Papers by Fabrizio Martelli
SPIE Proceedings, 2013
The optical properties of the human head in the range from 600 nm to 1100 nm have been non-invasi... more The optical properties of the human head in the range from 600 nm to 1100 nm have been non-invasively in-vivo investigated by various research groups using different diffuse optics techniques and data analysis methods.
Journal of the Optical Society of America A
Anomalous radiative transfer (ART) theory represents a generalization of classical radiative tran... more Anomalous radiative transfer (ART) theory represents a generalization of classical radiative transfer theory. The present tutorial aims to show how Monte Carlo (MC) codes describing the transport of photons in anomalous media can be implemented. We show that the heart of the method involves suitably describing, in a "non-classical" manner, photon steps starting from fixed light sources or from boundaries separating regions of the medium with different optical properties. To give a better sense of the importance of these particular photon step lengths, we also show numerically that the described approach is essential in preserving the invariance property for light propagation. An interesting byproduct of the MC method for ART is that it allows us to simplify the structure of "classical" MC codes, utilized, for example, in biomedical optics.
Sensors (Basel, Switzerland), 2022
The research in optical sensors has been largely encouraged by the demand for low-cost and less o... more 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: eli...
Optics Communications, 2019
In this paper we deal with the influence on absorption of the diffusive media characteristics fra... more 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.
Physical Review A, 2019
The peculiar characteristics of random laser emission have been studied in many different media, ... more The peculiar characteristics of random laser emission have been studied in many different media, leading to a classification of the working regimes based on the statistics of spectral fluctuations. Alongside such studies, the possibility to constrain light propagation by Lévy walks, i.e. with a 'heavy-tailed' distribution of steps, has opened the opportunity to investigate the behavior of a superdiffusive optical gain medium, that can lead to a "superdiffusive random laser." Here, we present a theoretical investigation, based on Monte Carlo simulations, on such a kind of medium, focusing on the widespread presence of fluctuation regimes, that, in contrast to a diffusive random laser, appears very hard to switch off by changing the gain and scattering strength. Hence, the superdiffusion appears as a condition that increases the value of the threshold energy and promotes the presence of fluctuations in the emission spectrum.
Journal of the Optical Society of America. A, Optics, image science, and vision, 2018
A generalized time-independent correlation transport equation (GCTE) is proposed for the field au... more A generalized time-independent correlation transport equation (GCTE) is proposed for the field autocorrelation function. The GCTE generalizes various models for anomalous transport of photons and takes into account the possible presence of a static background. In a tutorial example, the GCTE is solved for a homogeneous semi-infinite medium in reflectance configuration through Monte Carlo simulations. The chosen anomalous photon transport model also includes the classic and the "generalized" Lambert-Beer's law (depending on the choice of parameters). A numerical algorithm allowing generation of the related anomalous random photon steps is also given. The clear influence of anomalous transport on the field autocorrelation function is shown and discussed for the proposed specific examples by comparing the general results with the classical case (Lambert-Beer's law).
Optics Express, 2016
A set of time-domain analytical forward solvers for Raman signals detected from homogeneous diffu... more A set of time-domain analytical forward solvers for Raman signals detected from homogeneous diffusive media is presented. The time-domain solvers have been developed for two geometries: the parallelepiped and the finite cylinder. The potential presence of a background fluorescence emission, contaminating the Raman signal, has also been taken into account. All the solvers have been obtained as solutions of the time dependent diffusion equation. The validation of the solvers has been performed by means of comparisons with the results of "gold standard" Monte Carlo simulations. These forward solvers provide an accurate tool to explore the information content encoded in the time-resolved Raman measurements.
