Time-Resolved Diffuse Optical Spectroscopy: A Differential Absorption Approach PAOLA TARONI,* ANDREA BASSI, LORENZO SPINELLI, RINALDO CUBEDDU, and ANTONIO PIFFERI Dipartimento di Fisica, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133 Milan, Italy (P.T., A.B., R.C., A.P.); Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche (P.T., L.S.); National Laboratory for Ultrafast and Ultraintense Optical Science, Consiglio Nazionale delle Ricerche (A.B., R.C., A.P.); and Research Unit Politecnico di Milano, Istituto Italiano di Tecnologia (R.C., A.P.) A method is presented for the estimate of spectral changes in the absorption properties of turbid media from time-resolved diffuse optical spectroscopy. The method relies on the hypothesis of constant scattering over the wavelength range of interest, but no limitations come from the sample size and shape as the method is derived directly from the Beer– Lambert law. The effects of a moderate spectral dependence of the scattering properties and of the non-ideal instrument response function were investigated theoretically, and the results were confirmed experi- mentally, showing that the method can be profitably applied in cases of practical interest. Index Headings: Absorption spectroscopy; Beer–Lambert law; Photon migration; Turbid media. INTRODUCTION The optical properties of a medium depend on its composition and microscopic structure. A wealth of informa- tion on the medium can be gained from their assessment. Thus, optical techniques, which are also inherently noninvasive, are presently applied or investigated for their potential use as diagnostic means in a variety of fields, including—but not limited to—biology and medicine. Most often, the optical parameter of direct interest is the absorption, because its estimate at multiple wavelengths allows one to derive the composition of the medium under investigation. However, in many real situations, the absorption properties cannot be easily assessed by conventional means due to the strong scattering. When highly diffusive media are involved, operation in the time domain allows one to disentangle the absorption from the scattering contribution to light attenuation, provided that light propagation can be correctly modeled for the system under study. In most cases, in order to deal with an analytical solution of the problem, experimental data are interpreted using simple models that hold accurately only for infinite or semi-infinite media and typically rely on the diffusion approximation to the radiative transfer equation (see, for example, Ref. 1). An analytical solution of the radiative transfer equation itself has also been derived, but still for an infinite 2 or semi-infinite medium. 3 On the other hand, lately the diffusion approximation has also been extended to provide straightforward close-form solutions for specific sample geometries. 4–7 These models can be effectively applied in several situations, but various conditions of practical interest exist that are far from fulfilling their hypotheses. This typically occurs for samples of irregular shape and/or very small size. As mentioned above, optical techniques (ranging from Raman to vibrational spectroscopy) are often investigated for their potential diagnostic use or are even already applied effectively. As an example, this occurs when agricultural produce (either fruits or vegetables) is probed for nondestruc- tive quality evaluation, including nondestructive firmness testing and the assessment of sugars related to sweetness and ripening, or of carotenoid levels to provide an indication of oxidative deterioration. 8,9 Time-domain photon migration techniques have recently shown good promise in the field, 10,11 but the irregular shape of the samples can limit their accuracy in the estimate of the optical properties and consequently the potential to develop effective quantitative diagnostics. Furthermore, even samples characterized by cylindrical or parallelepiped geometry cannot be accurately modeled if their size is too small. 6 This is typically the case for pharmaceutical tablets that need to be checked for content uniformity. Conventional quality control methods such as high-perfor- mance liquid chromatography (HPLC) and mass spectroscopy (MS) are time consuming, expensive, and require sample preparation. Even more important, they are destructive, so that only small samples may be tested from given production batches. Furthermore, they do not provide any information about the spatial distribution of components within a sample. Chemical imaging, which combines conventional imaging and vibrational spectroscopy, is thus emerging for process monitoring and control at all stages, from raw material to packaged product characterization. 12,13 Near-infrared and— more generally—optical techniques require no sample prepa- ration, are fast and cheap, and provide capacity for remote measurements through fiber-optic probes. Thus, they could prove very effective if quantitative results were obtained in real measurement conditions. Several years ago an experimental approach relying on the Beer–Lambert law was introduced, specifically for use in oximetry. Its aim was the estimate of blood content and oxygenation level in living tissue from time-resolved reflection measurements performed at two wavelengths. 14 The present work is essentially founded on the same theoretical base, the Beer–Lambert law, to derive the spectral dependence of the absorption coefficient from time-resolved reflection measure- ments performed over a certain wavelength range. Because the Beer–Lambert law comes directly from the radiative transport equation, the proposed method is not affected by the hypotheses that typically limit the application of the diffusion approximation for an infinite/semi-infinite medium, such as high albedo or sample size large enough to make boundary effects negligible. However, a strong assumption is made that the scattering properties should not change with wavelength. Thus, the performances of the proposed method were tested Received 26 March 2010; accepted 5 August 2010. * Author to whom correspondence should be sent. E-mail: paola.taroni@ fisi.polimi.it. 1220 Volume 64, Number 11, 2010 APPLIED SPECTROSCOPY 0003-7028/10/6411-1220$2.00/0 Ó 2010 Society for Applied Spectroscopy