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High-quality vision correction: Spherical aberration and the pupil are the keys

While measurement technologies have improved, the challenge now is cost-effectively mass-manufacturing corrective devices.

by Louis J. Catania, OD, FAAO PCON Editorial Board member
and Ernst Nicolitz, MD, FACS Special to Primary Care Optometry News

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A number of years ago the television industry introduced “high definition” TV (HDTV) and revolutionized viewing (and purchasing) through increased picture resolution. Such a phenomenon strongly indicates the level of sensitivity and desire the human visual system and the visual cortex seek in their resolution and quality of vision.

Eye care practitioners (ECPs) have addressed quality of vision issues for many years in measuring and correcting human vision at the lower, second radial order (sphere [defocus] and cylinder). However, it was not until the application of adaptive optics, wavefront science and aberrometry into vision care in the past 10 years that ECPs have been able to move to a new level of measurement at the “higher orders” of vision, particularly third order coma and fourth order spherical aberration (SA).

Figure 1. Spherical aberrations are caused by light rays focusing in front of or behind the retinal plane.
Figure 2. Spherical aberrations produce a symmetrical Zernike polynomial (map) in the “circle of least confusion.”
Figure 3. Positive spherical aberration is produced when peripheral rays deviate and cross in front of the retinal plane.
Figure 1. Spherical aberrations are caused by light rays focusing in front of or behind the retinal plane.
 Figure 2. Spherical aberrations produce a symmetrical Zernike polynomial (map) in the “circle of least confusion.”
Figure 3. Positive spherical aberration is produced when peripheral rays deviate and cross in front of the retinal plane.

Images: Catania LJ

Now with adaptive optics, the “circle of least confusion” (the blurred retinal image surrounding the macula) can be color mapped or projected as points of light onto a black background to present a reconstruction of a patient’s Zernike polynomial and point spread function (PSF), respectively.

During this wavefront evolution from lower order to higher order aberration (HOA) measurements, technologies (e.g., lenslet arrays, diffraction gratings, dynamic skiascopy, pixilated optics, nanotechnologies) have begun to be applied to corrective devices including – but not limited to – spectacles, contact lenses and IOLs. These corrective applications verify the philosophy in vision care: If an aberration can be measured, it can be corrected.

Of course, vision correction is a multifactorial process with numerous variables that must be controlled at both the lower and higher order levels. Thus, while lower order corrective devices have been relatively refined over decades of development, the early emergence in correction of HOAs requires careful considerations in its practical implementation. Which HOAs produce the most profound effects on the quality of vision? Which have the highest incidence and prevalence in human vision? Which must be prioritized for the successful development of HOA corrective strategies and devices?

Figure 4. Pupil constriction reduces or eliminates positive spherical aberrations.
Figure 5. Point spread function (PSF) with increasing pupil diameter. Increasing higher order aberrations occur with increasing pupil diameter.
Figure 4. Pupil constriction reduces or eliminates positive spherical aberrations.

Figure 5. Point spread function (PSF) with increasing pupil diameter. Increasing higher order aberrations occur with increasing pupil diameter.

Of equal, practical consideration in vision correction at the lower and higher orders is the effects and dynamics pupil diameter manifests on human vision during dilated and constricted conditions in relationship to light, accommodation, aging and other factors. Such a consideration has produced the realization that the pupil in the measurement and correction of HOAs, especially fourth order SA (the most prevalent HOA, according to Thibos and colleagues) is of greatest importance in ECPs’ efforts to create a new level of quality of vision. This article will attempt to impart an understanding of the clinical measurement and correction of SA and its relation to the pupil in “customized,” high quality (high definition) vision correction.

Clinical considerations

Spherical aberration is defined as light rays from a curved periphery of a lens or mirror producing a shorter or longer focal length (focal point) than light rays from the central (apical) portion. SA generates a symmetrical Zernike polynomial or map in the circle of least confusion. The more or less spherical or steeper the peripheral curve is in relationship to the central or apical curve, the more or less SA (in small clinical amounts) is produced.

This relationship can be stated in a quotient or “Q value” (QV), which is a ratio of the radius of the apex of a curve (R1 in “positive spherical aberration” figure below with darker blue) to the radius of a variable point (R2 in figure) in the curve’s periphery (i.e., peripheral radius [R2]2/apical radius [R1]2 – 1 = QV). This QV can help estimate – though not precisely calculate due to variable peripheral points – the SA of a curve.

Figure 6. Positive SA produces vision reduction at distance and depth-of-focus at near.
Figure 7. Negative SA reduces or eliminates the circle of least confusion. Its peripheral light rays meet behind the retina (red light rays).
Figure 6. Positive SA produces vision reduction at distance and depth-of-focus at near.

