The nature, significance, and evaluation of the Schwarzschild-Villiger (SV) effect in photometric procedures

Abstract

The Schwarzschild-Villiger effect has been experimentally demonstrated with the optical system used in this laboratory. Using a photographic mosaic specimen as a model, it has been shown that the conclusions of Naora are substantiated and that the SV effect, in large or small magnitude, is always present in optical systems. The theoretical transmission error arising from the presence of the SV effect has been derived for various optical conditions of measurement. The results have been experimentally confirmed. The SV contribution of the substage optics of microspectrophotometers has also been considered. A simple method of evaluating a flare function f(A) is advanced which provides a measure of the SV error present in a system. It is demonstrated that measurements of specimens of optical density less than unity can be made with less than 1 per cent error, when using illuminating beam diameter/specimen diameter ratios of unity and uncoated optical surfaces. For denser specimens it is shown that care must be taken to reduce the illuminating beam/specimen diameter ratio to a value dictated by the magnitude of a flare function f(A), evaluated for a particular optical system, in order to avoid excessive transmission error. It is emphasized that observed densities (transmissions) are not necessarily true densities (transmissions) because of the possibility of SV error. The ambiguity associated with an estimation of stray-light error by means of an opaque object has also been demonstrated. The errors illustrated are not necessarily restricted to microspectrophotometry but may possibly be found in such fields as spectral analysis, the interpretation of x-ray diffraction patterns, the determination of ionizing particle tracks and particle densities in photographic emulsions, and in many other types of photometric analysis.