CN103217223B - Method for improving measurement precision of transfer matrix of adaptive optical system - Google Patents

Abstract

The invention relates to a method for improving the measurement precision of a transfer matrix of a self-adaptive optical system, which is characterized by comprising the following steps of: in the process of measuring the transfer matrix of the adaptive optical system, the voltage applied to the deformable mirror driver comprises a signal voltage and a compensation voltage; the compensation voltage is used for pre-correcting the static aberration of the adaptive optics system. The invention effectively solves the problem that the measurement of the transfer matrix of the adaptive optical system is restricted by static aberration, and further improves the measurement precision of the transfer matrix.

Description

A kind of method improving ADAPTIVE OPTICS SYSTEMS transfer matrix measuring accuracy

Technical field

The invention belongs to the technical field of ADAPTIVE OPTICS SYSTEMS, relate to a kind of method improving ADAPTIVE OPTICS SYSTEMS transfer matrix measuring accuracy.

Background technology

Adaptive optics (Adaptive Optics, AO) system can the wavefront distortion that causes due to factors such as atmospheric turbulences of real time correction, improve the resolving power of imaging system and the focusing power of transmission laser system, therefore have a wide range of applications in fields such as astronomical sight, Laser Transmission and eyes imaging.AO system is made up of parts such as Wavefront detecting, wavefront process and wavefront corrections usually.Wave front detector the most frequently used is at present Hartman wavefront detector, and wave-front corrector is distorting lens.AO system transfer matrix is the relational matrix that wave-front corrector actuator voltage vector is converted into wave front detector sub-aperture slope vector.Before measuring transfer matrix, the static aberration of AO system is less, and the facula mass center that Calibrating source is formed in each sub-aperture of Hartman wavefront detector is more close to sub-aperture center, and the precision of the transfer matrix recorded is higher.Because the transfer matrix recorded with this understanding more presses close to the actual Closed loop operation situation of AO system on the one hand; On the other hand, when facula mass center is positioned at sub-aperture immediate vicinity, the larger signal voltage of amplitude can be applied to improve signal to noise ratio (S/N ratio), and not worry the measuring error that the range of linearity that hot spot exceeds sub-aperture causes.But, along with increasing rapidly of optical telescope bore, the wavefront slope of the static aberration of the large-scale AO system matched with it also can increase relatively (comprising the fluctuating of distoring mirror shape to introduce, through the wavefront slope of contracting beam system amplification and the wavefront slope etc. of the aberration introducing of Hartman wavefront detector own).Wavefront slope increases and will directly cause facula mass center polaron aperture center position greatly in each sub-aperture of Hartman wavefront detector.If when measuring transfer matrix, apply slightly large voltage to driver again, under extreme case, hot spot may be caused to cross over the phenomenon of sub-aperture, the facula mass center position now recorded just can not characterize real wavefront variation, and the measuring accuracy of transfer matrix will reduce greatly.For suppressing static aberration on the impact of transfer matrix measuring accuracy, improve ADAPTIVE OPTICS SYSTEMS transfer matrix measuring accuracy, need before measurement transfer matrix, the static aberration of first corrective system, can utilize distorting lens that facula mass center in each sub-aperture is corrected to the immediate vicinity of sub-aperture, then carry out the measurement of transfer matrix.For this reason, need first obtain one rough but ADAPTIVE OPTICS SYSTEMS can be made to stablize the transfer matrix of closed loop.S.Oberti etc. propose for comprising the MACAO system of curvature sensor with two piezoelectric deforming mirror the alignment error (S.Oberti utilizing the symmetry characteristic of MACAO system transfer matrix first to measure distorting lens and sensor, H.Bonnet, E.Fedrigo, et.al., Calibration of a curvature sensor/bimorph mirror AO system:interaction matrix measurement on MACAO systems, Proc.SPIE, 2006, then obtain the result of calculation of AO system transfer matrix Vol.5490).But, the method is only applicable to the special case that transfer matrix is square formation, most of AO system, the transfer matrix of the most widely used AO system be such as made up of Hartman wavefront detector and distorting lens is not square formation usually, and therefore the method does not possess versatility.

Summary of the invention

The technical problem to be solved in the present invention is: overcome the deficiencies in the prior art, provide a kind of method improving ADAPTIVE OPTICS SYSTEMS transfer matrix measuring accuracy, the method effectively can solve the problem at hot spot substantial deviation sub-aperture center in the Hartman wavefront detector sub-aperture that static aberration causes, and contributes to the measuring accuracy improving ADAPTIVE OPTICS SYSTEMS transfer matrix.

The technical scheme that the present invention solves the problems of the technologies described above is: a kind of method improving ADAPTIVE OPTICS SYSTEMS transfer matrix measuring accuracy, it is characterized in that in the measuring process of transfer matrix, the voltage applied to distorting lens driver comprises signal voltage and bucking voltage two parts, and concrete steps are as follows:

Step (1): measure the distorting lens of ADAPTIVE OPTICS SYSTEMS and the alignment error of Hartman wavefront detector;

Step (2): the alignment error obtained according to step (1) and the design parameter of ADAPTIVE OPTICS SYSTEMS obtain the result of calculation of transfer matrix and recovery matrix;

Step (3): utilize the result of calculation of recovery matrix to make ADAPTIVE OPTICS SYSTEMS Closed loop operation correct the static aberration of ADAPTIVE OPTICS SYSTEMS, and after recording closed-loop stabilization the voltage of each driver of distorting lens as bucking voltage;

Step (4): apply the measuring voltage be made up of signal voltage and bucking voltage to distorting lens driver, and record corresponding wavefront slope;

Step (5): the measurement result obtaining transfer matrix according to measuring voltage and wavefront slope.

