Machine-Aided Selection of Optical Glasses for Two-Element, Three-Color Achromats

Abstract

The work of Herzberger and Stephens dealing with the neces­ sary conditions and optical glass selection needed to achieve fourcolor achromats stimulated our interest in seeking combinations of glasses that would give four-color correction for longitudinal chromatic aberration. We have not been successful in finding such a pair of glasses, but we have as a result found several glass pairs which give three-color correction. These may prove to be of some value to astronomers. The general methods used to find these combinations are discussed herein. The methods that we have used are, in principle, those of Stephens but we have adapted them for use in our high-speed digital computers ( IBM 7090, Philco 2000). The first step (see Fig. 1) is to transfer the index of refraction data from the glass manufacturers' catalogs to punched cards. The identification of the glass and manufacturer are put on the card, and weathering, acid, availability, etc., codes can be included as desired. This process need be done only once, except where errors need to be corrected Secondly, the index data are fitted by the method of least squares to Herzberger's Universal Function formula to mini­ mize the effects of measured and typographical errors in the glass tables. The form of the dispersion formula currently used is shown at the bottom of Fig. 1. This program produces a deck of cards which constitutes a Universal Glass Catalog. Each card of the deck has the four fitted indices for the glass at the A', C, F, and h Fraunhofer lines of the spectrum and the identi­ fication of the manufacturer and glass type. The durability coded may be included, and additional comments can be added to the cards at a later date as desired. This fitting step need be done only once also, unless it is desired to fit data to some other formula such as has been done by Sutton and Stavroudis. The third step is to compute from these fitted indices the re­ ciprocal dispersion and whatever partial dispersions are desired. Since the interpolation formula above is used for finding the index at any wavelength, the dispersions can be found for any wavelength within the region of validity of the particular inter­ polation formula used. This fact should prove to be of value since the best partials to be examined will depend on the wave­ length region in which the residual spectrum is to be minimized. If the region from C to F light is not included in the region of