Photoacoustic frequency-domain depth profiling of continuously inhomogeneous condensed phases: Theory and simulations for the inverse problem

Abstract

Photoacoustic frequencydomain depth profiling of continuously inhomogeneous solids. Theory and quantitative profilometry of octyleyanobiphenyl (8CB) liquid crystals An application is presented of the Hamilton-Jacobi formulation of thermal-wave physics [A. Mandelis, J. Math. Phys. 26, 2676( 1985] to the problem of photoacoustic depth profiling of inhomogeneous solids with arbitrary, continuously varying thermal diffusivity profiles. Simple expressions for the modulation frequency dependence of the photoacoustic signal in the case of exponential thermal diffusivity profiles are obtained, and a working general method for solving the inverse problem and obtaining arbitrary diffusivity depth profiles is demonstrated through computer simulations. The method was found to possess excellent profile reconstruction fidelity.

Study of thermal properties of metallic samples AZ91E/ALN

“…These applications include the study of solid and semi-solid organic, inorganic and biological [1][2][3][4][5] . This technique is sensitive to changes in the physical characteristics of the sample and is widely used to measure the thermal diffusivity of many materials.…”

Thermal characterization of nanocrystalline porous CePO4ceramics

“…Since the Rosencwaig-Gersho (R-G) theory was proposed for the photoacoustic effect in solids [14], photothermal methods have been used to determine several material properties in different states of matter where conventional spectroscopic methods fail [15][16][17]. Amongst various photothermal techniques, the photoacoustic (PA) method has become more popular due to it simplistic approach.…”

Thermal depth profile reconstruction by neural network recognition of the photothermal frequency spectrum

“…If the thermal profile of a material is known, then the corresponding photothermal signal can be calculated in a straighforward way. Although a general analytical relation expressing the thermal depth profile as a function of the photothermal spectrum does not exist, several approximate methods [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] have been proposed to extract the depth dependence of the thermal properties from the signal. In essence these methods are all based on one global or many sequential fits of the signal, minimizing the difference between the measured signal and the signal corresponding to the estimated profile.…”