A μrad Accuracy and nW Detection Sensitivity Four-Quadrant Heterodyne Coherent Angular Measurement System

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript investigates the performance of a coherent detection angle measurement system based on QD. The measurement accuracy of coherent detection and direct detection angle measurement systems was compared based on experimental results. Some suggestions are as follows:

1. Some parameters in equations (such as Q/I in Fig. 3) are not described.
2. In Fig. 11，when the loop bandwidth is smaller than 10Hz，how the measurement accuracy changes.
3. English expression needs improvement.
4. What is the reason for the poor measurement accuracy of the direct detection angle measurement system used as a comparison object in the manuscript, and is it related to the current selection of detector types.

Author Response

Comments 1:

Some parameters in equations (such as Q/I in Fig. 3) are not described.

Response 1:

Thank you for your valuable suggestions. Based on your opinions, we have described and supplemented the I and Q variables of Equation 3 in the manuscript in both textual and formula forms, and rearranged all the formula number references in the manuscript text. The specific content has been revised in lines 166-171 on page 5 of the manuscript.

Comments 2:

In Fig. 11, when the loop bandwidth is smaller than 10Hz, how the measurement accuracy changes.

Response 2:

Thank you very much for the valuable suggestions of the reviewers. Based on your suggestion, while keeping other conditions the same, we conducted supplementary experiments on the system Angle measurement performance when the loop bandwidth is lower than 10Hz. And the experimental results were updated in Figure 11 of the manuscript. The experimental results show that when the loop bandwidth of the system is lower than 10Hz. The measurement accuracy of azimuth and pitch axis angles has decreased significantly. We analyze that the reason for this phenomenon is that if the loop bandwidth is too small, it will cause a large systematic error. At this time, the adjustment step size of the phase-locked loop is too small, making it difficult to correctly track and detect the phase of the received signal. Excessive loop bandwidth will result in significant random errors. At this time, the adjustment step size of the phase-locked loop is too large, resulting in significant jitter in the phase locking result. Therefore, in the Angle measurement system, it is necessary to select an appropriate loop bandwidth value to ensure the optimal performance. The specific content has been revised in lines 514-521 on page 15 and lines 523-525 on page 16 of the manuscript.

Comments 3:

English expression needs improvement.

Response 3:

Thank you for your suggestions. Regarding your opinion. We carefully examined the english expressions of all the contents of the manuscript and made adjustments and supplements to the problematic and unclear sentences. The specific content has been revised in lines 86-88 on page 2, 95-96 on page 3, 105-109 on page 3, 178-182 on page 5, 204-209 on page 6, 286-293 on page 8, 320-324 on page 9, 347-351 on page 10, 398-401 on page 11, 404-409 on page 11, 434-443 on page 13, 485-490 on page 14, 553-556 on page 17, lines 594-596 on page 18 of the manuscript.

Comments 4:

What is the reason for the poor measurement accuracy of the direct detection angle measurement system used as a comparison object in the manuscript, and is it related to the current selection of detector types.

Response 4:

Thank you very much for your suggestions. We believe that the main reason for the low accuracy of the direct detection angle measurement system used as the comparison object in the manuscript lies in the signal-to-noise ratio of the system. In the direct detection system, thermal noise dominates among noise factors and has a significant impact on the signal-to-noise ratio of the system. In the heterodyne coherent detection system, due to the power gain of the local oscillator laser beam, the proportion of thermal noise in the noise factors becomes very small, and the signal-to-noise ratio of the system is correspondingly improved, thereby enhancing the angular measurement performance of the system. We supplemented the analysis and comparison of the four-quadrant detector (QD), charge-coupled device (CCD), and position-sensitive detector (PSD) in lines 71-76 on page 2 of the manuscript. We believe that the main reason for the low accuracy of the direct detection system does not lie in the selection of the detection type.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript describes a heterodyne coherent angle measurement system under an inter-satellite long-range laser transmission link. By locking and tracking the phase of the beat frequency signal, high accuracy and high sensitivity measurement of the deflection angle is realized. With minor modifications, this work will meet the publication standards of Photonics. Specific improvements to this manuscript are 
suggested below. 
1.The introduction part of the manuscript mentions the reconfigurable properties of laser communication terminals and the space-based adaptive communication node program. It is suggested that the authors elaborate on the correlation between the heterodyne coherent angle measurement system built in this paper and the reconfigurability of laser terminals. 
2.Compared to charge-coupled devices and position-sensitive detectors in conventional systems. What are the distinct advantages of using a four-quadrant detector as the photodetection unit of the heterodyne coherent angle measurement system in the manuscript? It is recommended that the authors provide a detailed explanation of the reasons for the selection of this particular detector. 
3.In Figure 3 of the manuscript, the meaning of the waveform above the "Phase Locked Loop Input Signal" module is somewhat vague and does not well reflect the connection between the beat signals in each quadrant. Also, the format of the two "MULT" modules does not seem to be quite the same. It is suggested that the author adjust and supplement the contents of Figure 3. 
4.The manuscript builds a desktop experimental system to test the accuracy and sensitivity of angle measurements. In order to facilitate the reproduction of the experimental results, it is recommended that the authors list and describe the key parameters in the experimental system in text or table form. 
5.Figure 4 of the manuscript simulates the phase locking results and NCO index values, but does not explicitly show the difference between the signals. The authors are advised to further describe the key information in Figure 4. 

Author Response

Comments 1:

The introduction part of the manuscript mentions the reconfigurable properties of laser communication terminals and the space-based adaptive communication node program. It is suggested that the authors elaborate on the correlation between the heterodyne coherent angle measurement system built in this paper and the reconfigurability of laser terminals.

Response 1:

We thank the reviewer for the valuable comments. In response to your comments, we have described the amount of change in optical frequency corresponding to different wavelengths in the Space-BACN system and the frequency of the beat signal, respectively. The isolation characteristics of the heterodyne interferometric angular measurement technique investigated in this paper in the area of laser terminal repeatable configuration and its application in multi-node laser communication network systems are clarified. The details are revised in lines 61-68 on page 2 of the manuscript.

Comments 2:

Compared to charge-coupled devices and position-sensitive detectors in conventional systems. What are the distinct advantages of using a four-quadrant detector as the photodetection unit of the heterodyne coherent angle measurement system in the manuscript? It is recommended that the authors provide a detailed explanation of the reasons for the selection of this particular detector.

Response 2:

We thank the reviewer for the comments. We compare the advantages of four-quadrant detector (QD) over charge-coupled device (CCD) and position-sensitive detector (PSD) in the introduction section of the manuscript and describe the reasons for choosing QD as photodetectors in this study. The details are revised in the manuscript on page 2, lines 71-76.

Comments 3:

In Figure 3 of the manuscript, the meaning of the waveform above the "Phase Locked Loop Input Signal" module is somewhat vague and does not well reflect the connection between the beat signals in each quadrant. Also, the format of the two "MULT" modules does not seem to be quite the same. It is suggested that the author adjust and supplement the contents of Figure 3.

Response 3:

We thank the reviewer for the valuable comments. Based on your suggestions, we have optimized and adjusted the details of Fig. 3. In the upper right corner of Fig. 3, we added the beat frequency signals of each quadrant of QD and characterized the phase difference between the signals. The format of the two MULT modules was also harmonized. The details are revised in the manuscript on page 10, line 344-346.

Comments 4:

The manuscript builds a desktop experimental system to test the accuracy and sensitivity of angle measurements. In order to facilitate the reproduction of the experimental results, it is recommended that the authors list and describe the key parameters in the experimental system in text or table form.

Response 4:

Thank you for your valuable comments. Based on your suggestion, we have added the key parameters of the desktop experimental system for heterodyne coherent angular measurements in the experimental section of the manuscript in the form of a table. The details are revised in lines 416-419 on page 12 in the manuscript.

Comments 5:

Figure 4 of the manuscript simulates the phase locking results and NCO index values, but does not explicitly show the difference between the signals. The authors are advised to further describe the key information in Figure 4.

