Analysis of multi-band pyrometry for emissivity and temperature measurements of gray surfaces at ambient temperature

A multi-band pyrometry model is developed to evaluate the potential of measuring temperature and emissivity of assumably gray target surfaces at 300 K. Twelve wavelength bands between 2 and 60 μm are selected to define the spectral characteristics of the pyrometers. The pyrometers are surrounded by an enclosure with known background temperature. Multi-band pyrometry modeling results in an overdetermined system of equations, in which the solution for temperature and emissivity is obtained through an optimization procedure that minimizes the sum of the squared residuals of each system equation. The Monte Carlo technique is applied to estimate the uncertainties of temperature and emissivity, resulting from the propagation of the uncertainties of the pyrometers. Maximum reduction in temperature uncertainty is obtained from dual-band to tri-band systems, a small reduction is obtained from tri-band to quad-band, with a negligible reduction above quad-band systems (a reduction between 6.5% and 12.9% is obtained from dual-band to quad-band systems). However, increasing the number of bands does not always reduce uncertainty, and uncertainty reduction depends on the specific band arrangement, indicating the importance of choosing the most appropriate multi-band spectral arrangement if uncertainty is to be reduced. A reduction in emissivity uncertainty is achieved when the number of spectral bands is increased (a reduction between 6.3% and 12.1% is obtained from dual-band to penta-band systems). Besides, emissivity uncertainty increases for pyrometers with high wavelength spectral arrangements. Temperature and emissivity uncertainties are strongly dependent on the difference between target and background temperatures: uncertainties are low when the background temperature is far from the target temperature, tending to very high values as the background temperature approaches the target temperature.