CN103134660B - Method acquiring telescope primary and secondary mirror alignment error based on astigmatism decomposition - Google Patents

Abstract

The invention relates to a method acquiring telescope primary and secondary mirror alignment error based on astigmatism decomposition. The method includes the steps of measuring four misalignment rates of a secondary mirror and the proportionality coefficient of exit pupil wavefront error astigmatism coefficient to coma coefficient, wherein the proportionality coefficient is expressed through a zernike polynomial, measuring a real-time exit pupil wavefront error, placing a misalignment rate dx and a misalignment ty of the secondary mirror in one group, placing a misalignment rate dy and a misalignment rate tx of the secondary mirror in one group, decomposing a astigmatism item Ast into Astx and Asty, constructing a relation model of the misalignment rates and the astigmatism item, solving a coupling coefficient Alpha x and a coupling coefficient Alpha y, constructing a relation model of the misalignment rates and a coma item, and solving the misalignment rates of the secondary mirror according to a constructed relation model of the misalignment rates and the wavefront error.

Description

The method obtaining telescope primary and secondary mirror alignment error is decomposed based on astigmatism

Technical field

The invention belongs to field of photodetection, relate to the decomposition method of alignment error, is exactly the method calculating axis reflector formula telescope primary and secondary mirror alignment error according to emergent pupil wavefront information specifically.

Background technology

The alignment error of axis reflector formula telescope primary and secondary mirror directly can affect the optical characteristics of whole telescopic system, in order to allow telescope as far as possible by designing requirement work, needs the alignment error reducing primary and secondary mirror as far as possible.Particularly for large telescope and the space telescope of more than bore 1m, be not easy to direct labor's aligning and debug, if primary and secondary mirror alignment error crosses senior general greatly reduce telescopical image quality, even make it complete assigned tasks.In addition for the telescope in work, due to factors such as vibrations, thermal deformation, weight distortion, also can cause the alignment error of primary and secondary mirror, in order to ensure that telescope is in optimum Working always, the alignment error of primary and secondary mirror must be revised in real time.Technique of alignment based on emergent pupil wavefront error has all done more research both at home and abroad, but because mathematical model is complicated or it is loaded down with trivial details to debug process, is not easy to quick, high precision alignment primary and secondary mirror.

Common alignment algorithm has CAA algorithm, reverse optimization algorithm, SPGD algorithm etc.GaoZhishan, the people such as Chen Lei are at article " Computer aided alignment for a referencetransmission sphere of an interferometer ", (" Optical Engineering ", 43 (1), 69-74 (2004)) in use CAA algorithm to aim at a spherical wave generator, but this algorithm can not good decoupling zero astigmatism for axis reflector telescope, and when actual measurement, higher order aberratons is comparatively large by such environmental effects, is not easy to as evaluation index.Seonghui Kim, the people such as Ho-SoonYang are at article " Merit function regression method for efficient alignmentcontrol of two-mirror optical systems " (" Optical Express ", 15 (8), 5059-5068 (2007)) in propose and use merit function decay algorithm (i.e. reverse optimization algorithm) to aim at the method for cassette telescope primary and secondary mirror, but this algorithm is uncertain for computing time, and likely converges on local extremum.Han Xingzi, the people such as Yu Xin are in paper " random paralleling gradient descent algorithm is used for the simulation study of secondary mirror calibration " (" laser and optoelectronics progress ", 47, 042201 (2010)) propose in utilize SPGD algorithm (random paralleling gradient descent algorithm) when without the secondary mirror aiming at coaxial three-mirror system when Wavefront sensor and systematic parameter the unknown, it is uncertain equally to there is convergence time in this algorithm, and likely converge on the drawback of local extremum, owing to being rigid motion when secondary mirror adjusts, the wavefront error that the misalignment rate of each degree of freedom causes is not identical yet, affect size also not identical, convergence when droop error and centrifugal error are likely different, the reliability and stability of algorithm are not high.

Summary of the invention

In order to overcome the deficiencies in the prior art, the object of this invention is to provide a kind of based on astigmatism decomposition, setting up the mathematical model between axis reflector telescope primary and secondary mirror misalignment amount and emergent pupil wavefront error.

To achieve these goals, method of decomposing acquisition telescope primary and secondary mirror alignment error based on astigmatism provided by the invention, the step obtaining telescope primary and secondary mirror alignment error comprises following:

Step S1: the secondary mirror in optical system is measured, scale-up factor between the emergent pupil wavefront error astigmatism item obtaining secondary mirror four misalignment rates and adopt zernike polynomial to represent and the zernike coefficient of coma item, when measuring one in misalignment rate, keep other misalignment rate constant; Described four misalignment rates comprise: dx is secondary mirror summit the first translation misalignment rate in the x-direction, dy is secondary mirror summit the second translation misalignment rate in the y-direction, tx is the following vertex point of secondary mirror is the first inclination misalignment rate that rotation center rotates around x-axis, and ty is the following vertex point of secondary mirror is the second inclination misalignment rate that rotation center rotates around y-axis;

Step S2: directional light or axle to be put into light source, measures the wavefront error at optical system emergent pupil place, obtains the zernike coefficient of emergent pupil astigmatism item and coma item Coma;

