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Higher Order Abberations

It has long been known that the human eye is not optically perfect. To a greater or lesser degree, many eyes exhibit wavefront aberrations in the eye’s optical path.

One of the simplest aberrations is a focusing error better known to optometrists as ‘defocus’. For myopic eyes, defocus is the result of the peripheral part of the wavefront propagating faster than the center; compared to a theoretically ‘perfect’ spherical reference wavefront which forms the focal point in front of the retina. Defocus is one of the so-called “lower order aberrations”, or LOAs, as shown in Figure 1 (left). The other LOA is astigmatism which causes different focal lengths of the eye along two perpendicular meridians.

Many eyes also have more complex types of aberrations collectively known as “higher order aberrations”, or HOAs, causing the irregular ray diagram shown in Figure 1 (right). These aberrations can significantly degrade visual quality, but unlike LOAs cannot be easily corrected with conventional solutions such as spectacles, contact lenses, or surgery.

Figure 1. Ray diagrams of perfect (red lines) and aberrated (blue lines) eyes.

In practice, an eye’s aberration profile is so complicated it is often easier to dissect it into individual aberrations. Typically, the wavefront map is described by Zernike polynomials, a set of orthogonal polynomials that arise in the expansion of a wavefront function for optical systems with circular pupils, such as eyes.

An arbitrary wavefront profile can be expressed by the sum of individual Zernike terms, multiplied by coefficients known as Zernike coefficients, as shown in Figure 2 (left). Each coefficient quantifies the relative contribution of individual aberrations to the entire ocular aberration. Figure 2 (right) shows individual Zernike aberrations. The first three terms represent sphero-cylindrical refractive errors or lower order aberrations. The other, more complex looking Zernike aberrations, are higher order terms.

Why should we care about such ocular aberrations, especially higher order aberrations? The quantitative ocular aberration makes it possible to objectively predict how image quality is altered by the aberrations by calculating various image quality metrics such as point spread function, Strehl ratio, and modulation transfer function.

Image convolution from the aberration can also visualize how the image of an object, for example a visual acuity chart or natural scene, looks like when imaged on the retina. This capability provides clinicians with precise insights into the visual quality a patient may experience on a day-to-day basis.

Figure 2. Mathematical relationship between an arbitrary aberration and Zernike aberrations (left), and  graphical representation of individual Zernike aberrations (right)

Today, the Shack-Hartmann wavefront sensor is the most commonly-used tool to measure such aberrations. Figure 3 illustrates the principle of the Shack-Hartmann sensor. One of the key components in this type of sensor is the lenslet array that projects a grid of focal spots on a CCD imaging device. Each spot contains local wavefront information at the corresponding location of each lenslet. Measuring the wavefront response from a theoretically ‘perfect’ eye would create a regularly-spaced spot array pattern. However, in the real world the spot pattern deviates from this reference position in an irregular fashion. Local wavefront slope is detected from deviation and wavefront aberration can be reconstructed from the local slopes.

Figure 3. Principle of Shack-Hartmann wavefront sensor.

Some of the higher order aberrations measured with the wavefront sensor can also characterize ocular pathologies. As seen in Figure 4 (left), it is very common to observe increased positive spherical aberration in eyes that have undergone laser refractive surgery. Results from keratoconic patients show large coma and secondary astigmatism, while patients with corneal transplant or radial keratotomy tend to have large trefoil and spherical aberration. As a result, these aberration patterns can provide useful information for diagnosing corneal diseases, or abnormalities.

It is also important to note that higher order aberrations in these pathologic corneas are considerably larger compared to normal eyes, suggesting that a much larger visual benefit is expected in these highly-aberrated eyes if we are able to correct the aberrations reliably. Figure 4 (right) illustrates the potential visual benefit of correcting HOAs, compared to the best spectacle correction of sphero-cylindrical refractive errors.

The visual benefit increases with pupil size simply because of the increased magnitude of the aberration. Even people with normal healthy eyes can achieve a significant visual performance improvement, especially large pupils. The benefit is more substantial when correcting HOAs in patients with keratoconus, even for small pupil sizes under photopic light conditions.

Figure 4. Characteristics of higher order aberrations in eyes with different corneal pathologies (left) and potential visual benefit of correcting the higher order aberrations (right)

There are many ways to correct the higher order aberrations.

