CN103744173B - A kind of telescope secondary mirror method for correcting position based on spot definition function - Google Patents

Abstract

A kind of telescope secondary mirror method for correcting position based on spot definition function.Step is as follows: (1) using visual field spot definition on axle as objective function, secondary mirror along the translation of optical axis and the orthogonal both direction of vertical optical axis translation and rotate as variable, by iterative algorithm, obtain the position that the secondary mirror of extreme value appears in objective function.If all variablees are carried out iteration simultaneously, then objective function may converge to local extremum.Therefore consider that iterative process comprises optical axis direction and the axial iteration of vertical light two steps each time, can make objective function converges to global extremum; (2) using the mean value of the sharpness function of multiple axle outer visual field hot spot as objective function, secondary mirror is rotated along orthogonal both direction system for winding zero coma point, and iteration seeks the extreme value of objective function, realizes the correction of secondary mirror relative position.The method, without the need to carrying out Wavefront detecting and reconstruction, makes the adjustment of telescopic system have objective standard, and can carry out Real-Time Monitoring to telescope image quality.

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 on-line tuning.

Background technology

Ideally telescope primary and secondary mirror relative position is certain, but in operational process, due to the impact of the factor 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 change of system architecture comprises secondary mirror along the translation of optical axis direction, the axial translation of vertical light and the axial rotation of vertical light.The change of primary and secondary mirror relative position can make telescope produce certain aberration.Wherein mainly comprise along optical axis direction translation produce out of focus and spherical aberration, vertical optical axis translation or rotate produce coma and astigmatism.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, visual field aberration on axle can be made to be corrected, can think that the aberration of telescopic system is corrected.But along with the increase of telescopic system visual field, astigmatism has become and can not ignore.Only the correction that can not realize whole visual field aberration is corrected to the aberration of visual field on axle.Therefore, carrying out in the correction of Large Area Telescope system aberration, needing to consider visual field and the outer visual field of axle on axle simultaneously.

At present, there is the multiple method utilizing the outer visual field in visual field and axle on axle to carry out aberration correction.The position angle of axle outer visual field far-field spot and excentricity is such as utilized to calculate wave front aberration coefficient, thus obtain around the method for the zero coma point anglec of rotation (see CollimationofFastWide-FieldTelescopes, BRIANA.MCLEOD, 1996); Utilize wave front detector to obtain wave front aberration coefficient, thus the opposing connection zero coma point anglec of rotation carry out calculating (see FinalalignmentoftheVLT, L.NoehteandS.Guisard, 2000); Sensitivity matrix is utilized to set up relation between misalignment rate and aberration coefficients, misalignment rate is oppositely solved (see Reverse-optimizationAlignmentAlgorithmusingZernikeSensit ivity by the measurement to aberration coefficients, EugeneD.Kim, etal, 2005).Said method all carries out indirectly or directly obtaining to wave front aberration coefficient, thus instructs correction.The shortcoming of first method is that computation complexity is higher, corrects result larger by the impact of computational accuracy.Second method needs wave front detector etc., adds the complexity of system.The matrix relationship that the third method is set up is being similar to when error is less, and when error is larger, matrix relationship exists relatively large deviation, and the acquisition of aberration coefficients simultaneously adds the complexity of system.As can be seen from the document published, the bearing calibration of telescopic system aberration is main relevant to wave front aberration coefficient, thus makes system there is certain complicacy, adds 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 the correction of telescope primary and secondary mirror relative position by the mode of iteration, 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-axis direction, the both direction of vertical optical axis is x, rectangular coordinate system is set up in y-axis direction, then the offset variable of secondary mirror comprises along optical axis direction and the translation in z direction and the x of vertical optical axis, translation totally three variablees in y direction, obtain by iterative computation the position that the secondary mirror of extreme value appears in objective function; Iterative process comprises two steps each time in an iterative process, 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 circulating, make objective function converges to global extremum; As shown in first step cyclic process in Fig. 1;

(2) using the mean value of the sharpness function of multiple axle outer visual field hot spot as objective function, secondary mirror is rotated namely along vertical optical axis x along orthogonal both direction system for winding zero coma point, y-axis direction rotates around 1 coma point, the distance Z wherein between secondary mirror culminating point and zero coma point _cfpmeet following formula, wherein L is secondary mirror culminating point and focal plane distance, m ₂for secondary mirror magnification, namely system focal length and the ratio of primary mirror focal length, meet 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, secondary mirror is along the translation of optical axis and vertical optical axis along the translation of orthogonal both direction and rotate as variable, by certain iterative algorithm, obtains the position that the secondary mirror of extreme value appears in objective function.If all variablees are carried out iteration simultaneously, then objective function may converge to local extremum.Therefore consider to carry out iteration to optical axis direction and vertical optical axis direction respectively, objective function converges can be made to global extremum.(2) using the mean value of the sharpness function of multiple axle outer visual field hot spot as objective function, make secondary mirror along orthogonal x, y-axis direction system for winding zero 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 objective function of sharpness function as aberration correction of telescopic system far-field spot, by CCD and computing machine to the acquisition of target function value, without the need to carrying out wavefront measurement and wavefront reconstruction, reduce system complexity, make the adjustment of telescope primary and secondary mirror relative position have objective standard.

