A High-Pointing-Accuracy Implementation Method for an 18m Antenna Based on a Multi-Error-Source Coupled Model

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The paper shows a framework for improving the pointing accuracy of an 18-meter VLBI antenna operating at 40 GHz by integrating multiple error sources into a unified modeling framework combined with a hierarchical compensation strategy. The systematic decomposition of geometric, gravitational, wind-induced, and dynamic errors, together with the explicit mapping to the TPOINT calibration model, constitutes a clear methodological contribution and provides a practical basis for antenna calibration.

However, the paper lacks of comprehensive experimental validation. The proposed methodology is assessed almost exclusively through simulations, with little or no evidence demonstrating that the coupled error model and compensation strategy can achieve the reported performance on a real antenna under operational conditions. Without experimental verification, the claimed pointing accuracy of 9.9 arcseconds remains difficult to substantiate.

Moreover, the analysis is conducted under relatively benign operating conditions, with wind speeds limited to 4 m/s and antenna scan rates below 0.1°/s. These assumptions considerably restrict the practical applicability of the proposed approach, as large radio telescopes are frequently required to operate under more challenging environmental and dynamic conditions. The paper does not discuss how the proposed framework would perform when subjected to stronger wind disturbances, higher tracking velocities, or rapidly varying external loads.

In addition, the paper shows an absence of a robustness or sensitivity analysis. Since the proposed framework combines multiple interacting error sources, it is important to quantify the influence of parameter uncertainties, installation tolerances, structural aging, thermal effects, and other unmodeled disturbances on the final pointing accuracy. Such an analysis would provide greater confidence in the stability and reliability of the proposed model.

Furthermore, although the hierarchical compensation strategy is logically organized, its effectiveness relies heavily on accurate mechanical alignment and precise model calibration. In practice, these assumptions may be difficult to maintain throughout the antenna's operational lifetime due to structural deformation, component wear, and environmental variations. The manuscript does not sufficiently address these practical implementation challenges.

Finally, the treatment of dynamic error compensation remains relatively limited. The paper does not investigate advanced adaptive or intelligent control techniques capable of updating the compensation parameters in real time to cope with changing operating conditions. Incorporating such approaches would significantly improve the robustness and long-term applicability of the proposed methodology.

Author Response

Reviewer's Responses to Question 1

1. The paper lacks of comprehensive experimental validation. The proposed methodology is assessed almost exclusively through simulations, with little or no evidence demonstrating that the coupled error model and compensation strategy can achieve the reported performance on a real antenna under operational conditions. Without experimental verification, the claimed pointing accuracy of 9.9 arcseconds remains difficult to substantiate.

Answer: We thank the reviewer for this important suggestion. We fully agree that experimental validation is essential to substantiate the claimed pointing accuracy. In the revised manuscript, we have added a comprehensive Section 5: Experimental Validation with Radio Source Tracking, which presents systematic experiments conducted on the actual 18‑m antenna under operational conditions.

Experimental Setup: The experiments were carried out at X‑band, under wind speeds ≤ 4 m/s and stable temperature conditions. Standard cross‑scanning procedures were used with calibration radio sources distributed across the sky to cover a wide range of elevation angles. The three‑level hierarchical compensation strategy (mechanical alignment + TPOINT model calibration + active servo suppression) was applied sequentially.

Static Pointing Accuracy (Figures 11 and 12): After TPOINT calibration, the residual pointing error was reduced to approximately 7.9″ (RMS@95%), compared to ~35″–50.5″ before compensation. This value agrees well with the theoretical budget of 8.64″ derived from the multi‑error‑source coupled model, confirming the effectiveness of the systematic error compensation.

Dynamic Tracking Performance (Figures 13 and 14): Two representative scenarios were tested—short‑range fast acquisition (0° to 2° step) and long‑distance large‑angle slew (0° to 60° step). With active servo suppression enabled, the settling time (defined as the time required for the tracking error to converge to within ±0.005° after the antenna velocity reaches 1°/s) was reduced from 2.986 s to 1.478 s (improvement of 50.5%) in the short‑range scenario, and from 3.356 s to 1.789 s (improvement of 46.7%) in the large‑angle scenario.

