Aberrometry and Wavefront Imaging

Snellen visual acuity was developed at a time when the only possible refractive correction of the optical system of the eye was spherocylindrical glasses, and the surgical techniques of treating eye diseases were less advanced. ^[1] The 20/20 Snellen visual acuity was considered normal vision and the goal of treatments and surgeries. This measurement of visual function does not suffice for a full understanding of vision quality, nor is it adequate for the current clinical practice of refractive surgery. Many people have visual acuity that is better than 20/20, and real-world visual performance also includes low-contrast objects under low or high illumination.

Wavefront analysis technology has enabled physicians to measure higher-order optical aberrations in addition to spherocylinders in clinical practice. These measurements can be used to describe the optical properties of the eye and to detect optical irregularities of the visual system that contribute to visual quality. ^{[2, 3]}

In physics, light can be described as either a wave or a particle. In the wave theory, all points of light that originate from the same point source and that are oscillating in the same state or phase are termed a "wavefront." When a wavefront of light travels through a vacuum, there is nothing to cause it to refract and scatter. Therefore, it has no imperfections or distortions. This does not happen in the real world, where even the atmosphere that light passes through modifies its path.

In ophthalmology, the eye is viewed as an optical system. A wavefront of parallel beams of light enters the eye and is distorted by the refractive error and imperfections of the eye's optical system. The total wavefront error is the difference between an ideal perfect wavefront and the actual real wavefront of the eye and gives an idea of the total distortion in the eye. Imperfections in the ocular system impair quality of vision.

Wavefront describes the curve corresponding to the position of multiple light rays exiting the eye that passed the different spots in the area of the pupil, emanating from the point source in the foveola after it passes through the optical system of the eye. The local slope of the wavefront curve at the particular spot within the pupil is derived from the actual image displacement of the point source from foveola as it passes through the optical system of the eye as compared with the ideal/predicted image of the ideal optical system.

All the rays from an object that are entering the eye with an ideal optical system should focus in the foveola. If it is presumed (that is not entirely true) that the light travels to the eye the same way as out of the eye, the wavefront directly measures the aberrations of the eye. Ideal wavefront of an optical system with no aberrations is plane.

Chromatic aberration

Light with short wavelength (blue) bends more than the longer wavelength (red). If yellow light focuses in the foveola, the blue and red lights focus in front of and behind the foveola, respectively. This is the basis of the red/green refractive test in clinical practice. This type of aberration currently cannot be corrected by any procedure.

Wavefront analysis instruments do not analyze degradation of the image caused by the chromatic aberrations.

Diffraction

Diffraction is an example of the properties of light, which is explained by the wave theory of light. When the wave encounters an obstruction, an aperture diffraction changes the direction of the wave. The image formed on the retina from the light entering through the pupil is not a perfect point but a light disc (airy disc) surrounded by concentric dark and light rings. Longer wavelengths (red) diffract more and, therefore, form a larger diameter airy disc.

The diffraction cannot be eliminated by changing the shape of refractive surfaces as is completed with laser vision correction.

The resolution of optical systems is limited by diffraction. If any optical system is within one-quarter wavelength of being perfect (Rayleigh criterion) further improvement of the optical system will not result in significantly better resolution of the optical system.

The aberrations caused by diffraction in the eye under usual conditions tend to be very small. When the pupil size is smaller than 2.5 mm, the diffraction increases and sets a limit for visual acuity.

Monochromatic aberrations

Monochromatic aberrations that depend on the shape of the refractive surfaces are measured and analyzed by the wavefront analysis instruments and theoretically could be corrected by changing the shape of the refractive surfaces. Theoretically, the laser vision correction enables creation of a customized shape for every eye with high precision. ^{[3, 4]}

Clinical terms of spherical correction, astigmatism, spherical aberration, and coma are all monochromatic aberrations. Total monochromatic aberrations correspond to the shape deformation of the wavefront.

Corneal and ocular aberrations can be decomposed into Zernike polynomials (ZP) consisting of Zernike coefficients (C). ^[5]

Each term C corresponds to a specific geometric pattern of the aberration (eg, C3 = astigmatism). The number (eg, C3 = 0.4) next to the particular term (eg, term C3) describes the amount of this particular type of aberration present. Zernike coefficients are grouped into orders of ZP (second order C are terms C3, C4, C5, see below).