 Figure 7. Negative SA reduces or eliminates the circle of least confusion. Its peripheral light rays meet behind the retina (red light rays).

The critical importance of the pupil diameter and its intimate relationship with SA in human vision becomes apparent at this point. When the pupil diameter is large (dilated in mesopia or scotopia – dim or night vision conditions) larger amounts of SA are produced by peripheral rays, as shown in the same figure. When pupil diameter decreases or constricts (miotic pupil, as in “Circle of least confusion” with lighter blue in photopic – bright light or day vision – conditions), SA is reduced, if not eliminated. Thus, the subjective effects of SA in human vision are directly related to pupil diameter.

Randazzo and colleagues have estimated that SA increases by 100% for every 1 mm of increased pupil diameter above 5 mm. The very measurement of vision (refraction) at the lower and higher orders is also directly affected by pupil diameter. The value of wavefront science and aberrometry is again demonstrated here through its ability to precisely measure or program a specific pupil diameter (pupillometry) during the capture of lower and higher order aberrations.

In the case of corneal curvature relative to its focusing of light on the retina, QV gives us an estimate of SA generated by the cornea. However, considering the multiple curved surfaces of the eyeball through which light must pass before reaching the retina (tear film, anterior and posterior cornea, and anterior and posterior lens surfaces), the total SA (effect of all curved surfaces) of the eye becomes a second factor, beyond corneal SA alone, that clinicians must address in measuring vision and correcting it with spectacles and contact lenses in the normal phakic eye. However, in aphakia and IOL considerations, the corneal SA alone, notwithstanding variables in HOAs from the tear film, becomes the critical SA measurement for proper IOL calculations.

Wavefront aberrometers can now provide separate measurements for corneal SA and for total ocular SA. As mentioned above, this is an important differentiation for respective clinical corrective devices. But relative to corrective strategies and devices, an equally important SA measurement aberrometers also provide is the positive or negative nature of SA. This becomes a primary consideration when analyzing the effects of oblate (flatter central than peripheral) vs. prolate (steeper central than peripheral) corneas.

Positive, negative SA

Positive SA does not necessarily mean “good SA.” In fact, there is probably more bad than good in positive SA, whereas “negative SA” might have more good than bad features.

Positive SA simply means that the peripheral rays cross in front of the retina or, if you will, the eye has too much “positive” convergence, and thus a large circle of least confusion results. The eye has too much plus (positive) power for its axial length.

So, positive SA will tend to produce the clinical effects – albeit in small degrees – of myopia, such as blurred distance vision, but magnification at the near point. Thus, positive SA has the adverse effect of reduced or degraded quality distance acuity but the beneficial effect of near magnification or depth-of-focus.

Negative SA is obviously the opposite of positive SA, that is, its peripheral rays meet behind the retina, produced by insufficient (negative) convergence of the light rays for the axial length of the eye. This generates only a small circle of least confusion, so it has the opposite clinical effects of positive SA. Negative SA will produce minimal reduction or degradation in distance vision, but it will not produce the depth-of-focus for near created by positive SA. As in life, “You can’t have your cake and eat it, too.”

With an understanding of positive and negative SA and QV, it flows that hyperopes who tend to have more oblate corneas (steeper peripheral, flatter central) will have more positive SA vs. myopes who have more prolate shaped corneas (flatter peripheral, steeper central) and, thus, tend to have more negative SA.

Because of this, a lower or second order corrected hyperope will not have the visual quality at distance, especially in scotopic or night conditions, as a lower or second order corrected myope. But the myope pays the price for that higher quality, lower order corrected distance vision with less depth-of-focus and, thus, potentially earlier presbyopic symptoms.

Practically speaking, this is usually not the observed effect because myopes “cheat” by removing their corrective lenses for near or sliding them down their nose for less minus (more plus) effect. Hyperopes, on the other hand, at the practical level, quickly begin to notice the adverse near effects of their refractive error as their accommodation begins to wane with age.

Figure 8. Increasing (cumulative or packing phenomenon) SA produces reduced contrast sensitivity.
Figure 9. The crystalline lens before age 20 (in blue) generates little SA due to a flat anterior surface and thin optic. Beyond age 20 (in red), the anterior surface becomes more spherical (oblate) and induces increasing amounts of SA.
Figure 8. Increasing (cumulative or packing phenomenon) SA produces reduced contrast sensitivity.

Figure 9. The crystalline lens before age 20 (in blue) generates little SA due to a flat anterior surface and thin optic. Beyond age 20 (in red), the anterior surface becomes more spherical (oblate) and induces increasing amounts of SA.

