Line Spectra Analysis: A Cumulative Approach

An optical spectrometer uses detector pixels that measure
the integrated intensity over a certain interval of wavelengths.
These integrated pixel values are divided by the interval
width and then interpreted as estimates of function values of the
wanted spectral irradiance. Hence each pixel measurement constitutes
an averaging process. But, averaging biases at maxima:
pixel data feature lower maxima. This paper proposes the conceptual
use of a cumulated spectrum to estimate spectral data.
The integrated quantities are placed in their natural habitat. The
motivation originates from the fact that pixel data as integrated
quantities are exact values of the cumulated spectrum. Averaging
becomes obsolete. There is no information loss. We start
with a single spectral line. This “true” spectrum is blurred mimicking
the instrument function of the spectrometer optics. For
simplicity we consider the instrument function to have Gaussian
shape. We integrate the blurred spectrum over subintervals
to simulate the pixel measurements. We introduce a cumulated
spectrum approach. We compare the cumulated approach with
the approach that interpolates the averaged function value estimates
of the non-cumulated spectrum. The cumulated approach
requires only basic mathematical concepts and allows fast computations.