CN103744173A - Telescope secondary mirror position correction method based on optical spot definition function - Google Patents

Abstract

A telescope secondary mirror position correction method based on an optical spot definition function. The method comprises the following steps: (1) and obtaining the position of the secondary mirror with an extreme value of the target function through an iterative algorithm by taking the definition of the field spots on the axis as a target function and the translation and rotation of the secondary mirror along the optical axis and in two orthogonal directions perpendicular to the optical axis as variables. If all variables are iterated simultaneously, the objective function may converge to local extrema. Therefore, each iteration process comprises two steps of iteration in the optical axis direction and the direction perpendicular to the optical axis, so that the objective function can be converged to a global extreme value; (2) and taking the average value of the definition functions of the light spots of the off-axis field of view as a target function, enabling the secondary mirror to rotate around a system zero coma point along two orthogonal directions, and iteratively seeking an extreme value of the target function to realize the correction of the relative position of the secondary mirror. The method does not need wavefront detection and reconstruction, so that the adjustment of the telescope system has an objective standard, and the imaging quality of the telescope can be monitored in real time.

Description

A kind of telescope secondary mirror method for correcting position based on spot definition function

Technical field

The present invention relates to a kind of telescope secondary mirror method for correcting position based on spot definition function.The method is applicable to telescopic system and debugs and adjust online.

Background technology

Ideally telescope primary and secondary mirror relative position is certain, but in operational process, due to the impact of the factors such as temperature, gravity, its primary and secondary mirror relative position can change.Using primary mirror culminating point as with reference to coordinate origin, the variation of system architecture comprises translation, vertical light axial translation and the vertical light axial rotation of secondary mirror along optical axis direction.The variation of primary and secondary mirror relative position can make telescope produce certain aberration.Wherein mainly comprise out of focus and spherical aberration, the vertical optical axis translation producing along optical axis direction translation or rotate the coma and the astigmatism that produce.For small field of view telescopic system, can ignore the impact of astigmatism on imaging, on axle, visual field is mainly coma.By regulating secondary mirror, can make visual field aberration on axle be proofreaied and correct, can think that the aberration of telescopic system is proofreaied and correct.But along with the increase of telescopic system visual field, astigmatism becomes and can not ignore.Only the aberration of visual field on axle is proofreaied and correct to the correction that can not realize whole visual field aberration.Therefore,, carrying out in the correction of Large Area Telescope system aberration, need to consider He Zhouwai visual field in visual field on axle simultaneously.

At present, there is the multiple method of utilizing visual field He Zhouwai on axle to carry out visual field aberration correction.For example utilize position angle and the excentricity of the outer visual field of axle far-field spot to calculate wave front aberration coefficient, thereby the method around the zero coma point anglec of rotation obtained is (referring to Collimation of Fast Wide-Field Telescopes, BRIAN A.MCLEOD, 1996); Utilize wave front detector to obtain wave front aberration coefficient, thereby the opposing connection zero coma point anglec of rotation is calculated (referring to Final alignment of the VLT, L.Noehte and S.Guisard, 2000); Utilize sensitivity matrix to set up the relation between misalignment rate and aberration coefficients, by the measurement to aberration coefficients, oppositely solve misalignment rate (referring to Reverse-optimization Alignment Algorithm using Zernike Sensitivity, Eugene D.Kim, etal, 2005).Said method all carries out indirectly or directly obtaining to wave front aberration coefficient, thereby instruct, proofreaies and correct.The shortcoming of first method is that computation complexity is higher, proofreaies and correct result and is subject to the impact of computational accuracy larger.Second method needs wave front detector etc., has increased the complexity of system.The matrix relationship that the third method is set up is that when error is larger, matrix relationship exists relatively large deviation hour approximate of error, and aberration coefficients obtains the complexity that has increased system simultaneously.From the document of publishing, can find out, the bearing calibration of telescopic system aberration is main relevant to wave front aberration coefficient, thereby makes system have certain complicacy, has increased engineering construction difficulty.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, a kind of telescope secondary mirror method for correcting position based on spot definition function is provided, the method can realize by the mode of iteration the correction of telescope primary and secondary mirror relative position, have and calculate simply, engineering construction is easy to feature.

