# Principles and Application of Polyimide Fiber Bragg Gratings for Surface Strain Measurement
## 1 Introduction  
Surface strain measurement is important and useful for civil engineering experiments. In traditional investigations, electronic strain gauges (ESGs) were commonly used. Recently, Fiber Bragg grating (FBG) sensors have been mounted to measure surface strain. Fiber Bragg gratings (FBGs) are functional fiber-optical sensors with excellent measurement precision, good stability, short response time, and provide quasi-distributed measurement. They have gradually become a preferred sensor and have wide applications in hydraulic engineering, electrical power engineering and the petrochemical industry in the measurement of structural defects and structural stress-strain [1; 2; 3; 4; 5; 6; 7; 8]. FBGs can be used in two ways. One is through encapsulation with some protection material; the other is through use of the bare FBG on its own. Encapsulation can provide protection but will increases cost and mounting complexity. Bare FBGs which means FBGs without encapsulation have many benefits, such as high strain transfer ratio, low cost and easy mounting. Although bare FBGs may not be fragile as researchers believe, the confidence of some users is still decreased. Therefore, polyimide FBG is a perfect solution. Polyimide FBGs are made from FBGs without coating. After the original coating is removed, a polyimide surface is painted outside the cladding of the FBGs. Surface strain measured by bare polyimide FBG can be compared with that measured by uncoated FBG in calibration experiment as shown in Figure 1. From the result, the polyimide coating did not influence the strain measured. Commonly, the polyimide coating can be negligible when mounted to the surface of the substrate [9]. As to say, the bare polyimide FBG can be always considered as uncoated FBG when mounted on the surface of substrate. Because the diameter of polyimide fiber is much smaller than commonly used fiber, the polyimide coating cannot be removed by fiber-stripping tools. Polyimide-recoated FBGs are stiff enough that fiber cutters cannot cut them off. It can be mounted to the surface of a substrate or specimen to measure the surface strain without any encapsulation or calibration. Since [PERSON] et al. [10] proposed shear-lag theory, many classical strain transfer models have been studied by researchers. [PERSON] et al. [11] proposed a strain transfer model for coated bare-fiber Bragg gratings for the first time. Strain transfer ratio of a coated FBG can be impacted by length bonded obviously. It also demonstrated that strain transfer ratio of a coated FBG cannot surpass 90% even the length bonded is over 18 cm. This strain transfer model is suited to cases where the interlayer between the fiber and substrate is a soft layer. For an FBG sensor, [PERSON] et al. [12; 13] proposed an FBG bonding layer substrate three-layer strain-transferring model, fiber-interlayer-substrate, by disregarding the structural differences between the fibers themselves, and conducted experiments on cantilever beams to assess the proposed model. The interlayer in [PERSON]'s model must be a stiff layer. That is to say, the modulus of the interlayer must be high enough. [PERSON] et al. [14] made an improvement on [PERSON]'s investigation by  
Figure 1: Samples of polyimide fiber Bragg gratings (FBGs). (**a**) Bare Polyimide FBG; (**b**) Strain transfer ratio experiment for polyimide FBG and uncoated FBG; (**c**) Bonding types for comparison; (**d**) Results of strain measured by polyimide FBG and uncoated FBG. taking into account temperature variations and non-axial stresses. The angle of stress and substrate is considered. [PERSON] et al. [PERSON] et al. (2015) proposed a novel theoretical model for the axial strain distribution of a clamped FBG sensor. Based on the research of [PERSON] and [PERSON], [PERSON] et al. (2016) investigated the influence of four geometric parameters of the adhesive, side width, top thickness, bond length, bottom thickness, and then proposed a strain transfer model to suit stiff-layer cases.