CN109308297A - A kind of telescope reflecting surface control algolithm based on nominal data library and interpolation calculation - Google Patents
A kind of telescope reflecting surface control algolithm based on nominal data library and interpolation calculation Download PDFInfo
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Abstract
The telescope reflecting surface control algolithm based on nominal data library and interpolation calculation that the invention discloses a kind of comprising building nominal data library and interpolation resolve two stages of actuator elongation；Wherein nominal data library must building be complete before interpolation resolves, and interpolation resolves actuator elongation can real-time perfoming in reflecting surface control.Control algolithm calculating speed provided by the invention is fast, can satisfy the calculating for completing actuator stroke needed for primary event face deforms in 0.5 second and is issued to actuator；The control precision of the algorithm can be effectively ensured by the stated accuracy and grid divergent density of control reflecting surface face shape in it；The dependence to reflecting surface face shape real-time measurement is got rid of, to evade boisterous interference, so that telescope control has the possibility of all weather operations；Without the additional electromagnetic interference of measuring instrument in real-time control, the EMC problem of telescope work is greatly alleviated；Solves the cable net structure safety problem of big zenith angle paraboloid deformation.
Description
Technical field
The present invention relates to the control algolithm fields of telescope reflecting surface, based on nominal data library and insert more particularly, to one kind
It is worth the telescope reflecting surface control algolithm calculated.
Background technique
500m bore spherical radio telescope (Five-hundred-meter aperture spherical radio
Telescope, FAST), it is under the jurisdiction of national Eleventh Five-Year Plan major scientific projects project, is that maximum single port diameter radio is hoped in the world
Remote mirror.The telescope reflecting surface is taken the initiative the unique job mode of displacement, can be according to the angle of observation celestial body, in 500m bore
The different zones of reflecting surface form the paraboloid that diameter is 300m.The working frequency of the telescope is between 70MHz~3GHz.
In order to realize the active displacement properties of reflecting surface, FAST is using flexible cable net as main supporting structure.Rope net knot
Structure includes 6670 main ropes and 2225 main rope nodes altogether, weighs about 1300 tons, rope net periphery is fixed on collar tie beam.The collar tie beam of FAST
For 11m × 5.5m annular truss that diameter is about 500m, about 5350 tons of weight, collar tie beam is supported on 50 height in 6m-50m etc.
Lattice column on.Single downhaul is arranged in each main rope node of rope net, drags downhaul by actuator come the change of control cord net
Position, so that the different zones within the scope of 500m bore form the paraboloid of 300m bore.
When FAST telescope carries out tracking observation to celestial body, need according to movement of heavenly bodies track, in FAST reflecting surface
Different location within the scope of 500m bore forms a series of continuous 300m bore paraboloids, this just needs reflecting surface control system
System constantly control actuator telescopic traction rope net deformation, tensioning goes out to meet the parabolic of surface precision on correct time, position
Face.Specific to reflecting surface control algolithm, seeks in predetermined time interval (0.5~1.0s) constantly to calculate and provide different positions
The target stroke of 2225 actuators corresponding to paraboloid is set, goes to execute to be handed down to actuator PLC.
Conventional reflecting surface control method uses the close-loop control scheme of laser total station real-time measurement reflecting surface face shape, i.e.,
The location information of about 700 rope net node targets is as control feedback in real-time measurement 300m paraboloid bore.But based on real
When measurement feedback reflecting surface close-loop control scheme encounter following 4 technology barriers: first, Real-time Feedback measuring speed is too slow:
Reflecting surface control requires to complete measurement to target points all in paraboloid in 0.5~1 second, through multiple actual test, 10
Laser total station combined measurement, 9 minutes must be needed at the soonest by completing primary above-mentioned measurement, be far from satisfying closed-loop control when
Between space requirement；Second, real-time measurement is very big by the restriction of live meteorological condition, is not able to satisfy round-the-clock high-acruracy survey
It is required that；Third, real-time measurement EMC outstanding problem will solve problems and have a significant impact again to measurement accuracy；4th, it is difficult to
Solve the cable net structure safety problem of big zenith angle paraboloid deformation.
The information disclosed in the background technology section is intended only to deepen understanding of the general background technology to the present invention, and
It is not construed as recognizing or implying in any form that the information constitutes the prior art known to those skilled in the art.