Step S3: the first translation misalignment rate of secondary mirror and the second inclination misalignment rate are divided into one group, second translation misalignment rate and the first inclination misalignment rate are divided into one group, with primary mirror optical axis during primary and secondary mirror ideal position for Z axis, secondary mirror summit is that true origin sets up left hand cartesian coordinate system, and the emergent pupil astigmatism item Ast recorded is decomposed into Ast _xand Ast _y, represent as follows:

$\mathrm{Ast}=\sqrt{{\mathrm{Ast}}_0^2+{\mathrm{Ast}}_{45}^2}---\left(1\right)$

${\mathrm{Ast}}_x=\frac{\mathrm{Ast}-{\mathrm{Ast}}_0}{2}---\left(2\right)$

${\mathrm{Ast}}_y=\frac{\mathrm{Ast}+{\mathrm{Ast}}_0}{2}---\left(3\right)$

Wherein, Ast _xfor the astigmatism produced by the first translation misalignment rate and the second inclination imbalance amount, Ast _yfor the astigmatism produced by the second translation misalignment rate and the first inclination imbalance amount, Ast ₀and Ast ₄₅be respectively 0 ° of astigmatism and 45 ° of astigmatisms;

Step S4: build and produce astigmatism Ast by the first translation misalignment rate and the second inclination misalignment rate acting in conjunction _xrelational model, build and produce astigmatism Ast by the second translation misalignment rate and the first inclination misalignment rate acting in conjunction _ybetween relational model, as follows:

Ka _dx·dx ²+2α _x·dx·ty+Ka _ty·ty ²＝Ast _x(4)

Ka _dy·dy ²+2α _y·dy·tx+Ka _tx·tx ²＝Ast _y(5)

Respectively to dx and dy differentiate, then have:

${\mathrm{Ka}}_{\mathrm{dx}}\·\mathrm{dx}+{\mathrm{\α}}_x\·\mathrm{ty}=\frac{1}{2}\frac{\∂{\mathrm{Ast}}_x}{\∂\mathrm{dx}}---\left(6\right)$

${\mathrm{Ka}}_{\mathrm{dy}}\·\mathrm{dy}+{\mathrm{\α}}_y\·\mathrm{tx}=\frac{1}{2}\frac{\∂{\mathrm{Ast}}_y}{\∂\mathrm{dy}}---\left(7\right)$

Wherein, α _xand α _yfor coupling coefficient, Ka _dxthe scale-up factor that a symbol represents between secondary mirror first translation misalignment rate and zernike coefficient astigmatism item, Ka _dythe scale-up factor that a symbol represents between secondary mirror second translation misalignment rate and zernike coefficient astigmatism item, Ka _txthat a symbol represents the scale-up factor that secondary mirror first tilts between misalignment rate and zernike coefficient astigmatism item, Ka _tythat a symbol represents the scale-up factor that secondary mirror second tilts between misalignment rate and zernike coefficient astigmatism item;

Step S5: build and produce coma item Coma by the first translation misalignment rate and the second inclination misalignment rate acting in conjunction ₀relational model, build and produce coma item Coma by the second translation misalignment rate and the first inclination misalignment rate acting in conjunction ₉₀relational model, meet following relation between them:

Kc _dx·dx+Kc _ty·ty＝Coma ₀(8)

Kc _dy·dy+Kc _tx·tx＝Coma ₉₀(9)

Wherein, Coma ₀and Coma ₉₀be respectively 0 ° of coma and 90 ° of comas, Kc _dxthe scale-up factor that a symbol represents between secondary mirror first translation misalignment rate and zernike coefficient coma item, Kc _dythe scale-up factor that a symbol represents between secondary mirror second translation misalignment rate and zernike coefficient coma item, Kc _txthe scale-up factor that a symbol represents between secondary mirror first translation misalignment rate and zernike coefficient coma item, Kc _tythat a symbol represents the scale-up factor that secondary mirror second tilts between misalignment rate and zernike coefficient coma item;

Step S6: need when combinatorial formula 4,5,8,9 solves to attempt moving, to determine correct moving direction; Combinatorial formula 6,7,8,9 needs when solving first to move a small quantity Δ dx and Δ dy, and then tries to achieve each misalignment rate of secondary mirror.

The present invention's tool compared with existing technical method has the following advantages:

(1) the present invention is based on astigmatism to decompose, calculate primary and secondary mirror misalignment amount in conjunction with coma, do not rely on tilt quantity, higher order aberratons, and locally face shape error is insensitive, environmental requirement is lower, reduces the installation requirement of surveying instrument to primary and secondary mirror simultaneously.

(2) the present invention directly can calculate misalignment rate, and computational accuracy improves along with the reduction of misalignment rate, reduces the blindness in alignment procedures, only needs just can realize high precision alignment several times, is convenient to realize real-time auto-alignment.

(3) mathematical model of the present invention is simple, only need measure several coefficient and just can calculate, convenient realization.

The present invention successfully achieves the decoupling zero of secondary mirror misalignment rate, thus provides foundation for primary and secondary mirror is aimed at accurately and fast, may be used for the real-time auto-alignment of primary and secondary mirror.