These are mathematic expressions describing how much of what type of geometric pattern (each coefficient of ZP) is contributing to the total optical (wavefront) aberration. This can be thought of in a similar way, as any curve (function) in geometry can be mathematically approximated with a polynomial function (ie, a function y = a + bx2 +cx3 + dx4 + …).

Other mathematic methods of analyzing the total optical aberrations are possible, but the decomposition to Zernike coefficients became commonly used and likely will develop into a standard way of reporting aberrations.

The most important and commonly used Zernikes are those of the first 6 orders consisting of 28 coefficients (C0 to C27) of ZP, as follows:

• 0-order ZP - C0  (piston)

• 1-order ZP - C1, C2 (tilt)

• 2-order ZP - C3, C5 (astigmatism), and C4 (defocus)

• 3-order ZP - C6, C9 (trefoil) and C7, C8 (coma)

• 4-order ZP - C10, C14 (quadrafoil), C11, C13 (secondary astigmatism), and C2 (spherical aberration)

• 5-order ZP -  C15, C20 (Pentafoil), C16, C19 (secondary trefoil), C17, C18(secondary coma)

• 6-order ZP - C16 to C27 (Hezafoil, secondary quadrafoil, tertiary astigmatism, secondary spherical aberration)

Lower-order aberrations included coefficients C0 to C5, and higher-order aberrations include coefficients C6 to C27.

In normal human eyes of young patients, third order ZP aberrations (ZPA) are responsible for most of the higher-order aberrations of the eye.

Point spread function

Point spread function (PSF) is a measure of how well one object point is imaged on the retina through the optical system of the eye. The PSF and image of an ideal optical system of the eye is zero (a point in the foveola).

Root means square

Root means square (RMS), also called the RMS of the optical path difference (OPD), in micrometers, is a measure of the deviation of an actual image from an ideal image of the source point object. The RMS of an ideal optical system is zero. The total RMS of the average human eye is 0.1 µm at younger than 40 years to 0.25 µm at age 60 years. Standard LASIK increases the RMS several times especially with larger pupil sizes. The RMS of high-quality telescope or microscope is less than 0.1µm, while the RMS of most cameras is several times higher.

Modulation transfer function

Modulation transfer function (MTF) is a set of numbers from 0-1 that characterizes the degradation caused by the tested optical system (eg, human eye), where 1 is a perfect optical system with no degradation of the image and for numbers close to 0, the image cannot be discerned at all.

More detailed explanation of modulation transfer function

The Snellen letters used for testing of visual acuity are high-contrast targets of standard width, and they do reflect the ability of human eyes to read letters but do not characterize the visual performance in different real-world conditions well.

The target often used to test the performance of optical systems (eg, microscopes) is a series of alternating light and dark bars of equal width or even more often its modification, where the brightness of the dark and light areas are changing in the form of the sine wave. The sine wave describes the testing object. This concept is used in ophthalmology in contrast sensitivity testing.

The particular sine wave is characterized by the spatial frequency in cycles per millimeters. Cycle is the width of the dark and light areas together similarly as frequency characterizes the sine wave in math.

Modulation is a number from 0-1, which characterizes the relative height of the sine wave. Modulation close to 1 characterizes high-contrast where the differences between the dark and light areas can be observed readily, whereas the modulation of 0.03 is close to the limit of visual detection of the dark and light area by the human eye. A sine wave pattern with modulation of much less than 0.03 appears as grey to the human eye and dark and light areas cannot be distinguished.

MTF plots a number from 0-1 (modulation), which characterizes the degradation of the image for every spatial frequency of the object sine wave. The testing object sine wave is degraded by the tested optical system to another sine wave characterizing the image. MTF of 1 describes a perfect optical system with no degradation. A sine wave with MTF close to 0 completely degrades the image, so it cannot be distinguished.

Hartmann-Shack aberrometry

Wavefront errors and higher-order aberrations can be measured with wavefront sensing devices called aberrometers. Hartmann-Shack style devices are currently the most commonly used. ^{[5, 6, 7]}  These devices analyze an outgoing light that emerge or is reflected from the retina and passes through the optical system of the eye. ^{[5, 7]}

Light of specific characteristics is projected into the eye onto the macula. Rays that emerges from a single point in the foveola and pass through the optical system of the eye are analyzed. Multiple tiny lenslets in newer devices simulate apertures in the Hartmann disc located in front of the eye that isolate a narrow pencil of light emerging through different parts of the pupil. A charge-coupled device (CCD) camera registers the true position of each ray and compares it to the calculated reference position of such a ray for a perfect optical system of the eye without aberrations. This difference enables calculation of the aberrations of the true optical system of the eye.