These experimental results demonstrate that the proposed three‑level hierarchical compensation strategy effectively reduces the pointing error to within the 1/10 HPBW requirement at 40 GHz, confirming the reliability of the approach in realistic operational scenarios. All experimental results have been added to Section 5 with the corresponding figures clearly marked in the revised manuscript. We believe these additions substantially strengthen the paper by providing direct experimental evidence for the claimed performance.

 

Reviewer's Responses to Question 2

2, The analysis is conducted under relatively benign operating conditions, with wind speeds limited to 4 m/s and antenna scan rates below 0.1°/s. These assumptions considerably restrict the practical applicability of the proposed approach, as large radio telescopes are frequently required to operate under more challenging environmental and dynamic conditions. The paper does not discuss how the proposed framework would perform when subjected to stronger wind disturbances, higher tracking velocities, or rapidly varying external loads.

Answer: We thank the reviewer for this important observation. We would like to clarify the rationale behind the chosen operating conditions as follows:

Regarding the 4 m/s wind speed limit: This value is not an arbitrary restriction but rather represents the prevailing operational condition for this specific 18‑m antenna. Based on long‑term site‑wind statistics, the majority of routine VLBI observations are carried out under wind speeds below 4 m/s. The antenna is designed to maintain its specified pointing accuracy under these typical conditions, which cover more than 80% of the annual observational hours at the site. For wind speeds exceeding this threshold, the antenna can still operate, but with a reduced performance margin; this is a common practice in large‑aperture antenna design, where a trade‑off between environmental robustness and structural cost is necessary.

Regarding the 0.1°/s scan rate: This antenna is primarily used for VLBI observations of compact radio sources, which require slow and stable tracking rather than rapid scanning. The 0.1°/s rate is representative of the maximum tracking speed encountered in such observations; higher slew rates are used only for source acquisition and repositioning, during which high pointing accuracy is not required. Therefore, the pointing accuracy budget is most meaningful at this representative tracking speed.

 

Reviewer's Responses to Question 3

3, The paper shows an absence of a robustness or sensitivity analysis. Since the proposed framework combines multiple interacting error sources, it is important to quantify the influence of parameter uncertainties, installation tolerances, structural aging, thermal effects, and other unmodeled disturbances on the final pointing accuracy. Such an analysis would provide greater confidence in the stability and reliability of the proposed model.

Answer: We thank the reviewer for this suggestion. In the revised manuscript, we have made the following additions:

Added a sensitivity analysis in Section 3, perturbing key error parameters (gravity coefficients, wind load, servo noise, assembly residuals) within expected tolerance ranges. Results show the total pointing error remains within 8.8″–9.5″, still well below the 1/10 HPBW requirement. Wind load is identified as the most sensitive parameter.

Added a sentence in the Conclusion stating that long‑term effects (e.g., structural aging, thermal fatigue) are not yet addressed and will be investigated in future work through periodic recalibration and in‑situ monitoring.

All changes are marked in the revised manuscript.

 

Reviewer's Responses to Question 4

4, Although the hierarchical compensation strategy is logically organized, its effectiveness relies heavily on accurate mechanical alignment and precise model calibration. In practice, these assumptions may be difficult to maintain throughout the antenna's operational lifetime due to structural deformation, component wear, and environmental variations. The manuscript does not sufficiently address these practical implementation challenges.

Answer: We thank the reviewer for this practical concern. In the revised manuscript, we have added a paragraph in Section 4 discussing the long‑term maintenance of the compensation strategy, covering mechanical alignment as a baseline setup, regular TPOINT recalibration (every 3–6 months), active servo suppression for short‑term disturbances, and health monitoring devices (inclinometers, temperature sensors) installed on the antenna. These measures ensure the strategy remains effective over the antenna's operational lifetime.

 

Reviewer's Responses to Question 5

5, The treatment of dynamic error compensation remains relatively limited. The paper does not investigate advanced adaptive or intelligent control techniques capable of updating the compensation parameters in real time to cope with changing operating conditions. Incorporating such approaches would significantly improve the robustness and long-term applicability of the proposed methodology.

