Speaker
Description
Among infrared thermal characterization techniques, scanning photothermal radiometry (SPR) stands out as an active technique that is simultaneously non-destructive, contactless, and allows for temporal resolutions on the order of nanoseconds and spatial resolutions down to the submicrometer scale, lower than 0.5µm [1]. It relies on measurements at different frequencies to investigate different depths of the sample under study. The drawback of this technique is that, as a scanning method, it can be time consuming to measure a 2D image at various frequencies while still keeping a large field of view and a small scanning step as usually at least 30min per frequency are needed in low noise scenarios for a precise map of a $50\times50$ µm area. This make it challenging to use as a screening method for instance.
In this work we show that it is possible to reduce the amount of measurements taken by 3 when using the SPR technique on a sample consisting of carbon fibers in an aluminum matrix. To achieve this reduction, leading to an equivalent reduction in measurement time, we rely on the general principle of compressive sensing [2,3], which is based on a few assumptions usually verified for most images that aren’t pure noise, among which the most important is the sparse nature of the measured signals. Compressive sensing has been previously used for single pixel imaging [5], i.e., reconstructing images from measurements with a mono-detector, or for increasing the number of pixels in an image.
Here, we specifically apply this technique to thermal measurements. Practically, we randomly undersample the measured image. We then accurately reconstruct the full image thanks to an $\ell_1$ norm minimisation algorithm. This compressive-sensing-based algorithm makes it possible to overcome the Shannon sampling limit of the equivalent regularly sampled image. We verify that the hypotheses required, such as the sparsity of the signal, are valid and compare the reconstructed image for different sampling ratios. We observe that it is possible to reconstruct the features of the sample with as little as 30% of the measurements while keeping the error low. In this communication, we will then discuss the specificities of using such technique in thermal characterization, in which thermal diffusion can filter out high frequency features, such as the fiber/matrix interfaces.
- Alejandro Mateos-Canseco, Andrzej Kusiak, Jean-Luc Battaglia, Matthieu Museau, François Villeneuve; Thermal characterization of vertical interface by scanning photothermal radiometry. Rev. Sci. Instrum. 1 October 2024; 95 (10): 104901. https://doi.org/10.1063/5.0225690
- E. J. Candes, J. Romberg and T. Tao, "Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information," in IEEE Transactions on Information Theory, vol. 52, no. 2, pp. 489-509, Feb. 2006, doi: 10.1109/TIT.2005.862083.
- D. L. Donoho, "Compressed sensing," in IEEE Transactions on Information Theory, vol. 52, no. 4, pp. 1289-1306, April 2006, doi: 10.1109/TIT.2006.871582.
- C. Li, “An efficient algorithm for total variation regularization with applications to the single pixel
camera and compressive sensing,” Ph.D. dissertation, 2011-01.
