In-Fiber Hybrid Structure Sensor Based on the Vernier Effect for Vector Curvature and Temperature Measurement

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors The authors present a manuscript to report a fiber sensor structure formed by a fiber Bragg grating, multimode fiber and single-hole dual-core fiber. The sensor structure is used for vector curvature monitoring and temperature monitoring. I recommend accepting the manuscript after revision:   1. Why does the curvature test range only go up to 0.865 m-1 and can a wider curvature range be tested?   2. The authors point out that the sensor can monitor curvature in four directions, but can it monitor curvature at other angles?   3. The illustration in Figure 9 is not clear enough and it is suggested to modify it.   4. The vertical coordinate of the graph in the article is not the relative light intensity, while the unit should be dBm, which needs to be changed.

Author Response

Comments1: Why does the curvature test range only go up to 0.865 m^-1 and can a wider curvature range be tested?  

Response1: Thank you for your suggestion. The measurement range is related to the structure design; this sensor has better accuracy in the curvature range of 0m^-1-0.865m^-1. When the signal light is transmitted in this structure sensor, the interference spectrum constitutes a vernier effect due to the joint action of the FP cavity and MZI interference mechanisms. When the curvature of the sensor changes, on the one hand, the air cavity in the sensor deforms, and the optical range difference of the transmitted light in the FP cavity changes, which makes the interference spectrum shift; on the other hand, the change in curvature also causes the fiber core to be squeezed or stretched, which likewise shifts the interference spectrum because of the change in the effective refractive index of the fiber. In the smaller range of 0 m^-1-0.865 m^-1 curvature, the refractive index of the fiber core changes less, the change of FP cavity length mainly causes the interference spectral shift, and the curvature and wavelength changes are linearly related. Beyond this curvature range, the change of the refractive index of the fiber core increases, and the influence on the interference envelope is enhanced, resulting in the interference spectral shift and curvature change relationship failing to show a good linear relationship. Therefore, the structural sensor was tested in this curvature range.

Comments2: The authors point out that the sensor can monitor curvature in four directions, but can it monitor curvature at other angles?  

Response2: Thank you for your suggestion. This structure sensor can monitor curvature in four directions when performing curvature experiments. If monitoring other directions is added, it will produce overlapping due to the curvature sensitivity changing the curvature and cannot be identified effectively. Therefore, this structure sensor can only monitor curvature in four vertical directions.

Comments3: The illustration in Figure 9 is not clear enough and it is suggested to modify it.  

Response3: Thanks to your suggestion, we have adjusted the unclear position in Fig. 9 and changed the manuscript.

 Initial manuscript：

Figure 9. The wavelength shifts of the envelope and the FBG with the temperature change.

Revision：

Figure 9. The wavelength shifts of the envelope and the FBG with the temperature change.

Comments4:  The vertical coordinate of the graph in the article is not the relative light intensity, while the unit should be dBm, which needs to be changed.

Response4： Thank you for your comments. In response to your suggestion, we have examined the legends in the text in detail. In each spectral legend in this paper, the change in transmittance of the interference spectrum is mainly shown as the change in wavelength, so dB is used as the vertical coordinate.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The paper proposes an in-fiber hybrid microstructure sensor with enhanced two-dimensional curvature and temperature sensitivities. The authors stated that the proposed sensor has minimal temperature cross-talk, making it suitable for high-sensitivity structural health monitoring of buildings and bridges. However, the novelty of this version is limited, with only minor improvements over previous works. Several concerns need to be addressed in the revision to strengthen the contribution and significance of this study.

 

