- Original Article
- Open Access
Effect of Facet Displacement on Radiation Field and Its Application for Panel Adjustment of Large Reflector Antenna
- Wei WANG^{1, 2},
- Peiyuan LIAN^{1},
- Shuxin ZHANG^{1, 2}Email author,
- Binbin XIANG^{1, 3} and
- Qian XU^{3}
https://doi.org/10.1007/s10033-017-0135-z
© The Author(s) 2017
Received: 9 May 2016
Accepted: 2 April 2017
Published: 13 April 2017
Abstract
Large reflector antennas are widely used in radars, satellite communication, radio astronomy, and so on. The rapid developments in these fields have created demands for development of better performance and higher surface accuracy. However, low accuracy and low efficiency are the common disadvantages for traditional panel alignment and adjustment. In order to improve the surface accuracy of large reflector antenna, a new method is presented to determinate panel adjustment values from far field pattern. Based on the method of Physical Optics (PO), the effect of panel facet displacement on radiation field value is derived. Then the linear system is constructed between panel adjustment vector and far field pattern. Using the method of Singular Value Decomposition (SVD), the adjustment value for all panel adjustors are obtained by solving the linear equations. An experiment is conducted on a 3.7 m reflector antenna with 12 segmented panels. The results of simulation and test are similar, which shows that the presented method is feasible. Moreover, the discussion about validation shows that the method can be used for many cases of reflector shape. The proposed research provides the instruction to adjust surface panels efficiently and accurately.
Keywords
- Reflector antennas
- Surface accuracy
- Radiation field
- Reflector antenna mechanical factors
- Electromechanical effects
- Panel adjustment
- Singular value decomposition (SVD)
1 Introduction
There are many methods to improve surface accuracy. A traditional method for panel adjustment is to measure the targets on the panel using theodolite and tape technique [7]. This kind of method takes much time with lower precision. Nowadays, many industrial measuring systems such as laser ranger are broadly used in panel adjustment [8, 9]. “Radio holography” is an advanced method to measure and adjust surface panels. This method makes use of a well-known relationship in antenna theory: the far-field radiation pattern of reflector antenna is the Fourier transformation of the field distribution in the aperture plane of antenna. Note that this relationship applies to the amplitude/phase distributions, not to the power pattern. Thus, if we can measure the radiation pattern, in amplitude and phase distribution in the antenna aperture plane with an acceptable spatial resolution. BENNETT, et al [10] presented a sufficiently detailed analysis of this method to draw the attention of radio astronomers. SCOTT and RYLE [11] used the new Cambridge 5 km array to measure the shape of four of the eight antennas, using a celestial radio point source and the remaining antennas to provide the reference signal Simulation algorithms were developed by RAHMAT-SAMII [12] and others [13–16], adding to the practicability of the method. Using the giant water vapour maser at 22 GHz in Orion as a source, MORRIS, et al [17] achieved a measurement accuracy of 30 microns and were set the surface of the IRAM 30 m millimeter telescope to an accuracy of better than 100 microns. NIKOLIC, et al [18] described phase-retrieval holography measurements of the 100-m diameter Green Bank Telescope using astronomical sources and produced low-resolution maps of the wavefront errors. YU [19] used radio holography to correct the surface profile of the Sheshan 25-m radio telescope. Moreover, SUBRAHMANYAN [20] presented the photogrammetry in antenna metrology and proposed that the complete antenna optics have been jointly surveyed at different elevation settings for the antenna with gravity deformation.
MARTINEZ-LORENZO, et al [21] investigated near field data and reconstructed the deformed reflector surface using least square method. TANAKA, et al [22] estimated the surface error of a space reflector antenna, and corrected its influence based on antenna gain analyses. HOERNER [23] calculated panel adjustment of four-cornered panels with least square method considering internal twist in surface plate of reflector antenna. In order to keep the same wave front, DAI, et al [24] derived a method to calculate the adjustment for segmented panels of space reflector. ZHOU, et al [25] developed a new technique of contour adjustment for high precision sandwich reflector panels. The core technologies are proposed to obtain the adjustors’ position and number.
In this research, a new method based on far field pattern of reflector antenna is proposed to improve the efficiency and accuracy of surface adjustment. In Sect. 1, the linear relationship between surface facet displacement in panel and electric field in far region is derived by using the method of PO. Then in Sect. 3, panel adjustment values are described as function of electric field variation with series of linear equations. The results are obtained by solving the equations with SVD. Consequently, the panel adjustment simulations and experiment results analysis are presented in Sect. 4, followed by discussions and conclusions.
