1. Introduction

White-light interferometry (WLI) has been widely adopted in absolute measurement systems [1–3], it is also a powerful tool for detection of distributed polarization coupling (DPC) in high-birefringence (Hi-Bi) fibers [4,5]. A typical white light interferometric measurement system consists of a sensing interferometer and a processing interferometer, as essential components. The former is used to convert the measurand into a variation of the optical path difference (OPD) between the two spatially separated wavetrains that are then delivered into the latter with an optic fiber link. The latter introduces an OPD with the same value as in the former, in order to recover the path length imbalance and create an interference fringe pattern. WLI can provide large dynamic range and high accuracy, and it is not sensitive to optical power fluctuation [4–6].

White light interferometry has been adopted to measure the distributed polarization coupling in Hi-Bi fibers in this work. The main structure is a Michelson interferometer with a scanning arm driven by a stepping motor and a fixed arm modulated by a piezo-electronic transducer (PZT). The scanning range of the moving arm is 150 mm with 0.2-μm resolution. It will incur a relatively large measurement error for the detection of DPC intensity. By adopting PZT scanning in the fixed arm, the measurement error can be reduced from 38% to 2%. It can be used to detect the polarization coupling intensity with an accuracy of up to –77 dB. This is limited by the coherent noises of the electronics and optical devices adopted in the testing system. The maximum fiber length that can be tested under this design is more than 1 Km, and the spatial resolution is 50 mm.

2. Experimental setup

The experimental setup of the distributed polarization coupling detection system is shown in Fig. 1. It consists of the following parts: (1) a superluminescent diode (SLD) as the broadband source; (2) the Hi-Bi fiber (HBF) coil under test; and (3) distributed polarization coupling detection module. The mail structure of part (3) is a scanning Michelson interferometer with a scanning arm driven by a stepping motor and a fixed arm modulated by a PZT. The light beam in the scanning arm is reflected three times. As a result, the OPD generated by the scanning arm is doubled. So the measurement range of the fiber length can be doubled compared to the systems only using one reflection mirror in the scanning arm.

 

Fig. 1 Structure of the distributed polarization coupling detection system

Download Full Size | PDF

The working procedure of the testing system can be expressed as follows:

3. Measurement accuracy improvement

3.1 Quality of the rail and stepping motor

The measurement accuracy of the testing system is decided by the resolution of the scanning parts in the Michelson interferometer. The scanning arm of the Michelson interferometer consists of a linear motion rail and a stepping motor. The quality of the rail affects the positioning accuracy of the DPC points in the HBF. It also influences the measurement accuracy of the polarization coupling intensity together with the stepping motor.

The resolution of the stepping motor decides how many steps a cycle of the motor movement can be divided, denotes it as n. If the displacement of the moving arm of the Michelson interferometer is x ₀ (mm) for a cycle of movement, then the minimum distinguishable displacement of the moving arm is Δx ₀ = x ₀/n. In this design, x ₀ = 2 mm, n = 10,000 , so we can get Δx ₀ = 0.2 μm. Since the light beam of the moving arm is reflected three times, the minimum distinguishable OPD is OPD _min = 4 ∙ Δx ₀. In this design, OPD _min=0.8μm.

Meanwhile, the maximum displacement of the moving stage on the rail will influence the measurement range. If the maximum displacement is L ₀, we can get the maximum OPD that can be generated by the moving arm of the Michelson interferometer as OPD _max = 4 ∙ L ₀. In this design, L ₀ = 160 mm, so the maximum OPD is 640 mm. If the modal birefringence of the high-birefringence fiber (HBF) is B, we can get the maximum length of the HBF that can be tested by the system as follows

If the modal birefringence of the HBF is B = 6×10^-4, the maximum fiber length can be longer than 1 Km. The spatial resolution of the DPC detection system is dependent on the coherent length L_c of the SLD. If L_c is 30 μm, then the spatial resolution can be calculated as follows

3.2 Influence of mechanical vibration

Mechanical vibration of the rail is another factor that affects the measurement accuracy. Then, the output current of the photo-detector is dependent on the location of the DPC, the OPD between the two arms of the interferometer, and the OPD uncertainty caused by mechanical vibration. For ease of analysis, we take the assumption that the auto-correlation function of the optical source has a Gaussian profile [7–9].