1. In the simulation section, the authors compare the transmission spectra of the PAHM sensor under different SHDCF lengths. What are the implications of varying the diameter of the internal air hole and the fiber cores in the SHDCF on the sensor's sensitivity and the formation of the Fabry-Perot interferometer (FPI) and Mach-Zehnder interferometer (MZI) spectra?
2. The term ‘Fiber Bragg Grating’ should be used in the abstract and introduction not ‘Fiber Grating’. This needs to be revised.
3. The page numbers beside each figure need to be removed.
4. The authors mentioned using a cascade Fiber Bragg Grating (FBG) to aid in distinguishing interference envelopes during the demodulation process. However, there is a lack of information regarding the fabrication method and parameters of the FBG. More details are needed for clarification.
5. The authors should provide additional information to elucidate the demodulation process in both curvature and temperature sensing experiments.
6. What are the optical mechanisms behind the different wavelength shift behaviors (red shift vs. blue shift) observed at various angles of curvature (0°, 90°, 180°, and 270°), and how do these shifts correlate with changes in the optical path length within the sensor's structure?
7. Figure 7 is confusing. The authors stated that a 0.1 mm movement of the micrometer generates curvature ranging from 0 to 0.865 m-1. However, it is unclear where the authors obtained the data points within this range. Additionally, it is important to clarify whether 0.865 m-1 represents the detection limit and provide detailed explanations to justify this.
8. Also, what equation did the author use to calculate the curvature? Need more clarification. ^​
9. Instead of plotting absolute temperature in Figure 10, it would be more informative for the sensor to plot the change in temperature versus the change in wavelength.
10. What are the optical principles underlying the linear response of the hybrid structure's spectra to simultaneous changes in curvature and temperature, and how do the distinct sensitivities at dip1 and dip2 facilitate accurate discrimination between these two parameters?
11. How does the thermo-optic effect in the fiber core and cladding contribute to the temperature sensitivity observed in the hybrid structure sensor, and what are the key factors affecting the accuracy of the temperature measurements?
12. Section 3.4 is weak as the authors did not demonstrate how the proposed sensor outperforms existing ones. The provided content lacks evidence of significant improvements.
13. The authors claim that the proposed sensor can be utilized for detecting structural health in buildings, bridge engineering, and other applications. However, they have not provided sufficient correlating results to substantiate this assertion. More detailed explanations and supporting evidence are needed to demonstrate the sensor's effectiveness in these specific fields.

Comments on the Quality of English Language

In general, there are several typos such as 'we probe', 'trough of', and others found in the current version. Significant language improvements are necessary to meet publication standards.

Author Response

Comments1: In the simulation section, the authors compare the transmission spectra of the PAHM sensor under different SHDCF lengths. What are the implications of varying the diameter of the internal air hole and the fiber cores in the SHDCF on the sensor's sensitivity and the formation of the Fabry-Perot interferometer (FPI) and Mach-Zehnder interferometer (MZI) spectra?

Response1： Thank you very much for your wise and practical professional advice. The area of the FP cavity's reflective surface directly affects the interference fringes' contrast and sharpness. The FP cavity length affects the interference spectrum's free spectral range and resonance wavelength. In this paper, the cavity length must be optimised to achieve a better interferometric spectral envelope of the vernier effect. In this structure, the core in the single-aperture dual-core fiber is a single-mode structure, and if the core size increases, more modes will be introduced into the core, and the interference spectrum will be more complex, which is not conducive to the construction of the vernier effect structure. Therefore, the simulation design in this paper only optimises the length of the single-hole dual-core fiber.

Comments2: The term ‘Fiber Bragg Grating’ should be used in the abstract and introduction not ‘Fiber Grating’. This needs to be revised.

Response2： We apologize for the text's lack of clarity. We have double-checked the article's formatting and presentation and made corrections, and changes in the text have been marked in red.

Comments3: The page numbers beside each figure need to be removed.

Response3: We apologise for the formatting error in the article and sincerely appreciate your suggestion. We have taken your advice very seriously and made significant changes to our manuscript.

Comments4: The authors mentioned using a cascade Fiber Bragg Grating (FBG) to aid in distinguishing interference envelopes during the demodulation process. However, there is a lack of information regarding the fabrication method and parameters of the FBG. More details are needed for clarification.

Response4： Thank you for your comment; your opinion is essential. I am sorry that the text did not include detailed information on fiber Bragg gratings. An external contractor supplied the fiber Bragg gratings used in this paper. We have added information about the supplier and parameters of the fiber Bragg gratings in subsection 2.1 of the paper.

Initial manuscript：

The fiber used in this work is a silica fiber with a diameter of 125 μm. It is a single-hole dual-core fiber (SHDCF) with a circular air hole and two arranged fiber cores. The cross-section of the fiber is shown in Figure 1b. The SHDCF has an internal air hole diameter of 40.6 μm, and both cores are eight μm in diameter. The Multimode fiber (MMF) has a core diameter of 105 μm and a cladding diameter of 125 μm. Wuhan Yangzi Optoelectronics Technology Co manufactures it. In the sensor manufacturing process, a 300 μm multimode fiber and a 750 μm single-mode dual-core fiber are sequentially fused at one end of the FBG. The second step fuses the single-mode fiber and a 300 μm multimode fiber. Finally, the multimode fiber is fused to the other end of the single-hole dual-core fiber to complete the sensor probe. Simply put, FBG-PAHM is the structure of parallel asymmetric hybrid microcavity cascading an FBG within a fiber.

