Bandpass-Correction Terms in Spectrophotometry

Abstract

Correction terms for errors arising from the finite width and spectral shape of the system bandpass of a dual-beam, ratio-measuring spectrophotometer are obtained by an extension and further development of the 1949 analysis of Hardy and Young. The analysis extension considers the spectral characteristics of the spectrophotometer’s sample-viewing geometry, optics transmittance, and reference standard, in addition to those spectral characteristics covered in the Hardy–Young analysis; namely, those of the spectrophotometer’s light source, photodetector, and wavelength-analyzing section. The analysis applies to dispersion spectrophotometers, or spectroradiometers, using prisms, gratings, or a combination of prisms and gratings and to abridged spectrophotometers that employ a multiplicity of narrow-band interference filters. Separate sets of correction terms are obtained for transmittance and for reflectance measurements. The analysis development shows how the wavelength centroid of the spectrophotometer system bandpass may be used to make the first-order correction term equal zero. A practical example is considered, wherein several sets of spectrophotometric correction terms, through the fourth-order, are presented. Spectrophotometric data with colorimetric application, which can have a photometric accuracy or precision of 0.1%, can benefit from the application of system-bandpass corrections. The application of system-bandpass corrections to any data having greater accuracy or precision is well warranted.