Optical Image Formation

For the greatest part of human history, visible light has been the only image forming medium. And until recently, visual telescopes and microscopes comprised the vast majority of image forming instruments. The image formation principles examined in this article derive from such venerable ancestry but are broader in their application. Whereas visible wavelengths span a range of less than 2 : 1 in the electromagnetic (EM) spectrum, the contents of this article can find application in devices operating across a wavelength range of ∼106, from nanometers to millimeters. However, the middle part of that range, from about 100 nm to about 10 µm, contains practically all of the devices that are classified as optical instruments, and those are our main concern here. The simplest device for whole-field imaging is the pinhole camera. It comprises a square or rectangular box that has a small opening on one side. The projection of the pinhole on the image plane, taken as approximately the same size as the pinhole itself, provides the resolution limit of the pinhole camera. Image details smaller than the pinhole size cannot be resolved. Any close examination of pinhole camera images reveals considerable blur. Thus, the pinhole camera has two fundamental problems: inferior resolution and a dim image. Both of these problems are resolved by introducing a lens in place of the pinhole. For any nonideal lens, the focal spot size depends on the specific construction of the lens, as well as on the object and image size or the angle at which rays strike the lens. When these realistic considerations are taken into account, it is found that increasing the lens size beyond a certain point normally leads to an increase in spot size or requires a complicated lens construction. The subject of this article is a more detailed appreciation of the contents and implications of the above. The necessary background for much of this material is that of a first-year college physics course. Specifically, some familiarity is assumed with the elementary concepts of a thin lens and its focal length/points and the basic concepts of wave optics. In addition to that, a proper understanding of the image formation concepts in a later section assumes some familiarity with the basic mathematics of Fourier transformations. Although some basic material of Fourier theory is reviewed in the Appendix, it is primarily useful as a refresher for those who already know something about the topic. However, a reader unfamiliar with such mathematics should still be able to appreciate that material because it is largely self-contained, although significantly compressed through omission of most mathematical proofs. A deliberate attempt has also been made to provide simple physical arguments for most equations, and many illustrations have been included. Clearly, for a detailed understanding, the reader must resort to the references given. Keywords: paraxial optics; image control; pinhole camera; size; magnification; lens assemblies; gaussian optics; image irradiance; image quality limitations; image formation; point-spread function; aberrations; frequency domain; optical transfer function; abbe theory; fourier analysis