Single Beam Interferometry of a Thermal Bump: II—Theory

Kuo and Munidasa [1] have reported a method by which a time-dependent optical intensity pattern is produced by the interference of laser light diffracted from a thermally induced bump with the light of the same laser reflected from the plane of the sample on which the bump was induced. In their experiment the thermal bump was induced by a second laser beam which was optically incoherent with the interfering light, but which was intensity modulated at frequencies ranging from the audio to the ultrasonic range. The resulting time-dependent patterns carry information about the thermal and elastic properties of the sample. The purpose of this work is to provide a first-principles calculation of those patterns so that those material properties can be measured with this technique. The starting point of the calculation is the solution to the coupled thermoelastic equations developed by Favro et al. [2–4]. That solution is expressed in terms of the three eigenmodes of the coupled equations: (1) a longitudinal acoustic wave consisting of propagating particle displacements and associated temperature variations arising from the compression and rarefaction of the material; (2) a transverse (shear) wave which consists only of propagating particle displacements and which does not cause any temperature variation as it propagates; and (3) a heavily-damped thermal wave which consists of propagating temperature variations and associated particle displacements arising from the thermal expansion it causes. The combination of surface displacements (i.e. “thermal bump”) resulting from these three kinds of waves when a modulated laser beam is incident on the surface of an opaque solid can be calculated in a straight forward fashion from expressions given in [4]

Long beating wavelength in the Schwarz-Hora effect

Thirty years ago, H.Schwarz has attempted to modulate an electron beam with optical frequency. When a 50-keV electron beam crossed a thin crystalline dielectric film illuminated with laser light, electrons produced the electron-diffraction pattern not only at a fluorescent target but also at a nonfluorescent target. In the latter case the pattern was of the same color as the laser light (the Schwarz-Hora effect). This effect was discussed extensively in the early 1970s. However, since 1972 no reports on the results of further attempts to repeat those experiments in other groups have appeared, while the failures of the initial such attempts have been explained by Schwarz. The analysis of the literature shows there are several unresolved up to now contradictions between the theory and the Schwarz experiments. In this work we consider the interpretation of the long-wavelength spatial beating of the Schwarz-Hora radiation. A more accurate expression for the spatial period has been obtained, taking into account the mode structure of the laser field within the dielectric film. It is shown that the discrepancy of more than 10% between the experimental and theoretical results for the spatial period cannot be reduced by using the existing quantum models that consider a collimated electron beam.Comment: 3 pages, RevTe

Thermal wave detection and analysis of defects in structural composite materials

One criticism which can be leveled at thermal wave images is that their resolution is often less than that of the very best ultrasonic images of similar targets. This reduction of the resolution arises from the transverse diffusion of heat in the thermal waves reflected from the subsurface defects in the sample. In this paper we describe a technique for removing the blurring of pulsed thermal wave images of planar defects through the reconstruction of the shape of the scatterer by use of inverse scattering techniques. Although the method at present is restricted to planar defects, this special class of defects includes delaminations and disbonds in layered materials, defects which are of great interest to a variety of industries. Therefore, the availability of a reconstruction algorithm provides a solution to an important problem in nondestructive evaluation. The algorithm produced we have developed is quite simple and very effective when it is applied to thermal wave images of such defects. The idea behind the design of the model is the manipulation of the equations of thermal wave scattering theory in such a way that the scattered wave at the surface of the sample ends up being expressed as a convolution of a “heat spread” function, with a function which describes the shape of the scatterer. The Fourier transform of the surface temperature contrast (the contrast in the image is essentially just a representation of the scattered wave) can then be expressed as a simple product of the Fourier transform of the heat spread function and the Fourier transform of the shape function of the scatterer. In principle, application of the algorithm consists of performing a two-dimensional spatial Fast Fourier Transform (FFT) on the experimental image of the (unknown) scatterer, dividing the resulting Fourier transform by the transform of the (known) theoretical heat spread function, and finally doing an inverse FFT to obtain the shape of the scatterer