2 Computation of Far Field with PO
3 Determination of Adjustment Value
3.1 Radiation Field with Facet Displacement
Based on Eq. (10), if all triangle facets displaced in the whole reflector, the influence of facet displacement on the radiation field forms a linear system.
3.2 Relationship Between Adjustment and Displacement
Actually, reflector panels are designed for curve fitting to a parabolic surface. As a result, facet displacement includes components in three different directions when different adjustors adjusted. Therefore, the whole offset vector is the superposition of three components.
3.3 Modeling of Linear System
3.4 Solution of Linear Equations Using SVD
4 Experiment and Analysis
4.1 Experimental Results and Analysis
According to PO, the surface is meshed into lots of triangle facets. The size of each facet is less than λ/4, therefore there are totally 262848 triangle facets all over the reflector surface. Utilizing the method mentioned above, the radiation field with and without facet displacements are calculated. At the same time, the electric field in far region is also tested.
Electrical performance comparison between simulation and experiment results
Performance | A_{0} | B_{0} | Error | A_{1} | B_{1} | Error |
---|---|---|---|---|---|---|
Gain (dB) | 52.84 | 52.23 | 0.61 | 52.21 | 52.00 | 0.21 |
HPBW (°) | 0.390 | 0.380 | 0.01 | 0.48 | 0.49 | 0.01 |
Left SLL (dB) | −14.33 | −14.54 | 0.21 | −17.3 | −17.8 | 0.5 |
Right SLL (dB) | −14.33 | −14.18 | −0.15 | −13.85 | −12.53 | −1.32 |
4.2 Simulations for Panel Adjustment
From Eq. (23), a vector of adjustment value can be obtained. Since the transformation matrix M is generally not a full rank matrix, the solution is not exclusive in Eq. (21). The adjustment values are not in accordance with the thickness of testing gaskets, because different panel positions have probably the same corresponding far field pattern. However, in practice, a feasible solution means that the electrical performance can be improved as well as possible with panel adjustment only once.
4.3 Discuss of the Validity Range
Error analysis for the linearization using Eq. ( 10 )
δ/rad | cosδ/% | sin δ/% | |E|/% | ɛ |
---|---|---|---|---|
−0.316 7~ + 0.316 7 | 5.23 | 1.69 | 5 | λ/40 |
−0.448 5~ + 0.448 5 | 10.98 | 3.43 | 10 | λ/28 |
−0.55~ + 0.55 | 17.3 | 5.23 | 15 | λ/23 |
Parameters of piecewise linear function for fitting real parts in Eq. (25) with p = 4 and q = 4
Amount of piecewise lines p | Phase error δ/rad | Path length error ɛ/λ | Parameter a | Parameter b | Fitting error e |
---|---|---|---|---|---|
1 | [−3.14, −1.86) | [−0.250, −0.148) | 0.977 8 | 0.713 4 | 0.049 4 |
2 | [−1.86, −1.58) | [−0.148, −0.126) | 1.562 3 | 0.995 5 | 0.011 9 |
3 | [−1.58, −1.49) | [−0.126, −0.119) | 1.574 6 | 1.003 | 0.04 |
4 | [−1.49, −0.73) | [−0.119, −0.058) | 1.413 9 | 0.883 1 | 0.049 3 |
5 | [−0.73, 0.37) | [−0.058, 0.029) | 0.965 4 | 0.173 6 | 0.049 4 |
6 | [0.37, 1.32) | [0.029, 0.105) | 1.256 2 | −0.731 | 0.048 2 |
7 | [1.32, 1.56) | [0.105, 0.124) | 1.558 8 | −0.992 5 | 0.012 5 |
8 | [1.56, 1.68) | [0.124, 0.134) | 1.576 2 | −1.004 | 0.040 6 |
9 | [1.68, 2.61) | [0.134, 0.208) | 1.327 | −0.87 | 0.048 9 |
10 | [2.61, 4.1) | [0.208, 0.326) | 1.167 3 | −0.765 6 | 0.049 6 |
Parameters of piecewise linear function for fitting Imaginary parts in Eq. (25) with p = 4 and q = 4
Amount of piecewise lines q | Phase error δ/rad | Path length error ɛ/λ | Parameter c | Parameter d | Fitting error e |
---|---|---|---|---|---|
1 | [−3.14, −3.03) | [−0.250, −0.241) | −3.646 3 | −1.184 4 | 0.045 |
2 | [−3.03, −2.49) | [−0.241, −0.198) | −3.115 3 | −1.005 1 | 0.049 6 |
3 | [−2.49, −1.41) | [−0.198, −0.112) | −1.606 4 | −0.371 4 | 0.049 9 |
4 | [−1.41, −0.39) | [−0.112, −0.031) | −0.204 4 | 0.605 2 | 0.048 7 |
5 | [−0.39, −0.01) | [−0.031, −0.001) | −0.002 1 | 0.976 4 | 0.035 |
6 | [−0.01, 0.01) | [−0.001, 0.001) | 0 | 1 | 0 |
7 | [0.01, 0.44) | [0.001, 0.035) | 0.003 | 0.970 1 | 0.047 8 |
8 | [0.44, 1.48) | [0.035, 0.118) | 0.246 6 | 0.557 8 | 0.049 2 |
9 | [1.48, 2.54) | [0.118, 0.202) | 1.700 1 | −0.417 7 | 0.048 9 |
10 | [2.54, 3.04) | [0.202, 0.242) | 3.150 2 | −1.017 3 | 0.042 9 |
11 | [3.04, 3.29) | [2.61, 4.1) | 3.760 3 | −1.221 3 | 0.048 2 |
5 Conclusions
- (1)
According to the method of PO, the effect model of facet displacement on the electric field in far region of reflector antenna is developed. Thus, the equation of integral for calculating far field pattern of antenna with distorted surface is transformed into a summation of many displaced facets.
