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Optimum parameters were selected for determining the total content (TC) of Freon R-12 (CCl2F2) from ground spectrometric measurements of solar radiation at the St. Petersburg NDACC station on a Bruker FS125HR Fourier interferometer. On the basis of the obtained optimum set of parameters the total content of R-12 over the station was established over the period of 2009–2018 with a systematic error of 2.7% and a random error of 2.5% over the whole period of the investigations. The preliminary trend estimate was –0.46 ± 0.06% per year.

Using the method of mathematical modeling, we consider the transformation of a random error of light intensity measurement into an error of determining elements of the light scattering matrix. We consider a device in which the polarization properties of probing radiation change depending on the setting of the phase plate and polarization analysis of scattered radiation is performed while the second phase plate located ahead of a stationary analyzer is rotated. A set of settings of the first phase plate has been revealed, which provides a minimum random error in determining the scattered light matrix elements.

An automated Stokes polarimeter of the dynamic type is created to measure the polarization characteristics of radiation emitted, reflected, and scattered by objects at different angles to a surface. An analysis of the versions of processing of measurement resuls has shown that the dependence of a random error in determination of the parameters on the number of positions N of a quarter-wave plate, at which the radiation intensity is measured, is of a similar nature as the dependence on the number of independent measurements of the same quantity $$( \sim 1/\sqrt N )$$ .

Spectroscopic data obtained under real conditions contain, aside from random errors, different instrumental distortions, owing primarily to the nonmonochromatic nature of the spectrum of the source of radiation and the finite resolution of the energy analyzer. Such distortions result in a significant complication of the spectra, whose unequivocal interpretation becomes difficult and often impossible.

where K is an operator describing the effect of the apparatus on the observed spectrum, and is the random error in the determination of the ordinate of the observed profile (see, e.g., [I]). In a real situation, when the measurement error is finite, the problem is mathematically improper. As shown in [1-4], it may be solved properly by the introduction of prior information obtained independently.

The effects of random errors in relation to working conditions are examined for various integral absorption functions. It is shown that the mean transmission ¯T should lie in the range 0.3 to 0.7 as regards minimization of the random errors in the integral quantities; this corresponds to transmission at band peaks TM of about 0.10. Optimum conditions are also deduced for extrapolated measurements and for structureless bands. Integral intensities can be measured to much higher precision if the optimal conditions are used.