Answer: Thank you for the reviewer's comments. In the revised manuscript, we have made the following additions:

n Section 2.2 (Dynamic Tracking Error), we have added a discussion acknowledging the limitations of the current dynamic compensation approach (feedforward control + active backlash elimination) and identifying advanced adaptive/intelligent control techniques as an important direction for future work.

In Section 5 (Experimental Validation with Radio Source Tracking), we have added a dedicated experimental section that validates the current compensation method through actual radio source tracking experiments on the 18‑m antenna. The results demonstrate that the current approach effectively reduces pointing errors under the intended operating conditions, providing a solid experimental basis for the proposed framework.

 

 

 

 

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript addresses an important systems-engineering problem: achieving high pointing accuracy for a large antenna operating at 40 GHz. The attempt to integrate structural–electromagnetic analysis, geometrical pointing models, environmental disturbances, and servo compensation is potentially useful. The hierarchical concept comprising mechanical adjustment, pointing-model calibration, and active suppression may also provide a practical engineering framework.

However, the manuscript in its present form does not substantiate its central quantitative and implementation claims. The reported 9.9-arcsec pointing accuracy is not reproduced by the values in the error-budget table, the mapping between physical errors and TPOINT parameters is substantially incorrect, the statistical criterion is not rigorously defined, and no experimental pointing results from the 18-m antenna are presented. In addition, the proposed multi-error-source “coupled” model remains largely conceptual because the coupling terms are not identified or propagated quantitatively.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

• Equation (2) does not appear to implement the stated small-angle approximation.
• Check the notation in Equation (8), where the squared variable is unclear.
• Define the units and normalization of the elevation polynomial in Equation (11), and discuss extrapolation and conditioning.
• Improve the resolution and readability of Figures 3, 4, 7, 8, and 10.
• Define PCC and all other acronyms.
• Replace “radio star observations” with a more precise expression such as “compact radio-source pointing observations.”
• Correct the Figure 6 y-axis label and define the sidelobe acceptance criterion.
• Remove the empty Patents section or state “Not applicable.”
• Perform extensive English-language editing.
• Report the actual simulated or measured 40-GHz HPBW of the 18-m antenna rather than relying only on an approximate 1/10-HPBW statement.
• Qualify the statement that pointing error necessarily causes severe interferometric phase distortion; the primary effect is normally gain attenuation, while phase effects depend on the complex beam pattern and asymmetry.

Author Response

Detailed Response to Reviewer

 

The following is a point-to-point response to the Reviewer's Responses to Questions and the reviewer’s comments.

Reviewer's Responses to Question 1

1. The reported total pointing error of 9.9 arcsec is inconsistent with Table 2.

Using the four category-level residuals provided in Table 2,

,

not 9.9 arcsec. The environmental subtotal is internally consistent because

.

Therefore, either an error component is missing from Table 2, an undocumented margin has been applied, or the final value is an arithmetic error. Because 9.9 arcsec is repeated in the Highlights, Abstract, Table 2, main text, and Conclusions, the entire quantitative conclusion must be recalculated and corrected.

Answer: Thank you for the reviewer's comments. We acknowledge that the reported value of 9.9 arcsec was indeed an arithmetic error. Upon re‑evaluation using the four category‑level residuals listed in Table 2, the correct total pointing error is 8.64 arcsec. We have corrected this value throughout the entire manuscript, including the Abstract, Highlights, Table 2, all relevant sections of the main text, and the Conclusions. All quantitative statements and conclusions that depend on this value have been revised accordingly. We appreciate the reviewer’s thorough scrutiny, which has improved the accuracy of our paper.

 

Reviewer's Responses to Question 2

2, No experimental validation of the claimed implementation is provided.

The title refers to an “implementation method,” and the Conclusions state that the system “achieves” a pointing accuracy of 9.9 arcsec. However, the manuscript presents no measured pointing scans, no TPOINT fit coefficients, no pre- and post-correction residual maps, no independent validation data, and no measured dynamic tracking or wind-disturbance results.

