Understanding the Science of Wavefront-Guided Correction

Optometric Management, Feb 2004 by Potvin, Rick

Here's a straighforward guide to the fundamentals of this promising technology.

You may not realize it, but you're already measuring wavefront error. Every time you perform a refraction, you determine several components of a patient's wavefront error - the lower-order aberrations of sphere and cylinder.

Wavefront technology represents a more sophisticated way to understand the eye's optical properties. It enables us to measure errors that normally would go undetected, and may explain why some patients are difficult to refract (for example, those with irregular astigmatism). Wavefront sensing may transform the way eyecare professionals measure and, coupled with the excimer laser, correct for optical error.

In this article, I'll explain how wavefront technology combined with the excimer laser allows surgeons to capture aberrations, register the captured wavefront measurements to the ablation and apply the appropriate ablation profile. This results in a wavefront-guided, customized refractive correction.

First, let's take a closer look at how wavefronts are measured.

The ideal wavefront

A point source of light from a distant object produces effectively parallel rays. This corresponds to a series of plane waves that meet the eye. (A wave is constructed by joining all the rays with perpendicular lines.) In an eye with no aberrations, these plane waves would travel through this perfect optical system and form a point focus on the retina, limited only by diffraction.

If an eye has aberrations, a plane wave entering the eye will never come to a distinct point focus. The resultant pattern on the retina is known as the "point-spread function," and its size and shape indicate the eye's aberrations. The rays entering the eye each would have a slightly different point of focus on the retina.

Measuring aberrations

Three techniques have been adapted for use in measuring the eye's optical aberrations:

* The Tscherning Principle. This technique involves projecting a regular clot or grid pattern onto the retina. A CCD fundus camera then captures the image of this grid on the retina. A sophisticated algorithm compares the observed dot pattern to the theoretical expectation, producing a map of the eye's wavefront error. This is similar to ray-tracing, but ray-tracing determines the wavefront error only one location at a time.

* Schemer's Principle. Sensors based on Schemer's Principle may be manual or automated. In the manual version, two small light beams with known separation are directed into the eye, and a patient adjusts his or her relative position until they overlap. The degree to which the beams must be moved indicates the wavefront error. Some neural effects may also be captured, as it is the patient's subjective impression that determines the end point. This is a time-consuming test. An automated variant involves the equivalent of point-bypoint retinoscopy, removing the subjective component and speeding data collection.

* The Shack-Hartmann Principle. Sensors based on this principle are the most common of the three. All laser systems approved for wavefront-guided treatment in the United States incorporate Shack-Hartmann technology.

This principle is based on the theory of light reversibility. A point source of light bounced off the fovea passes through the eye's optical components and is collected on a detector. This detector focuses distinct small areas of the resultant wave using a lenslet array. The difference in the location of the resulting focal points relative to the theoretical location from a plane (perfect) wave determines the wavefront error in each region. Mathematical algorithms then determine the combined wavefront error.

In the past, Shack-Hartmann wavefront sensors have been criticized for an inability to measure a large range of aberrations accurately. The LADARWave CustomCornea device has overcome this deficiency by incorporating a proprietary "proportional array technology," giving it the largest dynamic range commercially available.

Classifying aberrations

Wavefront sensors use a complex geometric formula to break down a wavefront into systematically identifiable components. Currently, the polynomial of choice is the Zernike polynomial, first used to classify the aberrations in optical systems such as telescopes.

The diagram shown here breaks down the first 14 optical aberrations identified in the Zernike polynomial by radial order (top to bottom) and angular frequency (center to periphery). The components of the second radial order (astigmatism, defocus) represent the spherocylindrical refraction we measure now and are known as low-order aberrations. Terms beyond the second order, known as higher-order aberrations, include such things as spherical aberration (the central fourth-order aberration).

While all Zernike terms combine to recreate the wavefront error in an eye, it can be instructive to examine the effects of specific aberrations. For example, if spherical aberration is simulated as the only wavefront error in an optical system, the potential outputs look as they do in the above diagram.