# Dual-Slope Diffuse Reflectance Instrument for Calibration-Free Broadband Spectroscopy  
[PERSON]  
Department of Biomedical Engineering, Tufts University, Medford, MA 02155, USA;  
[PERSON] (R.D. ); [PERSON]S] (S.M. ); [PERSON]RESS] (H.N. );  
that we present in this article aims to improve the accuracy and robustness of quantitative broadband spectroscopy of optically turbid media, and it is relevant to a variety of applications of diffuse optics, even though we mostly focus on its role in the area of biomedical optics. Quantitatively, light propagation in diffusive media is characterized by a lower probability of absorption (related to the absorption coefficient; \(\mu_{a}\)) compared to the probability of effectively isotropic scattering (related to the reduced scattering coefficient; \(\mu_{s}^{\prime}\)). These two optical properties are the chief quantities of interest in the field of diffuse optics and diffuse biomedical optics [2; 3; 16; 17], and they feature a wavelength dependence that is often of crucial importance. In the case of most biological tissues, the dominating scattering condition of diffuse optics is realized in the NIR optical window. Measurements of the wavelength dependent absorption of tissue yields information about the concentration of chromophores with known extinction spectra, while measurements of scattering spectra yields structural information related to the size and density of scattering centers [2]. These properties are often obtained in the reflectance geometry, where light is delivered onto the sample surface and detected at some distance away from the source on the same surface. The primary difficulty in these measurements is the decoupling of absorption and scattering contributions to the measured optical signal. One method to achieve this is by using a source light with a temporally varying intensity. These time-resolved methods fall into two categories: time-domain methods where the light emission has an impulse profile, and Frequency-Domain (FD) methods where the light emission has a sinusoidal profile [1; 18]. Focusing on FD-NIRS, the measurement of both absorption and scattering can be achieved via a calibrated measurement of the spatial dependence (as a function of the distance from the source on the tissue surface) of the amplitude and phase of the detected modulated intensity (which may be represented as a complex reflectance) [19; 20; 21]. This spatially dependent measurement of FD-NIRS data to achieve absolute optical properties is often summarized as measuring the slope (versus source-detector distance; \(\rho\)) of a modified intensity amplitude and phase (i.e., modified complex reflectance). The chief complication of this technique is calibration, since each source-detector pair may have differing instrumental contributions (because of the individual source emission and detector sensitivity properties) and differing coupling factors between source/detector and sample. A method which compensates for the differing instrumental contributions is the so-called Multi-Distance (MD) scanning, where either the source or the detector is moved across the surface of the optical medium [22]. In doing so, the instrumental factors remain the same for each distance (same source and same detector used for each distance); thus, the measurement of slope is independent of these factors. However, differing coupling factors may still be present if during the scan the source (or detector) moves away or toward the tissue surface (in a non-contact case), or experiences a variable contact pressure (in a contact case). Aside from MD scanning, a potentially more effective and more easily implemented calibration free method may be employed. This method is the Self-Calibrating (SC) method, where a symmetric optical probe that features two sources and two detectors is used such that instrumental and coupling factors cancel in the calculation of slopes [23].