In described step (1), the horizontal direction that the alignment error of distorting lens and Hartman wavefront detector comprises distorting lens pupil plane center and Hartman wavefront detector pupil plane center departs from, vertical direction departs from and distorting lens pupil plane relative to the rotation of Hartman wavefront detector pupil plane, its concrete measuring process is as follows:

(1) if make coordinate on distorting lens be (X _{_ act}(i), Y _{_ act}(i)) the influence function of i-th driver be $V_i(x,y)=\exp \left[{(\sqrt{{(x-X_{\_\mathrm{act}}\left(i\right))}^2+{(y-Y_{\_\mathrm{act}}\left(i\right))}^2}/d)}^{\mathrm{\α}}\ln \mathrm{\ω}\right],$ Wherein, d is driver pitch, and α is Gaussian index, and ω is commissure value, then without the result of calculation IM of transfer matrix in alignment error situation _{_ ideal}for:

$\begin{array}{cc}{\mathrm{IM}}_{\_\mathrm{ideal}}{(j,i)}_{2\mathrm{NsubXNact}}=-\frac{\underset{S_j}{\∫\∫}\frac{{\∂V}_i(x,y)}{\∂x}\mathrm{dxdy}}{A_j}& i=\mathrm{1,2},...,\mathrm{Nact},\\ {\mathrm{IM}}_{\_\mathrm{ideal}}{(j+\mathrm{Nsub},i)}_{2\mathrm{NsubXNact}}=-\frac{\underset{S_j}{\∫\∫}\frac{{\∂V}_i(x,y)}{\∂y}\mathrm{dxdy}}{A_j},& j=\mathrm{1,2},...,\mathrm{Nsub}\end{array}$

Wherein, S _jfor a jth sub-aperture is in the phase conjugation region of distorting lens pupil plane, A _jfor the area in this region, Nact is the effective driver number of distorting lens, and Nsub is the effective sub-aperture number of Hartman wavefront detector, IM _{_ ideal}in the i-th slope being classified as No. i-th driver corresponding affect column vector;

(2) the All Drives position in design relation is moved Δ d=[-d-0.9d ... d] in the horizontal direction, obtain distorting lens driver exist horizontal direction depart from Δ d under reposition, utilize the computing method in (1) to obtain corresponding transfer matrix result of calculation IM ₁, IM ₂..., IM ₂₁; Δ d is vertically moved in All Drives position in design relation, obtain distorting lens driver exist vertical direction depart from Δ d under reposition, utilize the computing method in (1) to obtain corresponding transfer matrix result of calculation IM ₂₂, IM ₂₃..., IM ₄₂;

(3) on distorting lens, four drivers are chosen as character-driven device, for measuring alignment error; If the character-driven device chosen is respectively a ₁, a ₂, a ₃, a ₄number driver, wherein, a ₁with a ₃number driver, a ₂with a ₄number driver is about distorting lens pupil plane Central Symmetry; Then apply separately 1 volt of voltage respectively to each character-driven device, Hartman wavefront detector records corresponding slope vector will with each transfer matrix result of calculation IM existed under alignment error ₀, IM ₁..., IM ₄₂in slope corresponding to each character-driven device affect column vector and carry out related operation, ask for correlation factor:

$\mathrm{\β}(i,k)=\frac{\underset{j=1}{\overset{{2N}_{\mathrm{sub}}}{\mathrm{\Σ}}}\stackrel{\→}{g_{\mathrm{ak}}}{\mathrm{IM}}_m(j,a_k)}{\sqrt{\underset{j=1}{\overset{{2N}_{\mathrm{sub}}}{\mathrm{\Σ}}}\stackrel{\→}{g_{\mathrm{ak}}}{\left(j\right)}^2}\sqrt{\underset{j=1}{\overset{{2N}_{\mathrm{sub}}}{\mathrm{\Σ}}}{\mathrm{IM}}_m{(j,a_k)}^2}},m=\mathrm{1,2},...42;k=\mathrm{1,2,3,4}$

Distorting lens driver again corresponding to each driver correlation factor maximal value obtains each character-driven device in the horizontal direction and departs from (dx relative to design attitude with the bias of vertical direction _a1, dy _a1), (dx _a2, dy _a2), (dx _a3, dy _a3), (dx _a4, dy _a4); Then, use following formula to obtain distorting lens pupil plane center to depart from relative to the pupil plane central horizontal direction of Hartman wavefront detector depart from vertical direction

$\mathrm{\Δx}=\frac{{\mathrm{dx}}_{a1}+{\mathrm{dx}}_{a2}+{\mathrm{dx}}_{a3}+{\mathrm{dx}}_{a4}}{4}$

$\mathrm{\Δy}=\frac{{\mathrm{dy}}_{a1}+{\mathrm{dy}}_{a2}+{\mathrm{dy}}_{a3}+{\mathrm{dy}}_{a4}}{4}$

Definition intermediate variable dx _r(k) and dy _rk () is respectively:

$\begin{array}{c}{\mathrm{dx}}_r\left(k\right)={\mathrm{dx}}_{\mathrm{ak}}-\mathrm{\Δx}\\ {\mathrm{dy}}_r\left(k\right)={\mathrm{dy}}_{\mathrm{ak}}-\mathrm{\Δy}\end{array},k=\mathrm{1,2,3,4}$

Again due to each drive location coordinate and distorting lens pupil plane center position coordinates difference (X in design _{r_act}, Y _{r_act}) be:

$\begin{array}{c}{X}_{r\_\mathrm{act}}\left(i\right)=X_{\_\mathrm{act}}\left(i\right)-X_{\_\mathrm{act}0}\\ Y_{r\_\mathrm{act}}\left(i\right)=Y_{\_\mathrm{act}}\left(i\right)-Y_{\_\mathrm{act}0}\end{array},i=\mathrm{1,2},...,\mathrm{Nact}$

Wherein, (X _{_ act0}, Y _{_ act0}) be the coordinate of distorting lens pupil plane center, then each character-driven device is relative to the anglec of rotation Δ θ of distorting lens pupil centre position _afor:

$\mathrm{\Δ}{\mathrm{\θ}}_a\left(k\right)=\arcsin \left(\frac{X_{r\_\mathrm{act}}\left(a_k\right)[Y_{r\_\mathrm{act}}\left(a_k\right)+{\mathrm{dy}}_r\left(k\right)]-Y_{r\_\mathrm{act}}\left(a_k\right)[X_{r\_\mathrm{act}}\left(a_k\right)+{\mathrm{dx}}_r\left(k\right)]}{X_{r\_\mathrm{act}}{\left(a_k\right)}^2+Y_{r\_\mathrm{act}}{\left(a_k\right)}^2}\right),$

k＝1,2,3,4

According to Δ θ _acan obtain distorting lens pupil plane relative to the anglec of rotation Δ θ of Hartman wavefront detector pupil plane is:

$\mathrm{\Δ\θ}=\frac{\underset{k=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\Δ\θ}}_a\left(k\right)}{4}$

Depart from Δ x relative to the horizontal direction at Hartman wavefront detector pupil plane center and vertical direction departs from Δ y with regard to obtaining distorting lens pupil plane center like this, and distorting lens pupil plane is relative to the anglec of rotation Δ θ of Hartman wavefront detector pupil plane.

The detailed process that the alignment error obtained according to step (1) in described step (2) and the design parameter of ADAPTIVE OPTICS SYSTEMS obtain the result of calculation of transfer matrix and recovery matrix is as follows:

(1) obtain according to Δ x, Δ y and Δ θ the coordinate (X considering each driver physical location of distorting lens that alignment error is later _{new_act}, Y _{new_act}), computing method are: when k is from 1 value to Nact:

If $\sqrt{X_{r\_\mathrm{act}}{\left(k\right)}^2+Y_{r\_\mathrm{act}}{\left(k\right)}^2}\≠0,$ Then

$X_{\mathrm{new}\_\mathrm{act}}\left(k\right)=\sqrt{X_{r\_\mathrm{act}}{\left(k\right)}^2+Y_{r\_\mathrm{act}}{\left(k\right)}^2}\cos (\arccos \left(\frac{X_{r\_\mathrm{act}}\left(k\right)}{\sqrt{X_{r\_\mathrm{act}}{\left(k\right)}^2+Y_{r\_\mathrm{act}}{\left(k\right)}^2}}\right)+\mathrm{\Δ\θ})+\mathrm{\Δx}+X_{\_\mathrm{act}0}$

$Y_{\mathrm{new}\_\mathrm{act}}\left(k\right)=\sqrt{X_{r\_\mathrm{act}}{\left(k\right)}^2+Y_{r\_\mathrm{act}}{\left(k\right)}^2}\sin (\arcsin \left(\frac{Y_{r\_\mathrm{act}}\left(k\right)}{\sqrt{X_{r\_\mathrm{act}}{\left(k\right)}^2+Y_{r\_\mathrm{act}}{\left(k\right)}^2}}\right)+\mathrm{\Δ\θ})+\mathrm{\Δy}+Y_{\_\mathrm{act}0}$

If $\sqrt{X_{r\_\mathrm{act}}{\left(k\right)}^2+Y_{r\_\mathrm{act}}{\left(k\right)}^2}=0,$ Then

X _{new_act}(k)＝Δx+X _{_act0}

Y _{new_act}(k)＝Δy+Y _{_act0}

(2) based on the distorting lens driver actual position coordinate (X of the consideration alignment error obtained above _{new_act}, Y _{new_act}), the actual influence function of distorting lens driver can be obtained

$V_i^{\′}(x,y)=\exp \left[{(\sqrt{{(x-X_{\mathrm{new}\_\mathrm{act}}\left(i\right))}^2+{(y-Y_{\mathrm{new}\_\mathrm{act}}\left(i\right))}^2}/d)}^{\mathrm{\α}}\ln \mathrm{\ω}\right]$

Then, the transfer matrix result of calculation IM under actual position coordinate can be obtained _{_ real}for:

$\begin{array}{cc}{\mathrm{IM}}_{\_\mathrm{real}}{(j,i)}_{2\mathrm{NsubXNact}}=-\frac{\underset{S_j}{\∫\∫}\frac{{\∂V}_i^{\′}(x,y)}{\∂x}\mathrm{dxdy}}{A_j}& i=\mathrm{1,2},...,\mathrm{Nact},\\ {\mathrm{IM}}_{\_\mathrm{real}}{(j+\mathrm{Nsub},i)}_{2\mathrm{NsubXNact}}=-\frac{\underset{S_j}{\∫\∫}\frac{{\∂V}_i^{\′}(x,y)}{\∂y}\mathrm{dxdy}}{A_j},& j=\mathrm{1,2},...,\mathrm{Nsub}\end{array}$

To IM _{_ real}generalized inverse matrix is asked namely to obtain the result of calculation R of AO system reset matrix _{_ real}.

The detailed process of the measurement result of transfer matrix is obtained according to measuring voltage and wavefront slope as follows in described step (5):

(1) R is utilized _{_ real}make ADAPTIVE OPTICS SYSTEMS work, each sub-aperture slope that closed-loop corrected Hartman wavefront detector records, after record closed-loop stabilization, the voltage of each driver obtains static aberration compensation voltage vector V _c;

(2) to i=l, 2 ..., Nact driver successively carries out following operation: apply bucking voltage vector V to distorting lens _c, then keep other actuator voltages constant, change No. i-th actuator voltage into V _c(i)+V _s, be recorded in the slope vector that Hartman wavefront detector records ; Change No. i-th actuator voltage into V again _c(i)-V _s, be recorded in the slope vector that Hartman wavefront detector records ; Wherein, V _sfor signal voltage.Utilize formula:

${\mathrm{IM}}_m=\frac{\left[\begin{array}{cccc}\stackrel{\→}{g_{m1\_1}}-\stackrel{\→}{g_{m2\_1}}& \stackrel{\→}{g_{m1\_2}}-\stackrel{\→}{g_{m2\_2}}& ...& \stackrel{\→}{g_{m1\_595}}-\stackrel{\→}{g_{m2\_595}}\end{array}\right]}{{2V}_s}$

The measurement result IM of the ADAPTIVE OPTICS SYSTEMS transfer matrix after static aberration correction can be obtained _m.

