# Simultaneous Transmission of Photonic Services over One Fiber with an ITU 100 GHz Grid
## 3 Measurement Setup
### Accurate Time Measurement Method  
Systems developed for highly accurate time scale comparison utilize a method based on a bidirectional transmission with a symmetrical transport delay in both directions [54; 55]. The principle can be seen in Figure 2.  
Figure 1: Measurement setup. Figure 2: Home-developed time adapter. The two adapters are connected by a two-way optical line. Each of the adapters is provided with the 1 PPS timing signal and 10 MHz frequency from a local clock at its input, and two electrical signals are internally generated, specifically \(T_{Ri}\) (\(i\) = A, B), representing the received and decoded 1 PPS signal from the remote adapter, and \(T_{Si}\), representing the moment when the encoded 1 PPS signal is sent to the optical line. The \(T_{Si}\) and \(T_{Ri}\) signals are fed into two time interval counters (TICs) that are started by the \(T_{i}\) signal--the 1 PPS input signal. The first TIC is used to measure the interval \(x_{i}\) between \(T_{i}\) and \(T_{Ri}\) (the difference between a local and a remote 1 PPS). The second TIC is used to measure the delay in the \(\varepsilon_{Si}\) adapter, i.e., the time between the \(T_{i}\) and \(T_{Si}\) signals. The internal structure of the adapter is shown in Figure 3.  
The 1 PPS pulse from the local clock arrives at adapter A at time \(t_{A}\). It is then sent to the optical line at time \(t_{SA}\) and received by adapter B at time \(t_{RB}\). By analogy, 1 PPS from the remote clock arriving at adapter B at time \(t_{B}\) is sent at \(t_{SB}\) and received by adapter A at time \(t_{RA}\). Thus, \(\Theta_{AB}=t_{B}-t_{A}\) is the offset of both clocks, \(\varepsilon_{Si}=t_{Si}-t_{i}\)\(i\) = A, B is the delay within the adapter \(i\), and \(\delta_{AB}=t_{RB}-t_{SA}\) (can also be defined as \(\delta_{BA}=t_{RA}-t_{SB}\)) is the line delay from A to B (B to A). By using TICs outputs (two in each location), it is possible to measure the internal delay of the \(\varepsilon_{Si}\) adapter and the following time intervals:  
\[x_{A}=t_{RA}-t_{A}=\Theta_{AB}+\varepsilon_{SB}+\delta_{BA}, \tag{5}\]  
\[x_{B}=t_{RB}-t_{B}=\ -\Theta_{AB}+\varepsilon_{SA}+\delta_{AB}. \tag{6}\]  
In the case of a symmetric line, the delay \(\delta\) in both directions will be the same, specifically: \(\delta=\delta_{AB}=\delta_{BA}\). In a real optical path, we can either transmit the signal unidirectionally with the same wavelength in a pair of optical fibers or bidirectionally in a single optical fiber at different wavelengths. In the first case, there will be a challenge with an asymmetry of the physical length of the fibers; in the latter case, the optical propagation velocity will slightly differ, as it is given by the coefficient of chromatic dispersion, which generally depends on the wavelength. In both of these cases, there will be an asymmetry of delay \(\Delta\):  
\[\Delta=\delta_{BA}-\delta_{AB} \tag{7}\]  
which needs to be computed in the case of a bidirectional transmission in a single fiber or evaluated during the calibration phase of the transmission route. Therefore, the time offset of the clock is given as follows:  
\[\Theta_{AB}=\frac{\left(\left(x_{A}-x_{B}\right)\right.+\left(\varepsilon_{ SA}-\varepsilon_{SB}\right)-\Delta\)}{2} \tag{8}\]  
Figure 3: Home-developed time adapter. By using TICs outputs (two in each location), it is possible to measure the internal delay of the \(\epsilon_{Si}\) adapter and the following time intervals:  
\[x_{A}=t_{RA}-t_{A}=\Theta_{AB}+\epsilon_{SB}+\delta_{BA}, \tag{9}\]  
Figure 1:0  
In the case of a symmetric line, the delay \(\delta\) in both directions will be the same, specifically: \(\delta=\delta_{AB}=\delta_{BA}\). In a real optical path, we can either transmit the signal unidirectionally with the same wavelength in a pair of optical fibers or bidirectionally in a single optical fiber at different wavelengths.