CN104268406B - The approximating method of space optional position parabola antenna - Google Patents
The approximating method of space optional position parabola antenna Download PDFInfo
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- CN104268406B CN104268406B CN201410506134.0A CN201410506134A CN104268406B CN 104268406 B CN104268406 B CN 104268406B CN 201410506134 A CN201410506134 A CN 201410506134A CN 104268406 B CN104268406 B CN 104268406B
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Abstract
The approximating method of space optional position parabola antenna, it is related to the fitting technique field of the parabola antennas such as large-scale radio telescope, Large Radar, first, determine and wait to be fitted paraboloidal two characteristic points, that is summit and focus, and square is created with the two characteristic points as reference point, with certain length of side, a series of supplemental characteristic point is constructed with square summit；Then the preferable parabola that the characteristic point construction with the supplemental characteristic point around summit and around focus assumes, computation and measurement point are preferable paraboloidal apart from extreme difference relative to assuming；By comparing, judging and characteristic point is reset come Step wise approximation desired characteristics point, realize tested paraboloidal Minimum Area fitting, obtain tested paraboloidal equation, position and attitude.The approximating method of the present invention can realize accurately, the Minimum Area evaluation of stable space optional position parabola antenna and fitting.
Description
Technical field
The present invention relates to the fitting technique of the parabola antenna such as large-scale radio telescope, Large Radar, and in particular to a kind of
The approximating method of space optional position parabola antenna.
Background technology
Space parabola is mainly used in parabola antenna, especially apply in large-scale parabola antenna more, such as：
In the military informations such as large-scale radio telescope, Large Radar Antenna equipment.Direct shadow during parabola antenna processing
It is exactly face shape error to ring the good and bad main cause of its electrical property, i.e. reality processing production parabolic shape and design parabola
Error between shape.At present, more be to processing after antenna surface data carry out secondary song using least square method is done
Face be fitted, that is, find out one with deformation after parabola normal distance minimum parabola as the best-fit paraboloid, so as to enter
Row error evaluation.This general quadric surface equation is carried out simplifying realizes that the method for parabola fitting can not be realized error and turn
Angle is than larger paraboloidal Accurate Curve-fitting.
Content of the invention
It is an object of the invention to provide a kind of space optional position parabola antenna approached based on geometry optimization search
Minimum Area approximating method, to realize tested paraboloidal Minimum Area fitting, solves existing approximating method and can not realize missing
Difference and corner are than larger paraboloidal Accurate Curve-fitting problem.
For achieving the above object, the technical scheme is that：The approximating method of space optional position parabola antenna, bag
Include following steps：
（1）, on parabola all measurement point coordinates average, obtain being fitted paraboloidal initial reference focus,
In the position for being close to parabola vertex, an optional measurement point is used as initial reference summit；
（2）, with step（1）Initial reference focus and initial reference summit be located straight line be paraboloidal symmetry axis,
Initial reference summit and described the symmetry axis origin of coordinates and coordinate overlapping of axles respectively with measurement coordinate system are made through coordinate transform,
Then each measurement point is calculated to the paraboloidal normal distance constructed with initial reference summit and initial reference focus, obtain most
The difference of big distance and minimum range, as extreme difference value；
（3）, respectively with step（1）Initial reference focus and initial reference summit centered on datum mark, withFor the length of side
Two squares are set to construct auxiliary magnet, using the summit of two squares as auxiliary magnet, then obtain 8 secondary focis and 8
Individual auxiliary summit, and then 64 parabolas can be constructed, each measurement point is then calculated to each paraboloidal normal distance,
64 extreme difference values are then obtained, and minimum extreme difference value therein is designated as；
（4）, by the square length of sideWith minimum extreme difference valueIt is compared, if, then two center reference points are not
Become, the length of side is reduced into original 0.5 times and two squares is reset to construct new auxiliary magnet, solve minimum extreme difference again
Value；If, then take withCorresponding two auxiliary magnets are new reference point, and datum mark centered on new reference point,
The constant construction square of the length of side, obtains new auxiliary magnet, and solves minimum extreme difference value；
（5）, repeat step（4）Process, until when the length of side of the square that is set up is less than 0.0001mm, now obtained
Square the length of side and minimum extreme difference value in reckling be Minimum Area parabolic Surface profile tolerance error, corresponding auxiliary
Summit and secondary foci are the paraboloidal summit and focus for meeting Minimum Area fitting, paraboloidal so as to obtain being fitted
Minimum Area fit equation and its position and attitude.