Summary of the invention
The purpose of the present invention is to provide a kind of controlled based on the telescope reflecting surface of nominal data library and interpolation calculation to calculate
Method, to solve the technical problems existing in the prior art.
To achieve the goals above, the invention adopts the following technical scheme:
The present invention provides a kind of telescope reflecting surface control algolithm based on nominal data library and interpolation calculation, the method
Two stages of actuator elongation are resolved including building nominal data library and interpolation；It is with steps are as follows:
1) triangular mesh mesh discretization is carried out to reflecting surface, one-dimensional discrete is carried out to temperature field, saves triangular mesh
The discrete and discrete topology information table of temperature field；
2) spherical surface is inputted, or inputs discrete parabola vertex coordinate and discrete temperature spot；
3) information tensioning/adjustment reflecting surface and reflecting surface face shape is measured by input；
4) whether assessment reflecting surface surface figure accuracy is up to standard, repeats step 2) if not up to standard；
5) actuator elongation/actuator stroke and corresponding discrete paraboloid/spherical surface and discrete temperature point are recorded, is updated
Nominal data library；
6) step 2)~step 5) is repeated, until the building of nominal data library finishes；
7) input needs the parabola vertex coordinate deformed, is believed according to the triangular mesh mesh discretization in topology information table
Breath search positions triangular mesh belonging to the vertex；
8) the temperature discrete point in topology information table is successively selected, according to nominal data library and parabola vertex coordinate,
Two-dimensional interpolation calculating is carried out in triangular mesh domain, finally obtains the actuator elongation under various discrete temperature spot；
9) actual ambient temperature is inputted, moment matrix is extended using the actuator in step 8), is carried out again in temperature field
One-dimensional interpolation calculates, and obtains final actuator elongation；
10) actuator elongation sends control plus final paraboloid actuator stroke is obtained after spherical surface actuator stroke
Device processed executes.
As a kind of further technical solution, the triangular mesh unit in step 1) is space spherical triangle,
Radius of curvature is 300 meters, and 3 vertex and 3 sides midpoint of the spherical triangle are the paraboloidal vertex for needing to demarcate.
As a kind of further technical solution, temperature field is the temperature range [- 10 that reflecting surface works normally in step 1)
DEG C, 45 DEG C].
As a kind of further technical solution, the topology information table in step 1) is compiled comprising triangular mesh unit
Number, calibration parabola vertex number and calibration parabola vertex number apex coordinate between mapping relations.
As a kind of further technical solution, actuator elongation described in step 5) refers to so that after distorted reflector
Deviate the actuator stroke increment of spherical surface.
It is controlled and is calculated based on the telescope reflecting surface of nominal data library and interpolation calculation as a kind of further technical solution
Method, which is characterized in that the two-dimensional interpolation calculating in step 8) refers to that fixed temperature domain is constant, builds inside spherical triangle
The area coordinate quadratic interpolation function formula of the vertical triangle comprising 6 nodes is as follows:
In formulaFor to the actuator elongation after parabola vertex P interpolation calculation any one in spherical triangle, subscript i
=1~3 represent 3 vertex of spherical triangle, the representative edge of i=4~6 midpoint, SiFor representated by i-th of vertex/side midpoint
Demarcate paraboloidal actuator elongation, NiFor the area coordinate quadratic interpolation shape function at corresponding i-th of vertex/side midpoint,
Expression formula is as follows:
L in formulaiFor interpolation point P relative to the area coordinate (being detailed in attached drawing 2) of vertex i, L in trianglei≤1；Convolution
(1) and formula (2), any paraboloid actuator elongation of the interpolation calculation vertex in triangle.
As a kind of further technical solution, 6 node is 3 triangular apex and 3 sides midpoint, corresponds to 6
Demarcate parabola vertex.
As a kind of further technical solution, the one-dimensional interpolation calculating in step 9) refers to fixed parabola vertex
It is constant, according to 5 DEG C of temperature interval totally 12 discrete temperature point x in the temperature field [- 10 DEG C, 45 DEG C]i, construct cubic spline and insert
Value function formula is as follows:
yi(x)=ai+bi(x-xi)+ci(x-xi)2+di(x-xi)3, (i=1~11) (3)
In formula, yi(x)(xi≤x≤xi+1) it is the segmentation guidable cubic spline functions of Second Order Continuous；H=xi+1-xi=
5℃；ai, bi, ci, diIt, can conducting bar part from segmentation Second Order Continuous for the parameter of i-th section of spline function:
Formula (4) is further simplified as solving unknown number being ciEquation group:
Free end condition is supplemented at temperature field both ends:
c1=c12=0 (6)
12 yuan of linear function groups representated by solution formula (5) and formula (6), obtain parameter ci, and then substitute into formula (4) and joined
Number ai, bi, di, then the paraboloidal final actuator elongation under actual ambient temperature obtained by formula (3) interpolation calculation.
