General Refracting Systems
Refracting systems can be built up from multiple combinations of lenses of arbitrary thickness and various compositions of optical media, such as types of glass with different refractive indices. Regardless of the complexity, for paraxial rays, such systems can be characterized by a single pair of principal planes and a single refractive power, P.
This is a remarkable simplification. We can ignore everything that takes place at the numerous optical interfaces within such an optical system, and proceed by simply determining the object vergence at the first principal plane, adding the power P, and then locating the image by referencing the exiting vergence to the second principal plane (Figure 1-15).
Figure 1-15 References for a compound optical system. Each lens has its own power and pair of principal planes, as indicated by subscripts 11 and 12, 21 and 22, and 31 and 32. The combined system has an equivalent or “net” power and a single pair of principal planes representing the entire system, indicated by H1 and H2.
(Courtesy of Edmond H. Thall, MD.)
To calculate the location of the principal planes, we must know the details of the refractive events within the lens system. In practice, this is usually done by means of an elegant formalism known as Gaussian optics (or Gaussian reduction). The details are beyond the scope of this book, but the basic idea is as follows: the paraxial approximation is effectively a linearization of Snell’s law. We can therefore express the approximation in terms of 2 types of “linear operators.” (1) The “translation operator” describes the propagation of a light ray through a medium of refractive index n over a distance t. This is, in essence, equivalent to the step of recalculating the vergence of light from a source object (or image created by a previous refracting surface) as referenced to the next refracting surface in an optical system. (2) The “refraction operator” describes the change in vergence at a curved optical interface of radius r between media of refractive indices n1 and n2. It is the equivalent of adding P to find the vergence of light exiting from a refractive interface. We can represent each of these operators in an appropriate coordinate system by a suitable 2 × 2 matrix. We can then use matrix multiplication to calculate the net action of a sequence of refractive events at the various refractive surfaces in a complex optical system.
Excerpted from BCSC 2020-2021 series : Section 3 - Clinical Optics. For more information and to purchase the entire series, please visit https://www.aao.org/bcsc.