Effect of radiometric errors on accuracy of temperature-profile measurement by spectral scanning using absorption-emission pyrometry

The spectral-scanning method may be used to determine the temperature profile of a jet- or rocket-engine exhaust stream by measurements of gas radiation and transmittance, at two or more wavelengths. A single, fixed line of sight is used, using immobile radiators outside of the gas stream, and there is no interference with the flow. At least two sets of measurements are made, each set consisting of the conventional three radiometric measurements of absorption-emission pyrometry, but each set is taken over a different spectral interval that gives different weight to the radiation from a different portion of the optical path. Thereby, discrimination is obtained with respect to location along the path. A given radiometric error causes an error in computed temperatures. The ratio between temperature error and radiometric error depends on profile shape, path length, temperature level, and strength of line absorption, and the absorption coefficient and its temperature dependency. These influence the choice of wavelengths, for any given gas. Conditions for minimum temperature error are derived. Numerical results are presented for a two-wavelength measurement on a family of profiles that may be expected in a practical case of hydrogen-oxygen combustion. Under favorable conditions, the fractional error in temperature approximates the fractional error in radiant-flux measurement.