Optical Systems, Design Methods for

An optical system is an assembly of optical parts, such as lenses, mirrors, prisms, plates, and dispersing elements, that forms the optical images of objects on a detector of light energy, such as the eye, a photosensitive layer, or a photocell, or that transforms beams of light according to prescribed laws, as in illumination systems. The designing of an optical system involves finding the structural elements—radii of curvature, indexes of refraction and dispersion of glass or other transparent materials, the distances between lenses, and lens thicknesses—that provide the optical system with the required characteristics. Such characteristics include numerical aperture, angular or linear field of view, magnification, size, image quality or resolution, and light energy distribution. The calculations here are carried out in two stages.

First, the methods of paraxial optics are used to calculate the overall layout and the dimensions of the optical parts. The number of components in the optical system, the distances between the components, and their diameters and focal lengths are thereby determined. On this basis a preliminary design of the system is drawn up and the system’s dimensions and weight are determined more precisely. It sometimes is found in this initial stage that the optical system is basically unconstructable—it may violate certain general laws of energetics, or the requirements for the system may be contradictory.

In the second stage of design the structural elements of individual subassemblies of the optical system are fixed so as to eliminate aberration. The number of aberrations corrected is related both to the purpose of the optical system and to the system’s basic characteristics. For example, only spherical aberration, chromatic aberration, and coma are corrected in astronomical objectives, which consist of two or three lenses and in which the field-of-view angle is small, the focal length great, and the relative aperture small. Both the relative aperture and the field-of-view angle are large in photographic objectives. A larger number of aberrations, seven or more, must be corrected in such objectives, a fact that accounts for the complexity of their design—modern high-power objectives consist of between 10 and 15 lenses. Objectives with a variable focal length, where aberrations must be corrected for several values of the focal distance, are still more complicated and have from 20 to 25 lenses. In the first approximation the design calculations are made on the basis of the third-order theory of aberrations; final adjustments are done with electronic computers for which special programs are written. The values of transverse or wave aberration, or else the magnitude of the frequency-contrast characteristic, which has to be preassigned, serve as the criteria of image quality.