F. Alan McDonald

Generalized theory of the photoacoustic effect

The theory of the photoacoustic effect is extended to include the contribution of mechanical vibration of the sample. Coupled equations for thermal and acoustic waves are solved in both sample and gas. It is shown that the pressure signal in the gas may be significantly affected by acoustic coupling in the sample, and experimental confirmation of this extended theory is given. The results of the fully coupled treatment are shown to be accurately reproduced by an extension of the Rosencwaig piston model: the pistonlike motion of the gas boundary layer adjoining the sample is superimposed on the mechanical vibration of the sample surface to give a composite piston displacement which then produces the pressure signal in the gas. The composite‐piston model provides relatively simple algebraic results applicable to many cases of physical interest.

Photoacoustic determination of absolute optical absorption coefficient

We propose and demonstrate that the photoacoustic effect can be used for absolute determination of the optical absorption coefficient. The photoacoustic signal is measured as a function of chopping frequency and compared to the theory of the photoacoustic effect. The essential agreement of theory and experiment over a restricted frequency makes possible the determination of the optical absorption coefficient (to within 10% in a test case). Observation of a characteristic leveling off of the photoacoustic signal at low frequencies for several materials is also reported.

Three‐dimensional heat flow in the photoacoustic effect

The theory of the photoacoustic effect is generalized to include three‐dimensional heat flow. For typical experimental conditions the predicted photoacoustic signal is precisely the same as that from previous one‐dimensional models, subject only to the restriction that thermal waves transverse to the incident beam do not reach the cell walls. This conclusion applies to both thermally thick and thermally thin sample or gas.

Subsurface‐structure determination using photothermal laser‐beam deflection

Photothermal imaging using laser‐beam deflection is shown to be a successful means of detecting subsurface structure in solids. Experimental data for known and unknown subsurface structures are reported. The existing theory agrees well with data on broad subsurface structures, but small subsurface structures produce signal variations which are better represented by a subsurface thermal contact resistance. The first photothermal‐image characterization of a microscopic, unknown subsurface defect is presented.

Three‐dimensional heat flow in the photoacoustic effect‐II: Cell‐wall conduction

The three‐dimensional treatment of heat flow in the photoacoustic effect is extended to allow for thermal conduction to the cell walls. The typical effect is to reduce the photoacoustic signal when thermal waves extend to the cell wall with appreciable amplitude, although small increases may also occur. Results are in good agreement with recent experimental data. Comparisons with predictions from one‐dimensional models are given.

Photoacoustic determination of small optical absorption coefficients: extended theory

Photoacoustic measurement of small absorption coefficients provides an important alternative to standard techniques. The theoretical basis for such measurements is extended to include the effects of thermally generated mechanical motion of the sample, by incorporating the thermoelastic equations for an isotropic solid in a cylindrical configuration. Sample calculations show that this thermoacoustic effect may dominate the photoacoustic signal for certain modulation frequencies and beam configurations.Photoacoustic measurement of small absorption coefficients provides an important alternative to standard techniques. The theoretical basis for such measurements is extended to include the effects of thermally generated mechanical motion of the sample, by incorporating the thermoelastic equations for an isotropicm solid in a cylindrical configuration. Sample calculations show that this thermoacoustic effect may dominate the photoacoustic signal for certain modulation frequencies and beam configurations.

Photoacoustic cell for liquids and solids: Generalization of one-dimensional models

The theory of the photoacoustic signal from a gas-filled sample cell is reconsidered, and it is shown that the results obtained from one-dimensional models are more generally applicable. In particular, for typical experimental conditions, a simple modification of the composite piston model presented previously gives an expression for the signal in any nonresonant cell.

Resolution and definition in photothermal imaging

The influences of pump and probe beam sizes, as well as chopping frequency, on resolution and definition in photothermal laser‐beam‐deflection imaging of subsurface structure are investigated experimentally and theoretically. It is shown that the resolution of nearby subsurface structures is improved by decreasing pump and probe beam sizes to dimensions less than, but not necessarily much less than, the characteristic dimension of the subsurface structures. It is also shown that the photothermal image width (full width at half maximum) may be different from the structure size, and that the width may vary with frequency, for certain structure geometry. A theoretical model of thermal‐wave scattering gives results consistent with the present experimental data and with previous, apparently contradictory, results in the appropriate geometric limits.

Scanned Photothermal Imaging of Subsurface Structure

Photothermal imaging using laser beam deflection (PTLBD imaging) has recently shown considerable potential for nondestructive detection of subsurface structure in solids.1 In this technique localized heating of a sample by a modulated laser beam produces a periodic temperature gradient in the fluid near the sample surface. The thermally induced gradient in the index of refraction of the fluid causes a periodic deflection of a laserprobe beam passing through the heated surface region. As the sample is translated relative to the beam intersection point, the magnitude and phase of the deflection signal give information about local variations in sample optical and thermal properties. Preliminary indication of the detection of subsurface structure with this technique has been given.2,3 The PTLBD technique has proved successful in studying surface structure, 2-4 and has also been used in spectroscopic studies.5 The potential advantages of PTLBD imaging over related photothermal approaches have already been identifieid. When compared to photoacoustic cell detection, this technique has much greater potential sensitivity,2 is not restricted to small sample size, and allows both excitation and detection to be spatially localized.7

Theory of photoacoustic signal generation for optimized photoacoustic cells

Recent advances in the theory of the photoacoustic effect are applied to the problem of cell optimization. Three‐dimensional heat flow, including conduction to the cell window and walls, is considered. A relatively simple theoretical expression for the signal is obtained, provided certain experimental conditions are satisfied.