## 4 Discussion  
The precision of the proposed approach is determined by the minimum detectable relative phase \(\Delta\phi^{min}=2\pi f_{s}\Delta t_{d}^{min}=\alpha\). Using \(\alpha=0.02\) rad [14] and \(f_{s}=20\) GHz leads to the minimum detectable relative DGD of \(\Delta t_{d}^{min}=159\) fs. The precision can be further improved by usage of commercially available 50 GHz electro-optic modulators allowing for \(f_{s}=100\) GHz and \(\Delta t_{d}^{min}=32\) fs. In the case of elliptical core PMF characterization, \(\Delta t_{d}^{min}\) is doubled because relative DGD in this case is obtained by the measurement of group delays of two principal axes, rather than by one direct measurement of DGD. Two measurements make \(\Delta t_{d}^{min}\) twofold. For the measurement of GBD, the limits of the proposed approach are estimated from the DGD variation rate \(\rho=D_{B}\times 2L/c\)[12]. Applications of Equation (4), Equation (5) and \(t_{d}(\lambda)=t_{ref}+\Delta t_{d}(\lambda)\) lead to \(\rho=\delta t_{d}/\delta\lambda\), where \(\delta t_{d}\) and \(\delta\lambda\) respectively are the DGD difference and wavelength separation between two adjacent scanning wavelengths. In the case of Panda PMF characterization, the minimum measurable DGD variation rate is \(\rho^{min}=\delta t_{d}^{min}/\delta\lambda^{max}\) with \(\delta\lambda^{max}\) being the maximum laser scanning range. In our experimental setup, the EDFA works in C band, and thus \(\delta\lambda^{max}\) is limited by 30 nm. Applications of \(\delta t_{d}^{min}=\Delta t_{d}^{min}=159\) fs and \(\delta\lambda^{max}=30\) nm lead to \(\rho^{min}=5.3\) fs/nm. The maximum measurable DGD variation rate is \(\rho^{max}=\delta t_{d}^{max}/\delta\lambda^{min}\) with \(\delta\lambda^{min}\) being the minimum laser scanning step. Accurate restoration of the sinusoidal power variation of \(P_{1}(\lambda)\) requires \(N\) sampling points within a sinusoidal variation cycle. This requirement restricts \(\delta\phi^{max}=2\pi/N\), where \(\delta\phi^{max}=2\pi f_{s}\delta t_{d}^{max}\) is the maximum phase difference associated with two adjacent scanning wavelengths. Accordingly, \(\delta t_{d}^{max}=1/Nf_{s}\) and \(\rho^{max}=1/Nf_{s}\delta\lambda^{min}\) are obtained. Applications of \(N=10\), \(f_{s}=20\) GHz and \(\delta\lambda^{min}=0.001\) nm of our tunable laser lead to \(\rho^{max}=5\) ns/nm. In the case of elliptical core PMF characterization, \(\rho^{max}\) is identical to that of the Panda PMF measurement, while \(\rho^{min}\) is double because the minimum detectable relative DGD \(\Delta t_{d}^{min}\) is twice that in the case of Panda PMF characterization. The maximum measurable fiber length \(L^{max}\) is determined by the maximum measurable DGD variation rate \(\rho^{max}=\delta t_{d}^{max}/\delta\lambda^{min}=D_{B}\times 2L^{max}/c\) and the intensity loss of the SMOSs traveling through the FUT. Applications of \(\rho^{max}=5\) ns/nm and \(D_{B}=5.55\times 10^{-7}\)/nm of the Panda PMF at  
Figure 6: Experimental results of (**a**) \(t_{f},t_{s}\) and calculated \(t_{d}\), (**b**) group birefringence \(B\) and (**c**) group birefringence dispersion \(D_{B}\) as a function of the laser wavelength \(\lambda\) in the case of elliptical core PMF characterization. \(\lambda=1550\) nm lead to \(L^{max}=c\rho^{max}/2D_{B}\approx 1.35\times 10^{6}\) m. Taking into account the intensity loss of SMOSs that travel through the FUT, one can place an EDFA after port 3 of the PMC in Figure 4 or Figure 5 to compensate the intensity loss and thus to extend the maximum measurable fiber length. Considering the loss of 0.2 dB/km, application of the EDFA offering 10 dB gain allows for a 50 km measurable fiber length. The measurement sensitivity of the proposed approach in comparison with that of the white-light-interferometry-based technique is also discussed. Essentially, the proposed approach interrogates the GBD of a PMF by measuring the DGD of two SMOSs. Therefore, the measurement sensitivity is governed by that of the DGD measurement.