Optical Aberrations and Wavefront Sensing

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.

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:

where F = frequency, V = velocity, n = index of refraction, λ = wavelength.

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 ).

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.

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:

Low spatial frequency corresponds to large angular spacing between white bars (wide grating) and high spatial frequency corresponds to fine grating ( Fig. 2.4 ). The spatial frequency of the images entering the eye can be influenced by the pupil size – the wider the pupil, the higher the spatial frequency of an object that can be perceived by the eye. However, the highest spatial frequency that can be detected by the visual system is also limited by the number of photoreceptors densely packed in the fovea also known as the Nyquist Sampling Limit. The Nyquist Sampling Limit states that spatial frequencies are only detected when they are less than one half the sampling frequency. The human eye cannot detect sampling frequencies higher than 60 c/deg, because the cones on the fovea provide a sampling rate of about 120 c/deg ( Fig. 2.5 ). Our brain compensates for much of this retinal undersampling, making us interpret images as being sharp.

Diffraction is a phenomenon which occurs when light waves are bent as they enter an aperture – in the case of the human eye, the pupil. In 1896, the German physicist, Arnold Sommerfeld, defined diffraction as “any deviation of light rays from a rectilinear path which cannot be interpreted as a reflection or refraction”. Diffraction is important in image quality because it sets limits to the resolution of an image. When a wavefront propagates without interruption, the array of point sources combine and interfere to form a new wavefront of similar shape as the previous one. When the same wavefront is interrupted by an aperture, the waves from the array of point sources combine and form a different shape. As the aperture's diameter increases, light is diffracted less. This principle was described by Huygens & Fresnel.

The Stiles–Crawford effect is another factor which influences image quality. This is the effect of light entering the cones transversely from the pupil margin, which is perceived half as bright as the light entering the center of the pupil. In simpler terms, light that passes through the edge of the pupil contributes less to image quality than light entering the center of the pupil.

Aberrations

Aberrations are dictated by the performance of any given optical system. They occur when light from one point of an object after transmission through the system does not converge into (or does not diverge from) a single point causing image blur. There are two classes of aberrations: chromatic and monochromatic. Theoretically, correcting both chromatic and monochromatic aberrations increases the contrast of images focused on the retina (contrast sensitivity).