We propose and validate the design of inhomogeneous phantoms for diffuse optical imaging purposes... more We propose and validate the design of inhomogeneous phantoms for diffuse optical imaging purposes using totally absorbing objects embedded in a diffusive medium. From Monte Carlo simulations, we show that a given or desired perturbation strength caused by an realistic absorbing inhomogeneity of a certain absorption and volume can be approximately mimicked by a small totally absorbing object of a so-called Equivalent Black Volume (Equivalence Relation). This concept can be useful to design realistic inhomogeneous phantoms using a set of black objects with different volumes. Further, it permits to grade physiological or pathological changes on a reproducible scale of equivalent black volumes, thus facilitating the performance assessment of clinical instruments. We have also provided a plot to derive the Equivalent Black Volume yielding the same effect of a realistic absorption object.
Journal of biomedical optics, 2014
Performance assessment of instruments devised for clinical applications is of key importance for ... more Performance assessment of instruments devised for clinical applications is of key importance for validation and quality assurance. Two new protocols were developed and applied to facilitate the design and optimization of instruments for time-domain optical brain imaging within the European project nEUROPt. Here, we present the "Basic Instrumental Performance" protocol for direct measurement of relevant characteristics. Two tests are discussed in detail. First, the responsivity of the detection system is a measure of the overall efficiency to detect light emerging from tissue. For the related test, dedicated solid slab phantoms were developed and quantitatively spectrally characterized to provide sources of known radiance with nearly Lambertian angular characteristics. The responsivity of four time-domain optical brain imagers was found to be of the order of 0.1 m² sr. The relevance of the responsivity measure is demonstrated by simulations of diffuse reflectance as a funct...
Biomedical Optics and 3-D Imaging, 2010
Abstract A multi-laboratory study for the accurate calibration of diffusive liquid phantoms based... more Abstract A multi-laboratory study for the accurate calibration of diffusive liquid phantoms based on Intralipid and Indian ink has been performed. Different techniques, instrumental set-ups and analysis methods led to compatible values for optical properties.
Applied Optics, 1998
A Monte Carlo procedure has been developed to study photon migration through highly scattering no... more A Monte Carlo procedure has been developed to study photon migration through highly scattering nonhomogeneous media. When two scaling relationships are used, the temporal response when scattering or absorbing inhomogeneities are introduced can be evaluated in a short time from the results of only one simulation carried out for the homogeneous medium. Examples of applications to the imaging of defects embedded into a diffusing slab, a model usually used for optical mammography, are given. Comparisons with experimental results show the correctness of the results obtained.
Optics Express, 2018
An heuristic model for ballistic photon detection in continuous-wave measurements of collimated t... more An heuristic model for ballistic photon detection in continuous-wave measurements of collimated transmittance through a slab is presented. The model is based on the small angle approximation and the diffusion equation and covers all the ranges of optical thicknesses of the slab from the ballistic to the diffusive regime. The performances of the model have been studied by means of comparisons with the results of gold standard Monte Carlo simulations for a wide range of optical thicknesses and two types of scattering functions. For a non-absorbing slab and field of view of the receiver less than 3 • the model shows errors less than 15% for any value of the optical thickness. Even for an albedo value of 0.9, and field of view of the receiver less than 3 • the model shows errors less than 20%. These results have been verified for a large set of scattering functions based on the Henyey-Greenstein model and Mie theory for spherical scatterers. The latter has also been used to simulate the scattering function of Intralipid, a diffusive material widely used as reference standard for tissue simulating phantoms. The proposed model represents an effective improvement compared to the existing literature.
Mechanically switchable solid inhomogeneous phantom for performance tests in diffuse imaging and ... more Mechanically switchable solid inhomogeneous phantom for performance tests in diffuse imaging and spectroscopy
The mean penetration depth of diffusely reflected photons is dependent on the arrival time t of p... more The mean penetration depth of diffusely reflected photons is dependent on the arrival time t of photons, but not on the source-detector distance. Thus, all photons collected at the same t have the same depth sensitivity, and can be used for the reconstruction. Following this concept, we have implemented a system for 3D tomography using a single injection fiber and a time-gated ICCD camera. The feasibility of the novel approach to reconstruct a local perturbation was demonstrated both with simulations and phantom measurements. Finally, preliminary measurements were performed in vivo following a standard protocol of motor cortex activation.