Technical solution of the present invention is: a kind of telescope secondary mirror method for correcting position based on spot definition function.Its characterization step is as follows:

(1) using visual field spot definition on axle as objective function, optical axis direction is z direction of principal axis, the both direction of vertical optical axis is x, y direction of principal axis is set up rectangular coordinate system, the offset variable of secondary mirror comprises that along optical axis direction be the translation of z direction and the x of vertical optical axis, the translation of y direction is totally three variablees, by iterative computation, obtains the position that the secondary mirror of extreme value appears in objective function; In iterative process, iterative process comprises two steps each time, the first step: along optical axis direction translation; Second step: the translation of vertical optical axis direction and rotation; Using above-mentioned two steps as once circulation, make objective function converge to global extremum; As shown in first step cyclic process in Fig. 1;

(2) using the mean value of the sharpness function of the outer visual field of multiple axles hot spot as objective function, secondary mirror is rotated along vertical optical axis x along orthogonal both direction system for winding 1 coma point, y direction of principal axis rotates around 1 coma point, wherein the distance Z between secondary mirror culminating point and 1 coma point _cfpmeet following formula, wherein L is secondary mirror culminating point and focal plane distance, m ₂for secondary mirror magnification, the ratio of system focal length and primary mirror focal length, meets m ₂=f ,/f ₁', the focal length that f ' is telescopic system, f ₁' be the focal length of primary mirror, b _s2for secondary mirror conic section constant.The extreme value of iterative objective function, realizes the correction of secondary mirror position, as shown in second step cyclic process in Fig. 1.

$Z_{\mathrm{cfp}}=\frac{2L(m_2^2-1)}{{(m_2+1)}^2[(m_2-1)-(m_2+1)b_{s2}]}$

(1), using visual field spot definition on axle as objective function, the translation of secondary mirror along the translation of optical axis and vertical optical axis along orthogonal both direction and rotation, as variable, by certain iterative algorithm, obtain the position that the secondary mirror of extreme value appears in objective function.If all variablees are carried out to iteration simultaneously, objective function may converge to local extremum.Therefore consider respectively optical axis direction and vertical optical axis direction to be carried out to iteration, can make objective function converge to global extremum.(2) using the mean value of the sharpness function of the outer visual field of multiple axles hot spot as objective function, make secondary mirror along orthogonal x, y direction of principal axis system for winding 1 coma point rotates, and the extreme value of iterative objective function, realizes the correction of secondary mirror relative position.

The present invention's advantage is compared with prior art:

(1) the present invention utilizes the sharpness function of telescopic system far-field spot as the objective function of aberration correction, the obtaining target function value by CCD and computing machine, without carrying out wavefront measurement and wavefront reconstruction, reduced system complexity, made the adjustment of telescope primary and secondary mirror relative position there is objective standard.

(2) utilize respectively on axle and the image sharpness function of the outer visual field of axle far-field spot as objective function, coupling is understood in vertical optical axis translation and rotation to secondary mirror, can make the outer visual field of axle because the astigmatism that primary and secondary mirror deviation causes is proofreaied and correct, there is simple, direct, the effective feature of method.

(3) do not need the orientation of the outer visual field of reference axis far-field spot and excentricity etc., the distribution of the far-field spot to the outer visual field of axle does not have strict requirement, can proofread and correct according to different hot spot distribution situations, meet the actual conditions in operational process, therefore both can be used for debuging, also can be used for online adjustment.

Accompanying drawing explanation

Fig. 1 is the large visual field high resolution imaging telescope primary and secondary mirror relative position bearing calibration process flow diagram that the present invention is based on many visual fields spot definition function.

Fig. 2 is pupil and visual field point coordinate schematic diagram.

Fig. 3 is that telescope primary and secondary mirror axis meets at zero coma point schematic diagram.

Fig. 4 is the outer visual field point distribution schematic diagram of telescope axle.

Fig. 5 be on axle visual field objective function and Si Telieer than with iteration convergence curve.