Examples of these devices are Wavefront analyzer made by Adaptive Optics, 20/10 Wavefront system by VISX, Wavefront analyzer made by Humphrey/Zeiss and Alcon/Summit/Autonomous, and Bausch & Lomb aberrometer based on Technolas design. ^[8] The images below sample show wavefront maps.

Tscherning aberrometry

Tscherning aberrometry analyzes the ingoing light, which forms an image on the retina. ^[9] A grid pattern formed by multiple spots is projected through the optical system of the eye and forms an image on the retina. This image is observed and evaluated by a method similar to indirect ophthalmoscopy and captured on CCD camera. The distortion of the grid pattern enables calculation of the aberrations of the optical system of the eye.

Tscherning aberrometry is used in Dresdner Wavefront Analyzer distributed by Technomed, Wavelight, and Schwind.

Ray tracing aberrometry

This device measures an ingoing light that passes through the eye's optical system and forms an image on the retina. ^[10] It measures one ray at a time in the entrance pupil rather than measuring all the rays at the same time like previously mentioned devices. This decreases the chance of crossing the rays in highly aberrated eyes. The total time of scanning is 10-40 milliseconds.

Ray tracing aberrometry is used in TraceyScan distributed by Tracey Technologies and in the new Pentacam® AXL Wave by Oculus. 

Scanning slit refractometer

Scanning slit refractometer is based on retinoscopic principles. Both the projecting system consisting of an infrared light source and the receiving system rotate at high speed around the optical axis synchronously, and 360° meridians are measured in 0.4 seconds. A group of photodetectors is located above and below the optical axis at 2.0, 3.2, 4.4, and 5.5 mm, which detect the time of its stimulation by reflected light. The time difference depends on the type and amount of refractive error and is converted into the refractive power.

This principle is used in ARK 10000 distributed by Nidek. ^{[11, 12]}

Traditional laser vision correction only treats spherocylindrical refractive errors, including defocus correction (Zernike C4) and astigmatism correction (C3 and C5). For example, a wavefront-optimized treatment will only treat C3 to C5 and will leave higher-order aberrations (C6 to C27) untreated. More recently "customized" interventions allow the simultaneous treatment of both spherocylindrical errors and higher-order aberrations. 

Both Corneal and ocular higher-order aberrations of the eye can be measured with aberrometry and treated by a customized excimer laser ablation of the corneal surface. Customized LVC treatments that address higher-order aberration include the 3 following technologies.

Topography-Guided

Topography-Guided LASIK is currently the most commonly performed customized LVC procedure. A Placido discs topographer scans the anterior corneal surface in detail and the anterior Zernike data is used to guide the excimer laser and regularize the anterior corneal surface. 

Wavefront-Guided

Wavefront-Guided LASIK is the second most commonly performed customized LVC procedure. A wavefront aberrometer scans the total ocular HOA in detail and the total ocular Zernike data is used to guide the excimer laser and regularize the ocular wavefront. 

InnovEyes Ray-Tracing-Guided

Developed by Alcon, InnovEyes ray tracing is the latest technology. ^[10] Firstly, axial length measurements from the Pentacam® AXL Wave (Oculus) provide an accurate representation of all anatomical refractive surfaces of the eye and a theoretical customized anatomical model of the eye is "built" for each patient by the InnovEyes software.

Corneal tomography measurements from the Pentacam® AXL Wave are then used to calculate the propagation of light from the anterior corneal surface to the anterior surface of the lens. The wavefront data is subsequently used to calculate theoretical light ray "trips" from the retina, through the vitreous and lens. Up to 2000 rays are traced in a retrograde fashion and calculated by the algorithm, hence the name “Ray-tracing”.

The InnovEyes software calculates the spherocylindrical treatment and ignores the actual subjective clinical refraction of the patient. It is currently unclear if a nomogram will be required. This technology has not been studied in detail, and more research will be needed. 

 

Before topography-guided for healthy primary eyes came along, excimer laser treatments always targeted manifest astigmatism in primary eyes and not the anterior corneal astigmatism. However, after Contoura's approval based on the 2016 FDA study, many surgeons and scientists, including us, believed that all-comer primary eyes that would undergo removal of higher amounts of anterior corneal HOAs with a topography-guided laser would result in lower predictability if treated on the manifest refraction.