- (2)
A linear system is constructed for calculating panel adjustment values. And then SVD is used to solve the linear equations. As a result, all adjustment values of panel adjustors are obtained. Therefore, the accuracy of reflector surface is improved significantly because the actual target of panel adjustment is to make the electrical performance better.
- (3)
A reflector antenna with 3.7 m diameter and 12 panels is taken to verify the effect model between facet displacement and radiation field. With sets of experiments, the method shows a good performance, and a good agreement is found between the simulation curves and experimental curves as well. The results verify the efficiency of presented method which has such an advantage that all panels over the reflector surface are adjusted as a whole.
- (4)
For larger phase error, the exponential function can be approximated with 4 piecewise lines and the fitting error is less than 5%. The validation range of the method is expanded by using piecewise lines to fit the exponential function.
Notes
Declarations
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
References
- RAHMAT-SAMII Y, DENSMORE A. Reflector antenna developments: a perspective on the past, present, and future[J]. IEEE Antennas and Propagation Magazine, 2015, 57(2): 85–95.Google Scholar
- WIJNHOLDS S J, TOL S V D, NIJBOER R, et al. Calibration challenges for future radio telescopes[J]. IEEE Signal Processing Magazine, 2010, 27(1): 30–42.Google Scholar
- USOFF J M, CLARKE M T, LIU Chao, et al. Optimizing the HUSIR antenna surface[J]. Lincoln Laboratory Journal, 2014, 21(1): 83–105Google Scholar
- LENG Guojun, WANG Wei, DUAN Baoyan, et al. Field-coupling model of reflector antenna with electromagnetic and displacement fields and its application to reflector antenna with the diameter of 65 m[J]. Chinese Journal of Mechanical Engineering, 2012, 48(23): 1–9. (in Chinese)Google Scholar
- WANG Meng, WANG Wei, WANG Congsi, et al. A practical approach to evaluate the effects of machining errors on the electrical performance of reflector antennas based on paneled forms[J]. IEEE Antennas Wireless and Propagation Letters, 2014, 13: 1341–1344.Google Scholar
- LIAN Peiyuan, DUAN Baoyan, WANG Wei, et al. A mesh refinement method of reflector antennas using quadratic surface construction over each structure element[J]. IEEE Antennas Wireless and Propagation Letters, 2014, 13: 1557–1560.Google Scholar
- KESTEVEN M J, PARSONS B F, YABSLEY D E. Antenna Reflector metrology: the australia telescope experience[J]. IEEE Transaction on Antennas and Propagation, 1988, 36(10): 1481–1484.Google Scholar
- IMBRIALE W A, BRITCLIFFE M J, BRENNER M. Gravity deformation measurement of NASA’s deep space network 70-meter reflector antennas[R]. JPN Progress Report, 2001: 42–127.Google Scholar
- WANG Jinjiang, YANG Zhiwen. A Surface measurement system from China for large antennas[J]. IEEE Instrumentation & Measurement Magazine, 2002, 5(1): 20–22.Google Scholar
- BENNETT J C, ANDERSON A P, MCINNES P A, et al. Microwave holographic metrology of large reflector antennas[J]. IEEE Transaction on Antennas and Propagation, 1976, 24(3): 295–303.Google Scholar
- SCOTT P F, RYLE M. A Rapid Method for measuring the figure of a radio telescope reflector[J]. Monthly Notices Roy. Astron. Soc., 1977, 178: 539–545.Google Scholar
- RAHMAT-SAMII Y. Microwave holography of large reflector antennas – simulation algorithms[J]. IEEE Transaction on Antennas and Propagation, 1985, 33(11): 1194–1203.Google Scholar
