Positive or negative spherical aberration- Which of the two provides better depth of focus by EDOF IOLs?

In the article in this blog 'Spherical Aberration, Q factor & choice of IOL' (https://www.quickguide.org/post/spherical-aberration-asphericity) I have provided an understanding on the subject of spherical aberration, the concept of positive and negative spherical aberration and how an IOL can be chosen for cataract patients based on the Q factor of the cornea. In this article, I will go a little deeper in understanding the 'best focus' or 'circle of least confusion' with spherical aberration and answer the following question:

Positive or negative spherical aberration, between the two what provides a better depth of focus?

To understand this we will first try to understand the concept of best focus with spherical aberration. In image 1, the axial or longitudinal spherical aberration is described as the distance between the paraxial focus and the marginal focus. We know spherical aberration provides depth of focus, but also degrades the image quality. This degradation of image quality is the result of the blur circle on the retina, as the marginal rays fall further away from the paraxial focal point. This is what typically happens in positive spherical aberration or negative spherical aberration.

Image 1: Image 1: Longitudinal SA and transverse SA in presence of positive SA

When the pupil is small, for example in day time, the marginal rays of light do not reach the retina. As a result the image is sharp with a significantly lower blur circle. As we enter into a mesopic condition, the pupil is large, as a result of which marginal rays of light that now pass the pupil fall in front of the paraxial focal point, creating a longitudinal positive spherical aberration.

The place where the patient best focus shift, that is the place where the image is a circle of least confusion is shown in image 2.

Image 2: The best focus of the patient in presence of positive spherical aberration.

To find the best focus of the patient in a dilated pupil in presence of positive spherical aberration (SA), follow the steps:

A) Identify the point where the marginal ray is meeting the paraxial ray (marked by green arrow)

B) Join this point to the paraxial focal point (green line).

C) Now identify the point where the inferior marginal ray (red line) is meeting the caustic (green line)

D) The point where the two lines meet is the 'best focus' for the patient.

The best focus is the place where an object at infinity will have the least blur circle, and the image would therefore be acceptable to the patient.

Image 3: Above picture shows how the marginal rays fall beyond the paraxial rays creating longitudinal negative SA and transverse negative SA. Below image depicts the location of best focus or the circle of least confusion. quickguie.org

The best focus therefore is not a fixed point on the image plane, and shift according to the pupillary diameter and the location of the object, either at infinity or any distance closer to the eye.

The best focus could be connected to the circle of least confusion concept from astigmatism. This is the place where the image of an object at infinity will have the least blur and therefore fairly acceptable to the patient. Thus with increasing amounts of ocular positive spherical aberration, the best focus shifts further away from the paraxial focal point. The more the spherical aberration, the larger the blur circle of the best focus and larger the drop in image quality. Night myopia is a term associated with patients who experience blurred vision in low light condition even though in the day time, they are normal. The shift in best focus of the patient as the pupil dilates explains such condition experienced by emmetropes with large spherical aberration.

Negative spherical aberration is a condition wherein the marginal rays of light fall beyond the paraxial rays of light (Image 3 top). Thus the best focus of the patient will be beyond the paraxial focal point (Image 3 bottom). Thus the following conditions will happen:

• For a emmetrope, with negative spherical aberration, the best focus will be on the hyperopic side.

• For an emmetrope with positive spherical aberration, the best focus will on the myopic side.

Karolinne Maia Rocha and co-authors found that higher positive spherical aberration provided better DCNVA than negative spherical aberration(1).

In an earlier study by the same first author in 2007, SN60AT ( a non aspheric spherical IOL) was shown to provide better DCNVA over the Acrysof IQ aspheric lens. Note, a spherical IOL adds to the positive spherical power for a cornea which is generally prolate. However, using adaptive optics (simulate different types of vision, including how aberrations affect vision), Rocha and co-authors in 2009 showed that both positive and negative spherical aberration could result in depth of focus for the patient(2). As described above, for an emmetrope with negative SA, the best focus will shift to the hyperopic side ( and the opposite for positive SA) the authors found that the shift of the best focus (authors describe as 'center of focus') is in the direction of the sign of the induced spherical aberration, that is best focus shifts on the positive side with positive SA and to the hyperopic side with negative SA. This may explain why intermediate or near vision improvement is noticed with positive SA rather than negative SA.

Contrary to work of Rocha and co-authors with Adaptive Optics, Khozaya and co-authors found no benefit of inducing positive SA in increasing depth of focus. The authors noted that only negative SA induced depth of focus. Positive SA decreased CDVA for both the enhanced monofocal and continuous range-of-vision IOLs and DCNVA for the monofocal IOLs with zero SA(3).

Damiel Gatinel (4) explains the surprise finding of Khozaya and co-authors.

Gatinel and Stern explains that inducing positive Zernike SA with adaptive optics introduces a hyperopic defocus in the center of the pupil, whereas inducing negative Zernike SA results in a myopic shift. As the paracentral rays of light shifts towards the myopic side with induction of negative SA, the patient's depth of focus improves, giving an impression that only negative SA works.

Gatinel and Stern advice that if adaptive optics have to be used to simulate negative and positive SA, then the patient's far focus has to be corrected for distance to negate any shift in focus of paraxial rays of light. Only then can we understand the effect of negative or positive SA on depth of focus.