Solutions such as adaptive optics, laser refractive surgery, corneal crosslinking, and ophthalmic lenses have been proposed and tested over many years. Among them, both wavefront-guided ophthalmic lenses (including spectacles) and soft and scleral contact lenses are practical and safe options for HOA correction. The surface of the wavefront guided lenses needs to be manufactured to have the opposite topology profile of the measured wavefront, with the magnitude scaled by the refractive index of the lens material. If correctly manufactured, the incoming wavefront becomes flat once the distorted wavefront from the eye propagates through the optics. Such wavefront guided optics can be manufactured using a standard CNC lathe machine, of the type currently used for commercial contact lens manufacture.

Figure 5 shows a brief summary of the correction performance with wavefront-guided ophthalmic lenses in keratoconic patients, as performed in Dr. Geunyoung Yoon’s research laboratory at the University of Rochester. It has been demonstrated that spectacles and both soft and scleral contact lenses can be customized to correct HOAs, resulting in substantial improvement in visual performance. Spectacles are a very good correction method as long as a fixed and accurate alignment between the lens and the eye’s pupil is maintained.

In practice, such a solution presents a number of real-world issues due to misalignment errors from dynamic eye movements. While a soft contact lens could alleviate this limitation, the lens still moves each time a patient blinks. This is one of the reasons why correction performance using soft contact lenses is sub-optimal when compared to well-aligned spectacles.

In contrast, scleral contact lenses are ideally suited to customized HOA correction. Assuming best practices in terms of measurement, manufacture, and fitting, scleral lenses move far less when in the eye. OVITZ has shown how using wavefront guided scleral lenses on patients with severe keratoconus can produce vision results superior to that from typical normal eyes.

Figure 5. Wavefront-guided ophthalmic lenses and their on-eye correction performance

When improving vision by correcting the ocular aberrations, it is important to take the aberrations of the whole eye into account (as opposed to corneal aberration only) since retinal image quality is determined by the total aberration.  quantifying aberrations of the cornea and internal optics as well as the whole eye found that corneal and internal optics aberrations can neutralize each other to certain degree.

This provides evidence that the whole eye aberration, when viewed as aggregated data, is actually smaller than the combined aberrations of the cornea and internal optics when considered (and measured) in isolation. This is clinically important because if an eye’s aberration correction is based, for example, on the corneal aberration measured with corneal topographer, the outcome will be sub-optimal.

It should be noted that with a conventional scleral lens, it is true that the majority of the corneal aberration is compensated due to the reduced refractive index difference between the cornea and tear/fluid lens created underneath the lens. However, the residual higher order aberration is still significantly larger (see the 3rd row in Figure 5) compared to measurements from typical normal eyes. Again, this is due to the various internal ocular components –  i.e. the posterior corneal surface and the crystalline lens – in addition to the uncorrected aberrations from the anterior corneal surface.

The other important factor to be managed carefully, in order to maximize correction performance, is the alignment of wavefront guided optics to the eye. This is because significant amounts of decenteration and/or rotational mis-orientation of the wavefront guided optics can make visual quality even worse, compared to conventional optics. It is therefore critical to identify the reference axis along which the correction is applied. More importantly, this reference axis varies significantly between different patients.

Until recently, such research and development on aberrometer and wavefront guided optics was done in scientific research labs. The aberrometer was built on an optical bench, and analysis and lens design were done somewhat manually. The resulting optical design meant contact lens manufacturers had to develop their own technological and engineering capabilities to transfer the data to their lathe machine in order to precisely manufacture the irregular surface. This entire process took considerable time and required significant resources from both research lab and lens manufacturer.

OVITZ believes this is the main reason why such technology has not been commercially available – until today.

We have dedicated our enthusiasm and resources to developing an all-in-one system consisting of a commercially affordable aberrometer, wavefront-guided lens design, and a streamlined lens manufacturing procedure. Considered together as an integrated, closed-loop system, they complete the entire measurement and manufacturing process in a totally automated fashion (Figure 6). The OVITZ xwave system addresses the aforementioned critical issues by measuring the whole eye aberrations and registering the correction axis – customized to the individual patient.

Figure 6. Patient Results

There are no ideal medical or surgical solutions for patients exhibiting significant ocular aberrations due to keratoconus, post corneal transplant, or other corneal ectasias such as post-surgical issues following laser refractive procedures.

The availability of a well-tolerated contact lens that optimizes visual potential provides a reliable, non-invasive therapeutic intervention. Moreover, it substantially alters the indications for invasive procedures, thereby  improving safety and quality of life for patients with irregular corneas.

The same wavefront-guided lens technology can also be applied to other ophthalmic/optometric fields including presbyopia correction, myopia control, sports vision, and visual training.

For more information on wavefront-guided scleral lenses and the OVITZ xwave system, please contact us at info@ovtiz.us