Response 5:

We thank the reviewer for the valuable comments. We have labeled the differences between the signals in Figure 4 of the manuscript. The details are revised in lines 376-378 on page 11 of the manuscript.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

I ask the authors to correct the following sentences and answer the questions:

1. Lines 26 and 27. The phrase is unclear: «This study is of great significance for the design of laser communication systems between gravitational wave measurements …». Make it easier to understand.
2. Figure 1. It is not clear where Figure (а) is positioned, and where Figure (b) is. The same is true for Figure 6. I recommend changing the position of the letters.
3. Figure 3 and lines 311-312: « …results are subjected to an atan operation to obtain the phase difference …» How is a phase difference greater than 2pi taken into account?
4. Figure 6. What were the distances L₁ and L₂ in the experiment?

Author Response

Comments 1:

Lines 26 and 27. The phrase is unclear: «This study is of great significance for the design of laser communication systems between gravitational wave measurements …». Make it easier to understand.

Response 1:

Thank you very much for your valuable suggestions. We sincerely apologize for the unclear expression of the sentences in the manuscript. The original meaning of this sentence is that the heterodyne coherence Angle measurement system proposed in this paper is of great significance simultaneously in the fields of gravitational wave detection and inter-satellite laser communication. We have restated this sentence in the manuscript. The specific content has been revised in lines 26-29 on page 1 of the manuscript.

Comments 2:

Figure 1. It is not clear where Figure (а) is positioned, and where Figure (b) is. The same is true for Figure 6. I recommend changing the position of the letters.

Response 2:

Thank you to the reviewers for your valuable comments. According to your suggestion, we have enlarged the font of (a)-(d) in Figure 1 and (a)-(b) in Figure 6 of the manuscript. And mark them all at the upper left corner of the corresponding dotted box. The specific content has been revised in lines 136-139 on page 4 and lines 410-412 on page 12 of the manuscript.

Comments 3:

Figure 3 and lines 311-312: « …results are subjected to an atan operation to obtain the phase difference …» How is a phase difference greater than 2pi taken into account?

Response 3:

Thank you very much for your valuable suggestions. Firstly, for the phase tracking process of the phase-locked loop (PLL), since the beat frequency sinusoidal signal is a continuous signal with a period of 2π. Therefore, signals with phase differences exceeding 2π will not have a significant impact on the operational results of the PLL phase tracking process. Secondly, if the initial angle deviation causes the phase difference to exceed 2π, it will have a certain impact on the final angle measurement result. In this case, it is necessary to initially acquire the beat frequency signal first, filter out the integer 2π parts of the phase difference, obtain the phase deviation within the (-π,+π) interval, and then perform phase tracking. Finally, for cases where the initial phase difference exceeds 2π, the method we currently envision is to use power angle measurement for initial acquisition, and then perform phase locking through phase angle measurement. This part of the content has also been supplemented simultaneously in lines 332-334 on page 9 of the manuscript.

Comments 4:

Figure 6. What were the distances L1 and L2 in the experiment?

Response 4:

Thank you for the suggestions put forward by the reviewers. The scene in Figure 6(b) of the manuscript is set up in a laboratory environment. L1 represents the distance from the collimator to the fast-steering mirror (FSM), which is 50mm. L2 represents the distance from the FSM to the screen, which is 1930mm. Among them, L2 selects a very large value because we believe that more accurate measurement results of the FSM deflection Angle can be obtained at a longer distance. Meanwhile, we supplemented the values of these two parameters in lines 451-452 on page 13 of the manuscript.

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Over a link distance of thousands of kilometers, the relative rotation and motion between the transmitter and receiver terminals introduces tiny angular deviations that must be measured with high sensitivity and accuracy in gravitational wave measurement and intersatellite laser communication systems. Compared to the conventional direct detection method, which measures angle using the beat frequency signal's phase, the heterodyne coherent angle measurement offers greater measurement accuracy and detection sensitivity.

The authors of this paper suggest a four-quadrant heterodyne coherent angle measurement method with nW-level detection sensitivity and μrad precision. A Monte Carlo simulation system is constructed for performance testing, and a mathematical model of the differential wavefront sensing (DWS) angle solution is developed. To evaluate the heterodyne coherent measuring method's sensitivity and accuracy and to compare its performance to that of the direct detection approach, an experimental setup has been developed. According to the experimental findings, this is true for the pitch and azimuth axes.