Biomedical optics express, 2012
In this paper a forward solver software for the time domain and the CW domain based on the Born a... more In this paper a forward solver software for the time domain and the CW domain based on the Born approximation for simulating the effect of small localized fluorophores embedded in a non-fluorescent biological tissue is proposed. The fluorescence emission is treated with a mathematical model that describes the migration of photons from the source to the fluorophore and of emitted fluorescent photons from the fluorophore to the detector for all those geometries for which Green's functions are available. Subroutines written in FORTRAN that can be used for calculating the fluorescent signal for the infinite medium and for the slab are provided with a linked file. With these subroutines, quantities such as reflectance, transmittance, and fluence rate can be calculated.
Scientific Reports
In this work, we present a robust and powerful method for the verification, with arbitrary accura... more 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 ...
Applied Sciences
Based on recent developments in both single-photon detectors and timing electronic circuits, we d... more Based on recent developments in both single-photon detectors and timing electronic circuits, we designed a compact and cost effective time-domain diffuse optical tomography system operated at 1 Hz acquisition rate, based on eight silicon photomultipliers and an 8-channel time-to-digital converter. The compact detectors are directly hosted on the probe in a circular arrangement around a single light injection fiber, so to maximize light harvesting. Tomography is achieved exploiting the depth sensitivity that is encoded in the arrival time of detected photons. The system performances were evaluated on simulations to assess possible the limitations arising from the use of a single injection point, and then on phantoms and in vivo to prove the eligibility of these technologies for diffuse optical tomography.
Biomedical Optics Express
The depth sensitivity functions for AC amplitude, phase (PH) and DC intensity signals have been o... more The depth sensitivity functions for AC amplitude, phase (PH) and DC intensity signals have been obtained in the frequency domain (where the source amplitude is modulated at radio-frequencies) by making use of analytical solutions of the photon diffusion equation in an infinite slab geometry. Furthermore, solutions for the relative contrast of AC, PH and DC signals when a totally absorbing plane is placed at a fixed depth of the slab have also been obtained. The solutions have been validated by comparisons with gold standard Monte Carlo simulations. The obtained results show that the AC signal, for modulation frequencies < 200 MHz, has a depth sensitivity with similar characteristics to that of the continuous-wave (CW) domain (source modulation frequency of zero). Thus, the depth probed by such a signal can be estimated by using the formula of penetration depth for the CW domain (Sci. Rep. 6, 27057 (2016)). However, the PH signal has a different behavior compared to the CW domain, showing a larger depth sensitivity at shallow depths and a less steep relative contrast as a function of depth. These results mark a clear difference in term of depth sensitivity between AC and PH signals, and highlight the complexity of the estimation of the actual depth probed in tissue spectroscopy.
PloS one, 2016
Non-invasive in vivo diffuse optical characterization of human bone opens a new possibility of di... more Non-invasive in vivo diffuse optical characterization of human bone opens a new possibility of diagnosing bone related pathologies. We present an in vivo characterization performed on seventeen healthy subjects at six different superficial bone locations: radius distal, radius proximal, ulna distal, ulna proximal, trochanter and calcaneus. A tailored diffuse optical protocol for high penetration depth combined with the rather superficial nature of considered tissues ensured the effective probing of the bone tissue. Measurements were performed using a broadband system for Time-Resolved Diffuse Optical Spectroscopy (TRS) to assess mean absorption and reduced scattering spectra in the 600-1200 nm range and Diffuse Correlation Spectroscopy (DCS) to monitor microvascular blood flow. Significant variations among tissue constituents were found between different locations; with radius distal rich of collagen, suggesting it as a prominent location for bone related measurements, and calcaneus...
Scientific Reports, 2016
In a random laser the optical feedback is provided by scattering rather than by an optical cavity... more 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.
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Papers by Fabrizio Martelli