Accompanying drawing explanation

Fig. 1 the present invention is based on astigmatism to decompose the method obtaining axis reflector formula telescope primary and secondary mirror alignment error;

Fig. 2 a to Fig. 2 c is that misalignment rate schematic diagram aimed at by primary and secondary mirror;

Fig. 3 is that primary and secondary mirror alignment error detects light path schematic diagram;

Fig. 4 a to Fig. 4 b is coupling coefficient α _xmensuration example.

Embodiment

Below in conjunction with accompanying drawing, embodiments of the invention are described.

As Fig. 1 illustrates the method for decomposing acquisition telescope primary and secondary mirror alignment error based on astigmatism, concrete steps are:

Step S1: the secondary mirror in optical system is measured, scale-up factor between the emergent pupil wavefront error astigmatism item obtaining secondary mirror four misalignment rates and adopt zernike polynomial to represent and the zernike coefficient of coma item, when measuring one in misalignment rate, keep other misalignment rate constant; Described four misalignment rates comprise: dx is secondary mirror summit the first translation misalignment rate in the x-direction, dy is secondary mirror summit the second translation misalignment rate in the y-direction, tx is the following vertex point of secondary mirror is the first inclination misalignment rate that rotation center rotates around x-axis, and ty is the following vertex point of secondary mirror is the second inclination misalignment rate that rotation center rotates around y-axis;

Step S2: directional light or axle to be put into light source, measures the wavefront error at optical system emergent pupil place, obtains the zernike coefficient of emergent pupil astigmatism item Ast and coma item Coma;

Step S3: the first translation misalignment rate dx of secondary mirror and the second inclination misalignment rate ty is divided into one group, second translation misalignment rate dy and the first inclination misalignment rate tx is divided into one group, with primary mirror optical axis during primary and secondary mirror ideal position for Z axis, secondary mirror summit is that true origin sets up left hand cartesian coordinate system, and the emergent pupil astigmatism item Ast recorded is decomposed into Ast _xand Ast _y, represent as follows:

$\mathrm{Ast}=\sqrt{{\mathrm{Ast}}_0^2+{\mathrm{Ast}}_{45}^2}---\left(1\right)$

${\mathrm{Ast}}_x=\frac{\mathrm{Ast}-{\mathrm{Ast}}_0}{2}---\left(2\right)$

${\mathrm{Ast}}_y=\frac{\mathrm{Ast}+{\mathrm{Ast}}_0}{2}---\left(3\right)$

Wherein, Ast _xfor the astigmatism produced by the first translation misalignment rate dx and the second inclination misalignment rate ty, Ast _yfor the astigmatism produced by the second translation misalignment rate dy and the first inclination misalignment rate tx, Ast ₀and Ast ₄₅be respectively 0 ° of astigmatism and 45 ° of astigmatisms;

Step S4: build and produce astigmatism Ast by the first translation misalignment rate dx and the second inclination misalignment rate ty acting in conjunction _xrelational model, build and produce astigmatism Ast by the second translation misalignment rate dy and the first inclination misalignment rate tx acting in conjunction _ybetween relational model, as follows:

Ka _dx·dx ²+2α _x·dx·ty+Ka _ty·ty ²＝Ast _x(4)

Ka _dy·dy ²+2α _y·dy·tx+Ka _tx·tx ²＝Ast _y(5)

Respectively to dx and dy differentiate, then have:

${\mathrm{Ka}}_{\mathrm{dx}}\·\mathrm{dx}+{\mathrm{\α}}_x\·\mathrm{ty}=\frac{1}{2}\frac{\∂{\mathrm{Ast}}_x}{\∂\mathrm{dx}}---\left(6\right)$

${\mathrm{Ka}}_{\mathrm{dy}}\·\mathrm{dy}+{\mathrm{\α}}_y\·\mathrm{tx}=\frac{1}{2}\frac{\∂{\mathrm{Ast}}_y}{\∂\mathrm{dy}}---\left(7\right)$

Wherein, α _xand α _yfor coupling coefficient, Ka _dxthe scale-up factor that a symbol represents between secondary mirror first translation misalignment rate dx and zernike coefficient astigmatism item, Ka _dythe scale-up factor that a symbol represents between secondary mirror second translation misalignment rate dy and zernike coefficient astigmatism item, Ka _txthat a symbol represents the scale-up factor that secondary mirror first tilts between misalignment rate tx and zernike coefficient astigmatism item, Ka _tythat a symbol represents the scale-up factor that secondary mirror second tilts between misalignment rate ty and zernike coefficient astigmatism item;

Step S5: build and produce coma item Coma by the first translation misalignment rate dx and the second inclination misalignment rate ty acting in conjunction ₀relational model, build and produce coma item Coma by the second translation misalignment rate dy and the first inclination misalignment rate tx acting in conjunction ₉₀relational model, meet following relation between them:

Kc _dx·dx+Kc _ty·ty＝Coma ₀(8)

Kc _dy·dy+Kc _tx·tx＝Coma ₉₀(9)

Wherein, Coma ₀and Coma ₉₀be respectively 0 ° of coma and 90 ° of comas, Kc _dxthe scale-up factor that a symbol represents between secondary mirror first translation misalignment rate dx and zernike coefficient coma item, Kc _dythe scale-up factor that a symbol represents between secondary mirror second translation misalignment rate dy and zernike coefficient coma item, Kc _txthe scale-up factor that a symbol represents between secondary mirror first translation misalignment rate tx and zernike coefficient coma item, Kc _tythat a symbol represents the scale-up factor that secondary mirror second tilts between misalignment rate ty and zernike coefficient coma item;

Step S6: need when combinatorial formula 4,5,8,9 solves to attempt moving, to determine correct moving direction; Combinatorial formula 6,7,8,9 needs when solving first to move a small quantity Δ dx and Δ dy, and then tries to achieve each misalignment rate of secondary mirror.

