Spectral Remote Sensing of Temperature Distribution in Semitransparent Solids Heated by an External Radiation Source

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Abstract
A spectral remote sensing method for recovering the temperature distribution in semitransparent solids from remotely sensed spectral emission data is studied. An analytical model that relates the emerging spectral intensity from a plane layer of solid heated by an external radiation source to the temperature distribution, spectral radiation properties, radiation characteristics of the interfaces of the solid, and the source is formulated. The temperature profile is expressed in the form of a finite series of Legendre polynomials; and the coefficients are obtained using an optimization scheme that, by iteratively solving the expressions for emerging intensity, reconstructs the distribution that best fits the spectral emission data. The validity and accuracy of the remote sensing method is evaluated by comparing the recovered temperature with independent measurements in two different experiments; one using surface thermocouples only and the other a Mach-Zehnder interferometer. Experimental results are reported for PPG clear float glass and Corning Code 7940 fused silica using a Perkin-Elmer spectrometer and Barnes Spectralmaster radiometer to measure the emerging spectral radiant energy. For clear float glass, the recovered temperatures were a maximum of 1.5% higher than those measured with surface thermocouples. For fused silica, the linear recovered and interferometrically measured temperature profiles agreed well, with the maximum deviation never exceeding approximately 2% up to about 1000 K.