Revision：

The fiber used in this work is a silica fiber with a diameter of 125 μm. It is a single-hole dual-core fiber (SHDCF) with a circular air hole and two arranged fiber cores. The cross-section of the fiber is shown in Figure 1b. The SHDCF has an internal air hole diameter of 40.6 μm, and both cores are eight μm in diameter. The Multimode fiber (MMF) has a core diameter of 105 μm and a cladding diameter of 125 μm. Wuhan Yangzi Optoelectronics Technology Co manufactures it. Zhixing Technology Nantong Co provides the fiber Bragg grating(FBG) used in this paper. The length of the fiber Bragg grating is 10mm, the central resonance wavelength is 1550nm, the 3dB bandwidth is 0.11nm, and the peak reflectance reaches 12dB. In the sensor manufacturing process, a 300 μm multimode fiber and a 750 μm single-mode dual-core fiber are sequentially fused at one end of the FBG. The second step fuses the single-mode fiber and a 300 μm multimode fiber. Finally, the multimode fiber is fused to the other end of the single-hole dual-core fiber to complete the sensor probe. Simply put, FBG-PAHM is the structure of parallel asymmetric hybrid microcavity cascading an FBG within a fiber.

Comments5: The authors should provide additional information to elucidate the demodulation process in both curvature and temperature sensing experiments.

Response5： Thank you for your comments, your suggestions are very helpful in improving the quality of the manuscript. We have added experiments for simultaneous sensing of curvature and temperature with two parameters to the manuscript.

Revision:

	Table 1. Simultaneous measurement of two parameters.
	The spectrum datum of actual measurement and calculation			dip1(nm)		dip2(nm)
	R	C=0°:0m-1, T=33℃
		Experiment		1386.28		1549.7
		Calculation
	Q1	C=0°:0.108m-1, T=43℃
		Experiment		1392.12		1549.92
		Calculation		1391.92		1549.86
	Q2	C=0°:0.216m-1, T=53℃
		Experiment		1395.28		1550.06
		Calculation		1394.96		1550.02
	Q3	C=0°:0.324m-1, T=63℃
		Experiment		1397.76		1550.22
		Calculation		1397.1		1550.16
	Q4	C=0°:0.433m-1, T=73℃
		Experiment		1401.12		1550.40
		Calculation		1400.06		1550.32
Table2. Difference between experimental results and theoretical calculation results.
The condition datum of calculation and actual measurement					ΔC		ΔT
R			actual		0		0
			measured
Q1			actual		0.108 m-1		10℃
			measured		0.116 m-1		11.5℃
Q2			actual		0.216 m-1		20℃
			measured		0.231 m-1		21.7℃
Q3			actual		0.324 m-1		30℃
			measured		0.337 m-1		31.2℃
Q4			actual		0.433 m-1		40℃
			measured		0.479 m-1		42.1℃

We measured four sets of transmission spectra of the sensor under different conditions: Q1 [C=0°:0.108m^-1, T=43°C], Q2 [C=0°:0.216m^-1, T=53°C], Q3 [C=0°:0.324m^-1, T=63°C] and Q4 [C=0°:0.433m^-1, T=73°C]. The transmission spectra of the sensors were measured at a temperature of 33°C with 0 m^-1 as the reference group. By comparing the four sets of spectra with the reference group, the wavelength shifts for the different cases can be derived. The derived values are shown in Table 1 and Table 2. The sensor's Measurement errors manifest as differences between the measured and actual values. The lack of accuracy of the curvature shift is one of the reasons for this, in addition to the resolution limitations of the spectra which also lead to test results, which also affects the accuracy of the data demodulation. In the following work, the sensor's sensitivity can be further improved to solve this problem.

Comments6: What are the optical mechanisms behind the different wavelength shift behaviors (red shift vs. blue shift) observed at various angles of curvature (0°, 90°, 180°, and 270°), and how do these shifts correlate with changes in the optical path length within the sensor's structure?