Fig. 6 is the outer visual field of axle objective function convergence curve.

Fig. 7 be on the outer visual field point of the axle chosen of table 2 and axle visual field point Si Telieer than (SR) with iteration convergence curve.

Embodiment

Below the present invention is described in further details.

The ultimate principle of a kind of telescope secondary mirror method for correcting position based on spot definition function of paper.According to three rank vector wave Aberration Theory, for two mirror telescope systems, due to the translation of secondary mirror vertical optical axis or around summit, rotate produced coma and astigmatism as shown in wave front aberration formula (1), (2).

$W_{\mathrm{coma}}^{\′}=[(W_{131}\stackrel{\→}{H}-\underset{j}{\mathrm{\Σ}}{W}_{131j}{\stackrel{\→}{\mathrm{\σ}}}_j)\·\stackrel{\→}{\mathrm{\ρ}}](\stackrel{\→}{\mathrm{\ρ}}\·\stackrel{\→}{\mathrm{\ρ}})$

$W_{\mathrm{ast}}^{\′}=\frac{1}{2}[\underset{j}{\mathrm{\Σ}}{W}_{222j}{\stackrel{\→}{H}}^2-2\stackrel{\→}{H}\left(\underset{j}{\mathrm{\Σ}}{W}_{222j}{\stackrel{\→}{\mathrm{\σ}}}_j\right)+\underset{j}{\mathrm{\Σ}}{W}_{222j}{\stackrel{\→}{\mathrm{\σ}}}_j^2]\·{\stackrel{\→}{\mathrm{\ρ}}}^2$

W ' _comabe three rank coma values, W ' _astbe three rank astigmatism values, j is the surperficial number of optical element in optical system, W _131jand W _222jbe respectively three rank comas and the astigmatism coefficient of j plane system wave aberration,

for normalization visual field vector, direction is determined by position angle a, big or small by determining apart from coordinate centre distance.

for normalization pupil vector, direction determines by θ, and size is by determining apart from corresponding coordinate centre distance, as shown in Figure 2,

it is the aberration center offset of j face.For the i.e. 1 visual field point in visual field on axle,

formula only comprises Section 2 in (1)

it is constant term coma.Formula comprises last in (2)

it is constant term astigmatism.Generally, due to Section 2 in a rear relative formula (1) in formula (2)

very little, can ignore.Therefore for two mirror telescopic systems, when there is afore-mentioned, on axle, visual field mainly produces coma.Because translation and the rotation of secondary mirror vertical optical axis are right respectively exert an influence.Therefore can by the translation of secondary mirror vertical optical axis and (or) around the rotation on its summit to axle on coma proofread and correct, make telescopic system

but for

with reference to figure 2 coordinate systems, be because secondary mirror is along x under normal circumstances, the coma that the translation of y axle produces and around x, the result that the coma that the rotation of y axle produces is cancelled out each other.When therefore different, meet

on axle, visual field is proofreaied and correct, and the outer visual field of axle may produce a large amount of astigmatisms.Therefore can reach a conclusion, for the correction of telescopic system aberration, need to consider He Zhouwai visual field in visual field on axle simultaneously.

According to theory, after on axle, coma is proofreaied and correct, the primary and secondary mirror central shaft of telescopic system meets at 1 coma point, as shown in Figure 3, around the rotation of this point, vertical optical axis translation and rotate produced coma around summit and can cancel out each other all the time.Therefore, after on axle, visual field is proofreaied and correct, can around zero coma point rotation, find by secondary mirror

position, realize final correction.Owing to rotating around 1 coma point, on axle, visual field far-field spot produces any variation hardly, and the outer visual field of axle hot spot exerts an influence.Therefore intend adopting the sharpness function of the outer visual field far-field spot (as Fig. 4) of axle as the basis for estimation of proofreading and correct, when the objective function of visual field outside axle reaches extreme value, realize the correction of telescope primary and secondary mirror relative position.