First, not taking into account of the influence of mechanical vibration, the output current of the photo-detector can be written as

where I_dc is the direct current, I_ac is the alternating current, h(l) is the local polarization coupling parameter of the HBF [4], l is the distance between the position of DPC and the end of the fiber coil, Δn_b is the refractive index difference of the two eigenmodes, Δs is the OPD of generated by the two arms of the interferometer, and k ₀ is the wave number in vacuum. Once the interferogram I(I, Δs) is detected, the local polarization coupling parameter h(l) can be calculated by

where I(l, Δs)_avg and I(l, Δs)_max denote the average value and maximum value of the photo-detector output current, respectively. Since the values of I(l, Δs) and I(l,Δs)_max can be calculated by a simple algorithm, the evaluation of the h(l) parameter can be simplified.

Since the spatial resolution of the rail is limited, the mechanical vibration will cause a deviation of Δs for each step of the stepping motor. This will cause a measurement error of the maximum value of I_ac, which can be achieved at Δs = 0. For ease of analysis, we take the assumption that the additional displacement caused by mechanical vibration is equally distributed at the range (0, Δx ₀). So the additional optical path difference (OPD) caused by mechanical vibration can be described by

where the function rand (1) gets a random value equally distributed between 0 and 1. In case of mechanical vibration, Eq. (2) and (3) should be rewritten as

or

The relationship between the measurement accuracy of h(l) and OPD deviation caused by mechanical vibration is shown in Fig. 2. It is a simulation result of 100 times averaging. From Fig. 2 we can see that the measurement accuracy of h(l) decreases with the increase of mechanical vibration, especially for the minimum value of h(l). In our design, the maximum mechanical vibration is less than 800 nm, the maximum measurement error is approximately 38% and the standard deviation is about 7% for 100 times measurement.

 

Fig. 2 Relationship between the measurement accuracy and mechanical vibration

Download Full Size | PDF

To achieve high measurement accuracy, a PZT is mounted at the fixed arm of the Michelson interferometer for high-resolution scanning. Under this configuration, the output current of the photo-detector should be modified as

when |Δn_bl - Δs + Δs_add + Δs_PZT| ≤ L_c and

where Δs_PZT is the OPD caused by the PZT scanning. The relationship between the normalized DPC intensity measurement value and OPD scanning resolution of the PZT is shown in Fig. 3.

In this design, a PZT with 20-μm scanning range and 20-nm resolution is adopted. Since the light beam is only reflected one time at the fixed arm of the interferometer, the OPD scanning resolution of the PZT is 40 nm. As a result, the maximum measurement error can be reduced to less than 2%, see Fig. 3. The costs of such a PZT and its driving circuits are less the $1,000, which will only contribute to a little cost increase of the testing system.

 

Fig. 3 Relationship between the measurement accuracy and PZT scanning resolution

Download Full Size | PDF

We do believe that experimental verification of the relationship between the measurement error and mechanical vibration is very important. But currently it is very difficult to measure the mechanical vibration of the order of tens of nanometers for a moving distance of more than 100 millimeters, especially to measure the mechanical vibration for each moving step. Due to the statistical property of mechanical vibration, the OPD uncertainty in each moving step is different for each time of measurement. This will further increase the measurement difficulty. As a result, it is hard to draw a conclusion on the relationship between the measurement error and mechanical vibration quantitatively just based on experimental results. The theoretical analysis results in this paper can be adopted as guidelines to decide the mechanical vibration requirements on the scanning parts of the Michelson interferometer for a given measurement error. By adopting a PZT-scanner in the fixed arm of the interferometer, the requirements on the linear motion rail and the stepping motor can be relaxed. This method can be used for optimization of the DPC detection system based on scanning white-light interferometry.

4. Conclusion

White light interferometry has been adopted to detect the DPC of Hi-Bi fibers. Its main architecture is a scanning Michelson interferometer, which deploys the advantages of white light interferometry. It is capable of testing a fiber coil with 1-km length at a spatial resolution of 50 mm for the position of the distributed polarization coupling point. The minimum detectable polarization coupling intensity is –77 dB. The measurement error of polarization-coupling intensity can be improved from 38% to 2% with a 20-nm resolution piezo-electronic transducer.