Response6： Thank you very much for your wise and practical professional counsel. Your questions have deepened our analysis of this structural sensor. When the signal light is transmitted in a sensor of this structure, it constitutes a vernier effect due to the FP cavity interference mechanism and the MZI interference mechanism. When the curvature of the sensor changes, on the one hand, the air cavity inside the sensor will be significantly deformed, and the optical path length of the FP cavity will change; on the other hand, the change of curvature will also cause the core to be squeezed or stretched, which will change the stress state received by the optical fiber, and thus affect its optical properties, especially the effect on the refractive index. During the curvature change, the combined impact of FP cavity interference and MZI interference produces a shift in the interference spectrum. In a small range of curvature change, the refractive index of the fiber core changes less, and the change of FP cavity length mainly causes the interference spectrum, and it is known that the interferometric resonance wavelength is directly proportional to the optical range of light in the FP cavity, so that the curvature and the amount of wavelength change are linearly related. Due to the asymmetry of the cross-sectional distribution of the single-hole dual-core fiber, the curvature change of the sensor at different angles causes different changes in the air cavity. In this experiment, during the curvature change of the sensor in the 0° and 90° directions, the air cavity is located above the central horizontal plane. The air cavity is stretched, and the cavity length becomes more extensive, increasing the optical range of light transmitted in the FP cavity. The interference spectrum produces a red shift. In the process of growing curvature of the sensor in the 180° and 270° directions, the air cavity is located below the center plane, the air cavity is squeezed, and the cavity length becomes shorter, which reduces the optical range of the light transmitted in the FP cavity, and the interferometric spectra are blue shifted.

Initial manuscript：

Under the elastic-optic effect, an increase in temperature causes the cavity length to increase. The thermo-optic effect of the fiber simultaneously causes a change in the effective refractive index. However, the air in the FPI cavity is less affected by temperature changes. Therefore, the temperature change affects the two structures differently. The sensitivity of FPI and MZI can be expressed as [18]:

Where k and ξ are constants and are expressed as thermo-optic and expansion coefficients, respectively. When transmitted light passes through an FBG, some of its energy is reflected. The Bragg resonance wavelength can be written as:

Where is the effective refractive index of the mode propagating in the FBG region and Λ is the grating period. The resonant wavelength of the FBG shifts as the temperature increases or the grating curvature changes [19,20].

Revision：

Temperature has a negligible effect on the refractive index of the air, so the Mach-Zende interference effect plays a vital role in the temperature sensitivity of the hybrid structure. The temperature sensitivity of the structure can be expressed as [18]:

Where k and ξ are constants expressed as thermo-optic and expansion coefficients, respectively. This structure is made of pure silicon dioxide with a small coefficient of thermal expansion, therefore the temperature sensitivity of this sensor is mainly related to the thermo-optic effect, and Equation (7) is rewritten to regain the temperature sensitivity equation：

Air cavity deformation and elastic-optical effects affect the interference spectrum during curvature sensing. The elastic-optical effect is weak within a slight curvature variation, and the curvature sensing sensitivity is mainly related to the FPI involved in the air cavity deformation. Therefore, the wavelength of the interference drift caused by the change in the FPI cavity length can be derived as[19]:

Where  is the change in length of the FPI chamber before and after bending, h is the distance between the center of the FP cavity and the bottom of the fiber, C is the curvature value to be measured. The FP cavity in this structured sensor is located at a non-centrosymmetric position on the cross-section with different values of h in different bending directions, thus having different sensitivities in the curvature sensing. In addition, the blue or red shift of the interference spectrum depends on the bending direction. When the sensor is bent in the 180° and 270° directions,  is less than 0, so  and C are negatively proportional, and the interference spectrum is shifted towards the short wavelength. Conversely,  and C are proportional in the 0° and 90° directions, and the interference pattern is correspondingly shifted in the long-wavelength direction.

When transmitted light passes through an FBG, some of its energy is reflected. The Bragg resonance wavelength can be written as:

Where is the effective refractive index of the mode propagating in the FBG region, and Λ is the grating period. The resonant wavelength of the FBG shifts as the temperature increases or the grating curvature changes [20,21].                    

Comments7: Figure 7 is confusing. The authors stated that a 0.1 mm movement of the micrometer generates curvature ranging from 0 m^-1 to 0.865 m^-1. However, it is unclear where the authors obtained the data points within this range. Additionally, it is important to clarify whether 0.865 m^-1 represents the detection limit and provide detailed explanations to justify this.

