CN117494338A - Full-movable radio telescope surface type pre-adjustment calculation method - Google Patents
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01Q—ANTENNAS, i.e. RADIO AERIALS
- H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
- H01Q15/14—Reflecting surfaces; Equivalent structures
- H01Q15/16—Reflecting surfaces; Equivalent structures curved in two dimensions, e.g. paraboloidal
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Abstract
The invention discloses a surface type pre-adjustment calculation method of a full-movable radio telescope, and relates to the field of radio telescopes; the method comprises the following steps: determining static response, including deformation due to dead weight load under a mean-flat working condition and deformation due to dead weight load under a supine working condition; determining the residual half-optical path difference of the caliber surface after the optimal anastomosis; determining a surface type preset quantity with minimum maximum deviation; after the preconditioning is determined, the face accuracy at each pitch angle is determined. According to the invention, under the dead weight load, after deformation of the telescope surface under the working conditions of upward rotation and downward rotation, the residual half-optical path difference of the caliber surface after the optimal anastomosis is calculated, and then the preset amount with the minimum maximum deviation is pushed forward. The surface type adjustment is carried out according to the preset quantity, so that the surface type precision under the whole pitching angle can be improved, and the worst surface type error can be effectively restrained.
Description
Technical Field
The invention relates to the field of radio telescope, in particular to a surface type pre-calculation method of a full-movable radio telescope.
Background
For large radio telescopes, the accuracy of the surface profile constrains the implementation of its electrical properties. In order for a telescope to function properly, its area accuracy must meet certain constraints, for example, the area accuracy is better than 1/20 of the operating wavelength. Deformation caused by dead weight load is unavoidable, and because the dead weight load has the characteristic of predictability, the accuracy of the radio telescope can be improved by calculating the deformation of the reflecting surface under the dead weight and adjusting the panel in advance.
For example, by searching, the large antenna reflecting surface gravity pre-adjusting method based on the optimal adjustment angle disclosed in Chinese patent publication No. CN100574007C and the large antenna reflecting surface gravity pre-adjusting method based on the optimal adjustment angle disclosed in Chinese patent publication No. CN 101179156A.
In practice, the radio telescope does not need to be optimized for accuracy under a certain angle, but only needs to meet accuracy constraints over the entire pitch angle range, and both of the above-mentioned patents improve the plane type accuracy over the pitch angle range to some extent, but neither consider suppressing worst-case plane type errors.
Therefore, the invention provides a surface type pre-adjustment calculation method of a full-movable radio telescope, which is used for minimizing the maximum deviation of the full-movable radio telescope under the dead weight load.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides a surface type pre-adjustment calculation method of a full-movable radio telescope.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a surface type pre-adjustment calculation method of a full-movable radio telescope comprises the following steps:
s1: determining static response, and determining deformation due to dead weight load under a finger-flat working condition and deformation due to dead weight load under a supine working condition;
s2: determining the residual half-optical path difference of the caliber surface after the optimal anastomosis;
s3: determining a preset amount of which the maximum deviation is minimized;
s4: after the preset amount is determined, the face precision at any angle is calculated.
Preferably: the specific steps of the step S1 are as follows:
s11: based on the finite element method, the displacement delta of the reflecting surface of the radio telescope under the working conditions of upward and downward pointing is obtained firstly h And delta z ；
S12: based on the deformation superposition principle, the displacement of the reflecting surface under any pitching angle can be obtained,wherein->Is the pitch angle.
Preferably: in the step S2, the calculation formula of the residual half-path difference of the caliber surface after the optimal anastomosis is as followsWherein ρ is h And ρ z Under the working conditions of upward and downward pointing, the matched half-range difference vector is shown as R, wherein R is a matrix related to the geometrical information of the nodes of the reflecting surface, and is related to the size of the reflecting surface of the radio telescope and is a known value.
