Theory of noncontact point thermal sensing by fiber-optic radiometry

This paper formulates a theory of noncontact point thermal sensing by fiber-optic radiometry. This theory covers the field of mid- and far-infrared fibers that are suitable for low-temperature radiometry. However, new problems arise in the infrared range, the emission of thermal radiation from the fiber itself due to infrared absorption introduces perturbations into the radiometry, and this must be taken into consideration. The model presented is based on three-dimensional optical geometry of bounded and tunneling skew rays and yields an analytical expression for the inclination and the skewness angle distribution of the guided power collected by the fiber from various layers of a thermal body. The effective field of view, the surface resolution, and the temperature resolution of fiber-optic radiometry are discussed. Thermal sensing by direct coupling is shown to have an advantage over the coupling of a focusing lens located behind the fiber tip. A formulation of fiber emissivity is presented that quantifies the suppression of radiometric perturbations in fiber-optic thermal sensing. Bulk and surface absorption in the fiber core and cladding absorption are all taken into consideration deriving emissivity. Combining the transmissivity and emissivity of the fiber, we propose a measurable criterion, a figure of merit, for fiber-optic radiometry.