CN115979593A - Method for improving wavefront error detection precision of large-aperture telescope - Google Patents
Method for improving wavefront error detection precision of large-aperture telescope Download PDFInfo
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- CN115979593A CN115979593A CN202211695854.7A CN202211695854A CN115979593A CN 115979593 A CN115979593 A CN 115979593A CN 202211695854 A CN202211695854 A CN 202211695854A CN 115979593 A CN115979593 A CN 115979593A
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Abstract
A method for improving the wavefront error detection precision of a large-aperture telescope. The method comprises the steps of firstly, constructing Zernike polynomial coefficient conversion matrixes of a telescope pupil and each local small-caliber pupil, combining the conversion matrixes into a new matrix, and calculating the condition number of the new matrix. The filling factor and the number of the local small-aperture pupils and the baseline distance between the local small-aperture pupils are respectively changed to calculate the corresponding new matrix condition number. The smaller the value of the condition number is, the higher the precision of calculating the telescope pupil wavefront error by using the wavefront of the local small-caliber pupil is, and the method provides an important parameter basis for detecting the telescope wavefront error.
Description
Technical Field
The invention relates to a method for improving the detection precision of a wavefront error of a telescope. In particular to a method for improving the wavefront error detection precision of a large-aperture telescope.
Background
Because the observation resolution of the astronomical telescope is in direct proportion to the clear aperture of the astronomical telescope, the aperture of the telescope needs to be continuously increased in order to obtain higher observation resolution, and the aperture size of the telescope becomes an index for measuring the observation capability of the astronomical telescope to a certain extent. In addition, imaging resolution of astronomical telescopes during observation is affected by wavefront errors caused by various factors, such as atmospheric turbulence of ground-based telescopes during observation. These wavefront errors can cause the reduction of the observation precision and imaging quality of the telescope, so that the wavefront errors of the telescope need to be detected by a proper method and corrected by a correction mechanism, so that the telescope is in the optimal working state; and an appropriate method is required to evaluate the accuracy of the above method.
For a small-caliber telescope, the wavefront error can be detected by methods such as an interferometer, a curvature sensor, a Hartmann-shack wavefront sensor and the like. Because the light path of the interferometer is complex and the light energy utilization rate is low, the application of the interferometer in weak target imaging systems such as astronomical observation and space observation is limited. The curvature sensor has a certain application in astronomical telescopes, but the measurement accuracy is relatively low. The Hartmann-shack sensor is a wavefront error detection device which is most widely applied and has the most mature technology at present, and generally comprises a micro lens array, a matched lens and a CCD camera, and when the wavefront error of a large-caliber telescope is measured, the micro lens array and the matched lens which are equivalent to the caliber of the telescope are needed, so that the hardware cost of the Hartmann-shack sensor is greatly increased. In addition, a sub-aperture splicing technology is also used for wavefront aberration measurement of a large-aperture optical system at present, full-aperture scanning is realized by controlling a three-position precision motion platform, when a large-aperture optical element reaches a meter level, a test process needs to consume longer time and higher cost, and meanwhile, other error sources such as temperature and platform return path difference also influence the wavefront error detection precision of the sub-aperture splicing method.
The document 'large-aperture reflector component surface shape detection system and method research' ([ J ] optics report 2016, 36 (2): 0212002-1-0212002-7) discloses a large-aperture optical element surface shape detection method, which is based on Hartmann-shack sensors and sub-aperture splicing detection technologies, and provides a hybrid splicing algorithm by improving the existing algorithm, so that the surface shape detection error caused by splicing is effectively reduced, but because the Hartmann-shack sensors and the sub-aperture splicing technologies are adopted at the same time, a more complex hardware structure is required. The document 'study and application of a large-aperture optical element surface shape detection neutron aperture splicing algorithm' ([ M ] Sun Lin, 2019, master graduation paper) discloses a method for detecting a large-aperture optical element wavefront error, and the method also adopts a Hartmann-shack sensor and a sub-aperture splicing technology to detect the large-aperture optical element.
Disclosure of Invention
The invention aims to provide a method capable of improving detection precision when calculating a telescope pupil wavefront error by using a local small-aperture pupil wavefront error.
1. For large aperture telescopes, the pupil wavefront error can be described by a combination of Zernike polynomials,
for a local small aperture pupil located in the telescope pupil, its wavefront error can be described by a combination of another set of Zernike polynomials
Wherein (A) and (B)r,θ) And (a)r’,θ’) Respectively representing the coordinates of the telescope pupil and the local small aperture pupil,a i anda i ’are respectively asZ i AndZ i ’the coefficient of (a).
For a point located in both the telescope pupil and the local small aperture pupilP，W(r,θ) AndW’(r’,θ’) Are equivalent, i.e.
MAndM'are respectively asZ i AndZ i ’the highest order of the order of (a) of (b),a i anda i ’the relationship between them can be expressed in the form of a matrix,
wherein
And &>
Respectively the telescope pupil and the secondkA Zernike polynomial coefficient vector of a local small-aperture pupil, i.e. </or>
= [a 1 ,a 2 , …,a M ]'，/>
= [a k, 1 ,a k, 2 , …,a k, M ]';z q (x,y,ρ) To characterize the pupil of the telescope and has a maximum order ofMThe (x, y) is the rectangular coordinate of the telescope pupil,z k,p (r k ,θ k ) Characterization ofkA local small aperture pupil of orderM’The zernike polynomial of (a), (ii) (r k ,θ k ) Is the polar coordinates of the local small aperture pupil;N k,p is a polynomialz k,p (r k ,θ k ) Norm of (d);
2 conversion matrix of Zernike polynomial coefficient according to each local small aperture pupil and telescope pupilT K Building a matrixNT；
3. Computing matricesNTMoore-Penrose generalized inverse matrix ofpinv(NT)；
4. Computing matricesNTCondition number ofCond(NT)
5. Respectively changing the filling factor and the number of the local small-aperture pupils and the baseline distance between the local small-aperture pupils, and repeating the steps (1) to (4) to obtain the condition numbers of the local small-aperture pupils corresponding to different filling factors, numbers and baseline distancesCond(NT) (ii) a According to the condition numberCond(NT) The detection precision of the telescope pupil wavefront error is judged according to the size of the calculated result,Cond(NT) The smaller the value of (b), the higher the detection accuracy.