Preferably: the specific steps of the step S3 are as follows:
s31: the panel is adjusted so that the reduction of the half-path difference of the aperture surface is delta=beta 1 ρ z +β 2 ρ h Wherein beta is 1 ，β 2 For the parameters to be solved, the value interval is [0,1]；
S32: determining a representation of a half-path difference vector at any pitch angle
S33: the plane deviation at any pitch angle can be expressed in terms of the root mean square value of the half-path difference, that is,wherein (1)>c hz ＝ρ h T Wρ z /N，/> W is a weight matrix, rms h 、rms z Before adjustment, the surface precision under the horizontal working condition and the upward working condition is indicated respectively. c hz Covariance of half optical path difference vector under working conditions of upward and downward;
s34: by traversing beta 1 ，β 2 Obtain different beta values 1 ，β 2 Maximum face bias under combination;
s35: determining the parameter (. Beta.) with the smallest maximum area deviation 1 * ,β 2 * )；
S36: according to the formula Δ=β 1 ρ z +β 2 ρ h And delta n ＝-Δ/cosφ＝-(β 1 * ρ z +β 2 * ρ h ) And (2) cos phi, and obtaining the normal adjustment vector of the corresponding panel node.
Preferably: the step S4 comprises the following specific steps:
s41: according to the formulaIs->The surface type precision at any preset pitching angle can be determined.
Preferably: in the step S34, the method includes the following steps:
S341：β 1 ，β 2 grid points are taken, and a plurality of data pairs (beta 1 ,β 2 )；
S342: each data pair (. Beta.) is then recorded 1 ,β 2 ) Carry to formulaTraversing the whole pitching angle range to obtain the maximum face type deviation corresponding to each grid point;
s343: of all the largest face deviations, the deviation with the smallest value is selected, and the corresponding data pair (beta 1 ,β 2 ) I.e. a parameter (beta) that minimizes the maximum area deviation 1 *,β 2 *)。
Preferably: in the step S342, the grid points are grid points on the two-dimensional orthogonal space [0,1] × [0,1 ].
Preferably: in the step S342, the interval between grid points is 10 -3 。
The beneficial effects of the invention are as follows:
1. according to the invention, the static response is determined, the residual half-optical path difference of the caliber surface after the optimal anastomosis is calculated, and then the preset amount with the minimum maximum deviation is pushed forward, so that the surface type adjustment compensation is carried out according to the preset amount, the surface type precision under the whole pitching angle can be improved, and the worst surface type error is effectively restrained.
Drawings
FIG. 1 is a schematic view of a radio telescope;
FIG. 2 is a schematic flow chart of a method for calculating the surface type presetting calculation of the full-movable radio telescope;
FIG. 3 is a schematic representation of the state of the radio telescope in the up-to-the-ground and flat-finger conditions;
FIG. 4a is a schematic diagram of a two-dimensional radiation Liang Ang day working condition in an example of a surface-type pre-calculation method of a full-movable radio telescope according to the present invention;
fig. 4b is a schematic diagram of a working condition of two-dimensional radiation Liang Zhiping in an example of a surface-type pre-calculation method of a full-movable radio telescope according to the present invention;
FIG. 5 is a schematic diagram showing the deviation of the chord node from the optimal fit parabola in the example of the method for calculating the surface-type preset calculation of the full-movable radio telescope according to the present invention, without using preset, for each pitch angle;
fig. 6 is a comparison of the deviation of each pitching angle under different preset strategies of the error of the chord node deviating from the optimal fit parabola in the example of the surface preset calculation method of the full-movable radio telescope provided by the invention.
Detailed Description
The technical scheme of the patent is further described in detail below with reference to the specific embodiments.
Example 1:
a surface type pre-adjustment calculation method of a full-movable radio telescope comprises the following steps:
s1: determining static response, and determining deformation due to dead weight load under a finger-flat working condition and deformation due to dead weight load under a supine working condition;
s2: determining the residual half-optical path difference of the caliber surface after the optimal anastomosis;
s3: determining a preset amount of which the maximum deviation is minimized;
s4: after the preset amount is determined, the face precision at any angle is calculated.
The specific steps of the step S1 are as follows:
s11: based on the finite element method, the displacement delta of the reflecting surface of the radio telescope under the working conditions of upward and downward pointing is obtained firstly h And delta z ；
S12: based on the deformation superposition principle, the displacement of the reflecting surface under any pitching angle can be obtained,wherein->Is the pitch angle.
In the step S2, the calculation formula of the residual half-path difference of the caliber surface after the optimal anastomosis is as followsWherein ρ is h And ρ z Under the working conditions of upward and downward pointing, the matched half-range difference vector is shown as R, wherein R is a matrix related to the geometrical information of the nodes of the reflecting surface, and is related to the size of the reflecting surface of the radio telescope and is a known value.
