# Recent Developments in Instrumentation of Functional Near-Infrared Spectroscopy Systems
## 4 Frequency-Domain fNIRS Instrumentation  
Continuous Wave modality is useful to measure light intensity attenuation. However, there are mainly two limitations to the use of CW fNIRS instruments. First, the CW instruments rely on the modified Beer-Lambert principle which assumes a constant scattering degree from all sites of light. The other limitation is the assumption to estimate the light traveled distance, the differential path length (L), where this mode contains no direct information about the time of flight. Hence, it is very difficult to separate the absorption from scattering in a heterogeneous medium using CW systems. Frequency Domain (FD) instruments are the evolution of the CW NIRS instruments. Thirty years ago, FD modality has been recognized as an alternative technique to measure the absorption and scattering coefficients. In the 1990s, the work was about developing the theory and building some prototypes [69; 70; 71; 72; 73]. Nevertheless, those developments led to what is now the only available commercially FD based instrument by ISS (Table 3). Since 2000, the main works focused on the applications mainly in the area of breast and brain imaging and validating these applications in large clinical studies [74; 75; 76; 77; 78; 79]. In FD fNIRS system, NIR light is modulated at a particular radio frequency (RF) usually in the range of a few hundred MHz. The selection of these frequencies is based on the distinct sizes and depths of the imaged object [76]. A high modulation frequency is suitable, for example, for imaging  
Figure 11: (a) The AOBI module (b) Top view of the flexible circuit board (c) A three-module configuration emphasizing. Reproduced from reference [62]. small breast lesions near the surface, while a low modulation frequency is suitable for imaging deeper and larger lesions as illustrated in Figure 12. Ideally, however, all modulation frequencies should be used to obtain the most accurate optical image reconstruction of the imaged object. On the other hand, acquiring NIR measurements with all modulation frequencies is unfavorable in the clinical setting to avoid patient motion. Therefore, one modulation frequency is usually selected for clinical studies based on the depth of the targeted area. As photon propagates into deeper tissue, its phase shift measurements quantify the degree of the scattered photon in tissue, therefore, tissue scattering parameter is no longer assumed. Both the phase and the amplitude intensity of the attenuated NIRS light can be extracted from the measurements of the FD system. Figure 13 illustrates the principle of dual-phase lock detection [80]. Primarily, the system consists of two mixers, two low-pass filters, and 90\({}^{0}\) phase-shifter. The first mixer mixes the signal and the reference, where the first lowpass filter ensures the output is a DC signal, \(S_{1}\) = 0.5 A cos(\(\phi\)). In the same manner, the 90\({}^{0}\) shifted reference signal is mixed with the original signal where the second lowpass filter ensures the output is a DC signal, \(S_{2}\) = 0.5 A sin(\(\phi\)). From \(S_{1}\) and \(S_{2}\), the amplitude-phase unit extracts both the amplitude and phase based on:  
\[\text{A}\ =\ 2\sqrt{S_{1}^{2}+S_{2}^{2}} \tag{1}\]  
\[\phi\ =\ \arctan\frac{S_{2}}{S_{1}} \tag{2}\]  
If the NIR probe consists of \"\(N\)\" number wavelengths sources, \"\(S\)\" number of sources, and \"\(D\)\" number of detectors, and since both the amplitude and phase at each source-detector pair can be extracted, the resulting total number of measurements for each set of measurements has a total of \(M\) = 2 \(\times\) (\(N\times S\times D\)). As stated earlier, when NIR light penetrates inside the human tissue, scattering of NIR light within human tissue dominates the absorption of the light propagation in such tissue. This imposes a significant challenge to FD-NIRS optical tomography with regard to its spatial resolution and localization accuracy.