The year 2022 marks the 200th anniversary of the publication of the monograph “Analytical Theory of Heat” by the outstanding French mathematician Jean-Baptiste-Joseph Fourier. In this work, historical aspects, mathematical foundations and the development of the Fourier method from an idea to an effective digital implementation are considered. Fourier’s idea, implemented in the 20th century in digital devices for processing large amounts of data, became one of the drivers of the technological revolution that began at the turn of the third millennium, the rapid development of which we are witnessing to this day. The authors have discussed the practice of applying methods of digital image processing of the latest materials and structures obtained using modern electron microscopy.
Fourier method as the basis of digital processing of microelectronic images
Written by N. A. Bogdanova, O. V. Podorozhny
Keywords: Fourier transform, spectral analysis, scanning electron microscopy, SEM, transmission scanning electron microscopy, TSEM, digital image.
References
- Bogdanova N. A. Fourier transform. From classical to quantum. Studiya onlaynkontenta MIET [Web]. 2021. Available at: https://miet.study/w/eeFqnseG1WmzCFrkZqxL8V (accessed: 20.08.2022).
- Bogdanova N. A. Mathematical processing of microelectronic images using MATLAB computational environment. Studiya onlayn-kontenta MIET [Web]. 2021. Access mode: authorization. Available at: https://bo.miet.ru/~EcJdx (accessed: 20.08.2022).
- Gonzalez R. C., Woods R. E., Eddins S. L. Digital Image Processing Using MATLAB. London, Pearson Education, 2004. 620 p.
- Descartes R. The Philosophical Works of Descartes, in 2 vols. Cambridge: Cambridge University Press, 1911.
- Rumyantsev A. V., Prikhodko A. S., Borgardt N. I. Study of gallium induced silicon amorphization by matching of experimental and simulated electron microscopy images. Poverkhnost’. Rentgenovskie, sinkhrotronnye i neitronnye issledovaniya, 2020, no. 9, pp. 103—108. (In Russian). https://doi.org/10.31857/S1028096020090174
- Nussbaumer H. J. Fast Fourier Transform and Convolution Algorithms. Berlin, Heidelberg, Springer, 1981. 248 p.
- Einstein A. The Albert Einstein Collection, vol. 1. S. l., Philosophical Library/Open Road, 2016. 386 p.
- Borgardt N. I., Rumyantsev A. V. Prediction of surface topography due to finite pixel spacing in FIB milling of rectangular boxes and trenches. Journal of Vacuum Science & Technology B, 2016, vol. 34, iss. 6, art. no. 061803. https://doi.org/10.1116/1.4967249
- Cooley J. W., Tukey J. W. An algorithm for the machine calculation of complex Fourier series. Math. Comp., 1965, vol. 19, pp. 297—301. https://doi.org/10.1090/S0025-5718-1965-0178586-1
- Fourier J.-B.-J. Théorie analytique de la chaleur. Paris, Firmin Didot Père et Fils, 1822. 639 p.