With the same signal power of -16 dBm, the heterodyne coherent angle measurement precision is 2.54 μrad and 2.85 μrad, which is five times better than direct detection. At the 20 μrad accuracy threshold, heterodyne coherent detection has a sensitivity of -50 dBm, 1000 times better than direct detection. The design of laser communication networks between satellites and gravitational wave experiments greatly benefits from this study.

Again, the need for high sensitivity and precision in measuring intersatellite long-range beams is addressed in this work. The concepts of spatial coherent mixing and DWS angular phase conversion are examined, and a theoretical model of heterodyne coherent angle measurement is developed. The specified angular deflection analog quantity is measured with high accuracy by combining a phase-locked loop with a simulation system of heterodyne coherent angle measurement based on the Monte Carlo approach. The experimental setup is further designed to examine the accuracy and detection sensitivity of heterodyne coherent angle measurement and compare it with direct detection. The heterodyne coherent angle measurement system developed in this study performs somewhat better than the coherent off-target detection system reported in other literature. At a high optical power level, the accuracy of the angle measurement increases from 5 μrad in the literature to 2.85 μrad. The design of inter-satellite laser communication terminals and gravitational wave measurements can both benefit from this study, which also supports inter-satellite long-distance beam measurements.

I recommend to publish the article as it is.

Author Response

Comments 1:

Over a link distance of thousands of kilometers, the relative rotation and motion between the transmitter and receiver terminals introduces tiny angular deviations that must be measured with high sensitivity and accuracy in gravitational wave measurement and intersatellite laser communication systems. Compared to the conventional direct detection method, which measures angle using the beat frequency signal's phase, the heterodyne coherent angle measurement offers greater measurement accuracy and detection sensitivity.

The authors of this paper suggest a four-quadrant heterodyne coherent angle measurement method with nW-level detection sensitivity and μrad precision. A Monte Carlo simulation system is constructed for performance testing, and a mathematical model of the differential wavefront sensing (DWS) angle solution is developed. To evaluate the heterodyne coherent measuring method's sensitivity and accuracy and to compare its performance to that of the direct detection approach, an experimental setup has been developed. According to the experimental findings, this is true for the pitch and azimuth axes.

With the same signal power of -16 dBm, the heterodyne coherent angle measurement precision is 2.54 μrad and 2.85 μrad, which is five times better than direct detection. At the 20 μrad accuracy threshold, heterodyne coherent detection has a sensitivity of -50 dBm, 1000 times better than direct detection. The design of laser communication networks between satellites and gravitational wave experiments greatly benefits from this study.

Again, the need for high sensitivity and precision in measuring intersatellite long-range beams is addressed in this work. The concepts of spatial coherent mixing and DWS angular phase conversion are examined, and a theoretical model of heterodyne coherent angle measurement is developed. The specified angular deflection analog quantity is measured with high accuracy by combining a phase-locked loop with a simulation system of heterodyne coherent angle measurement based on the Monte Carlo approach. The experimental setup is further designed to examine the accuracy and detection sensitivity of heterodyne coherent angle measurement and compare it with direct detection. The heterodyne coherent angle measurement system developed in this study performs somewhat better than the coherent off-target detection system reported in other literature. At a high optical power level, the accuracy of the angle measurement increases from 5 μrad in the literature to 2.85 μrad. The design of inter-satellite laser communication terminals and gravitational wave measurements can both benefit from this study, which also supports inter-satellite long-distance beam measurements.

I recommend to publish the article as it is.

Response 1:

Thank you very much for your affirmation of the content of our manuscript. Based on the currently established system and research results, we will continue to delve into the deeper theories and methods in heterodyne coherence angle measurement, and verify and analyze them through simulation and experiments, striving to achieve more research results in the future.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have addressed all the concerns raised by the reviewer and have revised the manuscript accordingly. Therefore, I recommend that the paper be accepted.