## Abstract

Temperature measurement based on pulsed photothermal radiometry is
described. In this technique a body is irradiated by a laser pulse
and its temperature is inferred from the shape of the emitted
photothermal-signal curve. A prototypical system based on a pulsed
CO_{2} laser, an IR detector, and IR-transmitting silver
halide optical fibers was constructed and used to evaluate the
feasibility of this technique. An important feature of the
technique is that changes in sample emissivity or geometric factors do
not introduce errors in the temperature determination. Theory,
simulation, and experimental results are given and
discussed.

© 1998 Optical Society of America

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### Equations (6)

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(1)
$$M\left(\mathrm{\lambda},T,\mathrm{\epsilon}\right)=\mathrm{\epsilon}\frac{{c}_{1}}{{\mathrm{\lambda}}^{4}}\frac{1}{exp\left(\frac{{c}_{2}}{\mathrm{\lambda}T}\right)-1}\mathrm{photons}{\mathrm{s}}^{-1}{\mathrm{cm}}^{-2}\mathrm{\mu}{\mathrm{m}}^{-1},$$
(2)
$$T\left(t\right)={T}_{0}+\mathrm{\Delta}Texp\left(-t/\mathrm{\tau}\right),$$
(3)
$$M\left(\mathrm{\lambda},{T}_{0},\mathrm{\Delta}T,t,\mathrm{\tau},\mathrm{\epsilon}\right)=\mathrm{\epsilon}\frac{{c}_{1}}{{\mathrm{\lambda}}^{4}}\frac{1}{exp\left\{\frac{{c}_{2}}{\mathrm{\lambda}\left[{T}_{0}+\mathrm{\Delta}Texp\left(-t/\mathrm{\tau}\right)\right]}\right\}-1}.$$
(4)
$$\frac{\partial}{\partial \mathrm{\lambda}}\left\{\frac{\partial \left[M\left(\mathrm{\lambda},T\right)\right]}{\partial T}\right\}=0.$$
(5)
$$\mathrm{\Delta}M\left(\mathrm{\lambda},{T}_{0},\mathrm{\Delta}T,t,\mathrm{\tau}\right)=M\left(\mathrm{\lambda},{T}_{0},\mathrm{\Delta}T,t,\mathrm{\tau}\right)-M\left(\mathrm{\lambda},{T}_{0}\right).$$
(6)
$$P\left(\mathrm{\lambda},{T}_{0},\mathrm{\Delta}T,t,\mathrm{\tau},\mathrm{\epsilon}\right)={\int}_{{\mathrm{\lambda}}_{1}}^{{\mathrm{\lambda}}_{2}}\mathrm{\epsilon}\mathrm{\Delta}M\left(\mathrm{\lambda},{T}_{0},\mathrm{\Delta}T,t,\mathrm{\tau}\right)F\left(\mathrm{\lambda}\right)\mathrm{d}\mathrm{\lambda},$$