In this work, we present a robust and powerful method for the verification, with arbitrary accuracy, of Monte Carlo codes for simulating random walks in complex media. Such random walks are typical ...of photon propagation in turbid media, scattering of particles, i.e., neutrons in a nuclear reactor or animal/humans' migration. Among the numerous applications, Monte Carlo method is also considered a gold standard for numerically "solving" the scalar radiative transport equation even in complex geometries and distributions of the optical properties. In this work, we apply the verification method to a Monte Carlo code which is a forward problem solver extensively used for typical applications in the field of tissue optics. The method is based on the well-known law of average path length invariance when the entrance of the entities/particles in a medium obeys to a simple cosine law, i.e., Lambertian entrance, and annihilation of particles inside the medium is absent. By using this law we achieve two important points: (1) the invariance of the average path length guarantees that the expected value is known regardless of the complexity of the medium; (2) the accuracy of a Monte Carlo code can be assessed by simple statistical tests. We will show that we can reach an arbitrary accuracy of the estimated average pathlength as the number of simulated trajectories increases. The method can be applied in complete generality versus the scattering and geometrical properties of the medium, as well as in presence of refractive index mismatches in the optical case. In particular, this verification method is reliable to detect inaccuracies in the treatment of boundaries of finite media. The results presented in this paper, obtained by a standard computer machine, show a verification of our Monte Carlo code up to the sixth decimal digit. We discuss how this method can provide a fundamental tool for the verification of Monte Carlo codes in the geometry of interest, without resorting to simpler geometries and uniform distribution of the scattering properties.
The research in optical sensors has been largely encouraged by the demand for low-cost and less or non-invasive new detection strategies. The invention of the random laser has opened a new frontier ...in optics, providing also the opportunity to explore new possibilities in the field of sensing, besides several different and peculiar phenomena. The main advantage in exploiting the physical principle of the random laser in optical sensors is due to the presence of the stimulated emission mechanism, which allows amplification and spectral modification of the signal. Here, we present a step forward in the exploitation of this optical phenomenon by a revisitation of a previous experimental setup, as well as the measurement method, in particular to mitigate the instability of the results due to shot-to-shot pump energy fluctuations. In particular, the main novelties of the setup are the use of optical fibers, a reference sensor, and a peristaltic pump. These improvements are devoted to: eliminating optical beam alignment issues; improving portability; mitigating the variation in pump energy and gain medium performances over time; realizing an easy and rapid change of the sensed medium. The results showed that such a setup can be considered a prototype for a portable device for directly measuring the scattering of liquid samples, without resorting to complicated numerical or analytic inversion procedures of the measured data, once the suitable calibration of the system is performed.
Random walks are common in nature and are at the basis of many different phenomena that span from neutrons and light scattering to the behaviour of animals. Despite the evident differences among all ...these phenomena, theory predicts that they all share a common fascinating feature known as Invariance Property (IP). In a nutshell, IP means that the mean length of the total path of a random walker inside a closed domain is fixed by the geometry and size of the medium. Such a property has been demonstrated to hold not only in optics, but recently also in the field of biology, by studying the movement of bacteria. However, the range of validity of such a universal property, strictly linked to the fulfilment of equilibrium conditions and to the statistical distributions of the steps of the random walkers, is not trivial and needs to be studied in different contexts, such as in the case of biological entities occupied in random foraging in an open environment. Hence, in this paper the IP in a virtual medium inside an open environment has been studied by using actual movements of animals recorded in nature. In particular, we analysed the behaviour of a grazer mollusc, the chiton Acanthopleura granulata. The results depart from those predicted by the IP when the dimension of the medium increases. Such findings are framed in both the condition of nonequilibrium of the walkers, which is typical of animals in nature, and the characteristics of actual animal movements.
Random lasers are optical sources where light is amplified by stimulated emission along random paths through an amplifying scattering medium. Connections between their physics and the one of quenched ...disordered nonlinear systems, notably spin glasses, have been recently suggested. Here we report a first experimental study of correlations of spectral fluctuations intensity in a random laser medium where the scatterers displacement significantly changes among consecutive shots. Remarkably, our results reveal that the replica symmetry breaking (RSB) phenomenology is robust with respect to an averaging over different realizations of the disorder. Moreover, besides opening new intriguing questions about the understanding of such a phenomenon, this work aims to clarify the connection between the RSB with the onset of the Lévy regime, i.e. the fluctuations regime that is a peculiar feature of the random lasing under critical conditions. Our results suggest that the former occurs independently of the latter and then the RSB phenomenology is a generic feature linked to the random laser threshold.