Response7： Thank you for your suggestion. Your suggestions are beneficial to improve the quality of the article. The data for the fitted curves in Fig. 7 come from the spectral translation record of the interference envelope for different angular curvature changes. If the interference envelope spectra of all curvature states are put in one plot, it is not easy to read the data due to the dense interference conditions. Therefore, we modify Fig. 6 by labelling the wavelength shift under the maximum curvature change for a clearer view by the reader.

The measurement range is related to the design of the structure; this sensor can detect curvature in the range of 0m^-1-0.865 m^-1 with high accuracy. The signal light in this structure sensor constitutes a vernier effect due to the FP cavity interference mechanism and MZI interference mechanism. When the curvature of the sensor changes, on the one hand, the deformation of the air cavity in the sensor is noticeable, and the optical path length of the FP cavity will change; on the other hand, the change of curvature will also cause the core to be squeezed or stretched, which will change the strain state of the optical fiber, and then affect its optical properties, especially the effect on the refractive index. During the curvature change, the shift of the interference spectrum is generated by the combined impact of FP cavity interference and MZI interference. In the range of 0 m^-1-0.865 m^-1, the refractive index of the fiber core changes less, the interference spectrum is mainly caused by the change of the FP cavity length, and the curvature is linearly related to the amount of wavelength change. Beyond the measurement range, the fiber core refractive index change increases, and the influence on the interference envelope is also apparent, resulting in the interference spectrum translation failing to show a linear relationship. Therefore, this sensor can perform high-precision sensing within a limited detection range.

Initial manuscript：

Figure 6. The sensor structure's response to curvature: (a) 0°, (b) 90°, (c) 180°, and (d) 270°.

Revision：

Figure 6. The sensor structure's response to curvature: (a) 0°, (b) 90°, (c) 180°, and (d) 270°.

Comments8: Also, what equation did the author use to calculate the curvature? Need more clarification.

Response8： We apologise for not clearly labelling the curvature formulae in the text. We have revised section 3.

Initial manuscript：

Figure 5 shows a schematic of the experimental setup that uses the vernier effect to detect curvature. The curvature can be obtained from the formula C = 2d/(d² +s²), where d is the downward distance from the end of the sensor, and s is half the distance between the fixtures at each end of the metal sheet. In the bending tests, the distance between the two fixtures was 74 mm, and the micrometer screw was moved 0.1 mm at a time to increase the curvature from 0 m^-1 to 0.865 m^-1. The Yokogawa AQ6370D optical spectrum analyzer operates in the wavelength range from 600 nm to 1700 nm. It has a power range of -90 dBm to 20 dBm and a spectral resolution of 0.02 nm. The broadband light source (YSL, SC-5-FC) can operate in the wavelength range 480-2200 nm with a total output power of 800mW. The optical fiber is attached to the bracket by two rotating clamps. The rotational angle scale of both rotators enables the sensor to detect various four-directional curvatures. The sensing probe is affixed to the center of a steel straight edge, and a push-pull gauge is employed to induce a minor displacement in the vertical direction of the steel straight edge, which subsequently alters the curvature of the sensor. One branch is connected to a broadband light source, while the other is connected to a spectrometer. The resulting transmission spectrum data were observed on the spectrometer.

Revision：

Figure 5 shows a schematic of the experimental setup that uses the vernier effect to detect curvature. The Yokogawa AQ6370D optical spectrum analyzer operates in the wavelength range from 600 nm to 1700 nm. It has a power range of -90 dBm to 20 dBm and a spectral resolution of 0.02 nm. The broadband light source (YSL, SC-5-FC) can operate in the wavelength range 480-2200 nm with a total output power of 800mW. The optical fiber is attached to the bracket by two rotating clamps. The rotational angle scale of both rotators enables the sensor to detect various four-directional curvatures. The sensing probe is affixed to the center of a steel straight edge, and a push-pull gauge is employed to induce a minor displacement in the vertical direction of the steel straight edge, which subsequently alters the curvature of the sensor. One branch is connected to a broadband light source, while the other is connected to a spectrometer. The resulting transmission spectrum data were observed on the spectrometer. The curvature can be obtained from the formula:

Where d is the downward distance from the end of the sensor, and s is half the distance between the fixtures at each end of the metal sheet. In the bending tests, the distance between the two fixtures was 74 mm, and the micrometer screw was moved 0.1 mm at a time to increase the curvature from 0 m^-1 to 0.865 m^-1.

Comments9: Instead of plotting absolute temperature in Figure 10, it would be more informative for the sensor to plot the change in temperature versus the change in wavelength.

