Functions of complex variable, derivatives, integrals. Theorem and formulas of Cauchy. Taylor and Laurent series. Residue theorem and application to integrals important for optics. Dispersion.
Special functions for optics and distributions. Fourier transform, convolution and image elaboration. Zernike polynomials. Use of special functions and transforms to understand the behaviour of optics instruments. Image instruments: telescopy
Notes are given to the students during the lectures.
Additional texts:
- G. Toraldo: "Metodi Matematici della Fisica", Volume di appunti raccolti da A. Consortini, Scuola di Specializzazione in Fisica 1961-62, (in Biblioteca)
- Franco Gori "Elementi di Ottica" Ed Accademica Srl, Roma 1995 (l'appendice "Supplemento")
- Arfken, Weber and Harris: "Mathematical Methods for Physicists: A Comprensive Guide" Elevier, Seventh Edition, 2013.
- Joseph W. Goodman "Introduction to Fourier Optics" Ed McGraw-Hill, Second Edition (Oppure Roberts 3th Edition). Il primo capitolo.
- Ronald N. Bracewell "The Fourier transform and its applications" Ed McGraw-Hill 2000. Cap. 15 e Cap 22.
- P. M. Duffieux "The Fourier Transform and its Application to Optics" John Wiley & Sons 1983, second edition. Duffieux pose le basi dell'ottica di Fourier.
- J. F. James "A Student's Guide to Fourier Transforms: With Applications in Physics and Engineering" Cambridge University Press; 3rd edition (May 9, 2011)
Learning Objectives
Knowledge of: Bases of advanced mathematics.
Bases for the use of mathematical functions needed for physics and mostly optics.
At the end of the course the students will be able to understand and describe in rigorous way the phenomena of physics and mainly of classic and modern optics
Prerequisites
Mathematics I and II are needed and strongly recommended
Teaching Methods
Front lectures, slides and laboratory demonstrations
CFU:6
Total number of course hours 150 (=6x25)
Number of hours for personal study and other individual activities:
Number of hours relative to the class activity: 48
Type of Assessment
oral examinations
Course program
Functions of complex variable, derivatives, integrals. Theorem of formulas of Cauchy. Series of Taylor and of Laurent. Theorem of residues and applications to the evaluation of integrals important for optics. Dispersion. Special functions used in optics and distributions. Fourier transforms. Convolution and image elaboration. Zernike polynomials and lens aberrations. Use of the special functions and transforms to understand the behaviour of optical instruments. Image instruments: telescope, binoculars, microscopy. Instruments for spectral analysis: prisms and greetings.