Distributed Strain Measurements Based on Rayleigh Scattering in the Presence of Fiber Bragg Gratings in an Optical Fiber

Round 1

Reviewer 1 Report

This work proposes an approach based on the windowed Fourier transform with the Hann window function for strain measurements using distributed fiber optic sensors based on Rayleigh scattering in presence of fiber Bragg gratings with reflectivity of 70%. The paper demonstrates that the proposed approach eliminates the presence of insensitive zones nearby the FBGs. A test on a specimen under tension embedding three FBGs placed in the region of some cutouts is performed and the effects of the windowed Fourier transform with the Hann window function are reported.

I suggest the paper can be accepted.

Some minor revisions:

- Fig. 9 should be divided in a), b), c), and d), such as to a description for each plot reported in Fig. 9 can be provided in the figure caption. Moreover, a legend in the last plot of Fig.9 should be inserted.

- Some typos should be corrected, e.g.:

- Line 72 (Introduction section) – Correct “rates” with “rate” and, after this word, a period is needed: “The larger reflection amplitude in this case improves the registration of strain at a higher sampling ratE. However, it significantly increases the cost of optical fiber production”.

- Line 257 (Results section) – a period is needed after “DFT”: “To mitigate the spectral leakage […] before applying the DFT. This window function ensures signal continuity at the boundaries of the measurement interval”.

Author Response

The authors are grateful to the reviewer for thorough analysis of the paper.

Point 1: Fig. 9 should be divided in a), b), c), and d), such as to a description for each plot reported in Fig. 9 can be provided in the figure caption. Moreover, a legend in the last plot of Fig.9 should be inserted.

Response 1: Based on the comment Figure 9 was divided into (a), (b) and (c). One of the plots was deleted from the figure as it is duplicating the plot of reflectograms presented in Figure 9a of the new version of the figure. A legend was added to this plot. Description of each plot is provided in the caption of the figure as well as expressed in the paper text with appropriate references.

Also, titles of plots in Figure 8 where corrected to emphasize that if the Hann window function is not applied, the rectangular window is still used to analyze signal of the finite length.

Point 2: Some typos should be corrected, e.g.:

- Line 72 (Introduction section) – Correct “rates” with “rate” and, after this word, a period is needed: “The larger reflection amplitude in this case improves the registration of strain at a higher sampling ratE. However, it significantly increases the cost of optical fiber production”.

- Line 257 (Results section) – a period is needed after “DFT”: “To mitigate the spectral leakage […] before applying the DFT. This window function ensures signal continuity at the boundaries of the measurement interval”.

Response 2: Thank you for your careful reading of the article. The mentioned typos where corrected and the paper was examined for remaining typos as well.

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript is about a novel technique based on the usage of windowed Fourier transform and the Hann window function to mitigate the FBG induced noise while interrogating the optical fiber during a distributed strain measurement.

I have some points to raise for a better understanding and some minor advise to improve the article:

- is this technique easy to be incorporated in any kind of interrogatio system for distributed sensors based on Rayleigh scattering? Or is it a technique to be used in post-processing?

- are there any application in which both puntual (FBG) and distributed sensing are necessary?

- Could be possible to simultaneously interrogate the FBG and the Rayleigh scattering?

- what is the central scanning wavelength in equation (2)?

- the quality of Figure 9 must be improved, please refer to the single figure with a number or a letter in the caption.

- In Figure 11 the legend is missing and the figures are not alligned.

- Refering to Figure 11, the optimal results shown in (b) should be compared with a reference one (always with Rayleigh scattering). Otherwise how to know if the strain measurement obtained is right?

- it is not clear to me the meaning of the green lines on Figure 11

- how this technique is affected in function of the FBG FWHM?

English is good, the text is very understandable with a good flow.

Author Response

The authors are grateful to the reviewer for thorough analysis of the paper.

Point 1: Is this technique easy to be incorporated in any kind of interrogation system for distributed sensors based on Rayleigh scattering? Or is it a technique to be used in post-processing?

Response 1: The ease of incorporation of this technique is related to the openness of the interrogation system. From the manufacturer point of view the application of the Hann window function can be easily done on the digitized signal acquired by photodetector before FFT. From the user point of view the simplicity of incorporating such technique depends on the availability of raw data to the user.

Point 2: Are there any application in which both puntual (FBG) and distributed sensing are necessary?

Response 2: Despite the advantages of distributed fiber-optic sensors (FOS), FBG interrogation systems still offer superior capabilities for dynamic strain measurements (several kHz versus 10-100 Hz for distributed FOS based on Rayleigh scattering). Additionally, FBG interrogators are more accessible in terms of price and market availability. Therefore, potential applications where both point and distributed sensors are necessary include cases where it is crucial to combine the benefits of both systems: measuring strain with a high acquisition rate at critical points of the structure, which FBG sensors can provide, and simultaneously requiring high spatial resolution to asses strain distribution in areas with potential strain gradients where damage may occur. This can be essential in aircraft SHM systems, where the structure is subjected to both dynamic and static loads, as well as in SHM systems for civil engineering structures. Another possible application is related to the research and development stage of various products, where distributed FOS can offer valuable information about the mechanical state of an object under different loads during laboratory tests. However, due to the high cost, it may be more appropriate to install point FBG sensors, calibrated with distributed FOS, in the final product.

In order to improve the content of the paper, the section “Results” was renamed into “Results and Discussion” and this paragraph was added to this section

Point 3: Could be possible to simultaneously interrogate the FBG and the Rayleigh scattering?