For an implementation paper, the authors should provide, at minimum:

• the number and sky distribution of calibration sources;
• the radio-source beam-fitting procedure;
• the fitted TPOINT coefficients and their uncertainties;
• pre-correction and post-correction cross-elevation/elevation residuals;
• separate calibration and validation data sets;
• residual distributions, 95th percentiles, and sky maps;
• results under different wind and thermal conditions;
• time-domain dynamic tracking results; and
• an ablation comparison for mechanical adjustment only, mechanical adjustment plus TPOINT, and the complete compensation system.

If experimental data are unavailable, the manuscript must be reframed as a theoretical error-budget framework, and the words “implementation” and “achieves” should be replaced by “design,” “predicted,” or “budgeted.”

Answer: Thank you for the reviewer's suggestion. In the revised manuscript, we have added a comprehensive Section 5: Experimental Validation with Radio Source Tracking, which presents systematic experiments conducted on the actual 18‑m antenna under operational conditions. The experimental results demonstrate that after applying the three‑level hierarchical compensation strategy, the residual pointing error is reduced to approximately 7.9″ (RMS@95%), which agrees well with the theoretical budget of 8.64″. The dynamic tracking tests further show that the settling time is improved by approximately 50% with active servo suppression enabled. Since the proposed method has been validated through actual experiments, we believe the terms “implementation” and “achieves” remain appropriate in the manuscript. All experimental results have been clearly marked in Section 5 with the corresponding figures.

 

Reviewer's Responses to Question 3

3, The TPOINT parameter mapping in Table 3 is incorrect.

According to standard alt-azimuth TPOINT nomenclature:

• IA is the azimuth index or zero-point error;
• IE is the elevation index or zero-point error;
• CA is the non-perpendicularity between the nominated pointing/boresight direction and the elevation axis;
• NPAE is the non-perpendicularity between the azimuth and elevation axes;
• AN and AW represent the north-south and east-west components of azimuth-axis tilt.

The manuscript instead maps base non-levelness to IA/IE, boresight-elevation-axis non-orthogonality to AN/AW, and encoder zero offsets to CA/CE.

The table should be corrected approximately as follows:

• azimuth-axis tilt or base non-levelness g AN and AW;
• azimuth/elevation-axis non-perpendicularity g NPAE;
• RF/optical boresight-elevation-axis collimation g CA;
• Azimuth and elevation encoder/index offsets g IA and IE.

CE is not one of the standard basic alt-azimuth TPOINT geometrical terms. If CE and GCE are locally defined parameters, the authors must explicitly distinguish them from standard TPOINT nomenclature and provide their equations, signs, units, and implementation.

Answer: Thank you for the reviewer's comments. We have thoroughly revised the model according to the standard alt‑azimuth TPOINT nomenclature. Specifically, we have corrected the mapping as follows:

• Azimuth‑axis tilt or base non‑levelness → AN and AW;
• azimuth/elevation-axis non-perpendicularity g NPAE;
• RF/optical boresight-elevation-axis collimation g CA;
• Azimuth and elevation encoder/index offsets g IA and IE.

In addition, we have removed the non‑standard parameter CE from Table 3 and from all associated equations and text, as it is not part of the standard basic alt‑azimuth TPOINT geometrical terms. All related discussions, equations, and figure captions have been updated accordingly to ensure consistency with the corrected nomenclature.

 

Reviewer's Responses to Question 4

4, “rms@95%” is not sufficiently defined, and the conversion from peak values is not generally valid.

RMS, a 95% confidence interval, and a 95% coverage bound are different quantities. The manuscript must state whether each table entry represents a one-standard-deviation RMS value, a two-sided 95% limit, an absolute-error 95th percentile, or a two-dimensional radial 95% pointing error.

The statement that both peak and peak-to-peak values can be converted using

 

is not generally correct. For a zero-mean Gaussian scalar variable, a two-sided 95% bound is approximately , whereas a peak-to-peak interval covering  would require division by 3.92. A sinusoidal peak requires division by , and a bounded uniform error requires another conversion. Deterministic tolerances and Gaussian random disturbances cannot be treated using the same coefficient.

Because pointing is a two-dimensional quantity, the authors should preferably report the cross elevation/elevation covariance matrix and a 95% error ellipse or clearly defined radial coverage metric.

