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. Reminds of geometrical optics. Thin and thick lens. Geometrical and chromatic aberrations. Applications to optical instruments. Propagation of light in anisotropic media.
- Notes are given by the teachers. - M. Born and E. Wolf “Principles of Optics”, Pergamon Press, 1980, 6th edition or subsequent one.- Joseph W. Goodman “Introduction to Fourier Optics” Mc Graw-Hill, II edition 1996.- F. Gori “Elementi di Ottica”, Accademica, Roma 1995.- G. Toraldo di Francia and P. Bruscaglioni “Onde Elettromagnertiche” II edition, Zanichelli 1988.-E.Hecht, "Optics", Addison Wesley, 2001- L.Abbozzo, D.Mugnai, "Ottica Classica, Teoria della Visione, Ottica Ondulatoria", CNR-Servizio Pubblicazioni, Roma 2008- and two “historical” books:G. Toraldo di Francia “La diffrazione della luce” Einaudi, 1958P.M. Duffieux “L’intégrale de Fourier et ses applications à l’optique” Masson, Paris 1970
Learning Objectives
Knowledge of the main phenomena and laws of Optics, including Fourier optics. Ability to recognize and understand and utilize the main optics phenomena and to test and use optical instruments
Teaching Methods
48 hours of lectures (6 CFU)
Type of Assessment
Oral examination
Course program
Wave Optics:Refreshment on the scalar approximation in optics and main wave forms (plane waves, spherical waves, cylindrical waves etc). Evanescent waves. Gaussian beams with application to laser cavities.Geometrical Optics approximation: ray equation, eiconal equation and examples.Time interference of waves having the same frequency; interference of two waves with different frequencies and importance of the sensor characteristics. Space interference of coherent waves of equal or different forms: two plane waves, one plane wave and one spherical wave, and two spherical waves. Examples of well known interferometers (Michelson, Young, Ronchi test) as particular cases.Diffraction: Huygens-Fresnel principle; diffraction from a slit; Fresnel zone and Fraunhofer zone. Helmholtz-Kirchhoff theory and diffraction from an aperture on a flat screen. Circular aperture: a) Fresnel zone and multiple foci, b) evaluation of the field in the Fraunhofer zone; Airy pattern c) resolving power of an optical system. Mention of: superresolution, the electronic microscope, and near field microscope. Fourier Optics: diffracted field from an object of any shape by means of a system of suitable waves. Inverse interference principle of Toraldo and bases of the holography. Plane screen: evaluation of the field diffracted from a periodic grating. Field diffracted from an aperture in terms of planes waves: diffracted field as Fourier transform of the field on the aperture.Images: some basic formulas and evaluation of the effect of a lens on the phase. Lens as a Fourier transformer. Role of the evanescent waves in the loss of the resolving power of an optical systems.Image theory: optics systems as linear systems. Coherent case: image formation in terms of field decomposition, by using the transformation properties of the lenses. Spread function, optical transfer function. Image as convolution. Spectrum of the convolution. Basics of the optics elaboration of images by using the properties of Fourier transform of a lens.Images by using incoherent radiation: Modulation Transfer function (MTF). Relationship between coherent and incoherent transfer functions. Examples of elaboration and/or correction of defects of images: Filtering; defocusing correction, Marechal experiment. Abbe-Porter experimant. Zernike phase contrast microscope. Effects of the systems and media, crossed by the radiation (eg.air), on images. Quality of an image and Strehl Ratio. Geometrical Optics:Fresnel formula for reflection/refraction at the interface between two media, Snell law, phase shift in total reflection, the Fresnel romb. The relation between intensity and electrical field.Application of the Fermat principle, optical properties of conical curves. Sign conventions in geometrical optics, formula of the conjugate points for spherical dioptres, thin lens. Graphical reconstruction of images, power of a lens, magnification. Combination of two thin lenses.Optics of matrices: free propagation, spherical dioptre, thin lens.The eye: optical properties, defects of vision, myopia and presbyopia compensation. The magnifying glass, the refracting telescope. Entrance and exit apertures and pupils of an optical system, brilliance and luminosity of the image. Relative aperture, f-number, field depth.The microscope: magnification, numerical aperture, resolving power. The Abbe sinus condition (enunciate). Meaning in the case of object at infinity.Thick lens: principal planes, cardinal points and nodes. Third order aberrations: classification. Image formation optical systems with aberration: the plane dioptre example. Definition of paraxial images, pupil of the system, the problem of the out-of-axis source, astigmatism.Spherical aberration. The spherical mirror case, reflecting telescopes. Spherical aberration in thin lens, spherical aberration cancellation in the meniscus lens, application to the microscope objective.Comatic aberration. Coma in thin lenses. Astigmatism. Images in sagittal and meridian planes. Effects of astigmatism on image formation.Mentions on field curvature and distortion.Chromatic aberration, achromatic doublet, Abbe number.Propagation of light in anisotropic media. Tensor of the dielectric constant, principal optical axes, direction of energy, refractive index ellipsoid, ordinary and extraordinary beams in uniaxial crystals, birefringence, Glan polarizer, halfwave plate