the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 06 Dec 2023
The development of a reference corner cube inertial suspension device
Abstract. The seismometer synchronous observation and zero crossing methods are applied to laser interferometer absolute gravimeter to suppress the vibration interference. However, during the synchronous observation of the seismometer and the gravimeter, the observation point of the seismometer does not coincide with the reference corner cube in space, resulting in spatial dislocation, which cannot accurately reflect the vibration state of the reference corner cube. So, it is necessary to hang the reference corner cube on the elastic element to directly measure its vibration acceleration measurement. In this paper, an open-loop reference corner cube inertial suspension device(RCCISD) hanging the reference corner cube was developed based on the principle of seismometer, which is used to measure the vibration acceleration of the reference corner cube of the laser interferometer absolute gravimeter. Experimental test results show that the power spectrum of gravitational acceleration calculated by an interference fringe observed jointly by the RCCISD is about 40 dB lower than that of the reference corner cube directly placed on the ground. RCCISD can restrain the vibration interference to a certain extent, not only can it measure the reference corner cube vibration more accurately than the seismograph synchronous observation method for the vibration compensation of gravity measurement, but also the volume is about 1 / 3 of the Super-Spring volume, which can greatly reduce the height of the gravimeter.
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RC1: 'Comment on gi-2023-16', Anonymous Referee #1, 25 Dec 2023
1 In this paper，the author introduces two transfer fucntions of the RCCISD. The first one is transfer fuction using the shake table test data (see section 4.2 ). The second one is transfer fuction using sinusoidal calibration data(see section 4.3 ). There are difference between these two transfer fuctions, especially from bandwidth 0.1Hz to 10Hz. Why use these two transfer fuctions in this paper? Does these two transfer functions have an impact on subsequent gravity acceleration measurements and experimental data analysis?
2 In section 4.4, during the experimental, where is the RCCISD? Be placed inside the vacuum chamber of the gravimeter? Or just be placed on the ground outside the vacuum chamber of the gravimeter? When the RCCISD was placed on ground outside the vacuum chamber of the gravimeter, Is the vibration acceleration data measured at different positions consistent? See following figure, near the A-pillar or B-pillar in the figure, the amplitude of vibration acceleration may be larger? In the figure, the vibration amplitude at the center position of the four pillar A, B, C, and D is smaller. But the small changes in the vibration acceleration signal measured by RCCISD may have a significant impact on the analysis of the gravity acceleration results of the gravimeter.
3 There are some unclear sentences in the article that need to be carefully revised.
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AC1: 'Reply on RC1', bing zhang, 23 Jan 2024
Thank you very much for your attention to and questions raised in our paper. In response to your questions, I made the following reply and revised the paper. Thanks again.
Answer 1：In section 4.2, The transfer fuction of the RCCISD using the shake table test data is used to roughly determine the natural frequency and frequency response curve of RCCISD, and to provide a reference for setting parameters for sinusoidal calibration.
In section 4.3, The main purpose of sinusoidal calibration test is to more accurately fit the transfer function of RCCISD in the joint experiment of gravimeter and RCCISD, so as to facilitate the more accurate removal of the frequency response of RCCISD in the subsequent gravity acceleration measurement data processing.
In response to your questions, I have added a description of the relevant content. Please see the attachment for details.
Answer 2：In section 4.4, during the experiment, the RCCISD is placed directly on the ground outside the vacuum of the gravimeter. Although the vibration acceleration data of the reference corner cube measured at different positions are different, the experimental scheme in this paper mainly measures the vibration acceleration data of the reference corner cube where the reference corner cube is located during the free fall of the free-falling corner cube. The data is the result of the comprehensive influence of the vibration of A, B, C, D and other positions of the cement pier in the figure, therefore, when the free-falling corner cube falls freely, the vibration of any position except the vibration of the reference corner cube is of no use to the algorithm in this paper.
Answer 3：The unclear sentences in the article have benn carefully revised.Please see the attachment for details.
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AC1: 'Reply on RC1', bing zhang, 23 Jan 2024
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CC1: 'Comment on gi-2023-16', zijian cui, 29 Mar 2024
1.The format of the Table 1 and 2 in the article need to be carefully revised.
2.Figure 7 is a data flow diagram that needs to be modified to meet standard graphical requirements, such as adding start and end boxes.Citation: https://doi.org/10.5194/gi-2023-16-CC1 -
AC2: 'Reply on CC1', bing zhang, 17 Jun 2024
Thank you very much for your attention to and questions raised in our paper. In response to your questions, I made the following reply and revised the paper.Answer 1： I corrected the format of the Table 1 and 2.
Answer 2：I modified Figure 7 to follow the standard process flow chart format.
Please see the attachment for details.Thanks again.
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AC2: 'Reply on CC1', bing zhang, 17 Jun 2024
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CC2: 'Comment on gi-2023-16', Junyan Yang, 12 Jun 2024
In this paper, the vibration data during a free fall in different stages and the PSD of gravitational acceleration calculated by an interference fringe observed jointly by the RCCISD are analyzed. The data analysis is detailed, and the results of magnitude are given for the first time, which is innovative. In view of the paper, I have the following suggestions for revision.
1.the statements "the 500th data in the sequence is one second" and "the peak and peak value" in section 4.5 are inaccurate and need to be revised.
2.It is recommended that the peak-to-peak values in Figure 11 and Figure 12 be comprehensively analyzed.Citation: https://doi.org/10.5194/gi-2023-16-CC2 -
AC3: 'Reply on CC2', bing zhang, 19 Jun 2024
Thank you for your recognition of our work and the questions raised in our paper. In response to your questions, I made the following reply and revised the paper.
Answer 1： I reworked the analysis text for Figure 11.
Answer 2：Combined with Figure 11 and Figure 12, I re-analyzed and described the corresponding data.
Please see the attachment for details.Thanks again.
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AC3: 'Reply on CC2', bing zhang, 19 Jun 2024
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RC2: 'Comment on gi-2023-16', Anonymous Referee #2, 10 Jul 2025
This work develops and characterizes an open-loop Reference Corner-Cube Inertial Suspension Device (RCCISD) that hangs the reference retro-reflector of a laser-interferometer absolute gravimeter on a force-balanced pendulum. The authors report a ≈40 dB reduction of reference-cube vibration above 7 Hz compared with a cube placed rigidly on the pier, while shrinking the isolator to one-third of the FG5 “Super-Spring” size.
I have some comments and questions:
- The authors performed sinusoidal shaker tests over 0.05–10 Hz at 17 discrete frequencies and obtained a fitted sensitivity of 387.7 V·m⁻¹·s; I think it’s important to include uncertainty bars on the Bode plots and to discuss the long-term stability or drift of this calibration constant—could you provide those details?
- Which mechanical component gives rise to the ~150 Hz resonance peak, and is there a way to damp it without compromising low-frequency isolation?
- Regarding thermal stability, I was wondering whether you have measured how temperature affects the suspension’s natural frequency (i.e., the flexure stiffness) as well as the voice-coil/magnet sensitivity.
- Have you characterized the attenuation of horizontal vibrations (and any cross-axis coupling into the vertical measurement) ?
- Have you measured the sensitivity of vertical acceleration read-out to horizontal tilt of the suspension frame?
- A similar idea, suspending the reference cube using a pendulum or spring, may have been explored before in the context of passive vibration isolation systems. It would be interesting to see a comparison with any prior systems, if they exist. How does your approach relate to or differ from those?
Citation: https://doi.org/10.5194/gi-2023-16-RC2
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