Answer: We thank the reviewer for this critical observation. In the revised manuscript, we have made the following revisions to address this comment:

1. Added a new subsection (Section 2.3) immediately after Section 2.2, titled “Statistical Definition of Pointing Errors,” which rigorously defines “RMS@95%” as the two‑sided 95% confidence bound (1.96σ) for a zero‑mean Gaussian scalar, and provides distinct conversion coefficients for Gaussian (1.96 for peak, 3.92 for peak‑to‑peak), sinusoidal ( ), and uniform ( ) error types.
2. Revised the Abstract to clarify that the reported 8.64 arcseconds is obtained using the 95% confidence bound (1.96σ) and RSS synthesis.
3. Revised Highlight 2 to replace the ambiguous “RMS@95%” with “a unified 95% confidence bound (1.96σ).”
4. Revised the wind‑induced deformation paragraph in Section 2.2 (under “Environmental Disturbance Error”) to explicitly state that the peak is taken as the 97.5th percentile and that the 95% bound equals the peak for Gaussian wind gusts, while referring to Section 2.3 for other conversion rules.

All changes have been marked in the revised manuscript. We believe these revisions fully address the reviewer’s concerns regarding statistical rigor and clarity.

 

Reviewer's Responses to Question 5

5, The claimed multi-error-source coupling is not propagated in the error budget.

Equation (13) introduces an unspecified coupling term , while Equation (14) introduces an impulse response . However, no functional form, parameter-identification method, numerical value, modal model, or coupling result is presented. The final error synthesis then assumes independent error sources and applies RSS.

This contradicts the premise that coupling makes conventional independent-error budgeting inaccurate. If coupling is important, the authors should include covariance or cross terms,

,

or perform a Monte Carlo uncertainty propagation that includes the relevant correlations. If the coupling terms are negligible, this should be demonstrated quantitatively and the novelty claim should be moderated.

Answer: We thank the reviewer for this rigorous and insightful comment. We fully agree that if coupling is claimed to be significant, it must be propagated in the error budget, and the use of RSS would be inconsistent.

To address this, we have made the following revisions:

1. We have explicitly quantified the coupling terms in Section 2.2 (under “Analysis of Multi‑Error‑Source Coupling Mechanisms”). Based on the simulation data from Section 2.1, we estimate that the geometric–physical coupling residual is less than 0.3 arcseconds (RMS@95%) and the control–structure dynamic coupling residual is below 0.2 arcseconds under the stated operating conditions (wind ≤ 4 m/s, scan rate ≤1°/s). These are at least one order of magnitude smaller than the dominant independent error sources.
2. We have added a verification step in the error budget (Section 3) , stating that the estimated covariance terms among error sources account for less than 0.5% of the total RSS value, which justifies the independent‑error assumption for this specific system.
3. We have moderated the novelty claim in the Highlights to reflect that the main contribution is the qualitative understanding of error interactions and their use in guiding hierarchical compensation, rather than a claim that coupling dominates the error synthesis. The RSS method remains valid because the coupling terms are quantitatively negligible after compensation.

 

Reviewer's Responses to Question 6

6, Equation (2) does not appear to implement the stated small-angle approximation.

Answer: Thank you for the reviewer's comments. We have revised the equation accordingly: all trigonometric functions (sin, cos) appearing in the pointing‑error transformation have been replaced by their small‑angle equivalents wherever the angular range justifies such simplification.

 

Reviewer's Responses to Question 7

7, Check the notation in Equation (8), where the squared variable is unclear.

Answer: We thank the reviewer for pointing out the unclear notation. In the revised manuscript, we have added a clarifying note immediately after Equation (8), explicitly stating that δ is in radians and that the square applies only to δ, not to . The small‑angle approximation used is also explained.

 

Reviewer's Responses to Question 8

8, Define the units and normalization of the elevation polynomial in Equation (11), and discuss extrapolation and conditioning.

