Introduction
Myopia, hyperopia and cylinder are refractive errors known as second-order aberrations. These aberrations result in the inability of the eye to focus images appropriately on the retina. In myopia, light rays entering the eye focus anterior to the retina. This is most often seen in an elongated eye. In contrast, hyperopia occurs in a short eye where light rays tend to focus behind the retina. Astigmatism results from an irregular-shaped cornea or early cataractous lens, which causes the light rays to focus at multiple points along the pathway to the retina. With regular astigmatism, the rays focus into a line oriented in the same axis of the cylinder, and yet another oriented 90° away. These basic optical errors related to the eye are what we have been correcting for the past 200 years with the aid of spectacles, contact lenses and even refractive surgery ( Fig. 2.1 ).
With the advent of wavefront technology, we have discovered a new way of conceptualizing how light rays behave when entering the eye. This technology allows us to visualize in two-dimensional images, the complex profile of refracted light as it passes through the cornea and the crystalline lens. We are able to now detect higher-order aberrations such as coma, trefoil and spherical aberrations. Laser technology for refractive surgery has evolved significantly over the past years. It now permits us to correct higher-order aberrations by performing a “customized” ablation of the cornea according to the data provided by wavefront sensors, improving the visual performance significantly. What is also exciting is how wavefront technology may be applied to customize contact lenses and even intraocular lenses.
This chapter intends to provide the reader with a basic understanding of optical aberrations, wavefront sensing technology and the benefit of correcting higher-order aberrations in the human eye.
Optical aberrations
In a perfect optical system, such as one free of aberrations, emerging image-forming rays are planar and converge onto a single point. In reality, however, we have learned that this is not true for our optical system, the human eye. In this section, we will review basic concepts of wavefront optics and explain the different types of optical aberrations.
Wavefront optics
In geometric optics, we study the relationships between refractive error and pupil size, which have an impact on the blur of an image. By reducing the pupil size of an eye with a given refractive error, the blur of an image improves by increasing the depth of focus. This can be understood by looking through a pin-hole, in which images appear to be sharper, but at the same time we decrease light and image resolution by inducing diffraction.
In physical optics, we describe light as energy which is transmitted in the form of a wave. The properties of a wave are wavelength, frequency, and velocity. In air, the speed of light remains relatively constant. When the light passes through a higher index of refraction, its properties change and aberrations are formed. This can be explained by the following equation:
F = V n / λ
The waves of light are joined at a single point in time by what is called a wavefront and always travel perpendicular to it. When the light waves emerge from a point source, the wavefront takes on a spherical shape. As the light waves move on, the wavefront becomes progressively more flat or planar. When light waves pass through an aberration-free optical system, they emerge from it perpendicular to the wavefront, forming a spherical shape which is either converging or diverging as if coming from a single point. When the wavefront is interrupted by an optical media with an irregular surface, the emerging wavefront is not planar, the light waves are irregular and unparallel to the wavefront. The distorted shape that a wavefront takes after emerging from an irregular optical media is called a wavefront aberration ( Fig. 2.2 ).
Optical limitations to vision
We cannot discuss the limitations that a human eye’s optics impose on the image quality without introducing the concepts of point spread function (PSF) and modulation transfer function (MTF). To further understand this, we must think of the eye as a camera. Where the cornea, crystalline lens and vitreous are the optical lenses of a camera, the pupil is the aperture, and the retina is the photographic film on which the images will be imprinted ( Box 2.1 ).
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Pupil size
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Nyquist sampling limit
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Diffraction
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Styles-Crawford effect
PSF is the intensity with which an optical system distributes an image from a point source onto the retina. The point source is influenced by the pupil size. The larger the pupil, the more irregular the shape of the point source imaged on the retina ( Fig. 2.3 ).
MTF is the ability of the eye’s optics to focus a sharp image on the retina with high contrast. As light passes through optical structures of the eye, it undergoes a process of “degradation” which can be measured by MTF. If we present an optical system with patterns of light and dark bars and measure their luminance, we are measuring the “modulation” or contrast of the light.
M = ( Maximum Luminance − Minimum Luminance ) ( Maximum Luminance + Minimum Luminance )
MTF involves spatial frequency and measures the sine waves (Fourier transformation) of the light source in cycles per degree (c/deg), which is similar to sound frequency being measured in Hertz (cycles per second). MTF is defined as the modulation of the image, Mi, divided by the modulation of the stimulus (the object), Mo, giving rise to the following equation:
MTF ( v ) = Mi / Mo
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