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

(1) the present invention can be applicable to the most widely used ADAPTIVE OPTICS SYSTEMS that is made up of distorting lens and Hartman wavefront detector.

(2) the present invention is applicable to and there is alignment error and transfer matrix is not the ADAPTIVE OPTICS SYSTEMS of square formation.

(3) the present invention is by carrying out precorrection to the static aberration of ADAPTIVE OPTICS SYSTEMS, facula mass center in each sub-aperture of Hartman wavefront detector is made to be positioned near center location, the measuring accuracy of ADAPTIVE OPTICS SYSTEMS transfer matrix can be improved, under equal conditions, reduce the closed loop residual error of ADAPTIVE OPTICS SYSTEMS.

Accompanying drawing explanation

Accompanying drawing described herein is used to provide a further understanding of the present invention, and form a application's part, schematic description and description of the present invention, for explaining the present invention, does not form inappropriate limitation of the present invention.

In the accompanying drawings:

Figure l is principle schematic of the present invention;

Fig. 2 is 595 element deformation mirror drivers and 676 unit Hartman wavefront detector sub-aperture design relation figure;

Fig. 3 is 595 element deformation mirror center driver influence function model horizontal direction schematic diagram;

Fig. 4 is 595 element deformation mirror drivers and 676 unit Hartman wavefront detector sub-aperture actual relationship figure;

Fig. 5 is distorting lens 78,89,507, No. 518 driver correlation factor schematic diagram;

Fig. 6 (a) is the initial facula mass center position of Hartman wavefront detector;

Fig. 6 (b) for after precorrection 50 step, Hartman wavefront detector facula mass center position;

Fig. 7 is the relation between Hartman wavefront detector sub-aperture facula mass center site error root-mean-square value and iterative steps;

Fig. 8 is Hartman wavefront detector sub-aperture facula mass center site error peak-to-peak (PV) relation between value and iterative steps.

Drawing reference numeral:

1. Calibrating source, 2. distorting lens, 3. catoptron, 4. contracting beam system, 5. Hartman wavefront detector, 6. precorrection controller.

Embodiment

Specifically introduce a kind of embodiment of the present invention below in conjunction with accompanying drawing 1 to accompanying drawing 8.

As shown in Figure 1, the ADAPTIVE OPTICS SYSTEMS used in the present embodiment comprises Calibrating source 1, distorting lens 2, catoptron 3, contracting beam system 4, Hartman wavefront detector 5, precorrection controller 6; Wherein, Calibrating source 1 produces the nominal light of mating with distorting lens 2 bore, contracting beam system 4 is imported by catoptron 3 after distorting lens 2 reflects, Hartman wavefront detector 5 is finally entered after contracting bundle, precorrection controller 6 applies voltage instruction to distorting lens 2, and receives the wavefront slope information that Hartman wavefront detector 5 records.A kind of concrete implementation step improving the method for ADAPTIVE OPTICS SYSTEMS transfer matrix measuring accuracy of the present invention is:

Step (1): measure the distorting lens 2 of ADAPTIVE OPTICS SYSTEMS and the alignment error of Hartman wavefront detector 5;

Step (2): obtain the transfer matrix of ADAPTIVE OPTICS SYSTEMS and the result of calculation of recovery matrix according to the alignment error that design parameter and the step (1) of distorting lens 2, contracting beam system 4 and Hartman wavefront detector 5 record

Step (3): utilize the result of calculation of recovery matrix to make ADAPTIVE OPTICS SYSTEMS Closed loop operation correct the static aberration of ADAPTIVE OPTICS SYSTEMS, and after recording closed-loop stabilization the voltage of each driver of distorting lens 2 as bucking voltage;

Step (4): apply the measuring voltage be made up of signal voltage and bucking voltage to distorting lens 2 driver, and the wavefront slope recording that Hartman wavefront detector 5 records;

Step (5): the measurement result obtaining transfer matrix according to measuring voltage and wavefront slope.

For easy analysis is for distorting lens driver and Hartman wavefront detector sub-aperture design relation 595 unit AO systems as shown in Figure 2, the method improving ADAPTIVE OPTICS SYSTEMS transfer matrix measuring accuracy is described.As shown in Figure 2, this AO system comprises the distorting lens having effective actuator unit number N act and equal 595, and drive number is 1 to No. 595 by the order of pressing from left to right, from top to bottom; This AO system also has the Hartman wavefront detector that effective sub-aperture number N sub equals 676, and sub-aperture is numbered 1 to No. 676 by the order of pressing equally from left to right, from top to bottom.595 element deformation mirror center driver influence functions in the horizontal direction (X-direction) schematic diagram as shown in Figure 3.The expression formula of the influence function of No. i-th driver is $V_i(x,y)=\exp \left[{(\sqrt{{(x-X_{\_\mathrm{act}}\left(i\right))}^2+{(y-Y_{\_\mathrm{act}}\left(i\right))}^2}/d)}^{\mathrm{\α}}\ln \mathrm{\ω}\right],$ Wherein, driver pitch d equals 12.25mm, and Gaussian index α is 2.14, and commissure value ω is 9.5%, (X _{_ act}(i), Y _{_ act}(i)) be the coordinate of No. i-th driver.Consider contracting beam system, when Hartman wavefront detector pupil plane is conjugated to distorting lens pupil plane, its size of sub-aperture d of equal value _hfor 10.42mm, and CCD camera number of pixels corresponding to each sub-aperture is 8X8.Actual debug after, there is horizontal direction-0.3d, the departing from of vertical direction 0.2d in distorting lens center and Hartman wavefront detector center, also there is 2 ° being rotated counterclockwise in distorting lens pupil plane and Hartman wavefront detector pupil plane simultaneously, driver when Fig. 4 is these alignment errors of existence and sub-aperture graph of a relation.Below for improving the implementation step of ADAPTIVE OPTICS SYSTEMS transfer matrix measuring accuracy:

One, the use driver of Fig. 2 and the driver influence function computing system transfer matrix IM of sub-aperture design relation and Fig. 3 are:

$\begin{array}{cc}{\mathrm{IM}}_{\_\mathrm{ideal}}{(j,i)}_{1352X595}=-\frac{\underset{S_j}{\∫\∫}\frac{{\∂V}_i(x,y)}{\∂x}\mathrm{dxdy}}{A_j}& i=\mathrm{1,2},...,595,\\ {\mathrm{IM}}_{\_\mathrm{ideal}}{(j+676,i)}_{1352X595}=-\frac{\underset{S_j}{\∫\∫}\frac{{\∂V}_i(x,y)}{\∂y}\mathrm{dxdy}}{A_j},& j=\mathrm{1,2},...,676\end{array}$

Wherein, S _jfor a jth sub-aperture is in the phase conjugation region of distorting lens pupil plane, A _ifor the area in this region.I-th row of IM characterize the relative effect degree to each sub-aperture slope when No. i-th driver adds separately 1V voltage, therefore, are referred to as the result of calculation of transfer matrix here.

Two, the All Drives position in design relation is moved Δ d=[-d-0.9d in the horizontal direction ... d], then according to the reposition of distorting lens driver under this alignment error of existence, the transfer matrix result of calculation IM under utilizing the transfer matrix computing method in step one to be there is this alignment error accordingly ₁, IM ₂..., IM ₂₁.Δ d is vertically moved in All Drives position in design relation, then according to the reposition of distorting lens driver under this alignment error of existence, the transfer matrix result of calculation IM under utilizing the transfer matrix computing method in step one to be there is this alignment error accordingly ₂₂, IM ₂₃..., IM ₄₂.

Three, a of distorting lens is chosen ₁=78, a ₂=89, a ₃=507 and a ₄=No. 518 drivers as character-driven device, for the anglec of rotation of departing from of measuring that distorting lens pupil plane center and Hartman wavefront detector pupil plane center in actual AO system exist and distorting lens.Wherein, No. 78 drivers and No. 518 drivers are about distorting lens Central Symmetry; No. 89 drivers and No. 518 drivers are about distorting lens Central Symmetry.Concrete measuring method is as follows:

3.1 apply separately the voltage of l volt respectively to each character-driven device, and Hartman wavefront detector records the slope variation vector that l volt voltage causes following related algorithm is utilized to obtain with the correlation factor affecting column vector in transfer matrix result of calculation under each alignment error to the slope that each character-driven device is corresponding:

$\mathrm{\β}(i,k)=\frac{\underset{j=1}{\overset{{2N}_{\mathrm{sub}}}{\mathrm{\Σ}}}\stackrel{\→}{g_{\mathrm{ak}}}{\left(j\right)\mathrm{IM}}_m(j,a_k)}{\sqrt{\underset{j=1}{\overset{{2N}_{\mathrm{sub}}}{\mathrm{\Σ}}}\stackrel{\→}{g_{\mathrm{ak}}}{\left(j\right)}^2}\sqrt{\underset{j=1}{\overset{{2N}_{\mathrm{sub}}}{\mathrm{\Σ}}}{\mathrm{IM}}_m{(j,a_k)}^2}},m=\mathrm{1,2},...42;k=\mathrm{1,2,3,4}$

In the present embodiment, a ₁, a ₂, a ₃, a ₄correlation factor as shown in Figure 5,

3.2 distorting lens drivers corresponding to each driver correlation factor maximal value obtain a at the displacement of X-direction and Y-direction ₁, a ₂, a ₃, a ₄number driver departs from (dx relative to design attitude _a1, dy _a1), (dx _a2, dy _a2), (dx _a3, dy _a3), (dx _a4, dy _a4), as shown in Figure 5, value corresponding in the present embodiment is (-0.6d, 0), (-0.5d, 0.4d), (0,0), (0,0.4d).

3.3 according to (dx _a1, dy _a1), (dx _a2, dy _a2), (dx _a3, dy _a3), (dx _a4, dy _a4) obtain distorting lens pupil plane center offset at X-direction shifted by delta x and Y-direction relative to the pupil plane center of Hartman wavefront detector: Δ y

$\mathrm{\Δx}=\frac{{\mathrm{dx}}_{a1}+{\mathrm{dx}}_{a2}+{\mathrm{dx}}_{a3}+{\mathrm{dx}}_{a4}}{4}$

$\mathrm{\Δy}=\frac{{\mathrm{dy}}_{a1}+{\mathrm{dy}}_{a2}+{\mathrm{dy}}_{a3}+{\mathrm{dy}}_{a4}}{4}$

In the present embodiment, Δ x=-0.275d, Δ y=0.2d, with actual value-0.3d and 0.2d closely.The coordinate difference of each driver coordinate and distorting lens pupil plane center is:

$\begin{array}{c}{X}_{r\_\mathrm{act}}\left(i\right)=X_{\_\mathrm{act}}\left(i\right)-X_{\_\mathrm{act}}\left(298\right)\\ Y_{r\_\mathrm{act}}\left(i\right)=Y_{\_\mathrm{act}}\left(i\right)-Y_{\_\mathrm{act}}\left(298\right)\end{array},i=\mathrm{1,2},...,595$

And intermediate variable dx _r(k) and dy _r(k) be:

$\begin{array}{c}{\mathrm{dx}}_r\left(k\right)={\mathrm{dx}}_{\mathrm{ak}}-\mathrm{\Δx}\\ {\mathrm{dy}}_r\left(k\right)={\mathrm{dy}}_{\mathrm{ak}}-\mathrm{\Δy}\end{array},k=\mathrm{1,2,3,4}$

Then according to geometric relationship, each character-driven device is relative to the anglec of rotation Δ θ of distorting lens pupil centre position _afor:

$\mathrm{\Δ}{\mathrm{\θ}}_a\left(k\right)=\arcsin \left(\frac{X_{r\_\mathrm{act}}\left(a_k\right)[Y_{r\_\mathrm{act}}\left(a_k\right)+{\mathrm{dy}}_r\left(k\right)]-Y_{r\_\mathrm{act}}\left(a_k\right)[X_{r\_\mathrm{act}}\left(a_k\right)+{\mathrm{dx}}_r\left(k\right)]}{X_{r\_\mathrm{act}}{\left(a_k\right)}^2+Y_{r\_\mathrm{act}}{\left(a_k\right)}^2}\right),$

k＝1,2,3,4

A in the present embodiment ₁, a ₂, a ₃, a ₄corresponding anglec of rotation Δ θ _a(1), Δ θ _a(2), Δ θ _a(3), Δ θ _a(4) be respectively 2.18 °, 1.70 °, 1.94 °, 1.94 °, then the average anglec of rotation of distorting lens pupil plane is:

$\mathrm{\Δ\θ}=\frac{\underset{k=1}{\overset{4}{\mathrm{\Σ}}}{\mathrm{\Δ\θ}}_a\left(k\right)}{4}$

The result of calculation of the present embodiment is 1.94 °, equally its also with actual value 2 ° closely.Like this we just obtain distorting lens pupil plane center relative to the departing from of Hartman wavefront detector pupil plane center (Δ x, Δ y) from and distorting lens pupil plane relative to the anglec of rotation Δ θ of Hartman wavefront detector pupil plane.

Four, the coordinate (X of each driver of distorting lens that alignment error is later can be considered according to Δ x, Δ y and Δ θ _{new_act}, Y _{new_act}), computing method are: when k is from 1 value to 595

If $\sqrt{X_{r\_\mathrm{act}}{\left(k\right)}^2+Y_{r\_\mathrm{act}}{\left(k\right)}^2}\≠0,$ Then

$X_{\mathrm{new}\_\mathrm{act}}\left(k\right)=\sqrt{X_{r\_\mathrm{act}}{\left(k\right)}^2+Y_{r\_\mathrm{act}}{\left(k\right)}^2}\cos (\arccos \left(\frac{X_{r\_\mathrm{act}}\left(k\right)}{\sqrt{X_{r\_\mathrm{act}}{\left(k\right)}^2+Y_{r\_\mathrm{act}}{\left(k\right)}^2}}\right)+\mathrm{\Δ\θ})+\mathrm{\Δx}+X_{\_\mathrm{act}}\left(298\right)$

$Y_{\mathrm{new}\_\mathrm{act}}\left(k\right)=\sqrt{X_{r\_\mathrm{act}}{\left(k\right)}^2+Y_{r\_\mathrm{act}}{\left(k\right)}^2}\sin (\arcsin \left(\frac{Y_{r\_\mathrm{act}}\left(k\right)}{\sqrt{X_{r\_\mathrm{act}}{\left(k\right)}^2+Y_{r\_\mathrm{act}}{\left(k\right)}^2}}\right)+\mathrm{\Δ\θ})+\mathrm{\Δy}+Y_{\_\mathrm{act}}\left(298\right)$

If $\sqrt{X_{r\_\mathrm{act}}{\left(k\right)}^2+Y_{r\_\mathrm{act}}{\left(k\right)}^2}=0,$ Then

X _{new_act}(k)=Δx+X _{_act}(298)

Y _{new_act}(k)＝Δy+Y _{_act}(298)

Based on the distorting lens drive location coordinate of the consideration alignment error obtained above, reuse the transfer matrix computing method in step one, the result of calculation IM of the transfer matrix of the AO system under new matching relationship can be obtained _real.Then to IM _realgeneralized inverse matrix is asked namely to obtain the result of calculation R of AO system reset matrix _real.If the initial position of Hartman wavefront detector sub-aperture light wave as shown in Figure 6 (a), utilize R _realcarry out closed-loop corrected to the sub-aperture slope that Hartman wavefront detector records, each sub-aperture facula mass center can be corrected to sub-aperture immediate vicinity.In the present embodiment, after 50 step iterative, each sub-aperture facula mass center as shown in Figure 6 (b), and because each sub-aperture hot spot has been positioned at sub-aperture immediate vicinity, now the static aberration of ADAPTIVE OPTICS SYSTEMS has obtained effective correction.In iterative process, the relation of root mean square and peak-to-peak (PV) value and iterative steps that each sub-aperture facula mass center departs from each sub-aperture center is distinguished as shown in Figure 7 and Figure 8, can see, along with the increase of iterative steps, root-mean-square value and PV value reduce all rapidly, after 40 steps, root-mean-square value is less than 0.04 pixel, and now static aberration is well compensated, and after record closed-loop stabilization, the voltage of each driver obtains static aberration compensation voltage vector is V _c.

Five, to i=1,2 ..., No. 595 drivers successively carry out following operation: apply bucking voltage vector V to 595 element deformation mirrors _c, get signal voltage V _sbe 1 volt, then keep other actuator voltages constant, change No. i-th actuator voltage into V _c(i)+V _s, be recorded in the slope vector that Hartman wavefront detector records change No. i-th actuator voltage into V again _c(i)-V _s, be recorded in the slope vector that Hartman wavefront detector records utilize formula:

${\mathrm{IM}}_m=\frac{\left[\begin{array}{cccc}\stackrel{\→}{g_{m1\_1}}-\stackrel{\→}{g_{m2\_1}}& \stackrel{\→}{g_{m1\_2}}-\stackrel{\→}{g_{m2\_2}}& ...& \stackrel{\→}{g_{m1\_595}}-\stackrel{\→}{g_{m2\_595}}\end{array}\right]}{{2V}_s}$

The measurement result IM of the ADAPTIVE OPTICS SYSTEMS transfer matrix after static aberration correction can be obtained _m.

The result of cumulated volume embodiment is known, a kind of method improving ADAPTIVE OPTICS SYSTEMS transfer matrix measuring accuracy provided by the invention effectively can carry out precorrection to the static aberration of ADAPTIVE OPTICS SYSTEMS really, thus improves the measuring accuracy of ADAPTIVE OPTICS SYSTEMS transfer matrix.

