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Shape-from-focus for real-time terahertz 3D imaging
Abstract. Thanks to significant advances in real-time terahertz imaging in terms of resolution and image quality, adapting and extending optical methods for 3D imaging at the millimeter scale is now promising. The shape-from-focus algorithm is a post-processing tool used in optical microscopy to reconstruct the external shape surface of a convex surface object. Images acquired at different distances from the object-side focal plane are implemented in this algorithm. We localize the best focus position in the stack of images for each pixel and then reconstruct the object in 3D due to the short depth of field. In this Letter, we propose an application of this algorithm in active and real-time terahertz imaging. We achieve the experimental reconstruction in 3D with a terahertz waves imaging system composed of a powerful source and a real-time terahertz camera. Full Article? ? 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Proven?al, P. Topart, C. Vachon, S. Verreault, and A. Bergeron, J. Infrared, Millimeter, Terahertz Waves 36, 922 (2015). [Crossref] Bousquet, B.. J. B. Sleiman, B. Bousquet, N. Palka, and P. Mounaix, Appl. Spectrosc. 69, 1464 (2015). [Crossref] J. P. Guillet, B. Recur, L. Frederique, B. Bousquet, L. Canioni, I. Manek-H?nninger, P. Desbarats, and P. Mounaix, J. Infrared, Millimeter, Terahertz Waves 35, 382 (2014). [Crossref] Canioni, L.. J. P. Guillet, B. Recur, L. Frederique, B. Bousquet, L. Canioni, I. Manek-H?nninger, P. Desbarats, and P. Mounaix, J. Infrared, Millimeter, Terahertz Waves 35, 382 (2014). [Crossref] Cariati, M.. M. R. Grootendorst, A. J. Fitzgerald, S. G. B. de Koning, A. Santaolalla, A. Portieri, M. Van Hemelrijck, M. R. Young, J. Owen, M. Cariati, M. Pepper, V. P. Wallace, S. E. Pinder, and A. Purushotham, Biomed. Opt. Express 8, 2932 (2017). [Crossref] Chevalier, C.. D. Dufour, L. Marchese, M. Terroux, H. Oulachgar, F. Généreux, M. Doucet, L. Mercier, B. Tremblay, C. Alain, P. Beaupré, N. Blanchard, M. Bolduc, C. Chevalier, D. D’Amato, Y. Desroches, F. Duchesne, L. Gagnon, S. Ilias, H. Jerominek, F. Lagacé, J. Lambert, F. Lamontagne, L. Le Noc, A. Martel, O. Pancrati, J.-E. Paultre, T. Pope, F. Proven?al, P. Topart, C. Vachon, S. Verreault, and A. Bergeron, J. Infrared, Millimeter, Terahertz Waves 36, 922 (2015). [Crossref] D’Amato, D.. D. Dufour, L. Marchese, M. Terroux, H. Oulachgar, F. Généreux, M. Doucet, L. Mercier, B. Tremblay, C. Alain, P. Beaupré, N. Blanchard, M. Bolduc, C. Chevalier, D. D’Amato, Y. Desroches, F. Duchesne, L. Gagnon, S. Ilias, H. Jerominek, F. Lagacé, J. Lambert, F. Lamontagne, L. Le Noc, A. Martel, O. Pancrati, J.-E. Paultre, T. Pope, F. Proven?al, P. Topart, C. Vachon, S. Verreault, and A. Bergeron, J. Infrared, Millimeter, Terahertz Waves 36, 922 (2015). [Crossref] de Koning, S. G. B.. M. R. Grootendorst, A. J. Fitzgerald, S. G. B. de Koning, A. Santaolalla, A. Portieri, M. Van Hemelrijck, M. R. Young, J. Owen, M. Cariati, M. Pepper, V. P. Wallace, S. E. Pinder, and A. Purushotham, Biomed. Opt. Express 8, 2932 (2017). [Crossref] Desbarats, P.. J. P. Guillet, B. Recur, L. Frederique, B. Bousquet, L. Canioni, I. Manek-H?nninger, P. Desbarats, and P. Mounaix, J. Infrared, Millimeter, Terahertz Waves 35, 382 (2014). [Crossref] Desroches, Y.. D. Dufour, L. Marchese, M. Terroux, H. Oulachgar, F. Généreux, M. Doucet, L. Mercier, B. Tremblay, C. Alain, P. Beaupré, N. Blanchard, M. Bolduc, C. Chevalier, D. D’Amato, Y. Desroches, F. Duchesne, L. Gagnon, S. Ilias, H. Jerominek, F. Lagacé, J. Lambert, F. Lamontagne, L. Le Noc, A. Martel, O. Pancrati, J.