This line of reasoning stemmed from the fact that the manifest astigmatism magnitude and axis were almost always significantly different from the topographically-measured anterior corneal astigmatism, even in primary virgin eyes. Therefore, many surgeons assumed that this discrepancy was mainly due to anterior corneal HOAs contributing to manifest astigmatism, similar to what they had experienced using topography-guided ablation in highly aberrated corneas.

Concerns were raised that primary virgin eyes with larger magnitude/axis discrepancies would result in outlier outcomes if treated on the manifest refraction. Since this belief was put forward by the vendor (Alcon) and key opinion leaders, it became widely spread and accepted even if no definitive evidence-based data supported that these assumptions were valid in virgin corneas.

Given the above, many surgeons moved away from using the manifest refraction and instead started to use the anterior corneal astigmatism as treatment input in all primary virgin eyes. In contrast, others treat in-between the manifest and anterior corneal astigmatism. More recently, some surgeons have also started to use analytical software to consider the refractive impact of anterior corneal HOAs in planning.

These new treatment paradigms were designed to improve primary topography-guided outcomes in all-comer eyes. Still, they all use the same unproved assumption to justify not using the manifest refraction: assuming that anterior corneal HOAs contribute to the subjective manifest refraction in healthy virgin eyes.Does this assumption hold in healthy virgin corneas?

Are anterior corneal HOAs truly contributing to manifest astigmatism in healthy primary eyes?

There are many examples in the recent literature of surgeons and clinicians that assume that the difference between Manifest and Topographical anterior astigmatism, in healthy primary corneas, is due to anterior corneal HOAs. The two italic quotations below are from published articles:

"Higher-order aberrations interacting with lower-order astigmatism is the main reason for the differences between manifest-refraction and Contoura measured astigmatism."  

"Manifest and Topo cylinder tend to differ in eyes with high-order aberrations because the subject may choose a spherocylindrical refraction in an attempt to correct high-order aberrations"

If such assumptions are valid in primary virgin eyes, and that the presence of anterior corneal HOAs mainly explains the discrepancy between refractive astigmatism (RA) and anterior corneal astigmatism (ACA), then there must be objective scientific proofs of that, such as a direct relationship between the amount of anterior corneal HOAs, and the amount of RA to ACA discrepancy. This is precisely what our Research Unit studied in nearly 40,000 all-comer eyes.

When calculated vectorially, the discrepancy between refractive astigmatism and anterior corneal astigmatism is termed ocular residual astigmatism (ORA). ORA is the best parameter to quantify the amount (in diopter) of the difference between Manifest and Topographical anterior corneal astigmatism because it considers both the magnitude and axis discrepancy.

Of the various types of anterior corneal HOAs, anterior corneal coma is believed to be the most significant contributor to ORA. Yet, we found no meaningful relationship between the anterior corneal coma magnitude and ORA magnitude nor between the anterior corneal coma axis and ORA axis, both with quasi-null correlation coefficients. The ORA was, in fact, against-the-rule (ATR) in 86% of eyes, whereas the anterior corneal coma was ATR in only 28% of eyes. 

Because no meaningful correlation was found between anterior corneal coma and ORA, anterior corneal coma cannot be a significant cause of the observed discrepancy between anterior corneal astigmatism and refractive astigmatism in healthy primary eyes. Therefore, the main contributors to the difference must stem from the posterior cornea, other internal ocular factors, and cortical perception.

Recent topography-guided protocols disregard refractive astigmatism and instead recommend treating the topography-measured anterior corneal astigmatism together with anterior corneal HOAs in primary eyes. This guidance wrongfully assumes that corneal HOAs are the leading cause of the discrepancy (ORA) between refractive astigmatism and anterior corneal astigmatism. If that assumption was valid and the corneal HOAs were treated, the anterior corneal astigmatism would equal refractive astigmatism, and then only anterior corneal astigmatism would need to be corrected. However, this logic neglects the impact of posterior corneal astigmatism, which is a much more significant contributor to ORA.

Although anterior corneal HOAs might affect refractive astigmatism in highly aberrated eyes with anterior corneal coma-dominant optics, this is not the case in primary eyes, as shown here. Healthy virgin corneas are markedly anatomically and physiologically different than highly aberrated pathological corneas. Virgin corneas don't have anterior corneal HOA-dominated optics. They have much smaller amounts of naturally occurring HOAs that contribute very little if anything at all to manifest astigmatism, as we debunked using those 37,454 all-comer primary eyes.