The part that the present invention does not elaborate belongs to techniques well known.

Claims (4)

1. improve a method for ADAPTIVE OPTICS SYSTEMS transfer matrix measuring accuracy, it is characterized in that: in the measuring process of transfer matrix, the voltage applied to distorting lens driver comprises signal voltage and bucking voltage two parts, and concrete steps are as follows:

Step (1): measure the distorting lens of ADAPTIVE OPTICS SYSTEMS and the alignment error of Hartman wavefront detector;

Step (2): the alignment error obtained according to step (1) and the design parameter of ADAPTIVE OPTICS SYSTEMS obtain the result of calculation of transfer matrix and recovery matrix;

Step (3): utilize the result of calculation of recovery matrix to make ADAPTIVE OPTICS SYSTEMS Closed loop operation correct the static aberration of ADAPTIVE OPTICS SYSTEMS, and after recording closed-loop stabilization the voltage of each driver of distorting lens as bucking voltage;

Step (4): apply the measuring voltage be made up of signal voltage and bucking voltage to distorting lens driver, and record corresponding wavefront slope;

Step (5): the measurement result obtaining transfer matrix according to measuring voltage and wavefront slope.

2. a kind of method improving ADAPTIVE OPTICS SYSTEMS transfer matrix measuring accuracy according to claim 1, it is characterized in that: in described step (1), the horizontal direction that the alignment error of distorting lens and Hartman wavefront detector comprises distorting lens pupil plane center and Hartman wavefront detector pupil plane center departs from, vertical direction departs from and distorting lens pupil plane relative to the rotation of Hartman wavefront detector pupil plane, its concrete measuring process is as follows:

(1) if make coordinate on distorting lens be (X _{_ act}(i), Y _{_ act}(i)) the influence function of i-th driver be $V_i(x,y)=\exp \left[{(\sqrt{{(x-X_{\_\mathrm{act}}\left(i\right))}^2+{(y-Y_{\_\mathrm{act}}\left(i\right))}^2}/d)}^{\mathrm{\α}}\ln \mathrm{\ω}\right],$ Wherein, d is driver pitch, and α is Gaussian index, and ω is commissure value, then without the result of calculation IM of transfer matrix in alignment error situation _{_ ideal}for:

$\begin{array}{c}{\mathrm{IM}}_{\_\mathrm{ideal}}{(j,i)}_{2\mathrm{NsubXNact}}=-\frac{\underset{S_j}{\∫\∫}\frac{\∂V_i(x,y)}{\∂x}\mathrm{dxdy}}{A_j}\\ {\mathrm{IM}}_{\_\mathrm{ideal}}{(j+\mathrm{Nsub},i)}_{2\mathrm{NsubXNact}}=-\frac{\underset{S_j}{\∫\∫}\frac{\∂V_i(x,y)}{\∂y}\mathrm{dxdy}}{A_j}\end{array},\begin{array}{c}i=\mathrm{1,2},...,\mathrm{Nact},\\ j=\mathrm{1,2},...,\mathrm{Nsub}\end{array}$

Wherein, S _jfor a jth sub-aperture is in the phase conjugation region of distorting lens pupil plane, A _jfor the area in this region, Nact is the effective driver number of distorting lens, and Nsub is the effective sub-aperture number of Hartman wavefront detector, IM _{_ ideal}in the i-th slope being classified as No. i-th driver corresponding affect column vector;

(2) the All Drives position in design relation is moved Δ d=[-d-0.9d in the horizontal direction ... d], obtain distorting lens driver exist horizontal direction depart from Δ d under reposition, utilize the computing method in step (1) to obtain corresponding transfer matrix result of calculation IM ₁, IM ₂..., IM ₂₁; Δ d is vertically moved in All Drives position in design relation, obtain distorting lens driver exist vertical direction depart from Δ d under reposition, utilize the computing method in step (1) to obtain corresponding transfer matrix result of calculation IM ₂₂, IM ₂₃..., IM ₄₂;

(3) on distorting lens, four drivers are chosen as character-driven device, for measuring alignment error; If the character-driven device chosen is respectively a ₁, a ₂, a ₃, a ₄number driver, wherein, a ₁with a ₃number driver, a ₂with a ₄number driver is about distorting lens pupil plane Central Symmetry; Then apply separately 1 volt of voltage respectively to each character-driven device, Hartman wavefront detector records corresponding slope vector will with each transfer matrix result of calculation IM existed under alignment error ₁..., IM ₄₂in slope corresponding to each character-driven device affect column vector and carry out related operation, ask for correlation factor:

$\mathrm{\β}(i,k)=\frac{\underset{j=1}{\overset{2N_{\mathrm{sub}}}{\mathrm{\Σ}}}\stackrel{\→}{g_{\mathrm{ak}}}\left(j\right){\mathrm{IM}}_m(j,a_k)}{\sqrt{\underset{j=1}{\overset{2N_{\mathrm{sub}}}{\mathrm{\Σ}}}\stackrel{\→}{g_{\mathrm{ak}}}{\left(j\right)}^2}\sqrt{\underset{j=1}{\overset{2N_{\mathrm{sub}}}{\mathrm{\Σ}}}{\mathrm{IM}}_m{(j,a_k)}^2}},m=\mathrm{1,2},...42;k=\mathrm{1,2,3,4}$

Distorting lens driver again corresponding to each driver correlation factor maximal value obtains each character-driven device in the horizontal direction and departs from (dx relative to design attitude with the bias of vertical direction _a1, dy _a1), (dx _a2, dy _a2), (dx _a3, dy _a3), (dx _a4, dy _a4); Then, use following formula to obtain distorting lens pupil plane center and depart from Δ x relative to the pupil plane central horizontal direction of Hartman wavefront detector and vertical direction departs from Δ y:

$\mathrm{\Δx}=\frac{{\mathrm{dx}}_{a1}+{\mathrm{dx}}_{a2}+{\mathrm{dx}}_{a3}+{\mathrm{dx}}_{a4}}{4}$

