In unique contexts such as orbiters, accurate real-time temperature measurement of the cabin structure is imperative. However, an orbiter’s sunlit side and its shaded side experience vast temperature differences, making the accurate assessment of the cabin surface temperature a pressing challenge. Fiber Bragg grating (FBG) sensors stand out because of their resistance to electromagnetic interference, compactness, ease of multiplexing, and other advantages [1, 2], leading to their wide application in aerospace, fire engineering, medical equipment and so on [3–5].

FBG temperature sensitivity is pivotal. Factors influencing this sensitivity and the thermal erase temperature [6] include the type of fiber material [7], the grating inscription method [8], and FBG packaging approach [6, 9].

Yin et al. [10] explored the nonlinear temperature sensitivity of bare FBG in the low-temperature range from −80 ℃ to 10 ℃. They found that sensitivity decreased from 8.96 to 6.72 pm/℃ as the temperature dropped. Similarly, Jin et al. [11] examined FBG temperature sensitivity in the range of −180.15 ℃ to 19.85 ℃, and observed a decline from 9.18 to 2.19 pm/℃ with decreasing temperature. Filho et al. [12] analyzed the thermo-optic and thermal expansion coefficients of FBGs made from three different fibers within the temperature range from −208.15 ℃ to 76.85 ℃. Shen et al. [13] studied a metal-coated FBG sensor for high-temperature measurements (50–240 ℃) and recorded a sensitivity of 19.5 pm/℃. The gilded germanium-doped fiber grating sensor, used for measurements between 200–800 ℃, showed an average temperature sensitivity of 15.6 pm/℃ [14]. Chah et al. [15] enhanced high-temperature sensing performance by regenerating an FBG at 450 ℃, achieving a sensitivity of 12.99 pm/℃ in the 100–900 ℃ range. An FBG created using overexposure with the femtosecond laser phase mask technique demonstrated a temperature sensitivity of approximately 15 pm/℃ between 0 ℃ and 1,000 ℃ [8]. Expanding the temperature measurement range can be achieved using FBGs inscribed by femtosecond lasers [16], specialty optical fibers [7], and transducers [17]. However, the associated FBG inscription processes are intricate and demand expensive equipment, which hinders their adoption in extensive FBG application scenarios.

Currently, most research on the temperature characteristics of conventional FBG concentrates on limited temperature ranges. Studies that delve into FBG temperature characteristics across a broad spectrum are scant. This paper intends to study the variations in conventional FBG sensitivity over a wide temperature range spanning from −196 ℃ to 900 ℃. Such insights can serve as the groundwork for FBG measurement calibration across expansive temperature ranges.

In situations where no axial strain is applied to the FBG, the relationship between the FBG Bragg wavelength and temperature change (ΔT) is represented as follows [14]:

where T is the ambient temperature, λ_B is the Bragg wavelength, ∆λ_B is the wavelength shift, α is the thermal expansion coefficient, ξ is the thermo-optic coefficient, n_eff is the effective refractive index of the fiber core, and Λ is the grating constant.

In general, both α and ξ are constants around room temperature. This implies a linear relationship between the FBG wavelength and temperature and suggests a consistent FBG temperature sensitivity. However, when accounting for a broad temperature range, the nonlinear responses of α and ξ come into play, meaning that this sensitivity is variable. In such scenarios, the relationship among n_eff, α, and temperature can be expressed as [18–20]:

where n₀ is the fiber core effective refractive index of the fiber core at 0 ℃, and a and b are the first- and second-order coefficients of the relationship between n_eff and T, respectively. α₀ is the thermal expansion coefficient of fiber at 0 ℃, and c and d are the first- and second-order coefficients of the relationship between α and T, respectively.

By iterating Eq. (1) through Eq. (4), the FBG temperature sensitivity can be derived, and is represented as:

From the Eq. (5), it is evident that FBG temperature sensitivity is subject to change with varying temperatures.

3.1. Experimental Scheme

For this study, FBGs were inscribed using ultraviolet light combined with a phase mask plate. The fiber coating around the grating area was carefully removed with acetone. Two types of tubes, a quartz capillary tube (with outer/inner diameters and length being 1 mm, 0.5 mm, and 600 mm, respectively) and a 304 stainless steel tube (with dimensions of 2 mm, 1.5 mm, and 600 mm, respectively), were chosen to package the FBG.

For packaging with the 304 stainless steel tube, the de-coated FBG was inserted to ensure no stress on the grating area. One end of the FBG was positioned 1cm from the end of the steel tube, while the other end was secured using a heat shrink tube. The packaging method using the quartz capillary was largely similar, but with 502 glue replacing the heat shrinkable tube. For dual protection, the FBG packaged inside the quartz capillary was then inserted into the 304 stainless steel tube. The one end of the steel tube was sealed using pliers, and the other end was capped with a heat shrink tube. Schematic diagrams and photographs of these FBG sensors are depicted in Fig. 1.

