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Accuracy of subsurface temperature distributions computed from pulsed photothermal radiometry

Derek J Smithies-+, Thomas E Milner-+, B Samuel Tanenbaum§, Dennis M Goodman§ and J Stuart Nelson-+

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Pulsed photothermal radiometry (PPTR) is a non-contact method for determining the temperature increase in subsurface chromophore layers immediately following pulsed laser irradiation. In this paper the inherent limitations of PPTR are identified.

A time record of infrared emission from a test material due to laser heating of a subsurface chromophore layer is calculated and used as input data for a non-negatively constrained conjugate gradient algorithm. Position and magnitude of temperature increase in a model chromophore layer immediately following pulsed laser irradiation are computed. Differences between simulated and computed temperature increase are reported as a function of thickness, depth and signal-to-noise ratio (SNR).

The average depth of the chromophore layer and integral of temperature increase in the test material are accurately predicted by the algorithm. When the thickness/depth ratio is less than 25%, the computed peak temperature increase is always significantly less than the true value. Moreover, the computed thickness of the chromophore layer is much larger than the true value.

The accuracy of the computed subsurface temperature distribution is investigated with the singular value decomposition of the kernel matrix. The relatively small number of right singular vectors that may be used (8% of the rank of the kernel matrix) to represent the simulated temperature increase in the test material limits the accuracy of PPTR. We show that relative error between simulated and computed temperature increase is essentially constant for a particular thickness/depth ratio.


PACS

87.19.Pp Biothermics and thermal processes in biology

42.62.Be Biological and medical applications

02.10.Yn Matrix theory

02.60.Dc Numerical linear algebra

87.50.W- Optical/infrared radiation effects

87.50.wp Therapeutic applications

Subjects

Mathematical physics

Computational physics

Optics, quantum optics and lasers

Medical physics

Biological physics

Dates

Issue 9 (September 1998)

Received 15 July 1997, in final form 14 April 1998



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