In two specular reflectance telescopic systems, according to formula, calculate and show, 1 coma point and secondary mirror vertex distance Z _cfpmeet formula (3).Wherein L is secondary mirror culminating point and focal plane distance, m ₂for secondary mirror magnification, the ratio of system focal length and primary mirror focal length, meets m ₂=f ,/f ₁', the focal length that f ' is telescopic system, f ₁' be the focal length of primary mirror, b _s2for secondary mirror conic section constant.

$Z_{\mathrm{cfp}}=\frac{2L(m_2^2-1)}{{(m_2+1)}^2[(m_2-1)-(m_2+1)b_{s2}]}---\left(3\right)$

Above-mentioned analysis shows that the basis for estimation that can use the objective function of the far-field spot of different visual field points to proofread and correct as secondary mirror must meet: (1) secondary mirror is along optical axis translation, and on axle, unique extreme value appears in visual field when ideal position.(2), when primary and secondary mirror central shaft intersects at 1 coma point, on axle there is unique extreme value in visual field point target function.(3), when secondary mirror is when 1 coma point rotates, there is unique extreme value in the outer visual field of axle objective function.The desirable objective function of comprehensive above-mentioned condition is as formula (5), (6).J is the mean radius of point target function in visual field on axle, for the correction judgement of visual field point on axle.I(x, y) be the light distribution of visual field point, wherein x, y is test surface normalization coordinate, x ', y ' is center-of-mass coordinate, meets formula (4).When wave front aberration reduces, mean radius is corresponding to be reduced.J ' is the basis for estimation of the outer visual field of axle point calibration, and i is the outer visual field of i axle point, and n is the number of the outer visual field point of axle, and J ' is the mean radius of the outer visual field of axle far-field spot.Due to timing is carried out in visual field on axle, axially proofread and correct and vertical axle correction existence coupling, therefore need respectively both to be carried out to iteration correction, correcting process is as Fig. 1, aligning step is as follows, and step (1) refers to the circulation process of translation and the axial translation of vertical light and (or) the rotation of optical axis direction in Fig. 1; Step (2) refers to the circulation process around zero coma point rotation in Fig. 1.Following step i.e. illustrating Fig. 1 trimming process.

$x^{\′}=\frac{\∫\∫\mathrm{xI}(x,y)\mathrm{dxdy}}{\∫\∫I(x,y)\mathrm{dxdy}}{y}^{\′}=\frac{\∫\∫\mathrm{yI}(x,y)\mathrm{dxdy}}{\∫\∫I(x,y)\mathrm{dxdy}}---\left(4\right)$

$J=\frac{\sqrt{{(x-x^{\′})}^2+{(y-y^{\′})}^2}I(x,y)\mathrm{dxdy}}{\∫\∫I(x,y)\mathrm{dxdy}}---\left(5\right)$

$J^{\′}=\left(\underset{i=\mathrm{1,2}....n}{\mathrm{\Σ}}{J}_i\right)/n---\left(6\right)$

(1) on axle, proofread and correct visual field

Consider that secondary mirror exists coupling along translation and the axial translation of vertical light, the rotation of optical axis direction, therefore respectively it is carried out to iteration convergence analysis.Utilize random paralleling gradient descent algorithm (SPGD, Stochastic Parallel Gradient Descent) to find the position that extreme value appears in visual field objective function J on axle.Its basic thought is the function that system function optimization index J can think to control parameter U, i.e. J=J(U), wherein U=(u ₁, u ₂, u ₃u _n), represent that U is the function of n variable.Because objective function is the fastest along gradient direction variation, this algorithm utilizes the variable quantity δ J of formula (7) performance index and meets random perturbation { the δ U that Bernoulli Jacob distributes _jthe product gradient of carrying out the k time iteration estimates, J(u in formula (7) ₁+ δ u ₁... u _n+ δ u _n) represent to add objective function after random perturbation, J(u ₁... u _n) represent not add the target function value of disturbance.After the k time iteration, control parameter for the k+1 time as formula (8), u _j ^k+1be the value of j variable after the k time iteration, r is fixing parameter, when objective function converges to minimal value r for negative, otherwise for just.Iteration J through certain number of times converges to a stationary value, completes the searching of objective function extreme value.

