JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Spectrophotometry in the Presence of Stray Radiation:A Table of Log[(100-k)/(T-k)]

ASCHER OLERResearch Department, Great Western Division, The Dow Chemical Company, Pittsburg, California

(Received January 12, 1950)

When spectrophotometry is conducted in the presence of unavoidable stray radiation, the usual expres-sion for the absorbance [A =log(100/T)] becomes log[(100-k)/(T-k)], where T is the percent trans-mittance (100I/Io) and k is the percent stray radiation. To meet the demands of routine infra-red spectro-photometry in the 15-22,u-region, a table of values of this function was prepared for 1 <T<99 and 0.5<k<20. The calculation of these values was performed by punched card machines.

V HEN spectrophotometry must be performed inthe presence of unavoidable stray radiation, it is

necessary to eliminate or to correct for the false energy.This is especially important when long wave-lengthsare used in infra-red spectrophotometry.

In the range above 15,4, the unfavorable energy ratiobetween the desired wave-length and the wave-lengthof the blackbody maximum of the source causes rapidincreases in the percent stray radiation with wave-length. This stray radiation may be virtually eliminatedby the use of a double monochromatorl or by judiciousselection and use of reflection plates. 2 Most standardprism spectrometers provide some means of reducingthe stray energy, e.g., rotating glass shutter, but thecorrection is never completely effective.

The extent of stray radiation may be estimated bytwo indirect methods:'-'

A. Measure the transmittance of a compound atvarious concentrations. Plot a family of curves usingthe formula A=log[(100-k)/(T-k)] for various k(percent stray light) values. Select the curve whichapproaches nearest to a straight line. The correspondingk is taken as the correct stray radiation.

B. The instrument is standardized at the desiredwave-length and slit width. The radiation at the de-sired wave-length is absorbed while radiations of shorterwave-lengths, which are assumed to account for mostof the stray radiation, are transmitted. This may be

I Hawes, Cary, Beckman, Madsen, Hare, and Stickney, "Adirect transmittancy recording infrared spectrophotometer,"presented before the Symposium on Molecular Structure andSpectroscopy, June 17, 1949, at Columbus, Ohio.

2 E. K. Plyler, J. Opt. Soc. Am. 37, 746 (1947).3Brattain, Rassmussen, and Cravath, J. App. Phys. 14, 418

(1943).Fry, Nusbaum, and Randall, J. App. Phys. 17, 158 (1946).

5 J. R. Nielsen and Don C. Smith, Ind. Eng. Chem. Anal. Ed.15, 609 (1943).

accomplished with a substance that absorbs stronglyat that wave-length or with a filter of glass, mica, LiF,CaF, or NaCl.

In performing routine spectrophotometry in the15-22/.z-range, stray radiation as high as 15 percent wasencountered. As large numbers of measurements weremade daily, considerable time was required for calcu-lating suitable corrections. To simplify this operation, atable giving the corrected absorbance values for differ-ent stray energies was prepared. The 2251 values werecomputed by International Business Machines Com-pany punched card machines.

The calculation was performed with an IBM No.405 Tabulator equipped with card cycle total trans-fer device and an IBM No. 519 Reproducer servingas a summary punch. The equation A = log[(100- k)]/(T-k)] was transformed to A= [log(100-k)]- [log(T- k)]. The calculation was performed stepwiseas follows:

A. 2500 Cards were prepared from 100 master "T"cards and 25 master "k" cards. Each card carried T k,(100-k), log(100-k), and (2-logT).

B. (T- k) values were found by subtraction. Nega-tive values were eliminated.

C. The logarithm values corresponding to the(T- k) values were automatically selected and punchedfrom a punched card table of logarithms.

D. The [log(T-k)] value was subtracted from the[log(100-k)] value.

E. The five-place table was checked by comparingrandom table values with individual calculations usinga seven-place logarithm table. No errors were found.

F. The table was rounded off to four places by adding5 to the last digit before dropping same.

The writer wishes to thank The Dow Chemical Com-pany for permission to publish this table.

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VOLUME 40, NUMBER 6 JUNE, 1950

402 ASCHER OPLER

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