instead, as the retina remains at the same location in the eye, the plane shift caused by focusing on a near object needs to be compensated, requiring some rays to focus before the retina, similar to what is observed in myopia. It is crucial to understand that in the case of negative Seidel-like SA, the extension of a useful depth of focus implies that for a distant target, paraxial rays are defocused in a plane anterior to the retina. Conversely, if this were not the case, nonparaxial rays would be defocused in a plane posterior to the retina, which would not allow for an extended depth of focus for near targets. In positive Seidel-like SA, the paraxial rays from a distant target need to be focused in a plane close to the retina as the peripheral rays provide additional power. In conclusion, both positive and negative SAs have the potential to enhance depth of focus when appropriately used in conjunction with manipulation of paraxial defocus. A recent clinical study supports the depth-of-focus enhancement potential of positive SA, demonstrating that lenses inducing positive SA can effectively improve depth of focus and produce favorable clinical outcomes.5
Authors: Benjamin Stern, Damien Gatinel
Language: English
Subfield: Ophthalmology
Field: Medicine
Domain: Health Sciences
Open Access status: green
OpenAlex ID: W4402897950