## Abstract

Each surface in an optical system reflects a small fraction of the incident flux, which thus is lost to the image; these surfaces singly and in combination form ghost images of the light source, in various locations in and about the system. The number of first-order ghosts is equal to the number of surfaces, and the number of second-order ghosts equals the number of pairs of surfaces. The total flux through the ghosts is shown to be *F*_{0}*ρ*(1−*t*^{2}* ^{n}*)/1−

*t*

_{2}for first-order ghosts, and

for the double reflection second-order ghosts, where *n* is the number of surfaces at which reflection can take place, *t* the transmittance, and *ρ* the reflectance at each surface. The left member has a simple interpretation.

In the general case of *s* interreflections, 1<*s*≤*n*, combinational theory indicates an expression:

for the number of ghosts, since (a) interreflection potentially can happen an unlimited number of times in any group, so that all multiplets of order less than *s* must be included, and (b) first reflection is prohibited at the first surface in all multiplets, because of the direction of light flow.

The relations are applied to a system of triplet condensers and projection lenses, coated and uncoated in all combinations. Even though the ghost flux is minimum in the condenser-unfilmed, objective-filmed objective, it offers no advantages over the all-filmed case, because of the lower transmission.

© 1949 Optical Society of America

Full Article | PDF Article## Corrections

Allen E. Murray, "Erratum: Reflected Light and Ghosts in Optical Systems," J. Opt. Soc. Am.**39**, 356-356 (1949)

https://www.osapublishing.org/josa/abstract.cfm?uri=josa-39-5-356