The specific steps of the step S3 are as follows:
s31: the panel is adjusted so that the reduction of the half-path difference of the aperture surface is delta=beta 1 ρ z +β 2 ρ h Wherein beta is 1 ，β 2 For the parameters to be solved, the value interval is [0,1]；
S32: determining a representation of a half-path difference vector at any pitch angle
S33: the plane deviation at any pitch angle can be expressed in terms of the root mean square value of the half-path difference, that is,wherein (1)>c hz ＝ρ h T Wρ z /N，/> W is a weight matrix, rms h 、rms z Before adjustment, the surface precision under the horizontal working condition and the upward working condition is indicated respectively. c hz Covariance of half optical path difference vector under working conditions of upward and downward;
s34: by traversing beta 1 ，β 2 Obtain different beta values 1 ，β 2 Maximum face bias under combination;
s35: determining the parameter (. Beta.) with the smallest maximum area deviation 1 *,β 2 *)；
S36: according to the formula Δ=β 1 ρ z +β 2 ρ h And delta n ＝-Δ/cosφ＝-(β 1 * ρ z +β 2 * ρ h ) The normal adjustment vector of the corresponding panel node can be obtained;
the step S4 comprises the following specific steps:
s41: according to the formulaIs->The surface type precision at any preset pitching angle can be determined.
Example 2:
a surface type pre-adjustment calculation method of a full-movable radio telescope comprises the following steps:
s1: determining static response, and determining deformation due to dead weight load under a finger-flat working condition and deformation due to dead weight load under a supine working condition;
s2: determining the residual half-optical path difference of the caliber surface after the optimal anastomosis;
s3: determining a preset amount of which the maximum deviation is minimized;
s4: after the preconditioning is determined, an angle is optionally selected, and then the face accuracy is adjusted.
The specific steps of the step S1 are as follows:
s11: based on the finite element method, the displacement delta of the reflecting surface of the radio telescope under the working conditions of upward and downward pointing is obtained firstly h And delta z ；
S12: based on the deformation superposition principle, can obtainThe displacement of the reflecting surface at the pitch angle is intended,wherein->Is the pitch angle.
In the step S2, the calculation formula of the residual half-path difference of the caliber surface after the optimal anastomosis is as followsWherein ρ is h And ρ z Under the working conditions of upward and downward pointing, the matched half-range difference vector is shown as R, wherein R is a matrix related to the geometrical information of the nodes of the reflecting surface, and is related to the size of the reflecting surface of the radio telescope and is a known value.
The specific steps of the step S3 are as follows:
s31: the panel is adjusted so that the reduction of the half-path difference of the aperture surface is delta=beta 1 ρ z +β 2 ρ h Wherein beta is 1 ，β 2 For the parameters to be solved, the value interval is [0,1]；
S32: determining a representation of a half-path difference vector at any pitch angle
S33: the plane deviation at any pitch angle can be expressed in terms of the root mean square value of the half-path difference, that is,wherein (1)>c hz ＝ρ h T Wρ z /N，/> W is a weight matrix, rms h 、rms z Before adjustment, the surface precision under the horizontal working condition and the upward working condition is indicated respectively. c hz Covariance of half optical path difference vector under working conditions of upward and downward;
s34: by traversing beta 1 ，β 2 Obtain different beta values 1 ，β 2 Maximum face bias under combination;
s35: determining the parameter (. Beta.) with the smallest maximum area deviation 1 *,β 2 *)；
S36: according to the formula Δ=β 1 ρ z +β 2 ρ h And delta n ＝-Δ/cosφ＝-(β 1 * ρ z +β 2 * ρ h ) The normal adjustment vector of the corresponding panel node can be obtained;
the step S4 comprises the following specific steps:
s41 according to the formulaIs->The surface type precision at any preset pitching angle can be determined.
In the step S34, the method includes the following steps:
S341：β 1 ，β 2 grid points are taken, and a plurality of data pairs (beta 1 ,β 2 )；
S342: each data pair (. Beta.) is then recorded 1 ,β 2 ) Carry to formulaTraversing the whole pitching angle range to obtain the maximum face type deviation corresponding to each grid point;
s343: of all the largest face deviations, the deviation with the smallest value is selected, and the corresponding data pair (beta 1 ,β 2 ) I.e. a parameter (beta) that minimizes the maximum area deviation 1 *,β 2 *)。
In the step S342, the grid points are grid points on the two-dimensional orthogonal space [0,1] × [0,1 ].
