One of the major applications of the wave theory of light is in wavefront analysis (see also BCSC Section 3, Clinical Optics). Currently, wavefront analysis can be performed clinically by 4 methods: Hartmann-Shack, Tscherning, thin-beam single-ray tracing, and optical path difference. Each method generates a detailed report of lower-order aberrations (sphere and cylinder) and higher-order aberrations (spherical aberration, coma, and trefoil, among others). This information is useful both in calculating custom ablations to enhance vision or correct optical problems and in explaining patients’ visual symptoms.
Measurement of Wavefront Aberrations and Graphical Representations
Although several techniques are available for measuring wavefront aberrations, the most popular in clinical practice is based on the Hartmann-Shack wavefront sensor. With this device, a low-power laser beam is focused on the retina. A point on the retina acts as a point source, and the reflected light is then propagated back (anteriorly) through the optical elements of the eye to a detector. In an aberration-free eye, all the rays would emerge in parallel, and the reflected wavefront would be a flat plane. In reality, the wavefront is not flat. To determine the shape of the reflected wavefront, an array of lenses samples parts of the wavefront and focuses light on a detector (Fig 1-1A). The extent of the divergence of the lenslet images from their expected focal points determines the wavefront error (Fig 1-1B). Optical aberrations measured by the aberrometer can be resolved into a variety of basic shapes, the combination of which represents the total aberration of the patient’s ocular system, just as conventional refractive error is a combination of sphere and cylinder.
Currently, wavefront aberrations are most commonly specified by Zernike polynomials, which are the mathematical formulas used to describe the surfaces shown in Figures 1-2 through 1-6. Each aberration may be positive or negative in value and induces predictable alterations in the image quality. The magnitude of these aberrations is expressed as a root mean square (RMS) error, which is the deviation of the wavefront averaged over the entire wavefront. The higher the RMS value is, the greater is the overall aberration for a given eye. The majority of patients have total RMS values less than 0.3 μm for a 6-mm pupil. Most higher-order Zernike coefficients have mean values close to zero. The most important Zernike coefficients affecting visual quality are defocus, spherical aberration, coma, and secondary astigmatism.
A, Schematic of a Hartmann-Shack wavefront sensor. As can be seen, the reflected wavefront passes through a grid of small lenses (the lenslet array), and the images formed are focused onto a charge-coupled device (CCD) chip. The degree of deviation of the focused images from the expected focal points determines the aberration and thus the wavefront error. B, An example of the images formed after the wavefront passes through the lenslet array. The green overlay lattice is registered to correspond to each lenslet in the array.
Fourier analysis is an alternative method of evaluating the output from an aberrometer. Fourier analysis involves a sine wave–derived transformation of a complex shape. Compared with shapes derived from Zernike polynomial analysis, the shapes derived from Fourier analysis are more detailed, theoretically allowing for the measurement and treatment of more highly aberrant corneas.
Excerpted from BCSC 2020-2021 series: Section 13 - Refractive Surgery. For more information and to purchase the entire series, please visit https://www.aao.org/bcsc.