-E. Paultre, T. Pope, F. Proven?al, P. Topart, C. Vachon, S. Verreault, and A. Bergeron, J. Infrared, Millimeter, Terahertz Waves 36, 922 (2015). [Crossref] Doucet, M.. D. Dufour, L. Marchese, M. Terroux, H. Oulachgar, F. Généreux, M. Doucet, L. Mercier, B. Tremblay, C. Alain, P. Beaupré, N. Blanchard, M. Bolduc, C. Chevalier, D. D’Amato, Y. Desroches, F. Duchesne, L. Gagnon, S. Ilias, H. Jerominek, F. Lagacé, J. Lambert, F. Lamontagne, L. Le Noc, A. Martel, O. Pancrati, J.-E. Paultre, T. Pope, F. Proven?al, P. Topart, C. Vachon, S. Verreault, and A. Bergeron, J. Infrared, Millimeter, Terahertz Waves 36, 922 (2015). [Crossref] Duchesne, F.. D. Dufour, L. Marchese, M. Terroux, H. Oulachgar, F. Généreux, M. Doucet, L. Mercier, B. Tremblay, C. Alain, P. Beaupré, N. Blanchard, M. Bolduc, C. Chevalier, D. D’Amato, Y. Desroches, F. Duchesne, L. Gagnon, S. Ilias, H. Jerominek, F. Lagacé, J. Lambert, F. Lamontagne, L. Le Noc, A. Martel, O. Pancrati, J.-E. Paultre, T. Pope, F. Proven?al, P. Topart, C. Vachon, S. Verreault, and A. Bergeron, J. Infrared, Millimeter, Terahertz Waves 36, 922 (2015). [Crossref] Dufour, D.. D. Dufour, L. Marchese, M. Terroux, H. Oulachgar, F. Généreux, M. Doucet, L. Mercier, B. Tremblay, C. Alain, P. Beaupré, N. Blanchard, M. Bolduc, C. Chevalier, D. D’Amato, Y. Desroches, F. Duchesne, L. Gagnon, S. Ilias, H. Jerominek, F. Lagacé, J. Lambert, F. Lamontagne, L. Le Noc, A. Martel, O. Pancrati, J.-E. Paultre, T. Pope, F. Proven?al, P. Topart, C. Vachon, S. Verreault, and A. Bergeron, J. Infrared, Millimeter, Terahertz Waves 36, 922 (2015). [Crossref] Duling, I. N.. J. Labaune, J. B. Jackson, S. Pagès-Camagna, I. N. Duling, M. Menu, and G. A. Mourou, Appl. Phys. A 100, 607 (2010). [Crossref] Dussopt, L.. F. Simoens, L. Dussopt, J. Meilhan, J.-A. Nicolas, N. Monnier, A. Siligaris, B. Hiberty, J.-B. Perraud, P. Mounaix, J. Lalanne-Dera, and O. Redon, Proc. SPIE 10531, 105310T (2018). [Crossref] Fitzgerald, A. J.. M. R. Grootendorst, A. J. Fitzgerald, S. G. B. de Koning, A. Santaolalla, A. Portieri, M. Van Hemelrijck, M. R. Young, J. Owen, M. Cariati, M. Pepper, V. P. Wallace, S. E. Pinder, and A. Purushotham, Biomed. Opt. Express 8, 2932 (2017). [Crossref] Frederique, L.. J. P. Guillet, B. Recur, L. Frederique, B. Bousquet, L. Canioni, I. Manek-H?nninger, P. Desbarats, and P. Mounaix, J. Infrared, Millimeter, Terahertz Waves 35, 382 (2014). [Crossref] Gagnon, L.. D. Dufour, L. Marchese, M. Terroux, H. Oulachgar, F. Généreux, M. Doucet, L. Mercier, B. Tremblay, C. Alain, P. Beaupré, N. Blanchard, M. Bolduc, C. Chevalier, D. D’Amato, Y. Desroches, F. Duchesne, L. Gagnon, S. Ilias, H. Jerominek, F. Lagacé, J. Lambert, F. Lamontagne, L. Le Noc, A. Martel, O. Pancrati, J.-E. Paultre, T. Pope, F. Proven?al, P. Topart, C. Vachon, S. Verreault, and A. Bergeron, J. Infrared, Millimeter, Terahertz Waves 36, 922 (2015). [Crossref] Garcia, M. A.. S. Pertuz, D. Puig, and M. A. Garcia, Pattern Recogn. 46, 1415 (2013). [Crossref] Généreux, F.. D. Dufour, L. Marchese, M. Terroux, H. Oulachgar, F. Généreux, M. Doucet, L. Mercier, B. Tremblay, C. Alain, P. Beaupré, N. Blanchard, M. Bolduc, C. Chevalier, D. D’Amato, Y. Desroches, F. Duchesne, L. Gagnon, S. Ilias, H. Jerominek, F. Lagacé, J. Lambert, F. Lamontagne, L. Le Noc, A. Martel, O. Pancrati, J.-E. Paultre, T. Pope, F. Proven?al, P. Topart, C. Vachon, S. Verreault, and A. Bergeron, J. Infrared, Millimeter, Terahertz Waves 36, 922 (2015). [Crossref] Grootendorst, M. R.. M. R. Grootendorst, A. J. Fitzgerald, S. G. B. de Koning, A. Santaolalla, A. Portieri, M. Van Hemelrijck, M. R. Young, J. Owen, M. Cariati, M. Pepper, V. P. Wallace, S. E. Pinder, and A. Purushotham, Biomed. Opt. Express 8, 2932 (2017). [Crossref] Guillet, J. P.. J. P. Guillet, B. Recur, L. Frederique, B. Bousquet, L. Canioni, I. Manek-H?nninger, P. Desbarats, and P. Mounaix, J. Infrared, Millimeter, Terahertz Waves 35, 382 (2014). [Crossref] Henneberger, R.. C. Am Weg, W. Von Spiegel, R. Henneberger, T. Loeffler, and H. G. Roskos, J. Infrared, Millimeter, Terahertz Waves 30, 1281 (2009). [Crossref] Hiberty, B.. F. Simoens, L. Dussopt, J. Meilhan, J.