Wherein: build individually measure each misalignment rate independent role of secondary mirror time and the zernike coefficient of astigmatism item between scale-up factor and each misalignment rate independent role time and the zernike coefficient of coma item between scale-up factor time fitting function model be:

Ast ₀＝Ka _dx·dx ²

Ast ₀＝Ka _dy·dy ²(10)

Ast ₀＝Ka _tx·tx ²

Ast ₀＝Ka _ty·ty ²

Coma ₀＝Kc _dx·dx

Coma ₉₀＝Kc _dy·dy (11)

Coma ₉₀＝Kc _tx·tx

Coma ₀＝Kc _ty·ty

Wherein, formula 10 is the fitting function model of astigmatism item, and formula 11 is the fitting function model of coma item.

Wherein: measure coupling coefficient α _xand α _ystep is as follows;

Step S41: a given second inclination misalignment rate ty, keep the second translation misalignment rate dy, the first inclination misalignment rate tx be zero, measure the second inclination misalignment rate ty non-vanishing time astigmatism item Ast ' _xastigmatism item Ast when being zero with the second inclination misalignment rate ty _xdifference DELTA Ast _dxvariation relation with the first inclination misalignment rate dx:

ΔAst _dx＝Ast′ _x-Ast _x| _ty＝0

＝Ka _dx·dx ²+2α _x·dx·ty+Ka _ty·ty ²-Ka _dx·dx ²(12)

＝2α _x·dx·ty+Ka _ty·ty ²

Coupling coefficient α is obtained according to above formula _x, in like manner, a given first inclination misalignment rate tx has:

ΔAst _dy＝Ast′ _y-Ast _y| _tx＝0

＝Ka _dy·dy ²+2α _y·dy·tx+Ka _tx·tx ²-Ka _dy·dy ²(13)

＝2α _y·dy·tx+Ka _tx·tx ²

And then obtain coupling coefficient α _y.

Wherein: the method building each misalignment rate of solving equations secondary mirror with formula 4,5,8,9 is as follows:

(1) build system of equations with formula 4,5,8,9, solve an equation and solve two groups of solutions, non trivial solution is the size of each misalignment rate of secondary mirror;

(2) first compensate according to the misalignment rate of first group of solution to secondary mirror, if emergent pupil wavefront error increases, adopt second group of solution to compensate.

Wherein: the method building each misalignment rate of solving equations secondary mirror with formula 6,7,8,9 is as follows:

A () allows secondary mirror carry out small translation Δ dx along the x-axis direction and carries out small translation Δ dy along the y-axis direction;

(b) measure secondary mirror carry out minute movement after emergent pupil wavefront, and calculate now Ast _xand Ast _yminor alteration amount Δ Ast _xwith Δ Ast _y, then have:

$\frac{\∂{\mathrm{Ast}}_x}{\∂\mathrm{dx}}\≈\frac{\mathrm{\Δ}{\mathrm{Ast}}_x}{\mathrm{\Δdx}},$ $\frac{\∂{\mathrm{Ast}}_y}{\∂\mathrm{dy}}\≈\frac{\mathrm{\Δ}{\mathrm{Ast}}_y}{\mathrm{\Δdy}}$

C () builds system of equations with formula 6,7,8,9, solve an equation and try to achieve unique solution, non trivial solution is each misalignment rate size of secondary mirror.

The definition of the primary and secondary mirror alignment error related in the present invention is as shown in Fig. 2 a to Fig. 2 c, it is the process realizing primary and secondary mirror optical axis coincidence that primary and secondary mirror is aimed at, if with primary mirror 4 for reference, then all alignment errors all can be considered as that secondary mirror 3 produces relative to primary mirror.Because change the change that primary mirror can cause incident light beam strikes angle in actual measurement process, and the visual field measured by measuring system also can be allowed to change.The correctness ensureing each arbitrary boundary conditions is difficult to like this in adjustment with computation process.In addition, re-use before the present invention aims at, first must carry out coarse alignment to primary and secondary mirror, at least ensure that measuring system can record emergent pupil wavefront error.With secondary mirror summit in idealized system for initial point, optical axis is that z-axis sets up left hand cartesian coordinate system xoy, and primary and secondary mirror alignment error is all given a definition at this coordinate system.Containing secondary mirror 3, primary mirror 4 in Fig. 2 a, symbol F, D, T are error signal label symbol in this figure, just in order to the space form of figuratively this several error bright, not there is strict mathematics define, symbol F represents defocus error, symbol D represents that the centrifugal error of primary optical axis is departed from secondary mirror summit, droop error when symbol T represents that secondary mirror optical axis and primary mirror optical axis exist certain angle; In Fig. 2 b, symbol tx represents the first inclination misalignment rate of secondary mirror optical axis when the rotation of x-axis and primary mirror optical axis exist angle, centrifugal second translation misalignment rate when symbol dy represents that primary mirror optical axis is departed from along y-axis in secondary mirror summit; In Fig. 2 c, symbol ty represents the second inclination misalignment rate of secondary mirror optical axis when the rotation of y-axis and primary mirror optical axis exist angle, centrifugal first translation misalignment rate when symbol dx represents that primary mirror optical axis is departed from along x-axis in secondary mirror summit.Following analytical calculation is all carried out under this definition, if adjusted with other rotation centers during adjustment, then needs will to calculate the margin of error of gained by changes in coordinates, under being converted to the coordinate system at place during actual adjustment.