Measurement of opaque film thickness

The theoretical and experimental framework for thickness measurements of thin metal films by low frequency thermal waves is described. Although it is assumed that the films are opaque and the substrates are comparatively poor thermal conductors, the theory is easily extended to other cases of technological interest. A brief description is given of the thermal waves and the experimental arrangement and parameters. The usefulness of the technique is illustrated for making absolute measurements of the thermal diffusivities of isotropic substrate materials. This measurement on pure elemental solids provides a check on the three dimensional theory in the limiting case of zero film thickness. The theoretical framework is then presented, along with numerical calculations and corresponding experimental results for the case of copper films on a glass substrate

Evaluation of Photoacoustic Microscopy Fatigue Crack Detection

The purpose of this paper is to evaluate the technique of scanning photoacoustic microscopy (SPAM) for the detection of fatigue cracks in metal alloys, and to describe an experimental arrangement for SPAM measurements on the inner surface of a cylindrical bolt hole. The experimental technique is based upon the physical mechanism of thermal wave imaging and has been described in detail at previous1, 2 Reviews of Progress in Quantitative NDE and elsewhere.3 In this paper we will also present some results of theoretical calculations for thermal wave scattering from closed, slanted cracks which intersect the surface of an opaque solid, and compare these results with our experimental data

Dynamic Thermal Tomography: New Nde Technique to Reconstruct Inner Solids Structure Using Multiple IR Image Processing

Nondestructive evaluation (NDE) technique appeared as the natural consequence of materials analysis by using a variety of physical fields and particles which being propagated through the specimen are able to produce the image of its inner structure. Disadvantage of traditional “shadow” or “backscattered” images is that the “weak” details are scarcely seen on the background of “stronger” ones. This is why the introduction of the tomographic principles, allowing to “slice” the solid into individual layers, was viewed as a revolution in vision techniques (especially in X-ray imaging). Ultrasonic, ultra-high frequency and nuclear magnetic resonance tomography are under quick development now

Photoacoustic Microscopy

Recent advances in scanning photoacoustic microscopy (SPAM) for NDE are described. Conventional and phase-contrast modes are used to detect a well-characterized subsurface flaw in Al, and the results are shown to be in good agreement with calculations based upon a three-dimensional thermal diffusion model. Applications of the technique are given which demonstrate surface and subsurface flaw detection in complex-shaped ceramic turbine parts. Photoacoustic pictures are presented of an integrated circuit semiconductor chip and show 6 μm resolution

Thermal Wave Characterization of Coated Surfaces

The experimental techniques and theory for utilizing the mirage effect, or optical probe beam detection, of thermal waves in opaque solids for determining their thermal diffusivities have been described in detail elsewhere. [1–4] An application to a coated nickel-based alloy has also been described elsewhere. [1] In previous papers [5,6] we presented a theoretical expression which describes the mirage effect signal in a three-layer medium (gas-coating-sample system), taking into consideration the effects of the sizes of the heating and probe beams. In this paper we extend the results of numerical calculations from that expression to the case of films which are thermally very thin (thicknesses of the order of 10-3 thermal diffusion lengths). A model system of 100–500 nm thick Cu films on glass substrates was studied experimentally at thermal wave frequencies below 1kHz, and in this paper we compare the results of those measurements to the numerical calculations

Parallel Box-Car Imaging of Adhesion Defects in Plasma-Sprayed Coatings

Thermal wave techniques have been successfully used for the characterization of adhesion defects of plasma-sprayed coatings on metal substrates. [1–3] With the advent of thermal wave infrared video imaging,[4–6] it is now possible to image large surface areas at video frame rates using an IR video camera. In this work we describe a novel parallel box-car imaging system, using an IR video camera and WSU-designed pixel by pixel time-gating and averaging and we demonstrate the ability of this system to detect adhesion defects in plasma-sprayed coatings on metal substrates. A particular advantage of our system is that the entire image can be obtain in parallel, thus making it a much faster technique than the conventional cw thermal wave imaging techniques