Course detail

# Wave Optics

The course consists of two parts.
The first part deals with the interference of light and related experiments. The following topics are explained and practised: Coherence of light, the contrast of the interference structure and the interpretation of the pattern obtained both by classical and by holografic interference methods.
The second part of the course is focused on the scalar diffraction in optics. The diffraction integral is discussed in detail and applied to the calculation of intensity and phase distribution in the diffraction patterns of the Fraunhofer and of the Fresnel types. The diffraction integral is derived in three ways:
(i) intuitively, from the Huygens-Fresnel principle,
(ii) from the wave equation by means of theorems of the integral calculus of functions of several variables,
(iii) by the superposition of plane waves.
Also the Rubinowicz representation of the boundary wave is derived and discussed. Interference and diffraction phenomena are demonstrated and practised in laboratories.

Learning outcomes of the course unit

1. Knowledge of the theory of optical interference and diffraction phenomena.
2. Experimental erudition for the work in laboratory of optical interferometry and diffraction.
3. Ability to interpret in detail diffraction and interference phenomena.

Prerequisites

Basic course of physics. Calculus of functions of several variables.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Born M., Wolf E.: Principles of Optics. 7th ed. Cambridge University Press 1999.
Sommerfeld A.: Optik. 2. Auflage. Akademische Verlagsgesellschaft Geest & Portig K.-G., Leipzig 1959. (Též Optics. Academic Press, New York 1954.)
Hecht, E.: Optics. Pearson Education, 2017.
Liška, M.: Optické sešity (texty k přednáškám). Brno, VUT 2013, 2014.
Saleh B. E. A., Teich C.: Základy fotoniky. Matfyzpress, Praha 1994.
Komrska, J.: Fourierovské metody v teorii difrakce a ve strukturní analýze. Brno: CERM, 2007. 242 s.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures. Teaching is suplemented by practical laboratory work.

Assesment methods and criteria linked to learning outcomes

Course-unit credit is conditional on active participation at seminars.
Examination: written test related to the interference and an oral examination from the diffraction.

Language of instruction

Czech

Work placements

Not applicable.

Aims

The aim of the course is to provide students with basic ideas of interference and scalar theory of diffraction and its applications.

Specification of controlled education, way of implementation and compensation for absences

Attendance at seminars is obligatory and is checked by the teacher. Absence may be compensated by the agreement with the teacher.

Classification of course in study plans

• Programme M2A-P Master's

branch M-PMO , 1. year of study, winter semester, 6 credits, compulsory

• Programme N-FIN-P Master's, 1. year of study, winter semester, 6 credits, compulsory

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Syllabus

Interference of light:
1. Intensity distribution in the area of superposition of two plane monochromatic waves of the same frequency. Width of the interference fringes. Contrast of interference structure. The Young experiment. Width of the fringes. Influence of the source size on an interference structure.
2. Light interference by means of the Fresnel mirrors. Width of fringes. Interference in a layer. Plan-parallel plate. A wedge layer. Fringes of equal inclination. Fringes of equal thickness.
3. Sensitivity of interference methods. Localization of interference fringes. Discussion of the localization of interference by a layer.
4. The Murty interferometer. Evaluate wavefront of elektromagnetic wave.
Thje Michelson interferometer. Equivalence with the interference by reflection on a thin layer. The use of the interferometer for length measurements and for the estimation of the quality of surfaces. Micro-interferometer. Mach-Zender interferometer. Visualization of phase objects.
5. Multiple-beam interferometer. The Fabry-Perot interferometer. High resolution spectroscopy. Optical resonators for lasers.
6. Holographic interferometry. Visualization of phase objects. Detection of small deformations and small shifts of objects with a diffuse surface.
7. Coherent speckles. Their applications.
.....................
Diffraction of light:
1. Scalar wave and its mathematical description. (Wave equation, harmonic waves, complex notation, the Helmholtz equation, the paraxial Helmholtz equation, the Fresnel approximation of the spherical wave.)
2. The Huygens-Fresnel principle and the diffraction integrals. The Fresnel and the Fraunhofer diffraction. The Soret plate.
3. The Fraunhofer diffraction phenomena. (Rectangular and circular apertures, the slit and the annular aperture.)
4. The Fresnel diffraction phenomena. (Half-plane, slit, strip, double-slit, circular aperture and circular obstacle, the Fresnel integrals, the Lommel functions of two variables.)
5. The Kirchhoff and the Rayleigh-Sommerfeld diffraction integrals.
6. The Fresnel diffraction as a transfer by a linear isoplanatic system.
7. The Rubinowicz representation of the boundary wave.

Laboratory exercise

14 hours, compulsory

Teacher / Lecturer

Syllabus

Young's experiment. Newton's fringes.
Shearing interferometry. Setting-up plane wave by reflection on plan-parallel plate. Estimation of the radius of curvature of the Gaussian-wave surface.
Visualization of the phase objects by Murty interferometer, Michelson interferometer and Mach-Zehnder interferometer.
Recognition of small defects and shifts by utilizing holographic interferometry.
Experimental arrangement for observation and registration of Fresnel and Fraunhofer diffraction patterns.
Fraunhofer and Fresnel diffraction by circular aperture.
Fraunhofer and Fresnel diffraction by a double-slit.

Exercise

12 hours, compulsory

Teacher / Lecturer

Syllabus

Calculation of the intensity distribution in Youngs experiment. Estimation of the coherence length from the visibility of interference fringes.
Localization of the interference fringes in different arrangement of two-beam interference measurements.
Calculation of the parameters of antireflection coatings. Calculation of the parameters of interference filters.
Size estimation of the Fresnel zones for typical experimental arrangements in light and X-ray optics. The Fresnel zones of convergent spherical wave. Focal lenghts of the Soret plates.
Calculation of the Fraunhofer diffraction phenomena. A detailed discussion of the Airy function.
Calculation and discussion of the Fresnel diffraction by a half-plane, slit, strip, double-slit and generally by obstacles with stright-line boundaries.
Calculations and discussion of the Fresnel diffraction by a circular aperture and disc.

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