Course detail
Applied Optics
FSI-TAOAcad. year: 2016/2017
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.
Language of instruction
Number of ECTS credits
Mode of study
Guarantor
Department
Learning outcomes of the course unit
2. Experimental erudition for the work in laboratory of optical interferometry and diffraction.
3. Ability to interpret in detail diffraction and interference phenomena.
Prerequisites
Co-requisites
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Examination: written test related to the interference and an oral examination from the diffraction.
Course curriculum
Work placements
Aims
Specification of controlled education, way of implementation and compensation for absences
Recommended optional programme components
Prerequisites and corequisites
Basic literature
Hecht, E.: Optics. Pearson Education, 2017.
Recommended reading
Liška, M.: Optické sešity (texty k přednáškám). Brno, VUT 2013, 2014.
Saleh, B. E. A., Teich, C.: Základy fotoniky. Matfyzpress, Praha 1994.
Classification of course in study plans
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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 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. The 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.
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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.
Exercise
Teacher / Lecturer
Syllabus
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.