The spatial resolution limit in photoacoustic/thermal imaging is derived from the irreversibility of attenuation of the pressure wave and of heat diffusion during propagation of the signals from the imaged subsurface structures to the sample surface, respectively. The acoustic or temperature signals are converted into so-called virtual waves, which are their reversible counterparts, and which can be used for image reconstruction by well-known ultrasound reconstruction methods, which is an ill-posed inverse problem. The resolution from entropy production is equal to the diffraction limit -which is noise limited. Incorporating sparsity and non-negativity in iterative regularization methods gives a significant resolution enhancement.
In the presented work the principle of super-resolution imaging using structured illumination is applied to thermography. Scattered light which can penetrate under the surface of a sample heats subsurface light absorbing structures. The diffused heat is measured on the sample surface e.g. with an infrared camera, which allows to image the subsurface structures. The deeper these structures are below the surface, the more blurred their images become.
Blind structured illumination inside the sample is used to calculate a super-resolution image which less blurring. The structured illumination inside the sample can be generated by interference of scattered light producing laser speckles.
Photothermal measurements with an infrared camera enable a fast and contactless part inspection. The main drawback of existing reconstruction methods is the degradation of the spatial resolution with increasing imaging depth, which results in blurred images for deeper lying structures. In this work, we propose an efficient image reconstruction strategy that allows prior information to be included to overcome the diffusion-based information loss. Following the virtual wave concept, in a first step we reconstruct from the measured photothermal signal an acoustic wave field that satisfies the standard wave equation. This wave is called a virtual one, because it is not the measured acoustic wave but mathematically calculated from the temperature signal measured on the sample surface. In the second step, stable and efficient reconstruction methods developed for photoacoustic tomography are used. We compensate for the loss of information in thermal measurements by incorporating the prior information positivity and sparsity. For that purpose we combine circular projections with an iterative regularization scheme. Using experimental data, this work demonstrates that the quality of the reconstruction based on photothermal measurements can be significantly enhanced. The main goal of this work was to illustrate that prior information significantly improves the regularized solution and, hence, the reconstructed field. Using an iterative non-linear regularization method, the prior information positivity and sparsity could be incorporated. The regularization and reconstruction results show that respecting information available about the data significantly increases the quality of the regularized solution.
KEYWORDS: Diffusion, Thermography, Signal to noise ratio, Aerospace engineering, Infrared cameras, Ultrasonics, Manufacturing, Testing and analysis, Time metrology, Wave propagation
High strength and light weight, justify the frequent use of carbon fibre reinforced plastics for aeronautical applications. The manufacturing process of such material systems is a multi-stage process and susceptible to the formation of air-filled voids. This porosity weakens the epoxy matrix and causes noticeable degradation of mechanical properties. Active thermography with optical-excitation is an advantageous photothermal method because due to the infrared camera it is a non-contacting, fast testing method for the estimation of material properties or for defect detection. We use the Virtual Wave Concept, which allows ultrasonic testing methods for photothermal measurement data. Based on this ability, we apply the through-transmission method to determine the Time-of-Flight of virtual waves, which is directly related to the porosity dependent diffusion time. A signalto-noise ratio dependent approach is used for the temporal truncation of measurement data to get the optimum evaluation time. This ensures to evaluate only time-ranges which contain information of the heat diffusion inside the sample. In addition, undesired effects of heat losses due to convection and radiation are reduced. After the evaluation procedure is shown for simulated data, we demonstrate the experimental pixel-wise estimation of the porosity affected thermal diffusion times on a real aerospace part in transmission configuration. The results are validated by X-ray computed tomography reference measurements, where a good match can be achieved with active thermography results.
In active thermography, the structure below the surface can be reconstructed from measured surface temperature signals. The main drawback in active thermographic is the degradation of the spatial resolution with imaging depth. Recently, we used a mathematical compensation method to transform each measured surface temperature signal into a virtual acoustic wave, which is the solution of the wave equation and therefore ultrasound image reconstruction methods can be used. This allows a 3D thermo-tomography, which combines the advantages of thermographic and ultrasonic imaging, but the degradation of spatial resolution for deeper lying structures is still significant. A possibility to overcome this degradation is to incorporate prior information such as positivity and sparsity in the reconstruction process. Based on pulsed thermography data we show that the thermographic detection limit is extendible by a factor of four.
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