Figures & data
FIGURE 1 Schematic of a typical blackbody optical fiber thermometer.
FIGURE 2 Predicted spectral signal measurements for the furnace temperature profile with corresponding uncertainty bands.
TABLE I Values used in the signal measurement equation
TABLE II Sensitivity coefficients, 
, for the uncertainty contributors, xi
, at several wavelengths [A/(W/m2)]
FIGURE 3 For a predicted uncertainty of 3% with a 95.4% confidence interval, the standard deviation for the distribution is 1.5% (σ = 0.5 normalized).
FIGURE 4 Laboratory furnace set-up with multipoint thermocouple for temperature characterization.
FIGURE 5 Measured furnace temperature and estimated temperature profile.
FIGURE 6 Reconstructed temperature profiles for profile A with confidence intervals on the uncertainty ranging from 86.6 to 99.7%.
FIGURE 7 Reconstructed temperature profiles for profile B with confidence intervals on the uncertainty ranging from 86.6 to 99.7%.
FIGURE 8 Reconstructed temperature profiles for profile C with confidence intervals on the uncertainty ranging from 86.6 to 99.7%.
TABLE III Results for three temperature profiles using a fourth-order polynomial
FIGURE 9 Reconstructed temperature profiles for profile A using the coefficients of an eighth order polynomial for the trial functions, CI = 99.7%.
TABLE IV Resulting tip temperature using the two-color method
FIGURE 10 Spectral signal measurements for profile C with a confidence interval on the uncertainty of 86.6%.
FIGURE 11 Spectral signal measurements for profile C with a confidence interval on the uncertainty of 99.7%.
FIGURE 12 Spectral signal components of the fiber emission calculated from Eq. (Equation12).
FIGURE 13 Log plot of the sensitivity coefficients for a fourth-order polynomial.
FIGURE 14 Temperature reconstruction using the genetic algorithm.
TABLE V Reconstruction statistics for the genetic algorithm
Table