In the previous chapter, we discussed paraxial optics, also referred to as âfirst-orderâ optics, in which we considered the properties of an optical system close to the optical axis. In effect, we have assumed that lenses form perfect images, with no aberrations.
Outside the paraxial region, this assumption is invalid. Real lenses have aberrations, which must usually be reduced. The reduction of aberrations is, of course, the function of the lens designer, and the main subject of this book.
Aberrations are calculated by a process known as ray tracing, probably first used by William Gascoigne, in which the exact form of Snell's law is used, rather than its paraxial approximation. Gascoigne died in 1641, at the Battle of Marston Moor, aged 24, without publishing his method. However, he is thought to have used it to design the telescopic sight and the micrometer eyepiece.
There are at least three methods of looking at such aberrations, but the transverse ray aberration, shown in Fig 3.1 is the most easy to understand, and often the most useful. (The other methods are wavefront aberrations, discussed below, and longitudinal aberrations, which are not considered here. All three methods give essentially the same information but in different ways; in some situations one method is more useful than the others, but this is very often a matter of personal preference.)
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