Thermal-wave Field Research Articles

Stimulated excitation of thermal diffusion waves in a magnetized plasma pressure filament

Results are presented from basic heat transport experiments using a magnetized electron temperature filament that behaves as a thermal resonator. Using a small cathode source, low energy electrons are injected along the magnetic field into the afterglow of a pre-existing plasma forming a hot electron filament embedded in a colder plasma. A series of low amplitude, sinusoidal perturbations are added to the cathode discharge bias that creates an oscillating heat source capable of driving large amplitude electron temperature oscillations. Langmuir probes are used to measure the amplitude and phase of the thermal wave field over a wide range of driver frequencies. The results are used to verify the excitation of thermal waves, confirm the presence of thermal resonances, and demonstrate the diagnostic potential of thermal waves through measurement of the parallel thermal diffusivity.

Quantitative photothermal lock-in thermography imaging of curved surfaces of cylindrical solids

We extend the applications of photothermal radiometric diagnostics to continuously curved cylindrical surface solids using lock-in thermography (LIT) imaging, in which both the photothermally induced surface temperature and the angularly dependent infrared radiation emitted by the curved surface are not constant. Specifically, a theoretical photothermal model is established based on the Green Function method from which the thermal-wave field distribution at different azimuthal angles on the curved surface is obtained and characteristics of the thermal-wave field with different material and measurement parameters/schemes are discussed. A laser-infrared photothermal lock-in imaging system for solid cylindrical samples is established, and the thermal diffusivity of AISI 304 cylindrical steel samples is measured directly based on the LIT images combined with empirically obtained infrared radiation angular distributions over the curved surfaces. The experimental results are in excellent agreement with the theory, which provides a fast and non-destructive quantitative tool for thermophysical evaluation of curved surface solids.

Localization of Subsurface Defects in Uncoated Aluminum with Structured Heating Using High-Power VCSEL Laser Arrays

We report on photothermal detection of subsurface defects by coherent superposition of thermal wave fields. This is made possible by structured heating using high-power VCSEL laser arrays whose individual emitter groups can be arbitrarily controlled. In order to locate the defects, we have developed a scanning method based on the continuous wavelet transformation with complex Morlet wavelet using the destructive interference effect of thermal waves. This approach can also be used for thermally very fast and highly reflective materials such as uncoated aluminum. We show that subsurface defects at an aspect ratio of defect width to defect depth down to $$ 1/3 $$ are still detectable in this material.

Quantitative lock-in thermography imaging of thermal-wave spatial profiles and thermophysical property measurements in solids with inner corner geometries using thermal-wave field theory

In this study, we established a theoretical photothermal model and its experimental validation for an infinitely long solid with an inner corner of arbitrary opening angle, with the solid being irradiated photothermally by a modulated laser beam of arbitrary spatial intensity distribution directed to the corner. The thermal-wave field distribution on the flat surfaces of the solid centered at the corner was obtained using the Green function method. Experimental results based on quantitative thermographic imaging were obtained and used to validate the theoretical model in which thermal diffusivity of an inner cornered stainless steel was measured. The thermal-wave theory based lock-in thermography imaging technique provides a quantitative tool for thermal property measurement and/or non-destructive evaluation of non-flat structures. It also generates valuable physical insights into the spatial distribution of the thermal-wave field in the neighborhood of geometric discontinuities such as inner corners in solids.

Finite element modelling of scattering of an acoustic wave by particles in a fluid: Shear and thermal effects

We investigate, using finite element modelling, the effects of viscous and thermal dissipation in the region around a particle in a liquid subjected to an acoustic field. The linearized thermo-acoustic equations for propagation in a viscous liquid are used in the model. In the Rayleigh scattering regime, with Mega-Hertz frequencies and nano- or micron-sized particles, the shear and thermal decay lengths are of order micrometres and are therefore challenging to resolve accurately using finite element models. We report investigations of the effect of particle size and frequency on the magnitude of the thermal and shear wave fields and their decay length and compare with analytical predictions. We present a determination of the viscous and thermal power dissipation around a single particle, and for small clusters of particles. Here we identify the effect of interaction of the shear and thermal fields with neighbouring particles through mode reconversion, leading to a reduction in dissipation losses when interparticle separation is of the order of the thermal or shear decay length.