In the step S342, the interval between grid points is 10 -3 。
According to the invention, the static response is firstly determined, then the residual half-optical path difference of the aperture face after the optimal anastomosis is calculated, and then the preset amount with the minimum maximum deviation is pushed forward, so that the correlation between the aperture face and the pitch angle is regulated and compensated according to the correlation, and the worst face type error can be restrained, and the precision is increased.
The following is the data predicted by the invention with the actual radio telescope, assuming that its upper chord is standard parabolic shape, caliber 6m, focal length 1.8m. The bottom end of the radiation beam is fixed, along with the change of the pitching angle, the radiation beam is always subjected to vertical downward acting force with the magnitude of 50N at 11 stress points, the height of the radiation beam is 2.5m, the thickness is 1mm, the elastic modulus is 1GPa, and the Poisson ratio is 0.3.
According to the pre-adjusting method provided by the invention, firstly, the structural deformation of the radiation beam under the working conditions of upward and downward pointing is calculated, and the precision after the optimal anastomosis is calculated. rms (rms) h ＝0.60mm、rms z ＝0.63mm、c hz =0.3. If the pre-regulation strategy is not considered, i.e. beta 1 ＝β 2 =0, bringing the above parameters intoThe error that the upper chord node of the radiation beam deviates from the optimal fit parabola under any pitching angle can be obtained,
next, based on the pre-tuning method presented herein, a pre-tuning parameter, β, can be obtained that minimizes the maximum deviation 1 *＝0.526，β 2 * =0.536. According toThe surface deviation after preconditioning at different pitch angles can be obtained, see fig. 6, with a maximum deviation of 0.20mm. FIG. 6 also shows the proposed inventionAnd comparing the method with the minimum optimal deviation and the minimum limit angle deviation. When the optimal deviation is minimum, the preset angle is 42.36 DEG, beta 1 ＝sin(42.36)＝0.674，β 2 =0.739, the minimum deviation is 0, and the maximum deviation is 0.31mm. Minimum limit angular deviation beta 1 ＝0.5，β 2 =0.5, the maximum deviation is 0.24mm. The results are summarized in Table 1.
| Pre-tuning strategy | β 1 | β 2 | Maximum deviation/mm |
| Without presetting | 0 | 0 | 0.82 |
| Minimum worst deviation | 0.526 | 0.536 | 0.20 |
| Minimum optimum deviation | 0.674 | 0.739 | 0.31 |
| Minimum limit angle deviation | 0.500 | 0.500 | 0.24 |
It can be seen that the method of the present invention is effective in reducing the worst bias, which indicates the effectiveness of the method.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art, who is within the scope of the present invention, should make equivalent substitutions or modifications according to the technical scheme of the present invention and the inventive concept thereof, and should be covered by the scope of the present invention.
Claims (8)
1. The surface type pre-adjustment calculation method of the full-movable radio telescope is characterized by comprising the following steps of:
s1: determining static response, and determining deformation due to dead weight load under a finger-flat working condition and deformation due to dead weight load under a supine working condition;
s2: determining the residual half-optical path difference of the caliber surface after the optimal anastomosis;
s3: determining a preset amount of which the maximum deviation is minimized;
s4: and determining the preset amount and calculating the surface precision under any angle.
2. The method for calculating the surface preset of the full-mobile radio telescope according to claim 1, wherein the specific steps of the step S1 are as follows:
s11: based on the finite element method, the displacement delta of the reflecting surface of the radio telescope under the working conditions of upward and downward pointing is obtained firstly h And delta z ；
S12: based on the deformation superposition principle, the displacement of the reflecting surface under any pitching angle can be obtained,wherein->Is the pitch angle.
3. The method for pre-calculation of total movable radio telescope surface type according to claim 1, wherein in said step S2, the calculation formula of the best-fit aperture surface residual half-optical path difference isWherein ρ is h And ρ z Under the working conditions of upward and downward pointing, the matched half-range difference vector is shown as R, wherein R is a matrix related to the geometrical information of the nodes of the reflecting surface, and is related to the size of the reflecting surface of the radio telescope and is a known value.