It by reflecting surface subdivision is 2004 equilateral spherical trigonometries of approximation in step 1) as a kind of further technical solution
Shape unit, triangular apex and side midpoint contain 4101 discrete parabola vertex.
By adopting the above technical scheme, the invention has the following beneficial effects:
Control algolithm calculating speed provided by the invention is fast, can satisfy needed for completing the deformation of primary event face in 0.5 second
The calculating of actuator stroke is simultaneously issued to actuator；It passes through the stated accuracy of control reflecting surface face shape and the grid of sufficient density
The control precision of the algorithm can be effectively ensured in subdivision；It gets rid of the dependence to reflecting surface face shape real-time measurement, to evade
Boisterous interference, so that telescope control has the possibility of all weather operations；Without measuring instrument in real-time control
Additional electromagnetic interference greatly alleviates the EMC problem of telescope work；Solves the rope net of big zenith angle paraboloid deformation
Structure safety problem.
Detailed description of the invention
It, below will be to specific in order to illustrate more clearly of the specific embodiment of the invention or technical solution in the prior art
Embodiment or attached drawing needed to be used in the description of the prior art be briefly described, it should be apparent that, it is described below
Attached drawing is some embodiments of the present invention, for those of ordinary skill in the art, before not making the creative labor
It puts, is also possible to obtain other drawings based on these drawings.
Fig. 1 is the telescope reflecting surface control algolithm provided in an embodiment of the present invention based on nominal data library and interpolation calculation
Flow chart；
Fig. 2 is that area coordinate of the interpolation point provided in an embodiment of the present invention in triangle relative to vertex calculates signal
Figure；
Fig. 3 is reflecting surface universe triangular mesh subdivision schematic diagram provided in an embodiment of the present invention.
Specific embodiment
Technical solution of the present invention is clearly and completely described below in conjunction with attached drawing, it is clear that described implementation
Example is a part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, ordinary skill
Personnel's every other embodiment obtained without making creative work, shall fall within the protection scope of the present invention.
In the description of the present invention, it should be noted that term " center ", "upper", "lower", "left", "right", "vertical",
The orientation or positional relationship of the instructions such as "horizontal", "inner", "outside" be based on the orientation or positional relationship shown in the drawings, merely to
Convenient for description the present invention and simplify description, rather than the device or element of indication or suggestion meaning must have a particular orientation,
It is constructed and operated in a specific orientation, therefore is not considered as limiting the invention.In addition, term " first ", " second ",
" third " is used for descriptive purposes only and cannot be understood as indicating or suggesting relative importance.
In the description of the present invention, it should be noted that unless otherwise clearly defined and limited, term " installation ", " phase
Even ", " connection " shall be understood in a broad sense, for example, it may be being fixedly connected, may be a detachable connection, or be integrally connected；It can
To be mechanical connection, it is also possible to be electrically connected；It can be directly connected, can also can be indirectly connected through an intermediary
Connection inside two elements.For the ordinary skill in the art, above-mentioned term can be understood as the case may be
Concrete meaning in the present invention.
Below in conjunction with attached drawing, detailed description of the preferred embodiments.It should be understood that this place is retouched
The specific embodiment stated is merely to illustrate and explain the present invention, and is not intended to restrict the invention.