Figure 1. Schematic diagrams and actual photos of fiber Bragg grating (FBG) sensors. (a) 304 stainless steel tube, (b) quartz capillary tube, and (c) quartz capillary tube inserted into 304 stainless steel tube for dual protection.

The experimental temperature range was bifurcated into two segments: High and low. The low-temperature span extended from −196 ℃ to 25 ℃, while the high-temperature span ranged from 25 ℃ to 1,200 ℃.

A schematic of the FBG testing system for high temperatures is depicted in Fig. 2. This system comprised a heat source, optical source, standard thermometer, optical spectrum analyzer, and a demodulator. High-temperature tube furnaces and liquid nitrogen Dewar bottles served as heat sources for high and low temperatures, respectively. Notably, the high-temperature tube furnace could attain a maximum of 1,600 ℃. Its furnace tube had a length of 1,100 mm and an internal diameter of 75 mm. For temperature measurements, a type K thermocouple sensor was used for high temperatures, and a PT100 sensor for low temperatures, and their respective measuring ranges were 0 to 1,200 ℃ and −200 to 600 ℃. Either the PT100 or the type K thermocouple was placed adjacent to the FBG to monitor its proximate temperature. The accuracy of the type K thermocouple is ±0.75%. The PT100 boasts class A accuracy, signifying an error margin of only ±0.15 ℃ at 0 ℃.

Figure 2. Schematic of the fiber Bragg grating temperature sensing system in a wide high temperature range.

The optical system worked as follows: Light emanating from the optical source was directed into port 1 of the circulator. This light was then channeled into the FBG via port 2. Light reflected by the FBG proceeded to a 3-dB coupler through port 3 of the circulator. Post-coupler, the light split into two beams: One was guided to an optical spectrum analyzer, and the other to a demodulator. The optical spectrum analyzer employed in this study was the AQ6370C model (Yokogawa Electric Co., Tokyo, Japan). Additionally, the SmartScan FBG demodulator (Smart Fibres Ltd., Bracknell, UK) was also used. The FBG spectra were recorded using the optical spectrum analyzer, and the accurate FBG wavelength determination was conducted by the demodulator.

During the high-temperature testing, the packaged FBG was positioned at the center of the tube furnace. The temperature of the furnace was elevated from 25 ℃ to 1,200 ℃ at a consistent rate of 5 ℃/min. Measurements for both the furnace temperature and the FBG wavelength were taken at 100 ℃ intervals. To ensure thermal equilibrium, the furnace temperature was held steady for 30 min at each measurement point. Once the furnace reached the designated temperature, the demodulator recorded the wavelength information every 5 min for a duration of 1 min. The average wavelength of these readings determined the FBG’s central wavelength at the varying temperatures.

For the low-temperature tests, the FBG, packaged in a quartz capillary, was affixed to the PT100 using 502 glue. This ensured that the grating area aligned precisely with the PT100 sensing region. Both the FBG and PT100 were then gradually submerged into a Dewar bottle filled with liquid nitrogen. Data recordings were spaced at intervals of 5 ℃ and 20 ℃ within the temperature ranges of −196 ℃ to −160 ℃ and −160 ℃ to 25 ℃, respectively. The FBG and PT100 were stationary for 10 min at each recording point, and data was collected during the final minute of this interval.

3.2. Temperature Sensing Characteristic

Figure 3 illustrates the relationships between time and FBG wavelengths with three different packaging methods. This figure reveals how the FBG wavelength varies linearly with time under different packaging conditions. The nonlinearity observed at the initial stage is attributed to the high-temperature furnace not being activated and slight fluctuations in ambient temperature.

Figure 3. Relationships between time and fiber Bragg grating wavelengths with different packaging methods.

The high-temperature tests showed the relationship between the FBG wavelength and temperature, as illustrated in Fig. 4. Figures 4(a), 4(b), and 4(c) show the relationships between the wavelength and temperature for the FBG packaged with the 304 stainless steel pipe, a combination of the 304 stainless steel pipe and quartz capillary tube, and quartz capillary tube, respectively. In Fig. 4, the black dots represent the FBG wavelength data measured by the demodulator at various temperatures and clearly show that the temperature rose in proportion to the wavelength. The red solid line and blue dotted line in Fig. 4 represent the quadratic and linear fits of the experimental data, respectively. Notably, the slope of the fitted curve changed in relation to the temperature. This indicates that the FBG temperature sensitivity was not a constant within the 25 ℃ to 1,000 ℃ range.