4. The method for calculating the surface preset of the full-mobile radio telescope according to claim 1, wherein the specific steps of the step S3 are as follows:
s31: the panel is adjusted so that the reduction of the half-path difference of the aperture surface is delta=beta 1 ρ z +β 2 ρ h Wherein beta is 1 ，β 2 For the parameters to be solved, the value interval is [0,1]；
S32: determining a representation of a half-path difference vector at any pitch angle
S33: the plane deviation at any pitch angle can be expressed in terms of the root mean square value of the half-path difference, that is,wherein (1)>c hz ＝ρ h T Wρ z /N，/> W is a weight matrix, rms h 、rms z Before adjustment, the surface precision under the horizontal working condition and the upward working condition is indicated respectively. c hz Covariance of half optical path difference vector under working conditions of upward and downward;
s34: by traversing beta 1 ，β 2 Obtain different beta values 1 ，β 2 Maximum face bias under combination;
s35: determining the parameter (. Beta.) with the smallest maximum area deviation 1 * ,β 2 * )；
S36: according to the formula Δ=β 1 ρ z +β 2 ρ h And delta n ＝-Δ/cosφ＝-(β 1 * ρ z +β 2 * ρ h ) And (2) cos phi, and obtaining the normal adjustment vector of the corresponding panel node.
5. The method for calculating the surface preset of the full-mobile radio telescope according to claim 1, wherein the step S4 comprises the following specific steps:
s41: according to the formulaIs->The surface type precision at any preset pitching angle can be determined.
6. The method of calculating the surface preset of the full-mobile radio telescope according to claim 4, wherein in the step S34, the method comprises the steps of:
S341：β 1 ，β 2 grid points are taken, and a plurality of data pairs (beta 1 ,β 2 )；
S342: each data is toCouple (. Beta.) 1 ,β 2 ) Carry to formulaTraversing the whole pitching angle range to obtain the maximum face type deviation corresponding to each grid point;
s343: of all the largest face deviations, the deviation with the smallest value is selected, and the corresponding data pair (beta 1 ,β 2 ) I.e. a parameter (beta) that minimizes the maximum area deviation 1 * ,β 2 * )。
7. The method according to claim 6, wherein in the step S342, the grid points are grid points on a two-dimensional orthogonal space [0,1] × [0,1 ].
8. The method of claim 6, wherein in the step S342, the grid point interval is 10 -3 。
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101013775A (en) * | 2006-12-22 | 2007-08-08 | 西安电子科技大学 | Method for adjusting precision of antenna surface based on multidimensional unconstrained optimization |
| CN101179156A (en) * | 2007-12-05 | 2008-05-14 | 西安电子科技大学 | Optimum setting angle based large-scale antenna reflecting plane gravity pre-regulation method |
| CN103926548A (en) * | 2014-04-18 | 2014-07-16 | 中国科学院新疆天文台 | Method for quickly measuring precision of reflection face of radiotelescope |
| CN105930570A (en) * | 2016-04-15 | 2016-09-07 | 西安电子科技大学 | Calculation method for parameter of optimally-fit shaped surface of shaped dual-reflector antenna |
-
2023
- 2023-11-03 CN CN202311458350.8A patent/CN117494338A/en active Pending
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|---|---|---|---|---|
| CN101013775A (en) * | 2006-12-22 | 2007-08-08 | 西安电子科技大学 | Method for adjusting precision of antenna surface based on multidimensional unconstrained optimization |
| CN101179156A (en) * | 2007-12-05 | 2008-05-14 | 西安电子科技大学 | Optimum setting angle based large-scale antenna reflecting plane gravity pre-regulation method |
| CN103926548A (en) * | 2014-04-18 | 2014-07-16 | 中国科学院新疆天文台 | Method for quickly measuring precision of reflection face of radiotelescope |
| CN105930570A (en) * | 2016-04-15 | 2016-09-07 | 西安电子科技大学 | Calculation method for parameter of optimally-fit shaped surface of shaped dual-reflector antenna |
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| Title |
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| SHUFEI FENG 等: "Novel Worst-Case Surface Accuracy Evaluation Method and Its Application in Reflector Antenna Structure Design", IEEE ACCESS, vol. 07, 8 October 2019 (2019-10-08), pages 140328 - 140335 * |
| 冯树飞: "大型全可动反射面天线结构保型及创新设计研究", 《中国博士学位论文全文数据库 信息科技辑》, no. 07, 15 July 2020 (2020-07-15), pages 136 - 16 * |
| 王伟 等: "重力作用下天线反射面变形及其调整角度的确定", 电波科学学报, vol. 23, no. 04, 15 August 2008 (2008-08-15), pages 645 - 650 * |
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