Response9： Thank you for your comments, your suggestions are constructive for the manuscript. We have modified Fig. 10 to plot temperature change versus wavelength change.

Initial manuscript：

Figure 10. Response of the sensor structure to the different temperatures.

Revision：

Figure 10. Response of the sensor structure to the different temperatures.

Comments10: What are the optical principles underlying the linear response of the hybrid structure's spectra to simultaneous changes in curvature and temperature, and how do the distinct sensitivities at dip1 and dip2 facilitate accurate discrimination between these two parameters?

Response10：

This paper's hybrid structure sensor has two interferometric structures, the Fabry-Perot interferometer (FPI) and Mach-Zehnder interferometer (MZI).

The fiber optic thermo-optic effect and the fiber optic thermal expansion effect play a role in the interference spectrum during temperature changes. The optical fiber used in this structure is made of pure silica, and the coefficient of thermal expansion of silica and air cavity is low. Therefore, the role of temperature on the interference spectrum is mainly the effect of the Mach-Zehnder interferometer (MZI) interference structure; the core and cladding of the fiber become more extensive refractive index under the impact of thermo-optic effect, which causes the interference spectrum to be shifted. Therefore, the temperature and wavelength change becomes approximately linear when only the temperature change is considered.

During the curvature change, it is the deformation of the air cavity and the elastic-optical effect that play a role in the interference spectrum. In a small range of curvature changes, the elastic-optical impact is weak, and the effect of curvature on the interference spectrum is mainly the Fabry-Perot interferometer (FPI) interferometric structure. In the curvature change, the air cavity is lengthened or shortened, which changes the optical path of light in the air cavity and thus causes a shift in the interference spectrum. A longer cavity length produces a red shift in the interference spectrum, and a shorter one produces a blue shift in the interference spectrum. Therefore, the curvature is approximately linearly related to the wavelength change when only the curvature change is considered.

In sensor systems, the similarity of the sensitivity of two observation points increases the error in the demodulation of the two-parameter signal. Suppose the sensitivities of the two observation points are very similar when a two-parameter signal passes through these two observation points. In that case, the resulting responses will be very close to each other, making it difficult for the demodulation system to distinguish between signals from different parameters. On the other hand, when the sensitivities of the two observation points are similar, the effect of noise during demodulation is amplified. The demodulation system tries to separate the signals by slight differences, which makes the effect of noise on the demodulation result more significant and further increases the error. Using two observation points with different sensitivities (dip1 and dip2) makes it possible to make each parameter's effects on different observation points uniquely characterised, thus reducing parameter coupling and improving demodulation accuracy. Different observation points may also have different sensitivities to noise. When the observation points have different sensitivities, the effect of noise can be filtered and cancelled out by combining the data from two observation points, thus improving the measurement accuracy. This approach helps to reduce measurement errors through multi-point calibration and data fusion.

 Comments11: How does the thermo-optic effect in the fiber core and cladding contribute to the temperature sensitivity observed in the hybrid structure sensor, and what are the key factors affecting the accuracy of the temperature measurements?

Response11：Thank you very much for your professional questions, which have deepened our understanding and thinking about this structure. We have added the appropriate analyses to the theoretical section to improve the manuscript's quality.

Temperature has a negligible effect on the refractive index of the air, so the Mach-Zende interference effect plays a vital role in the temperature sensitivity of the hybrid structure. The temperature sensitivity of the structure can be expressed as [18]:

 Where k and ξ are constants expressed as thermo-optic and expansion coefficients, respectively, this structure is made of pure silicon dioxide with a small coefficient of thermal expansion(opg.optica.org/col/abstract.cfm?URI=col-13-10-100601). Therefore, the temperature sensitivity of this sensor is mainly related to the thermo-optic effect, and Equation (1) is rewritten to regain the temperature sensitivity equation:

To improve temperature sensing accuracy, it is necessary to make the temperature and wavelength translation change as linear as possible. Measuring curvature sensing variations over a small area reduces the influence of photo-elastic effects on MZI interference, which can improve the accuracy of the temperature sensing process.                              

Comments12: Section 3.4 is weak as the authors did not demonstrate how the proposed sensor outperforms existing ones. The provided content lacks evidence of significant improvements.

Response12： Thanks to your suggestion, we have added in subsection 3.4 a comparison and analysis of the performance of the sensors proposed in this paper with other types of sensors.