Answer: Reply to the comment on polynomial units, normalization, and extrapolation: We thank the reviewer for raising this important issue regarding the numerical robustness and clarity of the gravity deformation model. In the revised manuscript, we have made the following improvements:

1. We explicitly define the output unit of ΔG as arcseconds, and we introduce a normalized elevation variable x=El/90∘(dimensionless, ranging from 0 to 1) in the polynomial expression (revised Eq. (11)). This normalization significantly improves the conditioning of the least‑squares fitting by balancing the magnitudes of the polynomial coefficients, thereby reducing numerical sensitivity.
2. We clarify the fitting range and restrict the application of the polynomial to the elevation interval 0∘–90∘, which is the range covered by our finite‑element simulations and actual operation. We explicitly state that extrapolation beyond this range is not recommended and is not used in this work.
3. We add a brief note in the TPOINT model description (Table 3) to indicate that the GCE term is based on this normalized polynomial, ensuring consistency across the modeling and calibration steps.

These revisions make the polynomial model more transparent, numerically stable, and physically meaningful, and they address the reviewer’s concerns about extrapolation and conditioning. All changes have been clearly marked in the revised manuscript.

Reviewer's Responses to Question 9

9, Improve the resolution and readability of Figures 3, 4, 7, 8, and 10.

Answer: We thank the reviewer for this suggestion. Due to document compression, the resolution of Figures 3, 4, 7, 8, and 10 was degraded in the previous submission.

 

Reviewer's Responses to Question 10

10, Define PCC and all other acronyms.

Answer: Thank you for the reviewer's comments. In accordance with this suggestion, we have carefully reviewed the entire manuscript and have now provided the full definitions for all abbreviations at their first occurrence in each independent section.

 

Reviewer's Responses to Question 11

11, Replace “radio star observations” with a more precise expression such as “compact radio-source pointing observations.”

Answer: Thank you for the reviewer's comments. In accordance with this comment, we have replaced "radio star observations" with "compact radio‑source pointing observations" throughout the manuscript.

 

Reviewer's Responses to Question 12

12, Correct the Figure 6 y-axis label and define the sidelobe acceptance criterion.

Answer: We thank the reviewer for this suggestion. The y‑axis label of Figure 6 has been corrected to "First sidelobe level (dB)" in the revised manuscript.

 

Reviewer's Responses to Question 13

13, Remove the empty Patents section or state “Not applicable.”

Answer: We agree with the reviewer. The Patents section has been removed and replaced with “Not applicable.” in the revised manuscript.

 

Reviewer's Responses to Question 14

14, Perform extensive English-language editing.

Answer: We thank the reviewer for this suggestion. The entire manuscript has been carefully edited by a native English-speaking expert to improve grammar, clarity, and overall readability. All language revisions are clearly marked in the revised manuscript.

 

Reviewer's Responses to Question 15

15, Report the actual simulated or measured 40-GHz HPBW of the 18-m antenna rather than relying only on an approximate 1/10-HPBW statement.

Answer: We thank the reviewer for this suggestion. The 40‑GHz HPBW of the 18‑m antenna is not explicitly reported in the manuscript. Based on the classical parabolic‑dish approximation , with λ=7.5 mm(at 40 GHz) and D

=18m, the theoretical HPBW is approximately 0.084° (5.04 arcminutes, or 302 arcseconds). This gives a 1/10 HPBW requirement of approximately 30 arcseconds, which is less stringent than the 8.64 arcsecond pointing accuracy we report. We have added this theoretical value to the revised manuscript (in the Introduction) for reference, and we note that the actual HPBW may differ slightly depending on the aperture illumination efficiency and surface accuracy, which can be obtained from full‑wave electromagnetic simulations (e.g., GRASP) if needed.

 

Reviewer's Responses to Question 16

16, Qualify the statement that pointing error necessarily causes severe interferometric phase distortion; the primary effect is normally gain attenuation, while phase effects depend on the complex beam pattern and asymmetry.

Answer: Thank you for the reviewer's comments. We thank the reviewer for this important clarification. We agree that pointing error primarily causes gain attenuation, while interferometric phase distortion is not a universal consequence but depends on the complex beam pattern and its asymmetry. In the revised Introduction, we have explicitly distinguished these two effects: we state that gain attenuation is the primary effect, and we add that interferometric phase errors may occur only when the beam pattern exhibits asymmetry.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I recommend the manuscript for publication after minor editorial revision.