Key Features
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Zernike polynomials and Fourier transforms are used to represent and analyze the ocular wavefront.
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Optical properties influence image quality.
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Different devices measure ocular aberrations differently.
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Wavefront-customized and wavefront-optimized ablations result in better visual acuity and mesopic contrast sensitivity.
Introduction
The eye is a complex, imperfect optical system. As light rays from distant objects pass through the optical components of the eye, they refract at the tear film and at corneal and crystalline lens interfaces. Any deviation from a perfectly focused optical system is referred to as aberration. Most of these aberrations reflect myopia, or hyperopia, and regular astigmatism, known as lower-order aberrations (LOA), which can be corrected with spherocylindrical spectacles. Other optical aberrations are commonly referred to as irregular astigmatism and include spherical aberration, coma, trefoils, and quadrifoils. Irregular astigmatism encompasses higher order aberrations (HOA).
HOA may decrease the quality of vision and cause symptoms in up to 15% of the general population. Rigid contact lenses can correct HOA that are generated at the anterior corneal surface. More advanced treatments involve the use of a personalized wavefront-guided laser refractive technique to reshape the surface of the cornea that leads to a more optically desired outcome.
A customized corneal shaping requires wavefront analysis of the eye (aberrometry). For reproducibility, the waveform can be decomposed into components, using either Zernike polynomials or Fourier analysis. The wavefront map is digitally interfaced with an excimer laser to control the delivery of a laser beam across the cornea in a customized fashion.
In the majority of the population, other noncustomized treatments may use epidemiological data to predefine ablation profiles that may be suitable to improve high-order aberration, especially spherical aberration. Although these treatments are not personalized for each patient, they are based on epidemiological information of wavefront analyses and are commonly known as wavefront optimized treatments.
Wavefront Optics
The wavefront is the locus of points in an optical pathway having the same phase. If all incoming rays are parallel, and the eye is free from any aberrations, the resultant emerging wavefront is a perfectly flat surface. In other words, all light rays coming from a point source located at infinity focus at a single point on the retina. In reality, though, the focusing properties of a real eye are not completely uniform: Some areas bend light more strongly than others. The wavefront aberration is the deviation of a particular eye’s wavefront from the ideal wavefront in the pupillary plane. Its magnitude is entirely dependent on the diameter of the pupil; a larger diameter leads to a larger wavefront error ( Fig. 3.6.1 ).
Higher-Order Aberrations
HOA are monochromatic refractive disorders that may limit the vision of healthy eyes to less than the retinal detection threshold. HOA cannot be corrected with spherocylindrical lenses or with standard refractive surgery. They have been categorized using Zernike polynomials by radial order and by angular frequency, with third order and higher constituting HOA. The higher the order, the less visually significant the aberration. The two most frequently discussed aberrations are spherical aberration (which causes halos and night vision disturbances) and coma (which is associated with monocular diplopia). The wavefront in spherical aberration is spherical in the center of the pupil but changes its curvature toward the edge of the pupil, giving concentric rings of focus that result in point images with halos. In coma, the wavefront is asymmetrical, producing a comet-shaped pattern ( Fig. 3.6.2 ). Trefoil, quadrifoil, pentafoil, and secondary astigmatism are other HOA (see Fig. 3.6.2 ).
Ideal Corneal Shape
The shape of the cornea is prolate (more curved in the center) to allow for a lower total HOA. The Q-value of the central cornea (5–7 mm) in a normal population varies from −0.21 to −0.27, meaning that the central cornea has a stronger curvature than the periphery. This aspherical shape allows for focusing of rays coming from the periphery and those coming from the center on one point, correcting for inherent spherical aberration of spherical lenses. Any change in the average prolate corneal shape toward a more oblate profile (less curved in its center) leads to induction of spherical aberrations and consequently a decrease in night vision and contrast sensitivity.
Measurements of Wavefront Aberrations
Zernike polynomials and Fourier transforms are used to analyze the detected ocular wavefront. Zernike polynomials are a sequence of polynomials based on a radial model, whereas Fourier transforms represent nonradial mathematical functions of frequency. Most aberrometers used for customized laser surgery rely on Zernike polynomials to decompose the wavefront aberrations ( Fig. 3.6.2 ). They can, in principle, measure an infinite number of aberration orders. Clinically, data up to the Zernike fifth order capture nearly all the aberration variance typically found in normal human eyes. The Fourier analysis can decompose an image into spatial frequency components with a higher resolution of the surface ( Fig. 3.6.3 ).
The measured wavefront errors are represented as root mean square deviations (RMS), which are correlated to the absolute deviation of an ideal wavefront. Applegate and colleagues evaluated the effect of individual Zernike modes on visual quality and noted large differences in their subjective impact, with those in the middle of a given Zernike order influencing vision more than those at the periphery. For example, in the second radial order, defocus degrades vision more than astigmatism. Similarly, in the third and fourth order, coma and spherical aberration degrade vision more than trefoil and quadrifoil, respectively (see Fig. 3.6.2 ).
Quality of Vision and Measures of Optical Quality
Visual assessment has two parts, acuity (quantity) and quality. A good visual acuity can be achieved on a high-contrast eye chart by correcting LOA using the standard refractive ablation. Vision quality refers to all fine details, colors, and shades of images after they are in focus—it is especially compromised in dim light. It can manifest as double vision, ghosting, glare, halos, starbursts, and reduced contrast sensitivity.
Standard approaches to quantification of the optical quality of the eye describe either the optical properties of the eye (aberration maps, wavefront error maps) or the effect these properties have on image quality (abnormality of an image of a point light source or of a sinusoidal grating).
Aberration maps measure the undulating wavefront from an aberrated eye at the pupillary plane; they are quantified by the RMS wavefront error. Despite the fact that RMS wavefront error is not a good predictor of the subjective impact of aberrations on vision, it usually gives a rough estimate of the overall aberrations of the eye.
Image plane metrics quantify the quality of the retinal image for both a point source of light (the point spread function, PSF) and a sinusoidal grating (optical transfer function, OTF). The theoretical retinal image of any object can be obtained by a convolution process based on the PSF. Any object can be thought of as a collection of points of light, each of which produces its own blurred image. The retinal image of the object is then the sum of these blurred images. An optical system can affect the quality of a sinusoidal grating by reducing its contrast or by causing a phase-shift. The ability of an optical system to transfer contrast and phase from the object to the image is called the modulation transfer function (MTF) and phase transfer function (PTF), respectively. The eye’s OTF includes both the MTF and PTF.
Wavefront-Measuring Devices
Several methods for assessing the wavefront aberrations in human eyes are currently available. Each method has its own way of measuring the displacement of a ray of light from its ideal position. They can be generally classified as outgoing or ingoing aberrometers.
Devices based on the Hartmann–Shack principle are currently the most widely used. These devices analyze an outgoing light that emerges or is returned from the retina and passes through the optical system of the eye. A narrow beam of light is projected onto the retina, and its image passes through the lens and the cornea and exits the eye. The Hartmann–Shack sensor has a lenslet array that consists of a matrix of small lenses. The light that emerges from the eye is focused on a charge-coupled device (CCD) camera through each lenslet to form a spot pattern. The spot pattern of an ideal subject with a perfect wavefront will be exactly the same pattern as the reference grid; a distorted wavefront will create an irregular spot pattern. Displacement of lenslet images from their reference position is used to calculate the shape of the wavefront. The advantages of this system include the fact that it measures wavefront in one shot; hence it is faster, leading to a higher resolution and a higher repeatability ( Figs. 3.6.4 and 3.6.5 ).
