# Detection of Thermal Strain in Steel Rails with BOTDA
## Laboratory Test  
### Test Setup  
The sensor system used in this test is based on differential pulse-width pair (DPP) BOTDA that was reported previously [8]. A conventional BOTDA system takes advantage of the loop configuration in which the counter-propagating probe pulse and CW pump are used to activate the stimulated Brillouin scattering along the optical fiber [9]. Using a shorter-width probe pulse can improve spatial resolution; however, Brillouin frequency-shift accuracy can be compromised, resulting from a broadened Brillouin gain spectrum (BGS) and weaker Brillouin gain. In a DPP-BOTDA system, the trade off between spatial resolution and Brillouin frequency-shift accuracy is prohibited since it employs pulse pairs with slightly different pulse width, and subtracts their corresponding BGS to simultaneously achieve a narrow BGS and fine spatial resolution. With a high spatial resolution of 20 cm, the BOTDA system has the ability to monitor the thermal strain caused by temperature variation in rail specimens with a length of 50 cm. It should be noted that the data collected at a specific point on the rail specimen correspond to the average value within the length of the spatial resolution, i.e., 20 cm. Accordingly, the measured Brillouin frequency captured from both edges of the specimen with a distance of less than 20 cm include some portion of the loose fiber between two glued fiber sections. Thus, only the data point in the middle of the rail along the longitudinal direction adequately represents the rail strain. The measurement accuracy is \(1\)\({}^{\circ}\)C or, equivalently, 20 \(\mu\)e. The scanning frequency range was set to be 10.4-11 GHz, with a scanning frequency interval of 6 MHz. The rail specimens under the test were 115 lbs RE rail formerly used in freight rail service in Canada. Each sample was approximately 61 cm in length. Each specimen was instrumented with three types of optical fiber and strain gauge at different sides of the rail specimen, as shown in Figure 1. According to the front and side view of the specimen in Figure 2a-c, five sensing fiber sections were mounted on the surface of the rail specimen at different positions, with 50 cm of loose fiber separating one sensing section from another. To evaluate the jacket effect on thermal-strain measurement, three types of fibers were tested, including two types of 900 \(\upmu\)m tightly buffered fiber from two different companies, and the carbon/polyimide coating fiber (BF04447, OFS, Norcross, GA, USA) with a diameter of 155 \(\upmu\)m. Each fiber was looped five times, and different types of fiber were fusion-spliced directly end-to-end or through an optical fiber patchcord. The overall connection diagram of the sensing fibers can be seen in Figure 2c, with plotting scale and fibers represented by Fiber A, B, and C in the following for simplicity. Detailed information on all the fibers can be found in Table 1. The sensing fibers were fixed with steel adhesive (Loctite 4861, Henkel, Dusseldorf, Germany) under pretension. The steel adhesive was firstly placed along the top line of the fiber, and then the adhesive gravity pulled itself into the gap between the fiber and the rail steel. In this manner, small bubbles that may have influenced the strain transfer into the fiber were prohibited and extra strain caused by gluing process was minimized. Figure 1: Rail specimen instrumented with strain gauge and optical fibers on each side. Figure 2: **(a)** Cross section of the rail specimen; **(b)** layout of a certain type of fiber (Fiber A, Fiber B, or Fiber C) glued on the surface of the rail specimen with a length of 61 cm; **(c)** overall connection diagram of three types of sensing fiber along the rail specimen. All the rail specimens instrumented with sensing fibers were placed inside a climate chamber that could be programmed to achieve the required temperature condition.