title: There's plenty of light at the bottom: statistics of photon penetration depth in random media.
abstract: We propose a comprehensive statistical approach describing the penetration depth of light in random media. The presented theory exploits the concept of probability density function f(z|ρ, t) for the maximum depth reached by the photons that are eventually re-emitted from the surface of the medium at distance ρ and time t. Analytical formulas for f, for the mean maximum depth 〈zmax〉 and for the mean average depth reached by the detected photons at the surface of a diffusive slab are derived within the framework of the diffusion approximation to the radiative transfer equation, both in the time domain and the continuous wave domain. Validation of the theory by means of comparisons with Monte Carlo simulations is also presented. The results are of interest for many research fields such as biomedical optics, advanced microscopy and disordered photonics.
authors.affiliation: Università degli Studi di Firenze, Dipartimento di Fisica e Astronomia, Via G. Sansone 1, 50019 Sesto Fiorentino, Firenze, Italy.
authors.forename: Fabrizio
authors.initials: F
authors.lastname: Martelli
authors.affiliation: Département de Neurosciences Fondamentales, University of Geneva, 1211 Geneva 4, Switzerland.|Département de l'Imagerie et des Sciences de l'Information Médicale, University Hospital, 1205 Geneva, Switzerland.
authors.forename: Tiziano
authors.initials: T
authors.lastname: Binzoni
authors.affiliation: Dipartimento di Fisica, Politecnico di Milano, Milano, Italy, Piazza Leonardo da Vinci 32, 20133 Milano, Italy.|Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche, Piazza Leonardo da Vinci 32, 20133 Milano, Italy.
authors.forename: Antonio
authors.initials: A
authors.lastname: Pifferi
authors.affiliation: Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche, Piazza Leonardo da Vinci 32, 20133 Milano, Italy.
authors.forename: Lorenzo
authors.initials: L
authors.lastname: Spinelli
authors.affiliation: Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche, Piazza Leonardo da Vinci 32, 20133 Milano, Italy.
authors.forename: Andrea
authors.initials: A
authors.lastname: Farina
authors.affiliation: Dipartimento di Fisica, Politecnico di Milano, Milano, Italy, Piazza Leonardo da Vinci 32, 20133 Milano, Italy.|Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche, Piazza Leonardo da Vinci 32, 20133 Milano, Italy.
authors.forename: Alessandro
authors.initials: A
authors.lastname: Torricelli