Juan Tabernero and co-authors(5), used adaptive optics to determine what amount of negative spherical aberration would help in near and intermediate without significantly affecting the distance. Starting from
0.07 to
0.3 mm of spherical aberration, the increase in depth of focus followed a linear trend, with a rate of change of 0.4 D of depth of focus per
0.1 mm of spherical aberration.

The authors showed that on average, when ocular spherical aberration increases more than
0.15 micron (all spherical aberration data in this section refer to a pupil diameter of 4.5 mm), the far distance visual acuity is worse than 0.15 logMAR units, which is hardly clinically acceptable. To be able to achieve a far visual acuity better than this value, the most effective EDOF IOL (on average) to extend the DoF would correspond to values of spherical aberration that range between
0.07 mm and
0.15 mm(5). Below is a video description from their study.

Current EDOF IOLs in market and there aspheric profile:

Here is a quick guide to the choice of EDOF or enhanced monofocal IOL according to the individual spherical aberration values. You see, all EDOF IOLs induce some amount of spherical aberration regardless of the optic design incorporated. It is important to see the individual spherical aberration values of the patient and then choose the particular EDOF. For example, a cornea with very high negative spherical aberration may not be ideal to be implanted with an EDOF IOL that induces more negative spherical aberration. Here is a chart that may help:

Current EDOF IOLs and the spherical aberration profile quickguide.org

The choice of EDOF IOL should not be based on the depth of focus provided alone, but a careful consideration of the aberration profile in these IOLs. Providing an EDOF IOL that adds high negative spherical aberration on a patient whose cornea already has negative spherical aberration, may lead to dissatisfaction and dysphotopsia. As already stated earlier, Juan Tabarnero and co-authors (5) showed that a spherical aberration value of beyond .15 micron (at an aperture size of 4.5 mm) is the borderline of tolerance for patients that may bring depth of focus without disturbing the distance at infiniti. Beyond a value of .15 micron, patients VA for distance (and therefore arguably the contrast) is lost at the cost of depth of focus.

While a positive spherical aberration value of .275 is largely regarded as an average value for human cornea, it is worthwhile to remember that these value is of 6mm cornea. The human pupil is hardly that dilated and therefore a more realistic figure to consider is around 4.0 to 4.5 mm of the cornea. Based on that thought, here is the average spherical aberration value of cornea for different pupillary apertures of the eye:

Average spherical aberration in microns against pupil aperture quickguide.org

A a careful choice of the right EDOF IOL based on its spherical aberration value should be based on not a 6 mm aperture of the human cornea, but on a context of more realistic pupillary aperture based on the patient's exit pupil. The average exit pupil, is around 15-20% less in size than the entrance pupil, the measured pupil size in the clinic (this aspect is detailed in the article https://www.quickguide.org/post/relationship-between-the-mesopic-pupil-size-and-diffractive-zone-of-multifocal-iol ).

To this extent, IOL companies should quote the spherical aberration value and ideally of an aperture size of 4.5 mm. This would help choose the right #EDOF IOL based on the induced spherical aberration values. The argument here is that all EDOF or enhanced monofocal IOLs, will induce some amount of spherical aberration, regardless of their mechanism of action or optical profile that induce depth of focus. Thus an EDOF IOL that generates significant amount of negative spherical aberration may not be ideal for a hyperopic lasik patient with a large negative spherical aberration. Doing so may lead to dysphotopsia and photic phenomenon.

In this article I have tried to throw some light on negative and positive SA, and what may be more useful in providing a depth of focus. More importantly, what amount of SA is tolerable to patient for far, and yet provide some depth of focus for the intermediate and near.

(this article is regularly being updated with more evidence as available from peer reviewed studies)

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References:

1. Karolinne Maia Rocha, MD, PhD, Larissa Gouvea, MD, George Oral Waring, IV, MD,

   Jorge Haddad, MD, Static and Dynamic Factors Associated with Extended Depth of Focus in Monofocal Intraocular Lenses, https://doi.org/10.1016/j.ajo.2020.04.014

2. Karolinne Maia Rocha 1, Laurent Vabre, Nicolas Chateau, Ronald R Krueger, Expanding depth of focus by modifying higher-order aberrations induced by an adaptive optics visual simulator, DOI: 10.1016/j.jcrs.2009.05.059

3. Kozhaya, Karim MD; Kenny, Peter I. BS; Esfandiari, Saina OD; Wang, Li MD, PhD; Weikert, Mitchell P. MD; Koch, Douglas D. MD, Effect of spherical aberration on visual acuity and depth of focus in pseudophakic eyes, Journal of Cataract & Refractive Surgery 50(1):p 24-29, January 2024. | DOI: 10.1097/j.jcrs.0000000000001314

4. Comment on: Impact of spherical aberration on visual quality and depth of focus, https://doi.org/10.1097/j.jcrs.0000000000001551

5. Juan Tabernero, PhD, Carles Otero, PhD, John Kidd, BSc, Laura Zahiño, OD, Ana Nolla, OD, Jose Luis Güell, MD, Pablo Artal, PhD, Shahina Pardhan, PhD, Depth of focus as a function of spherical aberration using adaptive optics in pseudophakic participants, J Cataract Refract Surg 2025; 51:307–313