Thin and thick lens in paraxial optics. Entrance and exit pupils, F-number and numerical aperture. Geometrical and chromatic aberrations. Applications to optical instruments. Use of optical design software.
Wave optics, including evanescent waves and paraxial beams, interference and diffraction. Imaging with coherent and incoherent radiation. Fourier optics and introduction to optical information processing. Applications to classic and modern systems.
- Notes given by the teacher.
- M. Born and E. Wolf “Principles of Optics”, Pergamon Press, 7th ed. 1999.
- Joseph W. Goodman “Introduction to Fourier Optics” Mc Graw-Hill, 2nd ed. 1996.
-E.Hecht, "Optics", Addison Wesley, 4th ed. 2002.
- G.Giusfredi, "Manuale di Ottica", Springer-Verlag 2015
Learning Objectives
Knowledge and understanding of the laws of paraxial geometrical optics and of geometric and chromatic aberations. Knowledge and understanding of the phenomena and laws of wave optics.
Ability to analyze the formation of the image in a complex optical system, also with the use of optical design software, to identify the limits to resolution induced by aberrations and diffraction. Ability to understand the characteristics and operating conditions of advanced optical instrumentation
Geometrical optics:
Recalls on Fresnel formulas for reflection / refraction on the surface of discontinuity between two media, Snell's law, phase shift of the wave in total reflection, Fresnel's rhomb.
Fermat principle, application to the optical properties of conic curves. Conventions of signs in geometrical optics, formula of conjugated points for spherical diopters and thin lenses. Graphic construction of images, power of the lens, magnification. Combination of two thin lenses.
Optics of matrices. Free propagation, spherical diopter, thin lens. The thick lens, principal planes, cardinal points and nodes.
The eye, optical characteristics, vision defects, compensation of myopia and presbyopia. The magnifying glass, the telescope, the reflecting telescopes.
Entrance and exit apertures, pupils of an optical system, brilliance and luminosity of the image. Numerical aperture, f-number, depth of field. Introduction to radiometry.
The microscope: magnification, resolving power.
Aberrations: Seidel classification of 3rd order aberrations. Image formation in an optical system with aberrations: example of the plane diopter. Definition of image in paraxial optics, pupil of the system, off-axis source problem, astigmatism.
Spherical aberration. Spherical mirror case. Spherical aberration in thin lenses, cancellation of spherical aberration in the meniscus lens, application to the microscope objective.
Comatic aberration. Coma in thin lenses. The Abbe sinus condition. Meaning in the case of object at infinity.
Astigmatism. Image point in the sagittal and meridian planes. Consequences of astigmatism on the formation of the image.
Notes on field curvature and distortion.
Chromatic aberration, achromatic doublet, Abbe number.
Use of optical software.
Wave optics:
The scalar approximation in optics and the main forms of waves (flat, spherical, cylindrical, dipolar spherical etc.). Evanescent waves. Bessel beams, Gaussian beams with application to the laser cavities.
Approximation of geometrical optics, rays equation and eiconal equation.
Interference of waves of the same frequency and different frequency. Interference in space of coherent waves of different shapes: two plane waves, one plane and one spherical and two spherical waves. Examples of some known interferometers (Michelson, Young, Ronchi test) as particular cases.
Diffraction: Huygens-Fresnel principle; diffraction from a slit; Fresnel and Fraunhofer aooriximation. Helmholtz-Kirchhoff theory. Circular aperture: Fresnel zones, evaluation of the field in the Fraunhofer zone and Airy figure, resolving power of an optical system.
Fourier optics: Development of the diffracted field and derivation of the Huygens.Fresnel formula. Inverse interference principle of Toraldo di Francia.
Effect of the lens on the incident wavefront, formation of the Fourier transform of the field in the focal plane of the lens.
Image theory: optical systems as linear systems. Coherent case: Amplitude Point Spread Function, Amplitude Transfer Function.
Images with incoherent radiation: Optical Transfer Function and Modulation Transfer Function. Relationship between the quantities of the coherent case and those of the incoherent case. Examples of image processing: filtering. Abbe-Porter experiment. The phase contrast microscope, super resolution, holography principles.