(2) to utilize respectively on axle and the image sharpness function of axle outer visual field far-field spot as objective function, understanding coupling is carried out to the vertical optical axis translation of secondary mirror and rotation, the astigmatism that the outer visual field of axle can be made to cause due to primary and secondary mirror deviation is corrected, and has simple, direct, the effective feature of method.

(3) orientation of axle outer visual field far-field spot and excentricity etc. are not needed to calculate, strict requirement is not had to the distribution of the far-field spot of the outer visual field of axle, can 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 on-line tuning.

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 telescope axle outer visual field point distribution schematic diagram.

Fig. 5 is that on axle, visual field objective function and Si Telieer compare with iteration convergence curve.

Fig. 6 is axle outer visual field objective function converges curve.

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

Embodiment

Below the present invention is described in further details.

First a kind of ultimate principle of the telescope secondary mirror method for correcting position based on spot definition function is introduced.According to three rank vector wave Aberration Theory, for two mirror telescope systems, due to the translation of secondary mirror vertical optical axis or rotate produced coma and astigmatism around summit 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 jth plane system wave aberration, for normalization visual field vector, direction is determined by position angle a, and size determines by apart from coordinate centre distance. for normalization pupil vector, direction is determined by θ, and size determines by apart from corresponding coordinate centre distance, as shown in Figure 2, for the aberration center offset in jth face.For visual field on axle i.e. 1 visual field point, formula only comprises Section 2 in (1) i.e. constant term coma.Formula comprises last in (2) i.e. constant term astigmatism.Generally, due to Section 2 in a relative formula (1) rear 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 the translation of secondary mirror vertical optical axis is right respectively with rotation have an impact.Therefore can be corrected coma on axle by the translation of secondary mirror vertical optical axis and (or) the rotation around its summit, make telescopic system but for with reference to figure 2 coordinate system, be because secondary mirror is along x under normal circumstances, the coma that y-axis translation produces and around x, y-axis rotates the result that the coma that produces is cancelled out each other.Therefore meet during difference on axle, visual field is corrected, and the outer visual field of axle may produce a large amount of astigmatism.Therefore can reach a conclusion, the correction for telescopic system aberration needs to consider visual field and the outer visual field of axle on axle simultaneously.

According to theory, after on axle, coma obtains correcting, the primary and secondary mirror central shaft of telescopic system meets at 1 coma point, as shown in Figure 3, rotates around this point, vertical optical axis translation and rotate produced coma around summit and can cancel out each other all the time.Therefore, after visual field obtains correction on axle, searching can be rotated by secondary mirror around 1 coma point position, realize final correction.Owing to rotating around 1 coma point, on axle, visual field far-field spot produces any change hardly, and axle outer visual field hot spot has an impact.Therefore intend adopting the sharpness function of outer visual field far-field spot (as Fig. 4) of axle as the basis for estimation corrected, the objective function when the outer visual field of axle reaches extreme value, then realize the correction of telescope primary and secondary mirror relative position.

In two specular reflectance telescopic systems, show according to formulae discovery, 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, namely system focal length and the ratio of primary mirror focal length, meet 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, can use the basis for estimation that the objective function of the far-field spot of different visual field point corrects as secondary mirror, must meet: (1) secondary mirror is along optical axis translation, and when ideal position, on axle, unique extreme value appears in visual field.(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 rotates around 1 coma point, there is unique extreme value in axle outer visual field 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, and on axle, the correction of visual field point judges.I(x, y) be visual field point light distribution, wherein x, y are test surface normalization coordinate, x ', y ' and be center-of-mass coordinate, meet formula (4).When wave front aberration reduces, the corresponding reduction of mean radius.J ' is the basis for estimation of axle outer visual field point calibration, and i is i-th axle outer visual field point, and n is the number of axle outer visual field point, and namely J ' is the mean radius of axle outer visual field far-field spot.Owing to carrying out timing to visual field on axle, axially correct and vertical axle correction existence coupling, therefore need to carry out iteration correction to both respectively, correcting process is as Fig. 1, aligning step is as follows, and step (1) refers to the translation of optical axis direction in Fig. 1 and the circulation process of the axial translation of vertical light and (or) rotation; Step (2) refers in Fig. 1 around the circulation process that 1 coma point rotates.Following step illustrating namely to 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, visual field corrects

