This course aims to provide the mathematical and conceptual tools for understanding modern optics, in the framework of optical imaging systems. Specifically, the theoretical foundations of physical optics will be introduced, together with a number of applications relevant in the field of nano-bioscience. Starting from the classical description of electromagnetic wave propagation, the geometrical and physical optics approximations will be introduced, while discussing their applicability limits. Image formation is addressed for both scalar and fully vectorial electromagnetic fields, by mean of a Fourier Transformation formalism. The image formation mechanism is explained through the concepts of spatial resolution, point spread function and transfer function of optical elements, for both coherent and incoherent illumination. As application examples, the wide-field microscope and the scanning confocal microscope will be considered, wherein aberrations and image distortion (chromatic aberrations, vignetting, coma, spherical aberration, etc.) are treated mathematically. More advanced microscopy techniques based on the use fluorescent probes will be also described, such as STED and FLIM. In the second part of the course, the principles of temporal and spatial coherence of electromagnetic radiation will be addressed, with particular attention to the relationships between extended sources and spatial coherence (Van Cittert-Zernike theorem), spectral distribution and temporal coherence (Weiner-Khinchin theorem). Interferometric approaches to optical imaging will be introduced based on speckle analysis and wavefront analysis. Finally, specific applications of holographic and interferometric imaging will be explained (e.g. Mach-Zehnder microscopy, Quantitative Phase Imaging, Optical Coherence Tomography), by means of optoelectronic devices such as Wavefront Analysers and Spatial Light Modulators.

The student is expected to acquire knowledge in: - fundamental principles of optical imaging - operation of most widely used microscopy/interferometric techniques with particular regard to the nano-bio domain Expected skills are: - ability to understand the underlying mechanisms of complex imaging systems - ability to design and operate optical systems for specific imaging purposes

Classical Electromagnetism Mathematical Analysis (Calculus).

- Brief summary of classical electromagnetism and wave propagation - Geometrical and physical Optics - Mathematical description of image formation theory, Fourier optics - Optical wide-field microscopy and scanning confocal microscopy - Advanced fluorescence microscopy techniques - Statistical Optics and speckles: spatial and temporal coherence of light - Interferometric, holographic and adaptive image formation systems - Control and manipulation of wave fronts: wavefront analysers, spatial light modulator devices - Imaging through turbid media

The course involves class lectures, supported with electronic slides and old-fashioned blackboard writing; and class exercises. During class exercises, exemplary applications will be considered, including calculations/simulations performed on laptop. In addition, practical “hands-on” sessions will be organized, depending on the availability of research laboratories and scientific personnel.

J.W. Goodman, Introduction to Fourier Optics J.W. Goodman, Statistical Optics B.E.A. Saleh and M.C. Teich, Fundamental of Photonics Additional supporting material provided during the course

Modalità di esame: Prova scritta (in aula); Prova orale facoltativa;

Exam: Written test; Optional oral exam;

... The exam includes a written and an oral discussion. The written part consists of : a) simple symbolic or numeric examples of the concepts explained in the course; b) multiple-answer questions; c) topical themes to be extensively discussed. The total allotted time is 2 hrs. A total score of at least 18/30 is required to access to the oral examination, which will last 20-30 mins on average.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.