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.

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References

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Transmittance T is related to optical density D by the equation B= —log T, and therefore when b=∞ the value of D required for the minimum σ_E/E is the arithmetic mean of the saturation density D_m and the density D_o of the processing fog level. For this case the T=0 for the photometer system should be set on the shadow of a simulated line of T_m=0 made by supporting a thin strip of metal about 0.3-mm wide on the plate or film in the immediate vicinity of the line to be measured. This technique compensates for scattered light and reduces bias in the determination of T_m from strongly exposed lines in the vicinity.

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