Abstract
A solution method is proposed to the inverse problem of determining the unknown initial temperature distribution in a laser-exposed test material from measurements provided by infrared radiometry. A Fredholm integral equation of the first kind is derived that relates the temporal evolution of the infrared signal amplitude to the unknown initial temperature distribution in the exposed test material. The singular-value decomposition is used to demonstrate the severely ill-posed nature of the derived inverse problem. Three inversion methods are used to estimate solutions for the initial temperature distribution. A nonnegatively constrained conjugate-gradient algorithm using early termination is found superior to unconstrained inversion methods and is applied to image the depth of laser-heated chromophores in human skin.
Highlights
Pulsed photothermal radiometry (PPTR) is a noncontact technique that utilizes an infrared detector to measure temperature changes induced in a test material exposed to pulsed radiation
Heat generated as a result of light absorption by subsurface chromophores in the test material diffuses to the surface and results in increased infrared radiant emission levels
In the following analysis we assume that the thermal diffusivity in a one-dimensional layered test material is constant following pulsed laser irradiation and derive an integral equation relating measured PPTR signal amplitude to the initial temperature distribution
Summary
Pulsed photothermal radiometry (PPTR) is a noncontact technique that utilizes an infrared detector to measure temperature changes induced in a test material exposed to pulsed radiation. In the following analysis we assume that the thermal diffusivity in a one-dimensional layered test material is constant following pulsed laser irradiation and derive an integral equation relating measured PPTR signal amplitude to the initial temperature distribution. Because we seek only to find the initial temperature distribution immediately following laser irradiation, analysis of the pulsed radiative transfer in the test material is not included. We deduce the initial temperature distribution from the measured PPTR signal amplitude by finding a solution estimate to the derived integral equation. We derive an expression for PPTR signal amplitudeDSt͒ in terms of the initial temperature distributionDTz, t 0͔͒ in a test material immediately following pulsed laser irradiation. From the Green’s function solution to the one-dimensional heat-transfer problem[7] the temperature distribution DTz, tat an arbitrary depth z and time t is written as DTz,
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