Consider secondary mirror along optical axis direction translation and the axial translation of vertical light, rotate and there is coupling, therefore respectively iteration convergence analysis is carried out to it.Utilize random paralleling gradient descent algorithm (SPGD, StochasticParallelGradientDescent) to find visual field objective function J on axle and occur the position of extreme value.Its basic thought is the function that system function optimization index J can think controling 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 change, this algorithm utilizes the variable quantity δ J of performance index in formula (7) and meets random perturbation { the δ U of Bernoulli Jacob's distribution _jproduct carries out the Gradient estimates of kth time iteration, J(u in formula (7) ₁+ δ u ₁... u _n+ δ u _n) represent the objective function after adding random perturbation, J(u ₁... u _n) represent the target function value not adding disturbance.After kth time iteration, kth+1 controling parameter is as formula (8), u _j ^k+1for the value of a jth variable after kth time iteration, r is fixing parameter, and objective function converges is negative to r during minimal value, otherwise is just.Converge to a stationary value through the iteration J of certain number of times, then complete 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 rotate decenterx, decentery, tiltx, tilty as correcting variable, J with the formula in (5) is as objective function, utilize above-mentioned algorithm to carry out iteration convergence analysis, visual field on axle is corrected.Adjusted rear secondary mirror central shaft and primary mirror central shaft meets at 1 coma point (as Fig. 3), relation meets formula (9), and wherein decenterx, decentery unit is rice, and tiltx, tilty unit is degree.Z _cfpfor the distance between secondary mirror culminating point and zero coma point, decenterx, decentery are respectively x, the skew in y direction, and tiltx, tilty are respectively around x, the rotation of y-axis.

(2) axle outer visual field point calibration

After completing correcting process (1), known four parameters are approximate between two meets linear relationship as formula (9).Rotate around 1 coma point (coma-freepoint) along x, y direction according to secondary mirror, control variable meets formula (9) neutral line relation, then can think that controling parameter is reduced to two by four.Utilize above-mentioned random paralleling gradient descent algorithm (SPGD), rotate as variable in x, y direction around 1 coma point, the mean value J ' of radius required by the far-field spot of (6) axis outer visual field is as evaluation function with the formula, realizes the correction of the outer visual field of axle.

Correct example:

Emulation employing two mirror reflection RC optical system carries out correction simulation, and systematic parameter is as shown in table 1.Parameter is brought formula (3) into and is obtained Z _cfp=-0.0106.ZEMAX optical design software and MATLAB programming software is utilized to simulate this trimming process.Analytic process is undertaken by the step in correcting process, and when considering to there is deviation, on axle, visual field astigmatism is almost nil, corrects initial parameter despace=80 μm, decenterx=600 μm, decentery=880 μm, tiltx=0.02 °, tilty=0.03 °.Aforementioned random paralleling gradient descent algorithm (SPGD) is all utilized to the translation of optical axis direction and other four parameters, makes both carry out iteration respectively.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, primary and secondary mirror axis is similar to and meets at 1 coma point.Finally, rotate around 1 coma point in x, y direction, adopt random paralleling gradient descent algorithm (SPGD), the outer visual field of axle is corrected.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 changes as shown in Figure 7 than with iteration, and axle outer visual field point far-field spot mean state 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

Table 2 normalization axle outer visual field point

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

Claims (3)

1., based on a telescope secondary mirror method for correcting position for 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-axis direction, the both direction of vertical optical axis is x, rectangular coordinate system is set up in y-axis direction, then the offset variable of secondary mirror comprises along optical axis direction and the translation in z direction and the x of vertical optical axis, translation totally three variablees in y direction, obtain by iterative computation the position that the secondary mirror of extreme value appears in objective function; Iterative process comprises two steps each time in an iterative process, 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 circulating, make objective function converges to global extremum;

(2) using the mean value of the sharpness function of multiple axle outer visual field hot spot as objective function, secondary mirror is rotated along orthogonal both direction system for winding zero coma point, namely rotate along the x of vertical optical axis, y direction around 1 coma point, the distance Z wherein between secondary mirror culminating point and zero coma point _cfpmeet following formula (1), wherein L is secondary mirror culminating point and focal plane distance, m ₂for secondary mirror magnification, namely system focal length and the ratio of primary mirror focal length, meet 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_{cfp}=\frac{2L(m_2^2-1)}{{(m_2+1)}^2\[(m_2-1)-(m_2+1)b_{s2}\]}---\left(1\right);$

In described step (1), (2), respectively using the sharpness function of visual field far-field spot outside visual field on axle and 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-StochasticParallelGradientDescent), simulated annealing, heredity, schema 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 change, this algorithm utilizes the variable quantity δ J of performance index in following formula (2) and meets random perturbation { the δ u of Bernoulli Jacob's distribution _jproduct carries out the Gradient estimates of kth time iteration; After kth time iteration, kth+1 controling parameter is as formula (3), and r is fixing parameter; Converge to a stationary value through the iteration J of certain number of times, then complete seeking of objective function extreme value;

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

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

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: 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 rotate decenterx, decentery, tiltx, tilty 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 corrected; 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), and wherein decenterx, decentery unit is rice, and tiltx, tilty unit is degree; Z _cfpfor the distance between secondary mirror culminating point and zero coma point, decenterx, decentery are respectively x, the skew in y direction, and tiltx, tilty are respectively around x, the rotation of y-axis;

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