Figure 4. Relationships between fiber Bragg grating (FBG) wavelength and temperature in the range of 0–1,000 ℃ for different FBG packaging methods. (a) 304 stainless steel tube, (b) 304 stainless steel tube combined with quartz capillary tube, and (c) quartz capillary tube.

Regarding the FBG enclosed within the 304 stainless steel tube, this tube began to develop precipitates as temperatures climbed, even leading to thermal deformation in some cases. These precipitates clung to the optical fiber and introduced thermal strain to the FBG, thereby potentially skewing measurements. As a result, this packaging technique proved unsuitable in high-temperature contexts. At 900 ℃, the FBG was thermally erased, and the quadratic fitting of the relationship between temperature and FBG wavelength achieved a coefficient of determination (COD) of 0.9948. Interestingly, when both the 304 stainless steel tube and the quartz capillary were employed to package the FBG, the quartz tube seemed to mitigate the negative impacts the steel tube had on the FBG. The data fitting COD improved by 0.0032, the thermal erase temperature increased to 1,000 ℃, and the COD registered at 0.9980. However, the COD reached an impressive 0.9999 using only the quartz capillary for packaging, although the thermal erase temperature dipped back to 900 ℃. The elevated thermal erasing temperature in the double-tube packaging method could be attributed to an insulating air layer trapped between the two tubes, given that the thermal conductivity of air is relatively low. This layer likely contributed some degree of thermal insulation.

The temperature sensitivities of the FBG in the range of 25–1,000 ℃ were derived from the experimental data curves presented in Fig. 4. The sensitivity fluctuations for the FBG packaged with the 304 stainless steel tube, a combination of the 304 stainless steel tube and quartz capillary, and solely the quartz capillary were 10.51–16.99, 9.87–19.55, and 11.26–16.62 pm/℃, respectively. The theoretical temperature sensitivity for the FBG in the 25–1,000 ℃ range can be determined using Eq. (5), given the parameters: n₀ = 1.447, a = 1.09 × 10⁻⁵, b = 1.611 × 10⁻⁹, α₀ = 5.36 × 10^–7, c = 1.24 × 10⁻¹⁰, and d = 0 [18–20]. A comparison of the experimental and theoretical FBG temperature sensitivity values is depicted in Fig. 5.

Figure 5. FBG temperature sensitivity variations in the 25–1,000 ℃ range.

From Fig. 5, it is evident that when packaged with the quartz capillary, the FBG temperature sensitivity aligns most closely with theoretical predictions. This consistency is attributable to the FBG and quartz capillary being composed of the same primary materials. A key factor contributing to the observed deviations is the presence of an air layer between the FBG and the tube. Due to the suboptimal thermal conductivity of air, there is an obstruction in temperature transmission. The most pronounced discrepancy observed was 1.3 pm/℃ at 25 ℃.

Regarding the FBG encased in the quartz capillary, Fig. 6 illustrates the time-dependent evolution of the normalized peak intensity of the FBG spectrum at varying temperatures. Associated FBG spectra are displayed in Fig. 7. After reaching the designated temperature, it is imperative to maintain this temperature for 30 minutes before employing an optical spectrum analyzer to obtain the FBG spectra depicted in Fig. 7.

Figure 6. Variation of normalized reflected intensity over time at various temperatures.

Figure 7. Fiber Bragg grating spectra across various temperatures.

At 25 ℃, the FBG peak intensity stands at 14.57 nW. As observed in Fig. 6, the reflection intensity remains fairly stable between 100–200 ℃. However, there is a marked decrease in intensity as temperatures climb from 300–500 ℃. This decline is attributed to the proximity of these temperatures to the phase change temperature range of pure silica fiber, which can modify the fiber’s inherent properties [21]. A new equilibrium is established within the 600–800 ℃ temperature bracket.

At 900 ℃, there is a stark decline in the FBG reflection intensity. The spectral variations over time, as depicted in Fig. 7, are in line with the reflection intensity changes shown in Fig. 6. It is noted in Fig. 7 that the FBG peak intensity dwindles to a mere 0.799 nW in a span of 30 min at 900 ℃. As temperatures continue to rise beyond this point, the optical spectrum analyzer fails to detect the FBG spectrum, indicating that the FBG has been entirely thermally erased.

For FBG packaged with the quartz capillary, the relationship between wavelength and temperature within the low-temperature range is depicted in Fig. 8. Data recordings were taken at 5 ℃ and 20 ℃ intervals for temperature ranges of −196 ℃ to −160 ℃ and −160 ℃ to 25 ℃, respectively. This adjustment is crucial when the temperature descends below −160 ℃ due to the pronounced nonlinear relationship between the FBG wavelength and temperature. Consequently, it is imperative to increase the frequency of measurements at temperatures below −160 ℃, and reduce the interval between temperature measurements to every 5 ℃.

