Propagation of Error from Densitometer Data to Spectrographic Results

Abstract

A treatment similar to that used by Slavin is combined with a logarithmic-logistic equation for a spectrographic-emulsion response curve and used to develop conditions for minimizing the propagation of random error in transmittance data into exposure and analytical results. In cases without spectral background, the optimum transmittance levels for reduced propagation depend sharply on behavior in the photometric system, but not on the slope or contrast terms in the emulsion equations. Optimum levels with spectral background involve contrast specifically and present prohibitive difficulties for direct algebraic treatment. Such cases can be studied by numerical computation and plotting techniques, and results for selected background situations are compared. A small effect of graininess on results obtained from Ilford Q2 plates is discussed.