Matched-Filter Thermography

Conventional infrared thermography techniques, including pulsed and lock-in thermography, have shown great potential for non-destructive evaluation of broad spectrum of materials, spanning from metals to polymers to biological tissues. However, performance of these techniques is often limited due to the diffuse nature of thermal wave fields, resulting in an inherent compromise between inspection depth and depth resolution. Recently, matched-filter thermography has been introduced as a means for overcoming this classic limitation to enable depth-resolved subsurface thermal imaging and improving axial/depth resolution. This paper reviews the basic principles and experimental results of matched-filter thermography: first, mathematical and signal processing concepts related to matched-fileting and pulse compression are discussed. Next, theoretical modeling of thermal-wave responses to matched-filter thermography using two categories of pulse compression techniques (linear frequency modulation and binary phase coding) are reviewed. Key experimental results from literature demonstrating the maintenance of axial resolution while inspecting deep into opaque and turbid media are also presented and discussed. Finally, the concept of thermal coherence tomography for deconvolution of thermal responses of axially superposed sources and creation of depth-selective images in a diffusion-wave field is reviewed.

Green functions of mass diffusion waves in porous media

A formulism of frequency-domain mass diffusion-waves in porous media is derived by means of Fourier transform. In analogy to conventional thermal-wave fields, internally consistent Green functions in Cartesian coordinates for linear mass diffusion-waves is also presented for infinite, semi-infinite and finite-size domains in three-dimensional spaces. The Green functions are utilized to analyze the response of a particular type of mass diffusion physical system to any arbitrary tracer source distributions. This method allows the introduction of frequency-dependent physically intrinsic properties of porous media. The Green functions presented in this letter may significantly advance understanding in linear mass diffusion-wave physics in porous media, and can be applied to retrieve spatial-temporal diffusive-wave fields from ambient mass fluctuations in geological reservoirs.

Local-stress-induced thermal conductivity anisotropy analysis using non-destructive photo-thermo-mechanical lock-in thermography (PTM-LIT) imaging

When tensile loading is exerted on a sample, internal stress will be generated to counterbalance the external force. The accumulation of local stress results in the change of thermal properties and the sample becomes locally anisotropic, wherein lies the significance of correlation between mechanical properties and thermal parameters. In this research, anisotropic thermal conductivity was considered as the direct result of tensile loading and was interpreted by a theoretical three-dimensional anisotropic diffusion-wave model. Photo-thermo-mechanical lock-in thermography (PTM-LIT) was introduced and used with a focused laser beam and a mid-infrared camera viewing an aluminum alloy sample fixed on a dynamic home-made tensile rig. A numerical two-dimensional Fourier transform was used to compute the thermal-wave field and the effects of several important factors were investigated. Both theoretical and experimental images were analyzed with an isothermal conductivity anisotropy contour fitting approach. It was demonstrated that PTM-LIT can qualitatively and quantitatively reveal otherwise hard-to- measure mechanical property behavior of materials subjected to tensile loading from the stress-free state to its ultimate level of mechanical strength before fracture.

Subsurface Defect Localization by Structured Heating Using Laser Projected Photothermal Thermography.

The presented method is used to locate subsurface defects oriented perpendicularly to the surface. To achieve this, we create destructively interfering thermal wave fields that are disturbed by the defect. This effect is measured and used to locate the defect. We form the destructively interfering wave fields by using a modified projector. The original light engine of the projector is replaced with a fiber-coupled high-power diode laser. Its beam is shaped and aligned to the projector's spatial light modulator and optimized for optimal optical throughput and homogeneous projection by first characterizing the beam profile, and, second, correcting it mechanically and numerically. A high-performance infrared (IR) camera is set up according to the tight geometrical situation (including corrections of the geometrical image distortions) and the requirement to detect weak temperature oscillations at the sample surface. Data acquisition can be performed once a synchronization between the individual thermal wave field sources, the scanning stage, and the IR camera is established by using a dedicated experimental setup which needs to be tuned to the specific material being investigated. During data post-processing, the relevant information on the presence of a defect below the surface of the sample is extracted. It is retrieved from the oscillating part of the acquired thermal radiation coming from the so-called depletion line of the sample surface. The exact location of the defect is deduced from the analysis of the spatial-temporal shape of these oscillations in a final step. The method is reference-free and very sensitive to changes within the thermal wave field. So far, the method has been tested with steel samples but is applicable to different materials as well, in particular to temperature sensitive materials.

Comparison of finite element and analytical modeling of scattering of an acoustic wave by particles in a fluid

Ultrasonic wave propagation through dispersions of particles in liquids is of interest for particle characterization and process monitoring applications. Interpretation of the measurements relies on a theoretical model; we typically use a multiple scattering model which builds on models of scattering by independent particles. We report finite element modeling of an acoustic wave propagating through a liquid and interacting with a particle, using the linearized thermo-acoustic equations for propagation in a viscous liquid. We demonstrate that the interaction of the acoustic field with the particle leads to decaying thermal and shear wave fields in the region very close to the particle. Since the length scale of the thermal and shear decay is orders of magnitude smaller than the propagational mode acoustic wavelength, fine meshing is necessary in the region of the particle/fluid boundary. The simulation results are compared with analytical solutions for scattering of a plane wave by a single spherical particle, provided by Epstein and Carhart [JASA, 25, 533, (1953)] and Allegra and Hawley [(JASA, 51, 1546 (1972)].

