Elementary Fourier optics for science and engineering students /

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"Version: 20250801"--Title page verso.Includes bibliographical references.1. Mathematical functions--a review -- 1.1. Introduction to mathematical functions -- 1.2. Trigonometry -- 1.3. Calculus -- 1.4. 2D functions -- 1.5. Introduction to complex variable functions -- 1.6. Harmonic functions -- 1.7. Special functions -- 1.8. Problems2. Optics fundamentals--a review -- 2.1. Basic concepts of geometric optics -- 2.2. Lenses and image formation -- 2.3. Basic concepts of waves -- 2.4. Interference of light -- 2.5. Diffraction of light -- 2.6. Problems3. Fourier transform in 1D -- 3.1. Periodic functions. Fourier series. Examples. Succession of square pulses. Frequency spectrum -- 3.2. Fourier transform in 1D. The square pulse -- 3.3. Properties of the Fourier transform. Linearity, scaling, translation. The Fourier transform of the Fourier transform -- 3.4. The Dirac delta function -- 3.5. The Fourier transform of the sine, cosine, and Gaussian functions -- 3.6. The negative frequencies -- 3.7. Problems4. Fourier transform in 2D -- 4.1. Fourier transform in 2D -- 4.2. Separable variables functions -- 4.3. Bidimensional images. Filtering. Use of 'Image J' program for image filtering -- 4.4. Fourier transform in polar coordinates (Fourier-Bessel transform) -- 4.5. Problems5. Linear and shift-invariant systems -- 5.1. Linear systems. Input and outputs. Examples -- 5.2. Shift-invariant systems -- 5.3. Decomposition in delta functions -- 5.4. Point spread function. The convolution integral. The image as a convolution -- 5.5. Graphic method for the solution of the convolution integral -- 5.6. Properties of the convolution -- 5.7. Convolution in 2D -- 5.8. Problems6. Fraunhofer diffraction and Fourier transform -- 6.1. Fraunhofer diffraction. Aperture function -- 6.2. Examples. One, two, three, several slits -- 6.3. Diffraction in 2D -- 6.4. Apodization -- 6.5. The array theorem -- 6.6. Problems7. Correlations. Transfer functions and images formation -- 7.1. Cross-correlation. Examples -- 7.2. Properties of the cross-correlation -- 7.3. The Parseval's theorem and the autocorrelation -- 7.4. The optical transfer function -- 7.5. The image formation : the lens and the Fourier transform. The 4F system -- 7.6. The evolution of the complex amplitude -- 7.7. Problems8. Advanced topics -- 8.1. Fourier transform infrared spectroscopy -- 8.2. Algorithms for the calculation of the Fourier transform -- 8.3. Holography -- 8.4. Problems.Full-text restricted to subscribers or individual document purchasers.Elementary Fourier Optics for Science and Engineering Students introduces the principles of Fourier optics, emphasizing their foundational role in modern optical systems. Designed for undergraduates and early graduates in physics, mathematics, or engineering, this book describes how wave propagation, diffraction, and linear systems theory unite under the Fourier framework to explain phenomena like image formation, holography, and optical signal processing. Important concepts such as convolution, cross-correlation, transfer function and their relationship with image resolution are also included. Among the key features of the book are a progressive learning path, visual explanations, use of a specialized program for graphic Fourier transform implementation, chapter abstracts, solved and non-solved exercises, and a list of relevant references. Part of IOP Series in Advances in Optics, Photonics and Optoelectronics.Students in science (physics) and engineering, particularly optics.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.H?el?ene Ollivier simultaneously obtained her engineer diploma from Institut d'Optique Graduate School (Palaiseau, France), completed her master's degree in lasers, optics and matter, and graduated from Ecole Normale Sup?erieure de Paris-Saclay as a normalien student in 2017. She completed her doctoral research in quantum photonics and cavity quantum electrodynamics in the Optics and Semiconductors nanoStructures Group under the supervision of Professor Pascale Senellart, a CNRS research director at the Center for Nanosciences and Nanotechnologies (C2N). She has authored three first-author publications, one in ACS Photonics and two in Physical Review Letters and co-authored five additional papers published in other top journals such as Nature Photonics, Nature Communications, and Optica. As a laureate of the 2016 physics aggregation, a highly competitive examination for the Education Nationale in France, she is deeply involved in physics education. She has held a permanent position as Associate Professor at the Foton Institute (University of Rennes) since September 2024. She currently teaches subjects related to photonics at ENSSAT (?Ecole Nationale Sup?erieure des Sciences Appliqu?ees et de Technologie) in Lannion and conducts research on room-temperature single-photon sources based on rare-earth-ion-doped optical fibers. Osvaldo de Melo is a distinguished physicist and educator specializing in semiconductor materials, thin-film growth, and nanotechnology. He earned his PhD in physical sciences from the University of Havana in 1992, focusing on ternary single crystal solutions of II-VI telluride compounds. A dedicated educator with over 40 years of experience, he served as Full Professor of Physics at the University of Havana (1993-2021), Dean of the Faculty of Physics (2001-2006), and visiting scholar at prestigious institutions including the Autonomous University of Madrid, the Instituto Polit?ecnico Nacional (Mexico), and the Universidade Federal de Minas Gerais (Brazil). His research, documented in more than 100 peer-reviewed scientific publications, spans materials preparation, nanostructured semiconductors, and 2D layered systems including molybdenum oxides and Bi2Te3. With an h-index of 19 (Google Scholar) and more than 1375 citations, his scientific contributions have earned numerous honors including Cuba's National Physics Prize (2016) and multiple awards from the Cuban Academy of Sciences for breakthroughs across various areas of Physics and Materials Science. He is currently affiliated with both the Escuela Superior de F?isica y Matem?aticas and the Escuela Superior de Ingenier?ia Mec?anica y El?ectrica at Mexico's Instituto Polit?ecnico Nacional (IPN), he investigates transition-metal oxides and dichalcogenides for next-generation electronic devices.Title from PDF title page (viewed on September 5, 2025).

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: .,

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1 online resource (various pagings) :illustrations (some color).

Language

English

ISBN/ISSN

9780750363921

Classification

621.36/01/5152433

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Subject(s)

Fourier transform optics.
SCIENCE / Physics / Optics & Light.
Applied optics.

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Statement of Responsibility

H?el?ene Ollivier, Osvaldo de Melo.

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