As shown in Figure 3, wherein, figure comprises parallel light tube 1 to the present invention's detection light path used, is Wavefront sensor 2, secondary mirror 3, primary mirror 4.Here adopt directional light to be reference light, parallel light tube 1 or starlight in reality, can be used as reference light.First ensure during measurement that reference light is parallel with the optical axis of primary mirror 4, if adopt starlight as with reference to light, then need to ensure that asterism is on the optical axis of primary mirror 4.Then, Wavefront sensor 2 is placed near telescope theoretical focal point position.The surface testing data obtaining primary mirror 4 and secondary mirror 3 are also needed, using as modified value during actual measurement before measurement.Six degree of freedom adjusting mechanism can be adopted when secondary mirror 3 adjusts.In order to the validity of estimation algorithm, a telescopical optical model of cassette is set up with optical design software ZEMAX, and the first translation misalignment rate setting secondary mirror 3 is dx=1mm, second translation misalignment rate dy=1mm, first inclination misalignment rate is tx=0.5 °, and second tilts to move misalignment rate ty=2 °.

In above definition with under requiring, the present invention realizes an embodiment according to the following steps:

The first step, measure each misalignment rate of secondary mirror 3 and the scale-up factor between wavefront error astigmatism item and coma term coefficient, when measure wherein one time, keep other misalignment rates of secondary mirror 3 constant, such as, when measuring the scale-up factor of dx, need to keep misalignment rate dy, tx, ty of secondary mirror 3 to be zero or remain unchanged, record each coefficient and be respectively: Ka _dxfor-0.104, Ka _dybe 0.104, Ka _txbe 0.6616, Ka _tyfor-0.6616, Kc _dxbe 1.2654, Kc _dybe 1.2654, Kc _txfor-3.3855 and Kc _tybe 3.3855;

Second step, using directional light as with reference to light, measures the wavefront error at primary mirror 4 and secondary mirror 3 emergent pupil place, obtains the zernike coefficient (adopting Fringe arrangement mode) of astigmatism item and coma item: Ast ₀for-1.961, Ast ₄₅be 1.425, Coma ₀be 8.043, Coma ₉₀for-0.4188, Ast ₀and Ast ₄₅be respectively the zernike coefficient of 0 ° of astigmatism and 45 ° of astigmatisms, Coma ₀and Coma ₉₀be respectively 0 ° of coma and 90 coma zernike coefficients;

3rd step, is divided into one group by the first translation misalignment rate dx of secondary mirror 3 and the second inclination misalignment rate ty, and the second translation misalignment rate dy and the first inclination misalignment rate tx is divided into one group.The astigmatism produced by the first translation misalignment rate dx and the second inclination misalignment rate ty is defined as Ast _x, the astigmatism produced by the second translation misalignment rate dy and the first inclination misalignment rate tx is defined as Ast _y, the emergent pupil astigmatism recorded is decomposed into Ast by profit with the following method _xand Ast _y:

$\mathrm{Ast}=\sqrt{{\mathrm{Ast}}_0^2+{\mathrm{Ast}}_{45}^2}=2.424$

${\mathrm{Ast}}_x=\frac{\mathrm{Ast}-{\mathrm{Ast}}_0}{2}=2.192$

${\mathrm{Ast}}_y=\frac{\mathrm{Ast}+{\mathrm{Ast}}_0}{2}=0.2316$

Wherein, due to Ka _dxand Ka _tyfor negative value, all Ast _xbe taken as-2.192;

4th step, measures α _xand α _y:

A given ty, measures astigmatism item Ast ' with this understanding _xwith the change of dx, as shown in fig. 4 a.In Fig. 4 a, horizontal ordinate represents that the distance of primary mirror optical axis is departed from along x-axis in secondary mirror summit, i.e. the size of misalignment rate dx; In Fig. 4 a, ordinate represents the Ast that emergent pupil wavefront error Ast obtains after decomposing _x; Ast when solid line represents that the second inclination misalignment rate ty of secondary mirror is 0 ° in Fig. 4 a _xwith the situation that the first translation misalignment rate dx changes, in figure, other line represents that secondary mirror second tilts misalignment rate ty Ast when being different value respectively _xwith the situation that the first translation misalignment rate dx changes.Then according to following formula:

