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 〈z_max〉 and for the mean average depth "Equation missing" 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.

In the present work, we investigated the scattering and spectrally resolved absorption properties of nanofluids consisting in aqueous and glycol suspensions of single-wall carbon nanohorns. The characteristics of these nanofluids were evaluated in view of their use as sunlight absorber fluids in a solar device. The observed nanoparticle-induced differences in optical properties appeared promising, leading to a considerably higher sunlight absorption with respect to the pure base fluids. Scattered light was found to be not more than about 5% with respect to the total attenuation of light. Both these effects, together with the possible chemical functionalization of carbon nanohorns, make this new kind of nanofluids very interesting for increasing the overall efficiency of the sunlight exploiting device. PACS 78.40.Ri, 78.35.+c, 78.67.Bf, 88.40.fh, 88.40.fr, 81.05.U.

In biomedical optics, the characterization of instrumentation with the help of appropriate tissue-simulating phantoms¹ plays an important role, ranging from proof-of-principle tests at early stages of the development to quality assurance during routine clinical application.² Numerous performance studies have been carried out by individual research groups; however, there are only a few multilaboratory efforts to characterize and to compare multiple instruments. Such approaches are essential to provide a sound basis for achieving quantitatively comparable results in clinical studies. They require the development of standardized guidelines to perform the same measurements on phantoms with the same properties in different laboratories. In the field of photon migration instruments, the first systematic study of different instruments was performed on the basis of the MEDPHOT protocol.³ Recently, the development and testing of phantoms has been reported for quality assurance in a multicenter clinical trial to measure the response of breast tumors to neoadjuvant chemotherapy by means of diffuse optical spectroscopic imaging.⁴ In the context of fluorescence imaging of tissues, phantoms were developed to characterize and compare imaging systems and to train surgeons.⁵

An exact solution of the time-dependent diffusion equation for the case of a two- and a three-layered finite diffusive medium is proposed. The method is based on the decomposition of the fluence rate in a series of eigenfunctions and upon the solution of the consequent transcendental equation for the eigenvalues obtained from the boundary conditions. Comparisons among the solution of the diffusion equation and the results of Monte Carlo simulations show the correctness of the proposed model.

The single scattering properties (extinction coefficient and scattering function at small forward scattering angles) of bovine and swine brain were obtained from transmissometric measurements on thin slices of tissues at l=633 nm. Large differences between the optical properties of white and gray matter were observed, whereas minor differences were found between bovine and swine samples. For gray matter, values between 10 and 30 mm^-1 were obtained for the extinction coefficient. The scattering function was strongly forward peaked, indicating a highly anisotropic scattering. For white matter, values between 100 and 250 mm^-1 were measured for the extinction coefficient. These values were so large that it was impossible to obtain a sample thin enough to measure the scattering function in single scattering conditions.

Diffuse optics¹ provides noninvasive tools to investigate highly scattering media (e.g., biological tissues in the wavelength range from 600 to 1300 nm) of large volumes (cubic centimeters) and depths up to a few centimeters beneath the surface. Both chemical (related to absorption) and structural (related to scattering) information can be retrieved by photons traveling through the diffusive medium. Numerous applications have been pursued, both in the medical field—ranging from functional brain imaging^2,3 and neuromonitoring,⁴ 5. ^{– 6} to cancer diagnostics^7,8 and therapy monitoring,^9,10—and in industrial sectors such as characterization of food,^11,12 wood,^13,14 and pharmaceuticals.^15,16 A key requirement for such applications to grow and gain a more widespread clinical or industrial acceptance is to achieve a high grade of reliability, reproducibility, accuracy in quantification, and comparability of clinical results.¹⁷ There is a compelling need to nurture the culture of quality assessment and quantitative grading of instruments in diffuse optics to support the parallel development of new instruments/techniques and applications on a stringent basis.¹⁸ 19. ^{– 20}