Laser-projected photothermal thermography using thermal wave field interference for subsurface defect characterization

The coherent superposition of two anti-phased thermal wave fields creates a zone of destructive interference which is extremely sensitive to the presence of defects without any reference measurements. Combining a high power laser with a spatial light modulator allows modulating phase and amplitude of an illuminated surface that induces spatially and temporally controlled thermal wave fields. The position and depth of defects are reconstructed from analysis of the amplitude and phase of the resulting photothermal signal. The proposed concept is experimentally validated and supported by numerical modeling.

Long-Wave Infrared Thermophotonic Imaging of Demineralization in Dental Hard Tissue

Dental caries remains the most prevalent chronic disease in both children and adults worldwide. To address this prevalence through disease prevention and management, dentists need tools capable of detecting caries at early stages of formation. Looking into the physics of light propagation in teeth, this study presents a clinically and commercially viable platform technology for thermophotonic detection of early dental caries using an inexpensive long-wavelength infrared (LWIR; 8 $$\upmu $$ m to 14 $$\upmu $$ m) camera. The developed system incorporates intensity-modulated light to generate a thermal-wave field inside enamel and uses the subsequent infrared emission of the thermal-wave field to detect early caries. It was found that the greater light absorption at caries sites shifts the thermal-wave field centroid, providing contrast between early caries and intact enamel. Use of LWIR detection band in dental samples is novel and beneficial over the conventional mid-wavelength infrared band (3 $$\upmu $$ m to 5 $$\upmu $$ m) as it suppresses the masking effect of the instantaneous radiative emission from subsurface features due to the minimal transmittance of enamel in the LWIR band. The efficacy of the LWIR system is verified though experiments carried out on nonbiological test samples as well as on teeth with natural and artificially induced caries. The results suggest that the developed LWIR technology is an affordable early dental caries detection system suitable for commercialization/translation to Dentistry.

Simulation of surface cracks measurement in first walls by laser spot array thermography

The inspection of surface cracks in first walls (FW) is very important to ensure the safe operation of the fusion reactors. In this paper, a new laser excited thermography technique with using laser spot array source is proposed for the surface cracks imaging and evaluation in the FW with an intuitive and non-contact measurement method. Instead of imaging a crack by scanning a single laser spot and superimposing the local discontinuity images with the present laser excited thermography methods, it can inspect a relatively large area at one measurement. It does not only simplify the measurement system and data processing procedure, but also provide a faster measurement for FW. In order to investigate the feasibility of this method, a numerical code based on finite element method (FEM) is developed to simulate the heat flow and the effect of the crack geometry on the thermal wave fields. An imaging method based on the gradient of the thermal images is proposed for crack measurement with the laser spot array thermography method.

Study on Lock-in Thermography Defect Detectability for Carbon-Fiber-Reinforced Polymer (CFRP) Sheet with Subsurface Defects

A simple theoretical expression is described to demonstrate the thermal response characteristics of the thermal wave field in the frequency domain by means of the Green’s function method. The defect detectivity using lock-in thermography (LIT) for a carbon-fiber-reinforced polymer (CFRP) with a subsurface defect is investigated, and theoretical analysis results of the defect depth resolution as well as the detection range determined by the thermal wave phase information have shown good agreement with experimental results. The detectable size of a lamination defect in a CFRP has also been studied using lock-in thermographic imaging. The experimental results indicate that LIT is reliably available for evaluating subsurface defects of a CFRP panel at the appropriate modulation frequency, and the defect diameter-to-depth ratio can be as low as 3.0.

Comparative Study of Thermal-Wave Fields in Bi-layered Semi-cylindrical and Fully Cylindrical Solids

A theoretical model for characterizing two-layered semi-cylindrical solid samples illuminated with a modulated incident beam on a curved surface using the Green function method is developed. The analytical expression for the thermal-wave (TW) field in such a semi-cylindrical sample is presented. Based on the model, characteristics of the TW field are simulated with different parameters, and comparisons with the whole cylinder model are conducted. It is found that TW properties of semi- and full cylinders show significant differences, especially in the low frequency range. Preliminary experimental validation is also presented with semi-cylindrical samples. The model provides a theoretical basis to quantitatively characterize semi-cylindrical samples using the TW method in a noncontact and nondestructive way.

