# Time-Domain Near-Infrared Spectroscopy and Imaging: A Review
## 3 Instruments for TD-NIRS
### Time-Correlated Single Photon Counting (TCSPC) Technique  
#### 3.2.1 Principle, Components, Characteristics, and Operation of the TCSPC Technique  
The TCSPC technique is a time-resolved spectroscopic measurement method based on a single photon counting, which is a way of light detection by counting photons one by one, combined with a pulsed light source with a narrow pulse width in the order of picoseconds and a stabilized repetition of pulse generation in the order of a mega-hertz, and has the capability of measuring temporal changes in very weak light intensity with a high-temporal resolution in the order of picoseconds. At time, \(t\), after the emission of a single ultra-short light pulse, photons reaching a detector with a probability of less than one photon per one light pulse are detected. This detection of single photon at time \(t\) is repeated many times in the order of a mega-hertz, and a histogram of the numbers of detected single photons as a function of time, \(t\), is produced, i.e., a TOF distribution is obtained [37]. As shown in Figure 7, a standard TCSPC instrument consists of a pulsed light source, a single-photon counting detector, such as a PMT, a time pick-off circuit, such as a constant fraction discriminator (CFD), a time-to-amplitude converter (TAC), an A/D converter, a histogram memory, etc. A pulsed light source must emit ultrashort light pulses with a pulse width much less than the characteristic response time of the optical phenomenon in a sample and with a stabilized and fast repetitive pulse generation. The TAC, one of the key components, receives output pulses (start signals) from the detector and reference pulses (stop signals) synchronized to the ultrashort light pulses from the light source, and outputs pulses with the intensities proportional to the time differences between the start and stop signals. The output pulses from the TAC are processed by the A/D converter and the histogram memory. The important factor in the measurement of the TCSPC technique is that the light intensity detected by the detector is adjusted so that the detection probability in a time-gate for one input pulse is constant at any time-gate. If more than one photon is detected in the time-gate for one input pulse, the TAC starts working at the arrival of the start signal generated by the first detected photon and neglects the start signals generated by the second, third,... detected photons until the next stop signal arrives. Then, measurement pile-up takes place causing a distortion in the TOF distribution. Resultantly, earlier times are enhanced because the detection probability in the time-gate is no longer constant, and a correct TOF distribution cannot be obtained due to a serious distortion. To solve this problem of pile-up distortion, the detection rate of the detector must be sufficiently smaller than the repetition rate of the input light pulses. Figure 7: Block diagram of a standard time-correlated single-photon counting (TCSPC) instrument. When \(m\) photons are detected in an average of one input pulse, the probability of detecting \(n\) photons for one input pulse is given by a Poisson distribution,  
\[P_{n}=\frac{m^{n}e^{-m}}{n!} \tag{26}\]  
As an example, when only one photon for 100 input pulses is detected in an average (\(m=0.01\)), the probability that more than one photon for one input pulse are detected becomes very small as,  
\[\frac{1-P_{0}-P_{1}}{1-P_{0}}=\frac{1-e^{-0.01}-0.01e^{-0.01}}{1-e^{-0.01}}=0. 0050\ (0.5\%). \tag{27}\]  
It is obvious that the appropriate value of \(m\) depends on the acceptable distortion of the measured TOF distributions, and it is a common understanding that \(m\) less than 5% (0.05) provides negligible distortions of the measured TOF distributions. Actually, \(m\) is often kept at small values of about 1% (0.01) or less than 2% (0.02). In principle, the errors will decrease with the decrease in \(m\), but at the same time the measuring time will be prolonged to assure good S/N ratios.