Here, again, with positive and negative SA the pupil diameter plays a crucial role in the quality of vision, particularly for the hyperope with the reduction of positive SA and proportional improvement in distance vision with a constricted pupil. For the myope, pupillary constriction does not completely eliminate the already small circle of least confusion but it is a favorable mitigating factor for both distance and near.

Finally, SA has one additional and quite profound effect on the quality of human vision. The visual cortex – the true level of sight and visual quality – uses gradient contrast between light to dark phases (spatial frequencies) as in a cycle from black to white or light to dark, to interpret vision. This highly sensitive interpretation of vision is called contrast sensitivity and is measured by modular transfer function (MTF).

At the “clinical awareness threshold” (= 0.4 µ RMS), cumulative SA (or the packing phenomenon – multiple imagery close together) in a visual pattern will exponentially reduce MTF and contrast sensitivity. Thus, increasing amounts of SA degrade the most sensitive degree of quality of vision (i.e., contrast sensitivity) at the cortical level. This is the major cause of night vision problems including reduced contrast, halos, glare and resultant reduced reaction times.

Epidemiologic considerations

There are more hyperopes than there are myopes, according to Bores. This is an epidemiologic fact of life and, as evidenced from our previous discussion about hyperopes and positive SA, it is inevitable that the clinical effects of SA with distance vision will be a highly prevalent cause of reduced quality of vision in the majority of the ametropic population.

Myopes, with their greater tendency toward negative SA, will not demonstrate much quality of vision loss in youth and early adulthood, assuming accurate lower order correction. But emetropes, hyperopes and myopes will all experience aging and other issues that make SA a mitigating factor in their photopic and, more so, in their mesopic/scotopic vision.

Three categories of epidemiologic factors dictate a predisposition toward SA. They include biologic and optical factors and aging of the crystalline lens. An understanding of each category makes it apparent as to why high quality or high definition vision correction depends on SA and the pupil. These factors will vary the degree of SA from person to person based on tear film effects, growth, aging, the dynamics of human vision (e.g., accommodation) and, mostly, the effects from variable pupil diameters.

The first epidemiologic category, biologic factors, has already been discussed above when defining SA as a product of curved surfaces and the eye’s multiple curved surfaces (tear film, anterior and posterior cornea and anterior and posterior lens surfaces). The innate nature of these ocular surfaces will produce varying degrees of innate SA in the human eye.

The second epidemiologic category with SA, optical factors, is apparent through the epidemiology of human vision itself.

The most common refractive abnormality is spherical correction, primarily as a product of variability of the curved surfaces of the eyeball and their relationship to axial length. Spherical correction through spectacle lenses, contact lenses, IOLs and all forms of refractive surgery uses or optically manipulates the eye’s curved surfaces and, thus, the correction itself generates its own degree of SA. This induced SA is not truly an inherent portion in vision; however, when considering its clinical correction, the SA of the correcting modality must be included.

The third and final epidemiologic category with SA, aging of the crystalline lens, relates to the crystalline lens’ dynamic changes – apart from near accommodation – with increasing thickness and curvature after about age 20.

Beyond about age 20, the lens curvatures, particularly the anterior surface, are constantly increasing in their spherical, oblate nature, according to Rocha and colleagues. By the onset of presbyopia, these physiologic lens changes, with or without cataractous changes, are generating increasing amounts of positive SA, which begin to degrade distance acuity and MTF (contrast sensitivity) with resultant insidious increases in subjective mesopic and scotopic (night vision) difficulties.

Measuring spherical aberrations relative to pupil diameter

The clinical understanding of HOAs, SA and their relationship to the pupil has progressed enormously with the advancement of wavefront aberrometry and its ability to capture a patient’s precise, Zernike polynomial at a given pupil diameter. The ability of new aberrometers to measure total SA as well as separate corneal and lenticular SA at specified pupil diameters can now provide ECPs with unique information to enhance and customize or personalize vision correction to higher levels, such as point-to-point correction of a patient’s Zernike polynomial.

To some degree, measuring capabilities are advancing more rapidly than the ophthalmic industry’s ability to design, fabricate and mass manufacture equivalent, customized vision correction devices. But it is just a matter of time before such challenges are met, and correction is customized to even adjust to varying pupil diameters and other dynamic features of human vision such as accommodation.

Figure 10. A dilated pupil (scotopic vision), with greater amounts of HOAs, will produce an entirely different Zernike polynomial than a constricted pupil (dotted black circle) in photopic vision.
Figure 11. Variability of cylinder power and axis results from increased HOAs in a dilated pupil.
Figure 12. Sufficient increases in SA with a dilated pupil can alter second order sphere.
Figure 10. A dilated pupil (scotopic vision), with greater amounts of HOAs, will produce an entirely different Zernike polynomial than a constricted pupil (dotted black circle) in photopic vision.
 Figure 11. Variability of cylinder power and axis results from increased HOAs in a dilated pupil.

