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B015501 - MATHEMATICAL METHODS FOR OPTICS
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Type of Assessment
Course program
Academic Year 2017-18
Course year
Second year - First Semester
Belonging Department
Physics and Astronomy
Course Type
Single education field course
Scientific Area
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS
Credits
6
Teaching Hours
48
Teaching Term
18/09/2017 ⇒ 22/12/2017
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Teaching Language
Italian
Course Content
Functions of complex variable, derivatives and
integrals. Cauchy’s theorem and formula.
Taylor and Laurent series.
Cauchy’s residue theorem and integrals of
interest in optics. Dispersion. Special functions
for optics and distributions. Fourier transforms.
Convolution and image elaboration. Zernike
polynomials. Use of special functions and
transforms to understand optical instrument
performances. Image instruments: telescope,
binoculars, microscope. Instruments for
sp
integrals. Cauchy’s theorem and formula.
Taylor and Laurent series.
Cauchy’s residue theorem and integrals of
interest in optics. Dispersion. Special functions
for optics and distributions. Fourier transforms.
Convolution and image elaboration. Zernike
polynomials. Use of special functions and
transforms to understand optical instrument
performances. Image instruments: telescope,
binoculars, microscope. Instruments for
sp
Suggested readings (Search our library's catalogue)
Appunti verranno dati agli studenti durante le lezioni.
Per alcune parti e/o approfondimenti:
- 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)
Per alcune parti e/o approfondimenti:
- 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
Knolewdge acquired:
Bases of advanced mathematics
Competence acquired
Main mathematical bases needed for physics and mostly for classical and modern optics.
Skills acquired (at the end of the course)
Ability to understand and rigorously describe the phenomena of physics and mainly of classic and modern optics.
Bases of advanced mathematics
Competence acquired
Main mathematical bases needed for physics and mostly for classical and modern optics.
Skills acquired (at the end of the course)
Ability to understand and rigorously describe the phenomena of physics and mainly of classic and modern optics.
Prerequisites
Courses to be used as requirements (required and/or recommended)
Matematica I e II
Courses required:
Courses recommmended Matematica I e II
Matematica I e II
Courses required:
Courses recommmended Matematica I e II
Teaching Methods
Blackboard lectures, slide projection, laboratory demonstrations
CFU: 6
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 150
Hours reserved to private study and other indivual formative activities:
Contact hours for: Lectures (hours): 48
CFU: 6
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 150
Hours reserved to private study and other indivual formative activities:
Contact hours for: Lectures (hours): 48
Type of Assessment
oral exam
Course program
Functions of complex variable, derivatives and
integrals. Cauchy’s theorem and formula.
Taylor series. Singularities and Laurent series.
Cauchy’s residue theorem and integrals of
interest in optics. Dispersion. Special functions
for optics and distributions. Fourier transforms.
Convolution and image elaboration. Zernike
polynomials. Use of special functions and
transforms to understand optical instrument
performances. Image instruments: telescope,
binoculars, microscope. Instruments for
spectral analysis: prisms and gratings.
integrals. Cauchy’s theorem and formula.
Taylor series. Singularities and Laurent series.
Cauchy’s residue theorem and integrals of
interest in optics. Dispersion. Special functions
for optics and distributions. Fourier transforms.
Convolution and image elaboration. Zernike
polynomials. Use of special functions and
transforms to understand optical instrument
performances. Image instruments: telescope,
binoculars, microscope. Instruments for
spectral analysis: prisms and gratings.