ΔAst _dx＝Ast′ _x-Ast _x| _ty＝0

＝Ka _dx·dx ²+2α _x·dx·ty+Ka _ty·ty ²-Ka _dx·dx ²

＝2α _x·dx·ty+Ka _ty·ty ²

Astigmatism item Ast ' when can to obtain the second inclination misalignment rate ty be not 0 ° _xastigmatism item Ast when being 0 ° with the second inclination misalignment rate ty _xdifference DELTA Ast _dx, as shown in Figure 4 b.In Fig. 4 b, horizontal ordinate represents that the distance of primary mirror optical axis is departed from along x-axis in secondary mirror summit; Astigmatism item Ast ' when ordinate represents that the second inclination misalignment rate ty is non-vanishing in Fig. 4 a _xastigmatism item Ast when being 0 ° with the second inclination misalignment rate ty _xdifference DELTA Ast _dx; Astigmatism item Ast ' when solid line represents that the second inclination misalignment rate ty of secondary mirror is 0.5 ° in Fig. 4 a _xastigmatism item Ast when being 0 ° with the second inclination misalignment rate ty of secondary mirror _xdifference DELTA Ast _dxwith the situation that the first translation misalignment rate dx changes, in figure, other line represents that secondary mirror second tilts misalignment rate ty Δ Ast when being different value respectively _dxwith the situation that the first translation misalignment rate dx changes.According to the straight line parameter of matching, just can in the hope of α _xnamely and Ka, be easyly taken as 0.104 here to calculate, _dxabsolute value equal.In fact, α _xbeing the number changed with the second inclination misalignment rate ty, if the computational accuracy in order to pursue large misalignment rate scope, then needing to carry out matching by the polynomial expression of the second inclination misalignment rate ty.Here be chosen at misalignment rate less time result of calculation, being on the one hand easy in order to what calculate, is to ensure the precision restrained, namely ensureing when misalignment rate is less by higher calculation accuracy on the other hand.

In like manner α can be obtained _ybe 0.104;

5th step, the misalignment rate calculating secondary mirror in two ways can be adopted:

(1) directly solve, solve rear dx and ty, dy and tx two groups has two groups of solutions respectively, because boundary condition is not enough, therefore need first to revise by wherein 1/2 or other Appropriates of one group, if the astigmatism item of emergent pupil wavefront and coma item all obviously reduce, then revise by this group solution; If emergent pupil wavefront astigmatism item and coma item all obviously increase, then direct by another group solution revise.

After aiming at according to computing method (1) first time, residual error is:

δdx＝-0.1357mm，δdy＝0.2459mm，δtx＝5.667′，δty＝2.921′，

Second time aims at rear residual error:

δdx＝0.126μm，δdy＝-0.264μm，δtx＝0.9792″，δty＝0.5616″。

(2) adopt the differential equation to solve, now need first to make secondary mirror 3 produce quantitative Δ dx and Δ dy misalignment rate, this active misalignment rate does not go out visual field with target and is advisable, then now have:

After aiming at according to computing method (2) first time, residual error is:

δdx＝1.03mm，δdy＝1.045mm，δtx＝23.59′，δty＝-2321′，

Second time aims at rear residual error:

δdx＝-34.68μm，δdy＝-34.65μm，δtx＝40.49″，δty＝40.66″。

Above two kinds of computing method are in first time to having the larger error of calculation on time, and second time computational accuracy obviously improves greatly, and this choosing with coupling coefficient is relevant.

From result of calculation, two kinds of method for solving all effectively can calculate misalignment rate.Wherein, computing method (2) solve with differential approximation, from ideal value very close to time not easily hold due to amount of movement, and due to the approximate relative error caused comparatively large, therefore when misalignment rate is very near apart from ideal value, this arithmetic accuracy is not high.Computing method (1) are although computational accuracy is high, but need to separate quadratic equation, calculate more complicated, and computing method (2) are also having enough computational accuracies away from during ideal value, so adopt computing method (2) when misalignment rate is far away apart from ideal value, adopt computing method (1) when distance ideal value is nearer.

The above; be only the embodiment in the present invention, but protection scope of the present invention is not limited thereto, any people being familiar with this technology is in the technical scope disclosed by the present invention; the conversion or replacement expected can be understood, all should be encompassed in of the present invention comprising within scope.