 Figure 12. Sufficient increases in SA with a dilated pupil can alter second order sphere.

Notwithstanding the challenges associated with the evolution of HOAs and high definition vision correcting devices, ECPs’ greater understanding of wavefront science is already providing clinical benefits in lower or second order correction, particularly as it relates to the pupil and photopic vs. scotopic (day vs. night) vision correction. The eternal subjective complaints of night vision problems can now be addressed more effectively in lower order correction as a result of a better understanding of SA and its relationship to pupil diameter.

The HOAs constituting the Zernike polynomial of a patient will vary significantly with varying pupil diameter. At the clinical awareness threshold (= 0.4 µ RMS), HOAs in a scotopic pupil will begin to corrupt the power and axis of the lower order cylinder measured at the photopic level for the same eye. Furthermore, increasing SA (increasing pupil diameter) will cumulatively add to the lower order spherical component as well as produce increasing distance blur and diminishing contrast sensitivity.

Sufficient enough differentials caused by HOAs – particularly SA with scotopic pupils – producing subjective night vision difficulties may require a modification in their lower order correction for improved scotopic vision. Through the use of an electronic phoropter with a programmed photopic and adjusted scotopic compound prescriptions in varying illuminations, the patient can make a comparative analysis of the differences in their respective day and night, lower order corrections.

Correcting spherical aberrations relative to pupil diameter

As stated earlier, the philosophy in vision care is: “If an aberration can be measured, it can be corrected.” Given the level of measurement technologies that have been achieved through wavefront science applications in vision care, this measurement-correction axiom is now a reality. In fact, given the similar nature of measuring and correcting technologies (e.g., lenslet arrays, diffraction gratings, pixilated optics, nanotechnologies), now the challenges are efficiently and cost-effectively mass-manufacturing corrective devices.

In spite of such technical challenges, the correction of SA has already begun to develop at a commercial level with aspheric designed optics. The ability to accurately measure HOAs, SA, QV, contrast sensitivity and MTF has produced a new generation of aspheric spectacles, contact lenses and IOLs. Already, a personalized correction can be selected from among multiple lens options of varying asphericity for a patient’s SA at a given pupil diameter in a phakic or aphakic eye.

Soon, the ECP will be able to specify the desired asphericity of spectacles, contact lenses or IOLs based on the patient’s SA measurements, corresponding pupil diameter and preferred lighting conditions for their vision correction. The ECP will be able to modulate the SA of a patient to perhaps enhance depth-of-focus (for example, as in an early presbyopic myope) or increase distance vision sharpness (as in night-driving correction for a hyperope). While other radial orders of HOAs (third, fifth, etc.) will require point-to-point corrective (adaptive optics) modalities for customized and personalized correction, fourth order SA can be customized based strictly on asphericity and pupil diameter.

Thus, the ultimate level of SA correction will include a dynamic component capable of sensing pupil diameter changes or its relationship to associated lighting conditions and adjusting the asphericity required to neutralize the resultant SA. This is not only “doable” technology, it is already being done. Consider auto-focusing digital cameras and other technologies that adjust to lighting conditions. Through modalities such as pixilated optics, photosynthetic membranes, micro-electro-mechanical systems and nanotechnologies, these capabilities are already being successfully integrated into ophthalmic optics correcting systems.

It is not the technological capabilities as much as it is the challenges of efficiently and cost-effectively mass-manufacturing corrective devices that dictate their rate of progress.

Continual quest for high quality correction

ECPs and their patients are continually striving for high quality vision correction. Perhaps the television industry has set the bar even higher with the successful introduction of HDTV, which has verified patients’ (and their visual cortex’s) strong desire for a level of correction beyond lower order sphere and cylinder. This patient desire along with the increasing role of wavefront science in vision and eye care have produced a growing understanding and clinical awareness of the role of HOAs, specifically fourth order SA and its relationship to the pupil.

SA is the most prevalent HOA in human vision and thus must be addressed in any efforts toward high quality vision correction. Its objective magnitude and subjective effects on vision are directly related to pupil diameter and, thus, that relationship must be addressed in the measurement and correction of SA. While such measurements have been effectively achieved and will continue to advance through the ever increasing sophistication of wavefront aberrometry, the correction of SA and its relationship to the pupil will present unique challenges, some of which have already been addressed with developing technologies and some of which are evolving in new generations of corrective devices.

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