Figure 8. Fiber Bragg grating wavelength variation in relation to temperature from −196 ℃ to 25 ℃.

The Fig. 8 shows that the wavelength exhibits a nonlinear change as the temperature decreases, indicating a variable FBG temperature sensitivity within this low-temperature range. The FBG wavelength exhibited significant changes in the temperature range of −160 ℃ to 25 ℃, a phenomenon attributed to the sharp decline in the quartz thermal expansion coefficient at temperatures below −40 ℃. Once removed from the liquid nitrogen, the FBG spectrum reverted to its initial state.

To determine the FBG temperature sensitivity between −196 ℃ and 25 ℃, we analyzed the derivative of the polynomial fitting curve displayed in Fig. 8. The theoretical correlation between FBG temperature sensitivity and temperature for this range can be calculated using Eq. (5), with n₀ = 1.447, a = 8.24 × 10⁻⁶, b = 1.18 × 10⁻⁸, α₀ = 4.53 × 10⁻⁶, c = 1.20 × 10⁻⁹, and d = −1.95 × 10⁻¹¹ [18–20].

Figure 9 illustrates the comparison between experimental and theoretical sensitivity values. Notably, the observed temperature sensitivity fluctuated between 1.55–10.61 pm/℃, aligning closely with theoretical predictions. The largest discrepancy between the two was a mere 1.1 pm/℃ at 25 ℃, which is attributed to the air gap between the tube and FBG, which acts as a thermal barrier.

Figure 9. Variation in fiber Bragg grating temperature sensitivity from −196 ℃ to 25 ℃.

By analyzing the experimental data at both high and low temperatures, the relationship between wavelength shift and temperature across a broad spectrum can be discerned. Figure 10 showcases this relationship for the FBG packaged with a quartz capillary. Notably, while the relationship between wavelength shift and temperature appears linear within a confined temperature range, it becomes nonlinear when viewed across a broader spectrum. For accurate temperature measurements in applications with alternating high and low temperatures, fitting the relationship between wavelength shift and temperature requires a quadratic polynomial or even higher-degree polynomial.

Figure 10. Fiber Bragg grating wavelength shift in relation to temperature from −196 ℃ to 900 ℃.

For the FBG housed in a quartz capillary, Fig. 11 illustrates the measurement errors of various fitting techniques across the temperature span of −196 ℃ to 900 ℃. The blue squares and red circles in Fig. 11 represent the measurement errors of linear and quadratic fittings, respectively. The black line represents a baseline with zero error, serving as a benchmark for error comparison. Notably, the quadratic polynomial fitting reduced the maximum temperature measurement error by 81.85% when compared to linear fitting in the −196 ℃ to 900 ℃ range. This experimental finding underscores that the quadratic polynomial fitting provides greater temperature measurement accuracy than its linear counterpart.

Figure 11. Comparison of measurement errors using different fitting methods from −196 ℃ to 900 ℃.

This study investigated the temperature sensitivity of conventional FBGs across an extensive temperature spectrum ranging from −196 ℃ to 900 ℃. The experimental results indicated that the COD for the relationship between FBG wavelength and temperature reached an optimum value of 0.9978 when the FBG was encapsulated in a quartz capillary. The temperature sensitivity in the spectrum of 25 ℃ to 900 ℃ varied between 11.26 to 16.62 pm/℃. At 900 ℃, the FBG reflectance intensity exhibited a rapid decline, culminating in a thermal erasure. Furthermore, in the temperature range from −196 ℃ to 25 ℃, the temperature sensitivity fluctuated between 1.55 and 10.61 pm/℃. The experimental data highlighted that the FBG wavelength’s relation with temperature deviates from linearity across broad temperature spectra. Additionally, the discrepancy between experimental and theoretical temperature sensitivities was exceptionally minimal for the FBG encased in a quartz capillary; the maximum discrepancy was approximately 1.3 pm/℃ at 25 ℃.

This research offers the significant potential of FBGs for accurate temperature monitoring in environments with extreme temperature variations and provides a crucial benchmark for the accurate calibration of FBG temperature sensors across broad temperature spectrums.

Fundamental Research Program of Shanxi Province (202303021212221), Shanxi Province Science Foundation for Youths (201901D211301); Taiyuan University of Science and Technology Scientific Research Initial Funding (20222122, 20232036); Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (2022L299, 2022L300).

The authors declare no conflicts of interest.

The data presented in this study are available on request from the corresponding author.