As shown in connection with fig. 1, the telescope reflecting surface control based on nominal data library and interpolation calculation that the present embodiment provides a kind of
Algorithm processed, the method includes building nominal data libraries and interpolation to resolve two stages of actuator elongation；Its with step such as
Under:
1) triangular mesh mesh discretization is carried out to reflecting surface, one-dimensional discrete is carried out to temperature field, saves triangular mesh
The discrete and discrete topology information table of temperature field, totally 3 arrays；The discrete topology information table of triangular mesh includes 2 arrays,
One is the two-dimensional array of 2004*6, and row number is triangular element number, and column number is respectively 6 for forming the triangle
Paraboloidal vertex number is demarcated, wherein preceding 3 parabola vertex represent 3 vertex 1,2,3 of triangle, rear 3 paraboloids
Vertex represents 3 sides midpoint 4,5,6 of triangle, and each point is detailed in attached drawing 2 in the position of triangle；Secondly being the two dimension of 4101*5
Array, row number are to demarcate paraboloidal vertex number, preceding 2 column numbers be the parabola vertex spherical coordinates (azimuth,
Zenith angle), rear 3 column numbers are the rectangular co-ordinate (x, y, z) of the parabola vertex；The discrete topology information table of temperature field includes
The one-dimension array of 12 discrete temperature points is spaced 5 DEG C；
2) spherical surface is inputted, or inputs discrete parabola vertex coordinate and discrete temperature spot；
3) information tensioning/adjustment reflecting surface and reflecting surface face shape is measured by input；
4) whether assessment reflecting surface surface figure accuracy is up to standard, repeats step 3) if not up to standard；
5) actuator elongation/actuator stroke and corresponding discrete paraboloid/spherical surface and discrete temperature point are recorded, is updated
Nominal data library；Nominal data library includes 2 arrays altogether, and one is the one-dimension array of 2225*1, is stored in spherical displacer at 20 DEG C
2225 actuator strokes in face；Secondly being the three-dimensional array of i*j art m=2225*4101*12, wherein the first dimension is represented and actuated
Device number, for the second dimension to demarcate paraboloidal vertex sum, the third dimension represents discrete temperature point quantity, each member of the array
Element is stored in respectively under m-th of discrete temperature point, j-th of paraboloidal i-th of actuator elongation of calibration.
6) step 2)~step 5) is repeated, until the building of nominal data library finishes；
7) input needs the parabola vertex coordinate deformed, is believed according to the triangular mesh mesh discretization in topology information table
Breath search positions triangular mesh belonging to the vertex；
8) the temperature discrete point in topology information table is successively selected, according to nominal data library and parabola vertex coordinate,
Two-dimensional interpolation calculating is carried out in triangular mesh domain, finally obtains the actuator elongation under various discrete temperature spot；
9) actual ambient temperature is inputted, moment matrix is extended using the actuator in step 8), is carried out again in temperature field
One-dimensional interpolation calculates, and obtains final actuator elongation；
10) actuator elongation sends control plus final paraboloid actuator stroke is obtained after spherical surface actuator stroke
Device processed executes.
In Fig. 1, I indicates discrete parabola vertex sum, I=4101；I indicates parabola vertex number；J indicates discrete temperature
Degree point sum, J=12；J: discrete temperature point number；- 10 DEG C≤temperature field Tj≤45℃
In this embodiment, as a kind of further technical solution, the triangular mesh unit in step 1) is space
Spherical triangle, radius of curvature are 300 meters, and 3 vertex and 3 sides midpoint of the spherical triangle are to need to demarcate
Paraboloidal vertex.
In this embodiment, as a kind of further technical solution, temperature field is that reflecting surface works normally in step 1)
Temperature range [- 10 DEG C, 45 DEG C].
In this embodiment, as a kind of further technical solution, the topology information table in step 1) includes three
Mapping between hexagonal lattice element number, calibration parabola vertex number and calibration parabola vertex number and apex coordinate
Relationship.
In this embodiment, as a kind of further technical solution, actuator elongation described in step 5) is to instigate
It obtains distorted reflector and retrodeviates the actuator stroke increment from spherical surface.
In this embodiment, the telescope as a kind of further technical solution based on nominal data library and interpolation calculation
Reflecting surface control algolithm, which is characterized in that the two-dimensional interpolation calculating in step 8) refers to that fixed temperature domain is constant, in spherical surface
The area coordinate quadratic interpolation function formula that triangle interior establishes the triangle comprising 6 nodes is as follows:
In formulaFor to the actuator elongation after parabola vertex P interpolation calculation any one in spherical triangle, subscript i
=1~3 represent 3 vertex of spherical triangle, the representative edge of i=4~6 midpoint, SiFor representated by i-th of vertex/side midpoint
Demarcate paraboloidal actuator elongation, NiFor the area coordinate quadratic interpolation shape function at corresponding i-th of vertex/side midpoint,
Expression formula is as follows:
L in formulaiFor area coordinate of the interpolation point P in triangle relative to vertex i；
Convolution (1) and formula (2), any paraboloid actuator elongation of the interpolation calculation vertex in triangle.In conjunction with
Shown in Fig. 2, Li=Ai/A0, L1+L2+L3=1, A0It is the triangle gross area.