Claims (5)

1. decompose the method obtaining telescope primary and secondary mirror alignment error based on astigmatism, it is characterized in that comprising the following steps:

Step S1: the secondary mirror in optical system is measured, scale-up factor between the emergent pupil wavefront error astigmatism item obtaining secondary mirror four misalignment rates and adopt zernike polynomial to represent and the zernike coefficient of coma item, when measuring one in misalignment rate, keep other misalignment rate constant; Described four misalignment rates comprise: dx is secondary mirror summit the first translation misalignment rate in the x-direction, dy is secondary mirror summit the second translation misalignment rate in the y-direction, tx is the following vertex point of secondary mirror is the first inclination misalignment rate that rotation center rotates around x-axis, and ty is the following vertex point of secondary mirror is the second inclination misalignment rate that rotation center rotates around y-axis;

Step S2: directional light or axle to be put into light source, measures the wavefront error at optical system emergent pupil place, obtains the zernike coefficient of emergent pupil astigmatism item and coma item Coma;

Step S3: the first translation misalignment rate of secondary mirror and the second inclination misalignment rate are divided into one group, second translation misalignment rate and the first inclination misalignment rate are divided into one group, with primary mirror optical axis during primary and secondary mirror ideal position for Z axis, secondary mirror summit is that true origin sets up left hand cartesian coordinate system, and the emergent pupil astigmatism item Ast recorded is decomposed into Ast _xand Ast _y, represent as follows:

$\mathrm{Ast}=\sqrt{{\mathrm{Ast}}_0^2+{\mathrm{Ast}}_{45}^2}---\left(1\right)$

${\mathrm{Ast}}_x=\frac{\mathrm{Ast}-{\mathrm{Ast}}_0}{2}---\left(2\right)$

${\mathrm{Ast}}_y=\frac{\mathrm{Ast}+{\mathrm{Ast}}_0}{2}---\left(3\right)$

Wherein, Ast _xfor the astigmatism produced by the first translation misalignment rate and the second inclination imbalance amount, Ast _yfor the astigmatism produced by the second translation misalignment rate and the first inclination imbalance amount, Ast ₀and Ast ₄₅be respectively 0 ° of astigmatism and 45 ° of astigmatisms;

Step S4: build and produce astigmatism Ast by the first translation misalignment rate and the second inclination misalignment rate acting in conjunction _xrelational model, build and produce astigmatism Ast by the second translation misalignment rate and the first inclination misalignment rate acting in conjunction _ybetween relational model, as follows:

Ka _dx·dx ²+2α _x·dx·ty+Ka _ty·ty ²＝Ast _x(4)

Ka _dy·dy ²+2α _y·dy·tx+Ka _tx·tx ²＝Ast _y(5)

Respectively to dx and dy differentiate, then have:

${\mathrm{Ka}}_{\mathrm{dx}}\·\mathrm{dx}+{\mathrm{\α}}_x\·\mathrm{ty}=\frac{1}{2}\frac{{\∂\mathrm{Ast}}_x}{\∂\mathrm{dx}}---\left(6\right)$

${\mathrm{Ka}}_{\mathrm{dy}}\·\mathrm{dy}+{\mathrm{\α}}_y\·\mathrm{tx}=\frac{1}{2}\frac{{\∂\mathrm{Ast}}_y}{\∂\mathrm{dy}}---\left(7\right)$

Wherein, α _xand α _yfor coupling coefficient, Ka _dxbe a symbol represent secondary mirror first translation misalignment rate quadratic sum zernike coefficient astigmatism item between scale-up factor, Ka _dybe a symbol represent secondary mirror second translation misalignment rate quadratic sum zernike coefficient astigmatism item between scale-up factor, Ka _txbe a symbol represent secondary mirror first tilt misalignment rate quadratic sum zernike coefficient astigmatism item between scale-up factor, Ka _tybe a symbol represent secondary mirror second tilt misalignment rate quadratic sum zernike coefficient astigmatism item between scale-up factor;

Step S5: build and produce coma item Coma by the first translation misalignment rate and the second inclination misalignment rate acting in conjunction ₀relational model, build and produce coma item Coma by the second translation misalignment rate and the first inclination misalignment rate acting in conjunction ₉₀relational model, meet following relation between them:

Kc _dx·dx+Kc _ty·ty＝Coma ₀(8)

Kc _dy·dy+Kc _tx·tx＝Coma ₉₀(9)

Wherein, Coma ₀and Coma ₉₀be respectively 0 ° of coma and 90 ° of comas, Kc _dxthe scale-up factor that a symbol represents between secondary mirror first translation misalignment rate and zernike coefficient coma item, Kc _dythe scale-up factor that a symbol represents between secondary mirror second translation misalignment rate and zernike coefficient coma item, Kc _txthat a symbol represents the scale-up factor that secondary mirror first tilts between misalignment rate and zernike coefficient coma item, Kc _tythat a symbol represents the scale-up factor that secondary mirror second tilts between misalignment rate and zernike coefficient coma item;

Step S6: need when combinatorial formula 4,5,8,9 solves to attempt moving, to determine correct moving direction; Combinatorial formula 6,7,8,9 needs when solving first to move a small quantity Δ dx and Δ dy, and then tries to achieve each misalignment rate of secondary mirror.