Response 3: It seems that simultanious interrogation of FBG sensors and distributed FOS based on Rayleigh scattering is possible. However, such a system should employ distinct operational wavelength ranges for point and distributed measurements to prevent interference between them. In the present study, the optical backscatter reflectometer (OBR4600) and the FBG interrogator had overlapping operational wavelength ranges (1530 – 1613 nm for OBR4600 and 1500 – 1600 nm for Hyperion si255 FBG interrogator). To separate the distributed interrogation system from the resonant wavelengths of FBGs, the scanning wavelength range of the OBR4600 was narrowed and shifted to longer wavelengths, which consequently reduced the maximum measured strain range. It is possible to develop an interrogation optical system that utilizes different operational wavelength ranges for distributed and point FOS, the input signals from which would be combined in the fiber under test and the reflected signals would be separated for subsequent analysis.

In order to improve the content of the paper, the section “Results” was renamed into “Results and Discussion” and this paragraph was added to this section

Point 4: What is the central scanning wavelength in equation (2)?

Response 4: Central scanning wavelength is the midpoint wavelength of the applied wavelength scanning range of the tunable laser source (TLS). For example for the applied wavelength scanning range of the tunable laser source (TLS) of 1590 – 1610 nm, central scanning wavelengh would be 1600 nm.

Article text was modified to “where  is the central scanning wavelength, which is the midpoint wavelength of the applied wavelength scanning range of the tunable laser source”

Point 5: The quality of Figure 9 must be improved, please refer to the single figure with a number or a letter in the caption.

Response 5: Figure 9 was divided into (a), (b) and (c). One of the plots was deleted from the figure as it is duplicating the plot of reflectograms presented in Figure 9a of the new version of the figure. A legend was added to this plot. Description of each plot is provided in the caption of the figure as well as expressed in the paper text with appropriate references.

Also titles of plots in Figure 8 where corrected to emphasize that if the Hann window function is not applied, the rectangular window is still used to analyze signal of the finite length.

Point 6: In Figure 11 the legend is missing and the figures are not alligned.

Response 6: Figure 11 was alligned and the legend was added to Figure 11b. Also the caption of the figure was modified to emphsize that the measurements were conducted under three loading levels and Figure 11b also presents the measurements by point FBG sensors shown as green segments.

Point 7: Refering to Figure 11, the optimal results shown in (b) should be compared with a reference one (always with Rayleigh scattering). Otherwise how to know if the strain measurement obtained is right?

Response 7: In Figure 11b strain measurements conducted with distributed FOS are compared with measurements by point FBG sensors. At each loading step the fiber under test was switched from OBR4600 reflectometer to Hyperion si255 FBG interrogator. So FBG strain data in this case act as reference measurements for distributed FOS.

Point 8: it is not clear to me the meaning of the green lines on Figure 11

Response 8: Green lines in Figure 11b represent strain measurements made by point FBG sensors with Hyperion si255 interrogator. At each loading step the fiber under test was switched from OBR4600 reflectometer to Hyperion si255 FBG interrogator. The length of these lines correspond to the length of FBGs which were 5 mm long and locations correspond to FBG locations in the optical fiber.

Point 9: how this technique is affected in function of the FBG FWHM?

Response 9: We are grateful for an interesting question. The influnece of the reflected spectral width was not studied in this work. Despite the fact that it seems that the reflectivity of the FBG produces the main impact on the noise level, FBG with high FWHM can demonstrate reflections on wider wavelength range and affect the noise level and insensitive zones. This problem could be the topic of the future studies.

Author Response File: Author Response.pdf

Reviewer 3 Report

The authors present in a well written paper, dealing with the  important issues and short enough, an approach to correct the disturbed distributed signal in presence of local FBGs. Even I am not quite convinced about its practical usefulness, the paper is interesting to understand a little better these systems

Author Response

The authors are grateful to the reviewer for thorough analysis of the paper.

Response: In order to improve the content of the paper, the section “Results” was renamed into “Results and Discussion”. Information about the potential applications of the proposed method and the possibility of implementing a system for simultaneously interrogation of point and distributed fiber-optic sensors has been added to this section.

“Combined measurements by point and distributed FOS on one optical fiber in this study was conducted sequentially by switching the FUT between two interrogation sys-tems (OBR4600 and Hyperion si255) at each loading step. However, simultaneous inter-rogation of FBG sensors and distributed FOS based on Rayleigh scattering is possible. Such a system should employ distinct operational wavelength ranges for point and dis-tributed measurements to prevent interference between them. In the present study, the OBR4600 and the FBG interrogator had overlapping operational wavelength ranges (1530–1613 nm for OBR4600 and 1500–1600 nm for Hyperion si255 FBG interrogator). To separate the distributed interrogation system from the resonant wavelengths of FBGs, the scanning wavelength range of the OBR4600 was narrowed and shifted to longer wavelengths, which consequently reduced the maximum measurement strain range. It is pos-sible to develop an interrogation optical system that utilizes different operational wave-length ranges for distributed and point FOS, the input signals from which would be com-bined in the fiber under test and the reflected signals would be separated for subsequent analysis.

Despite the advantages of distributed FOS, FBG interrogation systems still offer supe-rior capabilities for dynamic strain measurements. Additionally, FBG interrogators are more accessible in terms of price and market availability. Therefore, potential applications where both point and distributed sensors are necessary include cases where it is crucial to combine the benefits of both systems: measuring strain with a high acquisition rate at critical points of the structure, which FBG sensors can provide, and simultaneously re-quiring high spatial resolution to assess strain distribution in areas with potential strain gradients where damage may occur. This can be essential in aircraft SHM systems, where the structure is subjected to both dynamic and static loads, as well as in SHM systems for civil engineering structures. Another possible application is related to the research and development stage of various products, where distributed FOS can offer valuable information about the mechanical state of an object under different loads during laboratory tests. However, due to the high cost, it may be more appropriate to install point FBG sensors, calibrated with distributed FOS, in the final product.”

Author Response File: Author Response.pdf