An Optimization of Detector-Noise-Limited Infrared Multiwavelength Determinations

Abstract

The existence of optimal absorbance levels for absorption spectrophotometry is well known. The corresponding phenomenon in the multiwavelength measurements characteristic of correlation spectroscopy lends itself to a similar analysis. The resulting optimization equation is quite complex, but can be approximated for several simplified cases. For very similar absorbances among the set of used wavelengths, or for a situation where the absorbance multiplied by its weighting factor at a given wavelength is far greater than for all the others, the classical optimum at A = 0.434 still applies. For a uniform distribution of absorbance, the optimal maximum absorption is A = 0.868. The complex general case can be rearranged to calculate, given data at a given pathlength, what the optimum pathlength should be. In multiwavelength determinations, the optimal condition involves equal relative error in the largest and the smallest absorbance.