2. according to claim 1ly decompose the method obtaining telescope primary and secondary mirror alignment error based on astigmatism, it is characterized in that: fitting function model during scale-up factor when building scale-up factor when individually measuring each misalignment rate independent role of secondary mirror and between the zernike coefficient of astigmatism item and each misalignment rate independent role and between the zernike coefficient of coma item is:

$\left\{\begin{array}{c}{\mathrm{Ast}}_0={\mathrm{Ka}}_{\mathrm{dx}}\·{\mathrm{dx}}^{2^2}\\ {\mathrm{Ast}}_0={\mathrm{Ka}}_{\mathrm{dy}}\·{\mathrm{dy}}^2\\ {\mathrm{Ast}}_0={\mathrm{Ka}}_{\mathrm{tx}}\·{\mathrm{tx}}^2\\ {\mathrm{Ast}}_0={\mathrm{Ka}}_{\mathrm{ty}}\·\mathrm{ty}\end{array}\right.---\left(10\right)$

$\left\{\begin{array}{c}{\mathrm{Coma}}_0={\mathrm{Kc}}_{\mathrm{dx}}\·\mathrm{dx}\\ {\mathrm{Coma}}_{90}={\mathrm{Kc}}_{\mathrm{dy}}\·\mathrm{dy}\\ {\mathrm{Coma}}_{90}={\mathrm{Kc}}_{\mathrm{tx}}\·\mathrm{tx}\\ {\mathrm{Coma}}_0={\mathrm{Kc}}_{\mathrm{ty}}\·\mathrm{ty}\end{array}\right.---\left(11\right)$

Wherein, the fitting function model that formula (10) is astigmatism item, the fitting function model that formula (11) is coma item.

3. method of decomposing acquisition telescope primary and secondary mirror alignment error based on astigmatism according to claim 1, is characterized in that: measure coupling coefficient α _xand α _ystep is as follows;

Step S41: a given second inclination misalignment rate, keeps the second translation misalignment rate, the first inclination misalignment rate is zero, measure the second inclination misalignment rate non-vanishing time astigmatism item Ast ' _xastigmatism item Ast when being zero with the second inclination misalignment rate _xdifference DELTA Ast _dxvariation relation with the first inclination misalignment rate:

$\begin{array}{c}{\mathrm{\ΔAst}}_{\mathrm{dx}}={{\mathrm{Ast}}_x^{\′}-{\mathrm{Ast}}_x|}_{\mathrm{ty}=0}\\ ={\mathrm{Ka}}_{\mathrm{dx}}\·{\mathrm{dx}}^2+{2\mathrm{\α}}_x\·\mathrm{dx}\·\mathrm{ty}+{\mathrm{Ka}}_{\mathrm{ty}}\·{\mathrm{ty}}^2-{\mathrm{Ka}}_{\mathrm{dx}}\·{\mathrm{dx}}^2\\ ={2\mathrm{\α}}_x\·\mathrm{dx}\·\mathrm{ty}+{\mathrm{Ka}}_{\mathrm{ty}}\·{\mathrm{ty}}^2\end{array}---\left(12\right)$

Coupling coefficient α is obtained according to above formula _x, in like manner, a given first inclination misalignment rate has:

$\begin{array}{c}{\mathrm{\ΔAst}}_{\mathrm{dy}}={{\mathrm{Ast}}_y^{\′}-{\mathrm{Ast}}_y|}_{\mathrm{tx}=0}\\ ={\mathrm{Ka}}_{\mathrm{dy}}\·{\mathrm{dy}}^2+{2\mathrm{\α}}_y\·\mathrm{dy}\·\mathrm{tx}+{\mathrm{Ka}}_{\mathrm{tx}}\·\\ ={2\mathrm{\α}}_y\·\mathrm{dy}\·\mathrm{tx}+{\mathrm{Ka}}_{\mathrm{tx}}{\·\mathrm{tx}}^2\end{array},{\mathrm{tx}}^2-{\mathrm{Ka}}_{\mathrm{dy}}\·{\mathrm{dy}}^2---\left(13\right)$

And then obtain coupling coefficient α _y.

4. method of decomposing acquisition telescope primary and secondary mirror alignment error based on astigmatism according to claim 1, is characterized in that: the method building each misalignment rate of solving equations secondary mirror with formula 4,5,8,9 is as follows:

(1) build system of equations with formula 4,5,8,9, solve an equation and solve two groups of solutions, non trivial solution is the size of each misalignment rate of secondary mirror;

(2) first compensate according to the misalignment rate of first group of solution to secondary mirror, if emergent pupil wavefront error increases, adopt second group of solution to compensate.

5. method of decomposing acquisition telescope primary and secondary mirror alignment error based on astigmatism according to claim 1, is characterized in that: the method building each misalignment rate of solving equations secondary mirror with formula 6,7,8,9 is as follows:

A () allows secondary mirror carry out small translation Δ dx along the x-axis direction and carries out small translation Δ dy along the y-axis direction;

(b) measure secondary mirror carry out minute movement after emergent pupil wavefront, and calculate now Ast _xand Ast _yminor alteration amount Δ Ast _xwith Δ Ast _y, then now have:

$\frac{{\∂\mathrm{Ast}}_x}{\∂\mathrm{dx}}\≈\frac{{\mathrm{\ΔAst}}_x}{\mathrm{\Δdx}},\frac{{\∂\mathrm{Ast}}_y}{\∂\mathrm{dy}}\≈\frac{{\mathrm{\ΔAst}}_y}{\mathrm{\Δdy}}\≈\frac{{\mathrm{\ΔAst}}_y}{\mathrm{\Δdy}}$

C () builds system of equations with formula 6,7,8,9, solve an equation and try to achieve unique solution, non trivial solution is each misalignment rate size of secondary mirror.