Initial manuscript：

Table 1 gives a detailed comparison of the performance of the sensor designed in this paper with other curvature and temperature sensors. From the table 1, we can find that compared with other structural sensors, the sensor proposed in this paper has the advantages of simple fabrication, compact structure, higher curvature sensitivity, and low-temperature crosstalk, and it can achieve two-dimensional vector curvature detection in four directions. The maximum sensitivity in one direction is -25.55nm/m^-1.

Revision：

In this experiment, we use a single-hole dual-core optical fiber to construct a non-centrosymmetric optical fiber microstructure, which achieves higher curvature sensitivity detection in four vertical directions with low-temperature crosstalk. The performance comparison of this sensor with existing sensors is shown in Table 1. The curvature sensors constructed with single optical Bragg grating or special optical fibers have low sensitivity, can only achieve one-dimensional curvature sensing, and have considerable temperature crosstalk [24-27]. Special processing, over fusion and polishing of optical fibers can improve the sensor's sensitivity, but these methods are difficult to process and have poor repeatability. Moreover, sensors relying on these methods can only achieve unidirectional curvature sensing [28][30]. Literature [29] constructed a vernier effect to improve curvature sensitivity by cascading biased core fiber and double-edged hole fibers. Still, the sensitivity difference in different directions of this structured sensor is noticeable, and it cannot achieve two-dimensional curvature sensing, and the temperature crosstalk is considerable. Compared with other structural sensors, the sensor proposed in this paper has the advantages of simple fabrication, compact structure, higher curvature sensitivity, and low-temperature crosstalk, and it can achieve two-dimensional vector curvature detection in four directions. The maximum sensitivity in one direction is -25.55nm/m^-1.

Comments13: The authors claim that the proposed sensor can detect structural health in buildings, bridge engineering, and other applications. However, they have not provided sufficient correlating results to substantiate this assertion. More detailed explanations and supporting evidence are needed to demonstrate the sensor's effectiveness in these fields.

Response13：Thank you very much for your suggestions, which will help improve the manuscript's readability. We have added a discussion section to the text in subsection 3.5, which analyses the issue

Revision：

3.5 Discussion

The experimental results show that the curvature sensor based on single-hole dual-core optical fiber composite interference has lower temperature crosstalk, more compact size, and higher curvature sensitivity in all four vertical monitoring directions compared with the traditional structural curvature sensor. Conventional curvature sensors are usually made by fusion bonding, polishing, and cone pulling, which have poor structural robustness, are challenging to process, and are not easy to cascade other optical devices to build a vernier effect. On the other hand, due to the single interference structure of traditional curvature sensors, it isn't easy to improve the curvature sensitivity while maintaining a low-temperature crosstalk during the sensing process. In contrast, the curvature sensor proposed in this paper avoids the complex fabrication process. By constructing parallel FPI and MZI composite interferences within the optical fiber, the size of the sensor structure is further reduced, providing a new method to build a curvature and temperature sensor with a vernier effect. During the measurement process, a two-dimensional curvature sensing with low crosstalk and high sensitivity is achieved by taking advantage of the different responsiveness of the microstructures to curvature and temperature. In practical application scenarios, such as structural health monitoring of buildings and bridges, curvature sensors' sensitivity and low crosstalk characteristics are highly required. In addition, the location of potential hazards and the direction of deformation where safety occurs in buildings, bridges, and other structures have uncertainties and must be monitored from multiple angles. Therefore, the two-dimensional curvature sensor proposed in this paper has a specific application potential in structural health monitoring.

 Comments14: In general, there are several typos such as 'we probe', 'trough of', and others found in the current version. Significant language improvements are necessary to meet publication standards.

Response14： We thank you for your feedback and sincerely apologise for the large number of inappropriate English descriptions in the text, which detracted from the overall quality of the article. We have made the necessary corrections to the known inaccuracies and used the recommended English editing services available on the journal website.

Initial manuscript：

We probe the curvature and temperature with two observation points, dip1 and dip2. Dip1 is the trough of the interference envelope, and dip2 is the Bragg resonance wavelength.

Revision：

    Measuring the temperature and curvature requires two observation points, dip1 and dip2. Dip1 denotes the interference envelope's trough, and dip2 is the Bragg resonance wavelength.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have carefully addressed the concerns. I suggest accepting this paper for publication. 

Author Response

Please find the response file in the attachment.

Author Response File: Author Response.docx