Laser lock-in thermography for detection of surface-breaking fatigue cracks on uncoated steel structures

This paper develops a new noncontact laser lock-in thermography (LLT) technique for detection of surface-breaking fatigue cracks on uncoated steel structures with low surface emissivity. LLT utilizes a modulated continuous (CW) wave laser as a heat source for lock-in thermography instead of commonly used flash and halogen lamps. LLT has the following merits: (1) the laser heat source can be precisely positioned at a long distance from a target structure thank to its directionality and low energy loss, (2) a large target structure can be inspected using a scanning laser heat source, (3) no special surface treatment of the target structure is necessary to generate and measure thermal wavefields, (4) thermal image noises created by arbitrary surrounding heat sources can be effectively eliminated and (5) the use of a low peak power laser makes it possible to avoid surface ablation. The LLT system is developed by integrating and synchronizing a modulated CW laser, a galvanometer and an infrared camera. Then, a fatigue crack evaluation algorithm based on a holder exponent analysis is proposed. The performance of the proposed LLT technique is validated through thermal wavefield imaging and fatigue crack evaluation tests on an uncoated steel plate with emissivity of 0.8 and a welded T-shape joint with emissivity of 0.7. Test results confirm that thermal wavefield images are effectively captured even when surface-reflected background noises and laser-generated thermal waves coexist, and surface-breaking cracks are successfully evaluated without any special surface treatment.

Infrared emissivity determination using a thermal-wave resonant cavity: Comparison between the length- and frequency-scan approaches

The mechanisms of heat conduction and radiation through a thermal-wave resonant cavity heated up with a modulated laser beam are investigated. This resonator is made up of three layers in which the thickness of the middle can be changed moving one of the external layers. A modulated heat source is applied to one of the external layers, and the changes of temperature are registered at the surface of the opposite layer. The obtained results show that the continuous (dc) and oscillatory (ac) components of the temperature are coupled, and they can be described under a fully analytical and exact approach. It is shown that: 1) the ac temperature depends strongly on the third power of the dc temperature at the inner surface of the illuminated layer. 2) The contribution of the heat radiation to the ac temperature becomes more remarkable as the thickness of the cavity becomes much larger than the thermal diffusion length of the fluid inside of it, i.e. when the contribution of the heat conduction decreases. 3) Though the effect of the radiation does not show up strongly on the real and imaginary part of the thermal wave field, it does affect both its amplitude and phase. 4) The amplitude and phase as a function of the cavity thickness exhibit a stronger dependence on the radiation contribution than the corresponding ones as a function of the modulation frequency. Length scan is therefore more suitable than frequency scan to observe the radiation contribution on the photopyroelectric signal. Based on these facts, various promising methods to determine the infrared emissivity of materials can be devised.

Equivalence of Normalized Thermal-Wave Fields Between Curved and Flat Surfaces and Its Application in the Characterization of Curved Samples

Equivalence of the normalized thermal-wave fields between curved and flat surfaces under certain conditions is investigated based on theoretical models of cylindrical, spherical, and flat solids with multilayer structures. The principle and the physical mechanism of the elimination of the surface curvature effect from the overall photothermal signal of the curvilinear solid are suggested. The effects of the relative values of radii of curvature of the curvilinear solid, the thickness of the inhomogeneous surface layer, and the measurement azimuthal angle on the validity of the equivalence principle are discussed. Consistent experimental reconstructions of thermophysical depth profiles of hardened cylindrical steel rods of various diameters are performed and obtained based on both the curvilinear theory and the equivalent flat surface theory.

Thermal-wave fields in solid wedges using the Green function method: Theory and experiment

In this work, we establish a theoretical model for a cylindrical rod of radius R with opening angle θ illuminated by a modulated incident beam. The model uses the Green function method in cylindrical coordinates. An analytical expression for the Green function and thermal-wave field in such a solid is presented. The theory is validated in the limit of reducing the arbitrary wedge geometrical structure to simpler geometries. For acute angle wedges, it is shown that the thermal-wave field near the edge exhibits confinement behavior and increased amplitude compared to a flat (reference) solid with θ = π. For obtuse angle wedges, it is shown that the opposite is true and relaxation of confinement occurs leading to lower amplitude thermal-wave fields. The theory provides a basis for quantitative thermophysical characterization of wedge-shaped objects and it is tested using an AISI 304 steel wedge and photothermal radiometry detection.

Characterization of the Thermal-Wave Field in a Wedge-Shaped Solid Using the Green’s Function Method

In this study, a theoretical model is established for a wedge-like solid with an open sector surrounded by walls of radius $$R$$ of a cylindrical rod illuminated by a modulated circular Gaussian incident beam by means of the Green’s function method in cylindrical coordinates. An analytical expression for the thermal-wave field in such a sample is presented. The theory is validated by reducing the arbitrary geometrical structure of the wedge to simpler geometries. It is shown that the frequency dependence of the thermal-wave field near the edge exhibits a large phase lag compared with that at a location far from the edge. The theory provides a foundation for quantitatively characterizing wedge-shaped industrial samples, such as metals with sintered edges, using photothermal methods in a non-contact and non-destructive manner.