Beneficial effect：The inventive method has matched optimal preferable parabola in higher required precision, so as to realize
Parabolic Surface profile tolerance error Evaluation of Minimum Region, the evaluation for dimensional conicoide provide a kind of effective ways.
The inventive method is except obtaining the Minimum Area profile error of parabola antenna reflecting surface, additionally it is possible to obtain
The opening of the alignment error of parabola antenna, i.e. parabola antenna is towards deviation.Parabola is evaluated by the determination of focusing
Whether the installation of feed is ideal position.
When parabolic Surface profile tolerance error is evaluated, can effectively determine fixed reference feature point, calculating process beneficial to understanding and
Realize, and it is preferable to restrain effect.
Description of the drawings
Fitting theory figures of the Fig. 1 for the inventive method.
In figure：1 represents actual measurement parabola, and 2 represent preferable parabola,Initial reference summit is represented,Represent initial ginseng
Examine focus,Auxiliary summit is represented,Represent secondary foci.
Specific embodiment
Step one, selection initial reference characteristic point
Assume that measurement point is, initial reference focusWith initial
Datum vertexIt is calculated as follows：
(1)
Step 2, calculating initial error
For ease of calculating, initial reference summit is made by coordinate transformFormer with the coordinate of measurement coordinate system
Point overlaps, and makes initial reference summitWith initial reference focusLine and reference axis Z axis weight
Close.
Measurement point coordinates after conversion is usedRepresent, its calculating process is as follows：
(2)
In formula：
After coordinate transform, initial reference summitWith initial reference focusRespectivelyWith, then by summitAnd focusThe parabola side of determination
Cheng Wei：
(3)
In formula：
Assumed positionFor measurement point after coordinate transform
With formula（3）The paraboloidal orthogonal points of the auxiliary that determined, then pointCoordinate can use formula（4）Solve.
(4)
By formula（5）All measurement points can be drawn to the preferable paraboloidal beeline of hypothesis：
(5)
When measurement point position is on the outside of parabolaTake on the occasion of, otherwise take negative value；Initial errorBy formula（6）Obtain.
(6)
Step 3, construction supplemental characteristic point
With initial reference characteristic pointWithCentered on datum mark, withArrange for the length of side
Two squares, then each summit of two squares be supplemental characteristic point（Abbreviation auxiliary magnet）, with initial reference focusCentered on 8 summits of set square be secondary foci, with initial reference
SummitCentered on 8 summits of set square be auxiliary summit.
According to square geometric relationship, the coordinate for calculating square auxiliary magnet is
(7)
(8)
Step 4, computation and measurement point are to paraboloidal apart from extreme difference
Computing Principle is identical with step 2, and simply reference point is changed.In the same manner, for ease of calculating, made by coordinate transform
Auxiliary reference summitAuxiliary reference summit is overlapped and is made with the origin of coordinatesAnd auxiliary
With reference to focusLine is overlapped with reference axis Z axis.
Measurement point coordinates after conversion is usedTable
Show, its calculating process is as follows：
(9)
In formula：
After coordinate transform, first auxiliary reference summitWith auxiliary reference focusPoint
It is notWith, then thus summitAnd focusThe parabola equation of determination is：
(10)
In formula：
Assumed positionFor measurement point after coordinate transform
With formula（10）The paraboloidal orthogonal points of the auxiliary that determined, then pointCoordinate can use formula（11）Solve.
(11)
By formula（12）All measurement points can be drawn to the preferable paraboloidal beeline of hypothesis：
(12)
Due to 8 secondary focis and 8 auxiliary summit two-by-two engagement formation auxiliary parabola, therefore can obtain 64 auxiliary
Parabola, measurement point can all obtain one apart from extreme difference value to each auxiliary parabola, when measurement point position is outside parabola
During sideTake on the occasion of, otherwise take negative value, then 64 extreme difference values can be drawn by following formula：
(13)
The reckling that this 64 assume in preferable parabola extreme difference value is designated as, then：
(14)
WithCorresponding secondary foci and auxiliary summit are designated as respectivelyWith.