δJ＝J(u ₁+δu ₁,...,u _n+δu _n)-J(u ₁,...,u _n) （7）

$U^{(k+1)=\left\{u_j^{k+1}\right\}}=\{u_j^k-r\·\mathrm{\δJ\δ}{u}_j\}---\left(8\right)$

$Z_{\mathrm{cfp}}=-\frac{\mathrm{decenterx}}{\mathrm{tilty}}=\frac{\mathrm{decentery}}{\mathrm{tiltx}}---\left(9\right)$

Displacement despace using secondary mirror along optical axis direction and the translation of vertical optical axis and rotation decenterx, decentery, tiltx, tilty are as correcting variable, using the J in formula (5) as objective function, utilize above-mentioned algorithm to carry out iteration convergence analysis, visual field on axle is proofreaied and correct.After adjustment completes, secondary mirror central shaft and primary mirror central shaft meet at 1 coma point (as Fig. 3), and relation meets formula (9), wherein decenterx, and decentery unit is rice, tiltx, tilty unit is degree.Z _cfpfor the distance between secondary mirror culminating point and 1 coma point, decenterx, decentery is respectively x, the skew of y direction, tiltx, tilty is respectively around x, the rotation of y axle.

(2) the outer visual field of axle point calibration

Complete after correcting process (1), known four parameters are approximate between two meets linear relationship as formula (9).According to secondary mirror, along x, y direction is rotated around 1 coma point (coma-free point), and control variable meets formula (9) neutral line relation, can think that controlling parameter is reduced to two by four.Utilize above-mentioned random paralleling gradient descent algorithm (SPGD), at x, y direction is rotated as variable around 1 coma point, using the mean value J ' of the outer required radius of visual field far-field spot of formula (6) axis as evaluation function, realizes the correction of the outer visual field of axle.

Proofread and correct example:

Emulation adopts two mirror reflection RC optical systems to proofread and correct simulation, and systematic parameter is as shown in table 1.Parameter is brought formula (3) into and is obtained Z _cfp=-0.0106.Utilize ZEMAX optical design software and MATLAB programming software to simulate this trimming process.Analytic process is undertaken by the step in correcting process, and while considering to have deviation, on axle, visual field astigmatism is almost nil, proofreaies and correct initial parameter despace=80 μ m, decenterx=600 μ m, decentery=880 μ m, tiltx=0.02 °, tilty=0.03 °.The translation of optical axis direction and other four parameters are all utilized to aforementioned random paralleling gradient descent algorithm (SPGD), make both carry out respectively iteration.Objective function J converges to minimal value gradually with iteration, as shown in phantom in Figure 5.On axle, the Si Telieer of visual field hot spot increases gradually than with iteration, finally converges to 1, as shown in solid line in Fig. 5, finally realizes the correction of visual field on axle, makes the approximate 1 coma point that meets at of primary and secondary mirror axis.Finally, at x, y direction is rotated around 1 coma point, adopts random paralleling gradient descent algorithm (SPGD), and the outer visual field of axle is proofreaied and correct.Timing is normalized the outer visual field of axle, and field of view edge is 1, and selected visual field point is as shown in table 2.The outer visual field objective function J ' of axle progressively converges to minimal value with iteration, as shown in Figure 6.Different visual field point Si Telieer change as shown in Figure 7 than with iteration, and the outer visual field point far-field spot mean state of axle reaches best.

Telescope parameter in table 1ZEMAX

	R（m）	Thickness（m）	Semi-diameter（m）	conic（m）
					1	Infinity	5	0.155	0.000
2	-11.040	-4.906	1.200	-1.002
					3	-1.358	6.406	0.141	-1.497
IMA	-0.631	-	0.081	0.000

The outer visual field of table 2 normalization axle point

fields	1	2	3	4
					Positions	（0,0.9）	（0,-0.8）	（0.7,0）	（-1,0）

Claims (4)

1. the telescope secondary mirror method for correcting position based on spot definition function, its characterization step is as follows:

