Measurement Modeling and Performance Analysis of a Bionic Polarimetric Imaging Navigation Sensor Using Rayleigh Scattering to Generate Scattered Sunlight

Round 1

Reviewer 1 Report (Previous Reviewer 2)

Comments and Suggestions for Authors

I thank the authors for having replied to all my questions and clarifying some doubts about the manuscript. 

Author Response

I thank the authors for having replied to all my questions and clarifying some doubts about the manuscript.

Response: Thank you for your patience in reviewing our manuscript and for your suggestions on our manuscript.

Reviewer 2 Report (New Reviewer)

Comments and Suggestions for Authors

This work is well revised, and it can be accepted.

Some minor comments:

1. Please revise all "polarization imaging" to "polarimetric imaging".

2. The format of the formula needs adjustment, for instance, vectors should be in bold, and matrices in italics. Moreover, there's a significant inconsistency in the font sizes of the formulas.

3. Eq.6, \phi should be in -90<\phi<=90.

4. Please provide a more detailed description of Figure 5.

Comments on the Quality of English Language

none

Author Response

This work is well revised, and it can be accepted.

Some minor comments:

1. Please revise all "polarization imaging" to "polarimetric imaging".

Response 1: Thank you for your valuable comments. We have corrected “polarization imaging” to “polarimetric imaging” in the revised manuscript.

2. The format of the formula needs adjustment, for instance, vectors should be in bold, and matrices in italics. Moreover, there's a significant inconsistency in the font sizes of the formulas.

Response 2: Thank you for your valuable suggestions. We have corrected the formatting of the formulas in the revised manuscript, including the font size of the formulas.

3. Eq.6, \phi should be in -90<\phi<=90.

Response 3: Thank you for your valuable comments. We have corrected Eq.6 in the revised manuscript.

4. Please provide a more detailed description of Figure 5.

Response 4: Thank you for your valuable suggestions. As shown in Section 3 of the revised draft, we have added a more detailed description of Figure 5. The detailed description is as follows.

The specific steps are as follows:

1. Set different solar altitude and azimuth angles. We set the solar altitude angle to 5° during the simulation, and the solar azimuth angle to change every 10° between 10° and 80°.
2. Reconstruct the skylight polarization distribution pattern at a certain time, and the skylight polarization distribution pattern can be reconstructed in the local geographical coordinate system according to the set solar altitude angle and azimuth angle and Rayleigh scattering model.
3. Generate the truth values of AoE image and DoLP image in the field of view, and According to the theoretical BPINS projection model, CMOS and lens parameters, we can get the truth values of two-dimensional AoE image and DoLP image from the three-dimensional skylight polarization distribution pattern reconstructed in step 2.
4. Stokes vector representation and incidence of polarized skylight, the polarization state of incident light can be calculated from the truth value of two-dimensional AoE image and DoLP image obtained in step 3, and the polarization state of incident light is represented by Stokes vector.
5. BPINS measurement model, set the error parameters of each device (Table 1), and polarized skylight with known polarization state obtained from step 4 is incident into BPINS with measurement errors.
6. CMOS imaging, through the BPINS projection model, CMOS and lens parameters, we can get 0°, 45°, and 90° direction intensity images.
7. Polarimetric imaging calculation, the intensity images obtained in step 6 are used for polarimetric imaging calculation to obtain DoLP and AoE images containing measurement errors.
8. Analyze the effect of single and combined factors on the measurement performance of BPINS. Repeat the above steps 1-7 to obtain multiple sets of DoLP and AoE images containing measurement errors, and then analyze the influence of errors on the measurement performance of BPINS.

Reviewer 3 Report (New Reviewer)

Comments and Suggestions for Authors

This paper presents an error model for the measurement performance of BPINS, and analyzes the influence of linear polarization degree and angle of E-vector. Key error factors such as principal point coordinate offset, lens attenuation, and COMS grayscale response are investigated using a generated skylight with known polarization state. Here are some concerns from reviewers that need to be addressed.

1.     The author should emphasize the necessity of the work. This can be demonstrated by comparing the improvement in measuring errors brought about by the error model proposed in this paper with existing literature.