Step 5, optimization approach search
If, then fixed reference feature point（That is the center reference point of two squares）Constant, the length of side is reduced into original
0.5 times and new auxiliary magnet is constructed, then repeat step three is to step 5 process；If, then take withCorresponding hypothesis
Preferable paraboloidal two supplemental characteristics point, i.e.,WithFor new fixed reference feature point,
The length of side is constant, constructs new square and auxiliary magnet, and then repeat step three is to step 5 process.
When tried to achieveDuring very little, typically take, it is believed that the hypothesis ideal parabola for searching is
Through being sufficiently close to actual ideal parabola, terminate search, now obtainWithIn reckling be Minimum Area parabolic
Surface profile tolerance error；Now can be concluded that the secondary foci for searching and auxiliary summit are and meet lowest area principal
Paraboloidal focus and summit, with the parabola that the parabola that this summit and focus determine is Minimum Area fitting, by front
The inverse transformation of the coordinate transform that states is obtained the parabola equation of Minimum Area fitting；After inverse transformation, according to summit and focus
Coordinate the angle of the paraboloidal position that is fitted and the parabola axis of symmetry and each reference axis is obtained.
Claims (1)
1. the approximating method of space optional position parabola antenna, it is characterised in that：Comprise the steps：
（1）, on parabola all measurement point coordinates average, obtain being fitted paraboloidal initial reference focus, connecing
The optional measurement point in the position of nearly parabola vertex is used as initial reference summit；
（2）, with step（1）Initial reference focus and initial reference summit be located straight line be paraboloidal symmetry axis, through sit
Mark conversion makes initial reference summit and described the symmetry axis origin of coordinates and coordinate overlapping of axles respectively with measurement coordinate system, then
Each measurement point is calculated to the paraboloidal normal distance constructed with initial reference summit and initial reference focus, obtain maximum away from
From the difference with minimum range, as extreme difference value；
（3）, respectively with step（1）Initial reference focus and initial reference summit centered on datum mark, withArrange for the length of side
Two squares to construct auxiliary magnet, using the summit of two squares as auxiliary magnet, then obtain 8 secondary focis and 8 auxiliary
Summit is helped, and then 64 parabolas can be constructed, each measurement point is then calculated to each paraboloidal normal distance, then obtained
To 64 extreme difference values, minimum extreme difference value therein is designated as；
（4）, by the square length of sideWith minimum extreme difference valueIt is compared, if, then two center reference points are constant, side
Length is reduced into original 0.5 times and resets two squares to construct new auxiliary magnet, solves minimum extreme difference value again；If, then take withCorresponding two auxiliary magnets are new reference point, and datum mark, the length of side centered on new reference point
Constant construction square, obtains new auxiliary magnet, and solves minimum extreme difference value；
（5）, repeat step（4）Process, until when the length of side of square that is set up is less than 0.0001mm, now obtained just
Reckling in the length of side of cube and minimum extreme difference value is Minimum Area parabolic Surface profile tolerance error, corresponding auxiliary summit
The paraboloidal summit and focus for meeting Minimum Area fitting is with secondary foci, so as to obtain being fitted paraboloidal minimum
Region fit equation and its position and attitude.
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| CN104680016A (en) * | 2014-11-05 | 2015-06-03 | 河南科技大学 | Geometric optimization approximation based minimum region fitting method for profiles of parabolas |
| CN105246090A (en) * | 2015-08-28 | 2016-01-13 | 中国航天科工集团第三研究院第八三五七研究所 | In-cabin power coverage optimizing method based on distributed antennas |
| CN111256664B (en) * | 2020-01-20 | 2022-02-08 | 中国科学院国家天文台 | Spherical radio telescope reflecting surface measuring system and method |
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| CN101989682A (en) * | 2010-07-21 | 2011-03-23 | 中国科学院国家天文台南京天文光学技术研究所 | Antenna reflection surface fitting method |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN101989682A (en) * | 2010-07-21 | 2011-03-23 | 中国科学院国家天文台南京天文光学技术研究所 | Antenna reflection surface fitting method |
Non-Patent Citations (3)
| Title |
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| 《任意空间位置雷达天线反射面拟合与评定技术》;唐文彦;《现代雷达》;20060530;第58-62页 * |
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