# Dual-Slope Diffuse Reflectance Instrument for Calibration-Free Broadband Spectroscopy
## 2 Materials and Methods
### Techniques
#### 2.1.2 Broadband Diffuse Reflectance Spectroscopy  
Continuous-Wave broadband Diffuse Reflectance Spectroscopy (CW-bDRS) was implemented with the purpose of measuring absolute absorption spectra of optically diffusive media (Figure 2a). This was realized using a Dual-Slope (DS) optode geometry which allowed for calibration free measurements of the CW reflectance slope (versus source-detector distance). The DS optode configuration (Figure 2c) used was the same as described previously [26]; it contains two source positions and two detector positions. The linearly symmetric arrangement resulted in a calibrated measurement of the slope (versus source-detector distance) of CW reflectance from 25 to 35 mm.  
The DS CW-bDRS system was custom built to achieve the multiplexing needed for DS measurements. This measurement requires the reflectance signal be acquired from all combinations of sources (named 1 and 2) and detectors (named A and B; Figure 2c). To do so, both the sources and detectors must be multiplexed (Figure 2b). Sources were multiplexed by using two shuttered light sources (AvaLight-HAL-S-Mini, Avantes, Louisville, CO, USA), each connected to one source position. Shutter state was controlled via a Transistor-Transistor Logic (TTL) signal from a micro-controller (Uno R3, Arduino, Ivrea, Italy) which was connected to the control computer via Universal Serial Bus (USB). Light was delivered from the sources to the probe using \(\diameter\) mm fiber bundles. The light sources output an approximate black-body spectrum with a temperature of about 2650 K (peak at about 1000 nm). On the detector side, diffuse CW light was collected using a \(\diameter\)600 \(\upmu\)m fiber at each of the two detector positions. Multiplexing of the detector positions was done using a \(1\times 2\) fiber switch (LBMB, Photonwares, Woburn, MA, USA) where the common end was connected to a spectrometer (AvaSpec-HERO, Avantes) via a \(\diameter\)600 \(\upmu\)m fiber. The spectrometer was configured with a 500 \(\upmu\)m slit and collected 1024 wavelengths between about 498 nm and about 1064 nm.  
The bottleneck in the multiplexing sequence is the switching time of the fiber switch. Because of this, the cycle of source-detector position combinations was optimized to minimize fiber switch actuation. Naming source-detector combinations as source number (1 or 2), then detector letter (A or B; Figure 2c) as an example measurement sequence could be:  
\[\dots 1\text{A}]\rightarrow[1\text{A}\text{\textgreater}2\text{A}\text{\textgreater }2\text{B}\text{\textgreater}1\text{B}]\rightarrow[1\text{B}\text{ \textgreater}2\text{B}\text{\textgreater}2\text{A}\text{\textgreater}1\text{A}] \rightarrow[1\text{A}\dots\]  
where \"\(\diameter\)\" is a source switch, \"\(\blacktriangleright\)\" is a detector switch, and the square brackets show one full DS set acquisition. The reflectance from each source-detector combination is  
Figure 1: Frequency-domain near-infrared spectroscopy methods to achieve measurements of absolute optical properties. (**a**) Render of multi-distance scan done on diffuse optical phantoms. (**b**) Schematic of eleven different source positions realized during the multi-distance scan.  
linearly interpolated to the average absolute time for their corresponding DS set. The four reflectance measurements that contribute to a DS measurement are synchronous, thus preventing potential temporal artifacts when studying dynamic samples or biological tissue. The specific acquisition parameters (including sampling rate and wavelength range considered) are stated in Section 2.2, and the analysis of the DS data (slope of CW reflectance versus source-detector distance) to yield absolute absorption spectra is described in Section 2.3.