In this embodiment, as a kind of further technical solution, 6 node is 3 triangular apex and 3 sides
Midpoint, corresponding 6 calibration parabola vertex.
In this embodiment, as a kind of further technical solution, the one-dimensional interpolation calculating in step 9) refers to
Fixed parabola vertex is constant, according to 5 DEG C of temperature interval totally 12 discrete temperature point x in temperature field [- 10 DEG C, 45 DEG C]i,
It is as follows to construct cubic spline functions formula:
yi(x)=ai+bi(x-xi)+ci(x-xi)2+di(x-xi)3, (i=1~11) (3)
In formula, yi(x)(xi≤x≤xi+1) it is the segmentation guidable cubic spline functions of Second Order Continuous；H=xi+1-xi=
5℃；ai, bi, ci, diIt, can conducting bar part from segmentation Second Order Continuous for the parameter of i-th section of spline function:
Formula (4) is further simplified as solving unknown number being ciEquation group:
Free end condition is supplemented at temperature field both ends:
c1=c12=0 (6)
12 yuan of linear function groups representated by solution formula (5) and formula (6), obtain parameter ci, and then substitute into formula (4) and joined
Number ai, bi, di, then the paraboloidal final actuator elongation under actual ambient temperature obtained by formula (3) interpolation calculation.
It in this embodiment, by reflecting surface subdivision is 2004 close in step 1) as a kind of further technical solution
Like equilateral spherical triangle unit, triangular apex and side midpoint contain 4101 discrete parabola vertex.
To sum up, control algolithm calculating speed provided by the invention is fast, can satisfy and completes the deformation of primary event face in 0.5 second
The calculating of required actuator stroke is simultaneously issued to actuator；It passes through the stated accuracy and sufficient density for controlling reflecting surface face shape
The control precision of the algorithm can be effectively ensured in mesh generation；It gets rid of the dependence to reflecting surface face shape real-time measurement, thus
Boisterous interference is evaded, so that telescope control has the possibility of all weather operations；Without measurement in real-time control
The additional electromagnetic interference of instrument greatly alleviates the EMC problem of telescope work；Solves big zenith angle paraboloid deformation
Cable net structure safety problem.
Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention., rather than its limitations；To the greatest extent
Pipe present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that: its according to
So be possible to modify the technical solutions described in the foregoing embodiments, or to some or all of the technical features into
Row equivalent replacement；And these are modified or replaceed, various embodiments of the present invention technology that it does not separate the essence of the corresponding technical solution
The range of scheme.
Claims (9)
1. a kind of telescope reflecting surface control algolithm based on nominal data library and interpolation calculation, which is characterized in that the method
Two stages of actuator elongation are resolved including building nominal data library and interpolation；It is with steps are as follows:
1) triangular mesh mesh discretization is carried out to reflecting surface, one-dimensional discrete is carried out to temperature field, it is discrete to save triangular mesh
The topology information table discrete with temperature field；
2) spherical surface is inputted, or inputs discrete parabola vertex coordinate and discrete temperature spot；
3) information tensioning/adjustment reflecting surface and reflecting surface face shape is measured by input；
4) whether assessment reflecting surface surface figure accuracy is up to standard, repeats step 2) if not up to standard；
5) actuator elongation or actuator stroke and corresponding discrete paraboloid and discrete temperature point are recorded, nominal data is updated
Library；
6) step 2)~step 5) is repeated, until the building of nominal data library finishes；
7) input needs the parabola vertex coordinate deformed, is searched according to the triangular mesh mesh discretization information in topology information table
Triangular mesh belonging to the vertex Suo Dingwei；
8) the temperature discrete point in topology information table is successively selected, according to nominal data library and parabola vertex coordinate, in triangle
Two-dimensional interpolation calculating is carried out in shape grid domain, finally obtains the actuator elongation under various discrete temperature spot；
9) actual ambient temperature is inputted, moment matrix is extended using the actuator in step 8), is carried out again in temperature field one-dimensional
Interpolation calculation obtains final actuator elongation；
10) actuator elongation sends controller plus final paraboloid actuator stroke is obtained after spherical surface actuator stroke
It executes.