-A. Nicolas, N. Monnier, A. Siligaris, B. Hiberty, J.-B. Perraud, P. Mounaix, J. Lalanne-Dera, and O. Redon, Proc. SPIE 10531, 105310T (2018). [Crossref] Horn, B. K. P.. B. K. P. Horn, “Focusing,” Computer Science and Artificial Intelligence Lab, Memo No.?1 (1968). Ilias, S.. D. Dufour, L. Marchese, M. Terroux, H. Oulachgar, F. Généreux, M. Doucet, L. Mercier, B. Tremblay, C. Alain, P. Beaupré, N. Blanchard, M. Bolduc, C. Chevalier, D. D’Amato, Y. Desroches, F. Duchesne, L. Gagnon, S. Ilias, H. Jerominek, F. Lagacé, J. Lambert, F. Lamontagne, L. Le Noc, A. Martel, O. Pancrati, J.-E. Paultre, T. Pope, F. Proven?al, P. Topart, C. Vachon, S. Verreault, and A. Bergeron, J. Infrared, Millimeter, Terahertz Waves 36, 922 (2015). [Crossref] Jackson, J. B.. J. Labaune, J. B. Jackson, S. Pagès-Camagna, I. N. Duling, M. Menu, and G. A. Mourou, Appl. Phys. A 100, 607 (2010). [Crossref] Jerominek, H.. D. Dufour, L. Marchese, M. Terroux, H. Oulachgar, F. Généreux, M. Doucet, L. Mercier, B. Tremblay, C. Alain, P. Beaupré, N. Blanchard, M. Bolduc, C. Chevalier, D. D’Amato, Y. Desroches, F. Duchesne, L. Gagnon, S. Ilias, H. Jerominek, F. Lagacé, J. Lambert, F. Lamontagne, L. 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Simoens, L. Dussopt, J. Meilhan, J.-A. Nicolas, N. Monnier, A. Siligaris, B. Hiberty, J.-B. Perraud, P. Mounaix, J. Lalanne-Dera, and O. Redon, Proc. SPIE 10531, 105310T (2018). [Crossref] Other (1). B. K. P. Horn, “Focusing,” Computer Science and Artificial Intelligence Lab, Memo No.?1 (1968). Supplementary Material (3). NameDescription ? Visualization 1 ?????. Visualization 1 = video of the transmission images of a leaf at 2.5THz.. ? Visualization 2 ?????. Visualization 2 = video of the transmission images of 2 leaves at 2.5THz.. ? Visualization 3 ?????. 3D reconstruction of the two leaves by SFF algorithm.. Cited By. OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here. Alert me when this article is cited. Click here to see a list of articles that cite this paper Figures (8). Fig. 1. Fig. 2. Fig. 3. Fig. 4. Fig. 5. Fig. 6. Fig. 7. Fig. 8. Fig. 1. Description of (a)?the different calculation steps, (b)?the calculation of ML from I, (c)?the calculation of F from ML to extract the optimal image, and (d)?the height map. Download Full Size PPT Slide PDF Fig. 2. (a)?Photo of a dried oak leaf and (b)?selection among 250 images of absorbance (0–20?dB) at 2.5?THz of the oak leaf. Download Full Size PPT Slide PDF Fig. 3. Focus measure F(Z) of three pixels with coordinates (X, Y) of the dried oak leaf images. Download Full Size PPT Slide PDF Fig. 4. Gray-scale optimal absorbance image of the dried oak leaf processed by the SFF algorithm. Download Full Size PPT Slide PDF Fig. 5. Depth map of the oak leaf, with the unit in millimeters. Download Full Size PPT Slide PDF Fig. 6. Depth map of the oak leaf, with the unit in millimeters. Download Full Size PPT Slide PDF Fig. 7. Focus measure of the pixel (X=125, Y=175) revealing two peaks corresponding to the position of the two leaves. Download Full Size PPT Slide PDF Fig. 8. Focus measurement of the pixel (X=125, Y=175) revealing two peaks corresponding to the position of the two leaves. Download Full Size PPT Slide PDF Equations (3). Equations on this page are rendered with MathJax. Learn more. (1) ML(X,Y)=2I(X,Y)?I(X?p,Y)?I(X+p,Y)+2I(X,Y)?I(X,Y?p)?I(X,Y+p). (2) F(x,y,z)=∑X=x?Nx+N∑Y=y?Ny+NML(X,Y,z)if??ML>T. (3) F(x,y,z)=Fp(x,y)e?12(z?d(x,y)?σ)2, .
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