# Recent Developments in Instrumentation of Functional Near-Infrared Spectroscopy Systems
## 5 Time-Domain fNIRS Instrumentation  
In time-domain fNIRS systems, the tissue is irradiated with picosecond short pulses. At the detector side, detectors that feature very fast responses have to be used in order to record the amplitude of the light pulse as it leaves the tissue as shown in Figure 15. Typically, the received signal is smeared out compared with the original signal as a result of the randomly distributed lengths of photons interacting with different diffusive layers of the tissue and induce various scattering events and form the distribution of time-of-flight (DTOF) of the received photons. Hence, the absorption and scattering properties of the tissue can be assessed using the pulse peak and its time, area, and width. By integrating the temporal profiles, the intensity can be obtained. Next, the modified Beer-Lambert law can be used to evaluate the absorption variations. Moreover, the mean optical path lengths are calculated from the center of gravity of the temporal profile [96]. The computations of the mean path length and absorption variations are model-independent. Hence, the values of scattering and absorption coefficients (\(\mu_{\text{s}}\) and \(\mu_{\text{a}}\)) can be obtained using the nonlinear least-squares method after applying the diffusion equation in reflectance mode into all observed temporal profiles [97]. In turn, absolute concentration levels can be obtained using this technique, which enables time-resolved measurements with any given source-detector distance that in principle can go down to zero. The intracerebral and extracerebral absorption variations are determined then from moments (integral, mean time of flight and variance) of DTOFs [98]. One of the early fNIRS-TD systems is from Hamamatsu Photonics KK, Hamamatsu, Japan [99]. It utilizes three-wavelength with a generated light pulse width of 100 ps, a peak power of 60 mW, an average power of 30 \(\mu\)W, and a pulse rate of 5 MHz as depicted in Figure 16. On the detection side, a PMT was used in photon-counting mode. The received signals are then processed by a TRS circuit. It consists mainly of a time-to-amplitude converter, an ADC, and a histogram memory. Optical fibers are used to illuminate the tissues and to collect the diffuse light accordingly. Two transmitters and two detectors are used and hence two spots can be illuminated at the same time. Figure 16: Photograph and schematic diagram of a time-resolved spectroscopy system. Reproduced from reference [14]. Figure 15: Mechanism of TD NIRS showing the incident light short pulse and two detected signals successively along with the possible photon paths “banana shape” in different layers with various absorption coefficient and reduced scattering coefficient. There have been some other attempts from academia to build TD-fNIRS systems to assess intracerebral and extracerebral absorption changes as shown in Figure 17[100]. Indocyanine green (ICG) bolus tracking was utilized for the clinical assessment of brain perfusion at the bedside. Time-correlated single-photon counting (TCSPC) electronics [45] scheme has been utilized for this purpose. A supercontinuum light was generated by fiber lasers with 40 MHz repetition frequency for in-vivo measurements and 80 MHz for in phantom studies. Optical fibers (length = 2 m, NA = 0.22, diameter 400 \(\upmu\)m) with used to deliver light to the surface of the phantoms or tissue. A low power level of 20 mW was used. A power density of no more than 2 mW/mm\({}^{2}\) was used at the surface of the skin. A fiber bundle (length 1.5 m, NA = 0.22) was utilized to transfer the photons to the detection system. For in-vivo measurements, the source-detector separation was \(r=3\) cm and for phantom studies, it was \(r=1\), 2, 3, and 4 cm. A detector module PML equipped with polychromator (NA = 0.135 and uses 77,414 diffraction grating) and 16-channel PML. Additional losses of photons in the photodetection system were due to the discrepancy between numerical apertures of the detection bundles (0.22) and polychromator (0.135).