(1) using visual field spot definition on axle as objective function, optical axis direction is z direction of principal axis, the both direction of vertical optical axis is x, y direction of principal axis is set up rectangular coordinate system, the offset variable of secondary mirror comprises that along optical axis direction be the translation of z direction and the x of vertical optical axis, the translation of y direction is totally three variablees, by iterative computation, obtains the position that the secondary mirror of extreme value appears in objective function; In iterative process, iterative process comprises two steps each time, the first step: along optical axis direction translation; Second step: the translation of vertical optical axis direction and rotation; Using above-mentioned two steps as once circulation, make objective function converge to global extremum;

(2) using the mean value of the sharpness function of the outer visual field of multiple axles hot spot as objective function, make secondary mirror along the zero coma point rotation of orthogonal both direction system for winding, along the x of vertical optical axis, y direction is rotated around 1 coma point, wherein the distance Z between secondary mirror culminating point and 1 coma point _cfpmeet following formula (1), wherein L is secondary mirror culminating point and focal plane distance, m ₂for secondary mirror magnification, the ratio of system focal length and primary mirror focal length, meets m ₂=f ,/f ₁', the focal length that f ' is telescopic system, f ₁' be the focal length of primary mirror, b _s2for secondary mirror conic section constant; The extreme value of iterative objective function, realizes the correction of secondary mirror position;

$Z_{\mathrm{cfp}}=\frac{2L(m_2^2-1)}{{(m_2+1)}^2[(m_2-1)-(m_2+1)b_{s2}]}---\left(1\right).$

2. the telescope secondary mirror method for correcting position based on spot definition function according to claim 1, it is characterized in that: this bearing calibration is applicable to two mirror reflections or catadioptric telescope system, comprise Cassegrain system, Gregory system, RC system.

3. the telescope secondary mirror method for correcting position based on spot definition function according to claim 1, it is characterized in that: in described step (1), (2), respectively using the sharpness function of He Zhouwai visual field, visual field far-field spot on axle as objective function, by iterative algorithm, ask for the extreme value of objective function; Wherein iterative algorithm adopts random parallel optimization algorithm to ask for the extreme value of objective function: comprise climbing method and random paralleling gradient descent algorithm (SPGD-Stochastic Parallel Gradient Descent), simulated annealing, heredity, pattern extraction etc., realize the adjustment of secondary mirror relative position;

Described random paralleling gradient descent algorithm is, objective function J=J(U), wherein U=(u ₁, u ₂... u _n), represent n variable altogether; Because objective function is the fastest along gradient direction variation, this algorithm utilizes the variable quantity δ J of following formula (2) performance index and meets random perturbation { the δ u that Bernoulli Jacob distributes _jproduct carry out the k time iteration gradient estimate; After the k time iteration, control parameter for the k+1 time as formula (3), r is fixing parameter; Iteration J through certain number of times converges to a stationary value, completes seeking of objective function extreme value;

δJ＝J(u ₁+δu ₁,...,u _n+δu _n)-J(u ₁,...,u _n) （2）

$U^{(k+1)=\left\{u_j^{k+1}\right\}}=\{u_j^k-r\·\mathrm{\δJ\δ}{u}_j\}---\left(3\right).$

4. the telescope secondary mirror method for correcting position based on spot definition function according to claim 3, it is characterized in that: for the correction of visual field on axle, displacement despace using secondary mirror along optical axis direction and the translation of vertical optical axis and rotation decenterx, decentery, tiltx, tilty are as correcting variable, the sharpness function J of far-field spot is as objective function, carry out iteration convergence analysis, visual field on axle is proofreaied and correct; After correction completes, secondary mirror central shaft and primary mirror central shaft meet at 1 coma point, and side-play amount relation meets formula (4), wherein decenterx, and decentery unit is rice, tiltx, tilty unit is degree; Z _cfpfor the distance between secondary mirror culminating point and 1 coma point, decenterx, decentery is respectively x, the skew of y direction, tiltx, tilty is respectively around x, the rotation of y axle;

$Z_{\mathrm{cfp}}=-\frac{\mathrm{decenterx}}{\mathrm{tilty}}=\frac{\mathrm{decentery}}{\mathrm{tiltx}}---\left(4\right)$

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