- GODWIN M P, SCHOESSOW E P, GRAHL B H. Improvement of the Effelsberg 100 meter telescope based on holographic reflector surface measurement[J]. Astronomy and Astrophysics, 1986, 167: 390–394.Google Scholar
- ROCHBLATT D J, SEIDEL B L. Microwave antenna holography[J]. IEEE Transaction on Microwave Theory and Techniques, 1992, 40(6): 1 249–1 300.Google Scholar
- JAMES G C, POULTON G T, MCCULLOCH P M. Panel setting from microwave holography by the method of successive projections[J]. IEEE Transaction on Antennas and Propagation, 1993, 41(11): 1523–1529.Google Scholar
- LEGG T H, AVERY L W, MATTHEWS H E, et al. Gravitational deformation of a reflector antenna measurement with single-receiver holography[J]. IEEE Transaction on Antennas and Propagation, 2004, 52(1): 20–25.Google Scholar
- MORRIS D, BAARS J W M, HEIN H, et al. Radio-holographic reflector measurement of the 30-m millimeter radio telescope at 22 GHz with a cosmic signal source[J]. Astronomy and Astrophysics, 1998, 203: 399–406.Google Scholar
- NIKOLIC B, PRESTAGE R M, BALSER D S, et al. Out-of-focus Holography at the green bank telescope[J]. Astronomy and Astrophysics, 2007, 465: 685–693.Google Scholar
- YU Hong. Microwave holography measurement and adjustment of 25 m radio telescope of Shanghai[J]. Microwave and Optical Technology Letters, 2007, 49(2): 467–470.Google Scholar
- SUBRAHMANYAN R. Photogrammetric measurement of the gravity deformation in a Cassegrain antenna[J]. IEEE Transaction on Antennas and Propagation, 2005, 53(8): 2590–2596.Google Scholar
- MARTINEZ-LORENZO J A, GONZALEZ-VALDES B, RAPPAPORT C, et al. Reconstructing distortions on reflector antennas with the iterative-field-matrix method using near-field observation data[J], IEEE Transactions on Antennas and Propagation, 2011, 59(6): 2434–2437.Google Scholar
- TANAKA H. Surface error estimation and correction of a space antenna based on antenna gain analyses[J]. Acta Astronautica, 2011, 68: 1062–1069.Google Scholar
- HOERNER S. Internal twist and least-squares adjustment of four-cornered surface plate for reflector antennas[J]. IEEE Transactions on Antennas and Propagation, 1981, 29(6): 953–958.Google Scholar
- DAI Yanfeng, LIU Zaozhen. Research on cophasing optimized algorithms for space-based telescope segmented primary mirror[J]. Optical Technique, 2008, 34(3): 914–916. (in Chinese)Google Scholar
- ZHOU Xianbin, HAO Changling, LI Dongsheng, et al. New technique of contour adjustment for high precision reflector panels[J]. Journal of Beijing University of Aeronautics and Astronautics, 2009, 35(2): 127–131. (in Chinese)Google Scholar
- IMBRIALE W A. Large antennas of the deep space network[M]. 1st ed. New York: John Wiley & Sons, Inc., 2003.Google Scholar
- MARTINEZ-LORENZO J A, PINO A G, VEGA I, et al. ICARA: Induced-current analysis of reflector antennas[J]. IEEE Antenna and Propagation Magazine, 2005, 47(2): 92–100.Google Scholar
- YI Wei, JIANG Zhaoliang, SHAO Weixian, et al. Error Compensation of Thin Plate-shape Part with Prebending Method in Face Milling[J]. Chinese Journal of Mechanical Engineering, 2015, 28(1): 88–95.Google Scholar
- WANG Wei, DUAN Baoyan, LI Peng, et al. Optimal surface adjustment by the error transformation matrix for a segmented reflector antenna[J]. IEEE Antennas and Propagation Magazine, 2010, 52(3): 80–88.Google Scholar
- CHANAN G, MACMARTIN D G, NELSON J, et al. Control and alignment of segmented-mirror telescopes: matrices, modes, and error propagation[J]. Applied Optics, 2004, 43(6): 1223–1232.Google Scholar