2.     The proportion of recently published literature in the references should be increased. Please add up-to-date research results, such as those completed in the past three years.

Author Response

This paper presents an error model for the measurement performance of BPINS, and analyzes the influence of linear polarization degree and angle of E-vector. Key error factors such as principal point coordinate offset, lens attenuation, and COMS grayscale response are investigated using a generated skylight with known polarization state. Here are some concerns from reviewers that need to be addressed.

1. The author should emphasize the necessity of the work. This can be demonstrated by comparing the improvement in measuring errors brought about by the error model proposed in this paper with existing literature.

Response 1: Thank you for your valuable comments. We have emphasized the necessity of the work in the Introduction. For example, “Polarized skylight imaging measurements involve the coordinate transformations and polarization state calculation of skylight, and BPINS measurements should be considered in terms of the geometric and polarization parameters of the optical system, which are not considered in the current research work [37-41].” The work in this paper focuses more on exploring the extent to which the measurement error of the optical system affects the measurement performance of BPINS and proposes a method for analyzing the impact of measurement performance that is generalized for polarimetric imaging navigation sensors. This work can guide the calibration of BPINS and provide a theoretical basis for the optimal design of BPINS. In addition to BPINS, the idea of this work can be applied to other polarimetric imaging applications such as polarimetric underwater detection, polarimetric defogging, polarimetric medical diagnostics, and so on. Future work will compare this with the measurement errors considered in the existing literature.

2. The proportion of recently published literature in the references should be increased. Please add up-to-date research results, such as those completed in the past three years.

Response 2: Thank you for your valuable suggestions. We have added recent and relevant research results in the revised manuscript. These relevant literatures are listed below:

37. Wang, Z. Qiu, P. Huang, X. Yu, J. Yang and L. Guo, A Bioinspired Navigation System for Multirotor UAV by Integrating Polarization Compass/Magnetometer/INS/GNSS, IEEE Trans. Ind. Electron., 2023, 70, 8: 8526-8536.
38. Li, Y. Zhang, S. Fan, Y. Wang and F. Yu, Robust Heading Measurement Based on Improved Berry Model for Bionic Polarization Navigation, IEEE Trans. Instrum. Meas., 2023, 72, 8500211.
39. Cheng H., Zhang Q., Wan Z., Zhang Z., Qin J. Study on the polarization pattern induced by wavy water surfaces, Remote Sensing, 2023, 15, 18: 4565.
40. Cheng H., Zhang D., Zhu J., Yu H., Chu J. Underwater target detection utilizing polarization image fusion algorithm based on unsupervised learning and attention mechanism, Sensors. 2023, 23, 12: 5594.
41. Liu, J. Yang, W. Li, P. Huang and L. Guo, Tightly Coupled Modeling and Reliable Fusion Strategy for Polarization-Based Attitude and Heading Reference System, IEEE Trans. Ind. Inform., 2023, 19, 62-73.
42. Kong, Y. Guo, J. Zhang, X. Fan, X. Guo, Review on bio-inspired polarized skylight navigation, Chinese Journal of Aeronautics, 2023, 36, 9:14-37.
43. Li, Q., Dong, L., Hu, Y., Hao, Q., Wang, W., Cao, J., Cheng, Y. Polarimetry for Bionic Geolocation and Navigation Applications: A Review. Remote Sens. 2023, 15, 3518.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper proposed a measurement model of BPINS that takes into account the geometric and polarization errors of the optical system. In this paper, authors studied the key error factors affecting the measurement accuracy of BPINS, and established the measurement error model of BPINS. Finally, outdoor measurement model simulations were performed. In general, I think the originality and innovation of this paper is not enough. Therefore, I cannot recommend this paper for publication in sensors. The main reasons are listed as follows:

The error analysis of BPINS measurement accuracy and corresponding BPINS measurement error model have been described in the authors another paper called “Measurement error model of the bio-inspired polarization imaging orientation sensor” (https://doi.org/10.1364/OE.442244). Thus, the proposed model cannot be considered as the innovation of this paper.

Comments on the Quality of English Language

The manuscript is well written and clearly organized. 

Reviewer 2 Report

Comments and Suggestions for Authors

Please read the pdf uploaded. 

Comments for author File: Comments.pdf