In a random laser the optical feedback is provided by scattering rather than by an optical cavity. Then, since its emission characteristics are very susceptible to the scattering details, it is a ...natural candidate for making active sensors to use as a diagnostic tool for disordered media like biological samples. However, the methods reported up to now, requiring the injection of toxic substances in the sample, have the drawback of altering the physical-chemical composition of the medium and are not suitable for in-vivo measurements. Here we present a random laser based sensor that overcomes these problems by keeping gain and diffusion separated. We provide an experimental characterisation of the sensor by using a reference diffusive liquid phantom and we show that, compared to a passive method, this sensor takes advantage of the gain and spectral properties of the random laser principle.
In this paper we deal with the influence on absorption of the diffusive media characteristics framing the problem in connection with the invariance property (IP) of the mean path length. We show that ...the IP is an important issue that regulates but not prevent the search of absorption maximization by scattering characteristics. We find that the scattering may increase the absorption or even be detrimental, depending on the geometry of the medium and the conditions of its illumination.
In biomedical optics, the mean fluence rate of photons, assessed in a sub-volume of a propagating medium, is classically obtained in Monte Carlo simulations by taking into account the power deposited ...by the absorbed photons in the sub-volume. In the present contribution, we propose and analytically demonstrate an alternative method based on the assessment of the mean pathlength traveled by all the photons inside the sub-volume. Few practical examples of its applications are given. This method has the advantage of improving, in many cases, the statistics and the convergence of the Monte Carlo simulations. Further, it also works when the absorption coefficient is nil and for a non-constant spatial distribution of the absorption coefficient inside the sub-volume. The proposed approach is a re-visitation of a well-known method applied in radiation and nuclear physics in the context of radiative transfer, where it can be derived in a more natural manner.
Invariance properties of exact solutions of the radiative transfer equation Martelli, Fabrizio; Tommasi, Federico; Fini, Lorenzo ...
Journal of Quantitative Spectroscopy & Radiative Transfer/Journal of quantitative spectroscopy & radiative transfer,
December 2021, 2021-12-00, Letnik:
276
Journal Article
Recenzirano
Odprti dostop
•Invariance properties hold for all RTE solutions under uniform Lambertian illumination.•Lambertian illumination offers a unique reference standard for forward computational codes.•Uniform and ...isotropic radiance is the physical insight at the ground of the invariance property.•A Lambertian surface exists in a non-absorbing medium subjected to uniform isotropic radiance.
In this work, special invariance properties of a class of exact solutions of the radiative transfer equation (RTE) pertaining to a uniform Lambertian illumination of any non-absorbing homogeneous and inhomogeneous volume are presented and discussed. This class of solutions of the RTE traces a reference ground under which light propagation can be studied in a special simplified regime. Despite the difficulties to obtain general solutions of the radiative transfer equation, the condition of Lambertian illumination determines a unique regime of photon transport where quite easy and simple invariant solutions can be obtained in all generality for homogeneous and inhomogeneous geometries. These solutions are invariant both with respect to the geometry (size and shape of the volume) and with respect to the scattering properties, i.e. scattering coefficient, scattering function and homogeneity of the considered domain. Another evident advantage of these solutions is that they are exact solutions known with arbitrary precision and can thus be used as reference standard for photon migration studies.
The limits of applicability of scaling relations to generate new simulations of photon migration in scattering media by re-scaling an existing Monte Carlo simulation are investigated both for the ...continuous wave and the time domain case. We analyzed the convergence properties in various scenarios by numerical methods, trying to derive practical guidelines for the judicious use of this approach, as well as a deeper understanding of the physics behind such relations. In the case of scaling of the absorption coefficient, the convergence is always rigorous both for the forward and inverse problems, relying on the derivatives with respect to the absorption coefficient. Also, the regenerated simulation inherits the very same noise of the original Monte Carlo simulation. In the case of scaling of the scattering coefficient, the situation is more critical. For forward problems, even for just a 10% uniform increase in scattering, appreciable deviations are observed whenever a high number of scattering interactions is involved. We tested a practical criterion based on the number of scattering events in the original simulation to judge the convergence of the scaling factors. For inverse problems, the scaling relations provide accurate regenerated simulations apart from the noise level that is increased with respect to the initial simulation, although anyway lower than the noise level obtained by implementing the direct calculation. The results of this study are important whenever an increase of Monte Carlo code throughput is mandatory, e.g. , for fast data analysis of diffuse data, or in machine-learning scenarios, when generating huge datasets is needed.
Optical sensing is a very important method for investigating different kinds of samples. Recently, we proposed a new kind of optical sensor based on random lasing Sci. Rep.6, 35225 (2016), that ...couples the advantages of stimulated emission in detecting small variations on scattering properties of a sensed material, to the needs of no alteration of the sample under investigation. Here, we present a method to achieve a quantitative measurement of the scattering properties of a material. The results on samples of calibrated microspheres show a dependence of the peak intensity of the emission spectrum on the transport mean free path of the light within the sample, whatever the dimension (down to ≈100 nm of particle diameter) and the concentration of scatterers dispersed in the sensed material. A direct and fast measurement of the scattering properties is obtained by calibration with a well-known and inexpensive reference medium.
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