Objectives
After working through this chapter, you should be able to:
Define a wavefront aberration
Explain how aberrations can affect the resultant image
Explain a Zernike polynomial
Understand how aberrometers can quantify aberrations
Explain how adaptive optics systems can improve image resolution
Introduction
We’ve already discussed aberrations (imperfections in the image) in previous chapters when we’ve considered spherical aberrations and chromatic aberrations. This chapter will focus on aberrations more generally before explaining why they’re such a nuisance, and how to get rid of them.
Wavefront aberrations
In a perfect optical system that produces an image, all the light rays from the object would be perfectly focused to form a complete, comprehensive and accurate representation of the object (e.g. Fig. 16.1 A). For example, if we think of our eyes as optical systems, the goal of the eye is to focus a clear image of the world onto the back of our eyes so that we can see in perfect clarity. However, as you’ll be familiar with your own eyes, you know that this isn’t the case. If we need glasses, then we’ll see blurry images without our correction, and even if we don’t need glasses, we might struggle to focus on things too close or too far away. These are examples of imperfections in the image which are called wavefront aberrations (because these aberrations exist in the wavefront). In its most basic form, the term ‘aberration’ describes a failure of light rays to converge sensibly at a point of focus. This means that the rays will, in some way, be blurring (less focused; Fig. 16.1 B) or distorting (warped in shape somehow; Fig. 16.1 C) the image.
And, slightly frustratingly, these aberrations exist in almost all optical systems (lenses, imaging systems, eyeballs). This can lead to issues such as: blurry vision for people in the real world, or blurry images being taken of the back of a patient’s eye. We will go into more detail on these aberrations and their effects throughout this chapter.
Types of aberrations
Before we go into detail of how aberrations can cause problems, let’s start by discussing the type of aberrations that can be induced. In the previous section we started to distinguish between blurring relative to distorting, but in actuality, we can break it down a lot more by not only classifying the type of aberration but also classifying how impactful the aberration is. One way to do this is to use Zernike polynomials , which turn the induced aberrations into a mathematical construct so we can tell how disruptive one aberration might be relative to another. In this case, each aberration can be assigned a value that is either positive or negative, and these values will predict alterations in the shape and quality of the image. Zernike polynomials are expressed in the form <SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='Znm’>𝑍𝑚𝑛Znm
Z n m
, where the subscript n defines the order of the aberration, and the superscript m defines the angular frequency (how many times the wavefront pattern repeats itself every 2π radians). Fig. 16.2 shows a view of the polynomials labelled and described.
In optometric practice, the angular frequency aligns with the number of planes of the cornea that the aberration affects – for example, you can imagine that a ‘tilt’ aberration would only affect one plane (horizontal or vertical), so its angular frequency is 1 (−1 or +1 depending on the direction). Also, typically, aberrations with a negative angular frequency are aligned in the vertical plane, whereas aberrations with a positive angular frequency are aligned in the horizontal plane. To provide a clinically relevant example, in chapter 5 we discussed that people can have astigmatism (a refractive error along a particular plane within the eye). In Fig. 16.2 we can see that astigmatism is a second-order wavefront aberration with either a +2 or −2 angular frequency.
Aberrations in lenses
Lenses are used in optical instruments (and glasses) in order to focus light in a set way. This means that you could be forgiven for thinking that all light is refracted through the lens equally, but in reality this isn’t the case. The optical centre of the lens will possess the clearest image, but as light moves away from the optical centre, more and more aberrations (imperfections) will be induced ( Fig. 16.3 ). This is particularly true for high-powered lenses where the lenses need to be thicker in order to produce the power required.