Due to the adoption of the technical scheme, the invention has the advantages that: the optimal local small aperture parameter and combination are found by calculating the condition number of a new matrix formed by each local small aperture pupil and the telescope pupil conversion matrix, so that the detection precision of the wavefront error of the large-aperture telescope is improved.
Drawings
FIG. 1 is a schematic diagram of a telescope pupil and a local small aperture pupil provided by an embodiment of the invention;
FIG. 2 is a graph of the result of calculating the condition number of the matrix NT under different fill factors according to the embodiment of the present invention;
FIG. 3 is a structural diagram of the number of local small-aperture pupils at the same fill factor according to an embodiment of the present invention;
FIG. 4 is a graph of the condition number calculation results for matrices NT for different numbers of local small-aperture pupils at the same fill factor provided by an embodiment of the present invention;
FIG. 5 is a schematic diagram of an aperture structure with different baseline distances for the same fill factor and local small aperture pupil numbers of 3 and 5, respectively, provided by an embodiment of the present invention;
FIG. 6 is a graph of the condition number calculation results for the matrix NT for aperture structures with different baseline distances for the same fill factor and local small aperture pupil numbers of 3 and 5, respectively, as provided by an embodiment of the present invention;
FIG. 7 is a computational flow diagram of the present invention.
The specific implementation mode is as follows:
the technical scheme of the invention is further explained by combining the attached drawings and the embodiment
Example 1
Referring to fig. 1, the large circle and the small circle in the figure represent a telescope pupil and a local small aperture pupil, respectively, and the wavefront errors of the telescope pupil and the local small aperture pupil are described by a combination of 36-order zernike polynomials. The condition numbers of the matrix NT at different fill factors, defined as the ratio of the sum of the local small aperture pupil areas to the telescope pupil area, were calculated separately, and the results are shown in fig. 2. It can be seen that the condition number of the transition matrix decreases significantly with increasing fill factor. When the fill factor is equal to 1, the condition number of the conversion matrix takes a minimum value of 1.
When the filling factor is kept constant and the number of local small aperture pupils is increased from 1 to 6 respectively, as shown in fig. 3 (a) -3 (f), the corresponding matrixes are calculated respectivelyNTThe results are shown in FIG. 4. While the fill factor remains constant, the transformation matrix is increased as the number of sub-apertures increases from 2 to 6NTReduced from 267.44 to 7.44.
As shown in FIG. 5, three and five local small-aperture pupils are taken as examples, the baseline distance of the local small aperture is changed respectively, and the corresponding matrix under different normalized baseline distances is calculatedNTThe results are shown in FIG. 6. When the number of the local small apertures is 3, and the normalized baseline length is increased from 0.38 to 0.69, the corresponding matrixNTRapidly decreases from 795.95 to 126.49. When the number of local apertures is 5, the corresponding matrix increases from 0.46 to 0.76 as the normalized baseline increasesNTReduced from 183.07 to 12.24. The results show that when the number of subapertures is fixed, the matrix is transformedNTIs inversely proportional to the baseline length.
Claims (1)
1. A method for improving the wavefront error detection precision of a large-aperture telescope is characterized by comprising the following steps:
(1) Constructing a Zernike polynomial coefficient conversion matrix of the telescope pupil and each local small-caliber pupil according to the relative positions of a plurality of local small-caliber pupils in the pupil of the large-caliber telescopeT K
Wherein
And &>
Respectively the telescope pupil and the secondkA Zernike polynomial coefficient vector of a local small-aperture pupil, i.e. </or>
= [a 1 , a 2 , …, a M ]'，/>
= [a k, 1 , a k, 2 , …, a k, M ]'; z q (x,y,ρ) To characterize the pupil of the telescope and has a maximum order ofMThe (x, y) is the rectangular coordinate of the telescope pupil,z k,p (r k ,θ k ) Characterisation of the firstkA local small aperture pupil of orderM’Of ZerniaThe number of the gram-polynomial is, (ii) (r k ,θ k ) Is the polar coordinates of the local small aperture pupil;N k,p is a polynomialz k,p (r k ,θ k ) The norm of (d);
(2) Converting matrix according to Zernike polynomial coefficient of each local small-aperture pupil and telescope pupilT K Building a matrixNT；
(3) Computing matricesNTMoore-Penrose generalized inverse matrix of (1)pinv(NT)；
(4) Computing matricesNTCondition number ofCond(NT)
(5) Respectively changing the filling factor and the number of the local small-aperture pupils and the baseline distance between the local small-aperture pupils, and repeating the steps (1) to (4) to obtain the condition numbers of the local small-aperture pupils corresponding to different filling factors, numbers and baseline distancesCond(NT) (ii) a According to the condition numberCond(NT) The detection precision of the telescope pupil wavefront error is judged according to the size of the calculated result,Cond(NT) The smaller the value of (b), the higher the detection accuracy.
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