Description du contenu de l'enseignement
The aim of the course is to present the basic concepts and formalism of Fourier optics, i.e. to show how bi-dimensional Fourier analysis and linear system theory allow to describe free-space light propagation and diffraction-limited coherent and incoherent imaging. Many fields of optics can be addressed with the Fourier optics formalism, such as optical signal processing, imaging system analysis, and holography.
Modalités d'organisation et de suivi
Part I: Formalism and basics
- Free-space propagation as a 2D invariant linear system
- Space-time analogy between diffraction and dispersion
- The ideal thin lens as a 2D-Fourier-transform operato
Part II: Spatial filtering and analogue optical information processing
- Spatial filtering setup: the 4f configuration
- Analogue optical information processing with amplitude objects
- Optical imaging of phase objects
Part III: Frequency analysis of the performance of optical imaging systems
- Introduction to frequency analysis of optical imaging systems
- Frequency response of diffraction-limited optical imaging systems
- Case study: Microscope with Köhler illumination
Compétences à acquérir
After completing the course, the student will be able to:
- understand the concept of spatial frequency spectrum (or 2D-Fourier spectrum) of a diffractive object;
- understand the description of free-space propagation as a 2D linear system, and recall the expression of its impulse response and its transfer function;
- calculate the field distribution after propagation over a given distance in free space in the framework of the Fresnel approximation (three approaches);
- explain why and how a thin lens can be used to reproduce the Fraunhofer diffraction conditions;
- describe the 4f configuration and explain the principle of the following coherent optical filtering processes:
- "cleaning up" of a laser beam profile;
- raster detection or elimination;
- dark field method and phase contrast method;
- explain the difference between coherent and incoherent illumination in an optical imaging system;
- use the 2D linear-system analysis tools (impulse response, transfer function) to evaluate the performance of a diffraction-limited optical imaging system.
- Propagation of a plane or spherical wave in a linear homogeneous isotropic medium
- Scalar diffraction theory
- Fourier analysis
- Analysis of linear systems
Bibliographie, lectures recommandées
- J. W. Goodman, “Introduction to Fourier optics”, Freeman (2017, 4th ed.).
- W. Lauterborn, T. Kurz, and M. Wiesenfeldt, “Coherent optics”, Springer (2003, 2nd ed.).
- B. H. Kolner, “Space-time duality and the theory of temporal imaging”, IEEE J. Quant. Electron. 30, 1951 (1994).