2. the telescope reflecting surface control algolithm according to claim 1 based on nominal data library and interpolation calculation, special
Sign is that the triangular mesh unit in step 1) is space spherical triangle, and radius of curvature is 300 meters, the spherical surface three
Angular 3 vertex and 3 sides midpoint are the paraboloidal vertex for needing to demarcate.
3. the telescope reflecting surface control algolithm according to claim 1 based on nominal data library and interpolation calculation, special
Sign is that temperature field is the temperature range [- 10 DEG C, 45 DEG C] that reflecting surface works normally in step 1).
4. the telescope reflecting surface control algolithm according to claim 1 based on nominal data library and interpolation calculation, special
Sign is, the topology information table in step 1) include triangular mesh element number, calibration parabola vertex number and
Demarcate the mapping relations between parabola vertex number and apex coordinate.
5. the telescope reflecting surface control algolithm according to claim 1 based on nominal data library and interpolation calculation, special
Sign is that actuator elongation described in step 5) refers to so that distorted reflector retrodeviates the actuator stroke increment from spherical surface.
6. the telescope reflecting surface control algolithm according to claim 1 based on nominal data library and interpolation calculation, special
Sign is that the two-dimensional interpolation calculating in step 8) refers to that fixed temperature domain is constant, and establishing inside spherical triangle includes 6
The area coordinate quadratic interpolation function formula of the triangle of node is as follows:
In formulaFor to the actuator elongation after parabola vertex P interpolation calculation any one in spherical triangle, subscript i=1~
3 represent 3 vertex of spherical triangle, the representative edge of i=4~6 midpoint, SiFor the throwing of calibration representated by i-th of vertex/side midpoint
The actuator elongation of object plane, NiFor the area coordinate quadratic interpolation shape function at corresponding i-th of vertex/side midpoint, expression formula
It is as follows:
L in formulaiFor area coordinate of the interpolation point P in triangle relative to vertex i, Li≤1；
Convolution (1) and formula (2), any paraboloid actuator elongation of the interpolation calculation vertex in triangle.
7. the telescope reflecting surface control algolithm according to claim 6 based on nominal data library and interpolation calculation, special
Sign is that 6 node is 3 triangular apex and 3 sides midpoint, corresponding 6 calibration parabola vertex.
8. the telescope reflecting surface control algolithm according to claim 1 based on nominal data library and interpolation calculation, special
Sign is that the one-dimensional interpolation calculating in step 9) refers to that fixed parabola vertex is constant, at temperature field [- 10 DEG C, 45 DEG C]
The interior temperature interval according to 5 DEG C totally 12 discrete temperature point xi, it is as follows to construct cubic spline functions formula:
yi(x)=ai+bi(x-xi)+ci(x-xi)2+di(x-xi)3, (i=1~11) (3)
In formula, yi(x)(xi≤x≤xi+1) it is the segmentation guidable cubic spline functions of Second Order Continuous；H=xi+1-xi=5 DEG C；
ai,bi,ci,diIt, can conducting bar part from segmentation Second Order Continuous for the parameter of i-th section of spline function:
Formula (4) is further simplified as solving unknown number being ciEquation group:
Free end condition is supplemented at temperature field both ends:
c1=c12=0 (6)
12 yuan of linear function groups representated by solution formula (5) and formula (6), obtain parameter ci, and then substitute into formula (4) and obtain parameter ai,
bi,di, then the paraboloidal final actuator elongation under actual ambient temperature obtained by formula (3) interpolation calculation.
9. the telescope reflecting surface control algolithm according to claim 1 based on nominal data library and interpolation calculation, special
Sign is, by reflecting surface subdivision is the equilateral spherical triangle unit of 2004 approximations, triangular apex and side midpoint in step 1)
Contain 4101 discrete parabola vertex.
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| CN110322559A (en) * | 2019-07-04 | 2019-10-11 | 贵州正业工程技术投资有限公司 | The localization method of ball crown type center of surface point and curved surface fixed point line and ground intersection point |
| CN111256664A (en) * | 2020-01-20 | 2020-06-09 | 中国科学院国家天文台 | Spherical radio telescope reflecting surface measuring system and method |
| CN113281004A (en) * | 2021-04-30 | 2021-08-20 | 中国科学院紫金山天文台 | Astronomical optical telescope photoelectric efficiency calculation and actual measurement verification method |
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| CN113281004B (en) * | 2021-04-30 | 2022-08-02 | 中国科学院紫金山天文台 | Astronomical optical telescope photoelectric efficiency calculation and actual measurement verification method |
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