$\mathrm{\Δy}=\frac{{\mathrm{dy}}_{a1}+{\mathrm{dy}}_{a2}+{\mathrm{dy}}_{a3}+{\mathrm{dy}}_{a4}}{4}$

Definition intermediate variable dx _r(k) and dy _rk () is respectively:

$\begin{array}{c}{\mathrm{dx}}_r\left(k\right)={\mathrm{dx}}_{\mathrm{ak}}-\mathrm{\Δx}\\ {\mathrm{dy}}_r\left(k\right)={\mathrm{dy}}_{\mathrm{ak}}-\mathrm{\Δy}\end{array},k=\mathrm{1,2,3,4}$

Again due to each drive location coordinate and distorting lens pupil plane center position coordinates difference (X in design _{r_act}, Y _{r_act}) be:

$\begin{array}{c}{X}_{r\_\mathrm{act}}\left(i\right)=X_{\_\mathrm{act}}\left(i\right)-X_{\_\mathrm{act}0}\\ Y_{r\_\mathrm{act}}\left(i\right)=Y_{\_\mathrm{act}}\left(i\right)-Y_{\_\mathrm{act}0}\end{array},i=\mathrm{1,2},...,\mathrm{Nact}$

Wherein, (X _{_ act0}, Y _{_ act0}) be the coordinate of distorting lens pupil plane center, then each character-driven device is relative to the anglec of rotation Δ θ of distorting lens pupil centre position _afor:

$\begin{array}{c}\mathrm{\Δ}{\mathrm{\θ}}_a\left(k\right)=\arcsin \left(\frac{X_{r\_\mathrm{act}}\left(a_k\right)[Y_{r\_\mathrm{act}}\left(a_k\right)+{\mathrm{dy}}_r\left(k\right)]-Y_{r\_\mathrm{act}}\left(a_k\right)[X_{r\_\mathrm{act}}\left(a_k\right)+{\mathrm{dx}}_r\left(k\right)]}{X_{r\_\mathrm{act}}{\left(a_k\right)}^2+Y_{r\_\mathrm{act}}{\left(a_k\right)}^2}\right),\\ k=\mathrm{1,2,3,4}\end{array}$

According to Δ θ _aobtaining distorting lens pupil plane relative to the anglec of rotation Δ θ of Hartman wavefront detector pupil plane is:

$\mathrm{\Δ\θ}=\frac{\underset{k=1}{\overset{4}{\mathrm{\Σ}}}\mathrm{\Δ}{\mathrm{\θ}}_a\left(k\right)}{4}$

Depart from Δ x relative to the horizontal direction at Hartman wavefront detector pupil plane center and vertical direction departs from Δ y with regard to obtaining distorting lens pupil plane center like this, and distorting lens pupil plane is relative to the anglec of rotation Δ θ of Hartman wavefront detector pupil plane.

3. a kind of method improving ADAPTIVE OPTICS SYSTEMS transfer matrix measuring accuracy according to claim 2, is characterized in that: the detailed process that the alignment error obtained according to step (1) in described step (2) and the design parameter of ADAPTIVE OPTICS SYSTEMS obtain the result of calculation of transfer matrix and recovery matrix is as follows:

(1) obtain according to Δ x, Δ y and Δ θ the coordinate (X considering each driver physical location of distorting lens that alignment error is later _{new_act}, Y _{new_act}), computing method are: when k is from 1 value to Nact:

If $\sqrt{X_{r\_\mathrm{act}}{\left(k\right)}^2+Y_{r\_\mathrm{act}}{\left(k\right)}^2}\≠0,$ Then

$X_{\mathrm{new}\_\mathrm{act}}\left(k\right)=\sqrt{X_{r\_\mathrm{act}}{\left(k\right)}^2+Y_{r\_\mathrm{act}}{\left(k\right)}^2}\cos (\arccos \left(\frac{X_{r\_\mathrm{act}}\left(k\right)}{\sqrt{X_{r\_\mathrm{act}}{\left(k\right)}^2+Y_{r\_\mathrm{act}}{\left(k\right)}^2}}\right)+\mathrm{\Δ\θ})+\mathrm{\Δx}+X_{\_\mathrm{act}0}$

$Y_{\mathrm{new}\_\mathrm{act}}\left(k\right)=\sqrt{X_{r\_\mathrm{act}}{\left(k\right)}^2+Y_{r\_\mathrm{act}}{\left(k\right)}^2}\sin (\arcsin \left(\frac{Y_{r\_\mathrm{act}}\left(k\right)}{\sqrt{X_{r\_\mathrm{act}}{\left(k\right)}^2+Y_{r\_\mathrm{act}}{\left(k\right)}^2}}\right)+\mathrm{\Δ\θ})+\mathrm{\Δy}+Y_{\_\mathrm{act}0}$

If $\sqrt{X_{r\_\mathrm{act}}{\left(k\right)}^2+Y_{r\_\mathrm{act}}{\left(k\right)}^2}=0,$ Then

X _{new_act}(k)＝Δx+X _{_act0}

Y _{new_act}(k)＝Δy+Y _{_act0}

(2) based on the distorting lens driver actual position coordinate (X of the consideration alignment error obtained above _{new_act}, Y _{new_act}), the actual influence function V ' of distorting lens driver can be obtained _i(x, y):

$V_i^{,}(x,y)=\exp \left[{(\sqrt{{(x-X_{\mathrm{new}\_\mathrm{act}}\left(i\right))}^2+{(y-Y_{\mathrm{new}\_\mathrm{act}}\left(i\right))}^2}/d)}^{\mathrm{\α}}\ln \mathrm{\ω}\right]$

Then, the transfer matrix result of calculation IM under actual position coordinate can be obtained _{_ real}for:

$\begin{array}{c}{\mathrm{IM}}_{\_\mathrm{real}}{(j,i)}_{2\mathrm{NsubXNact}}=-\frac{\underset{S_j}{\∫\∫}\frac{\∂V_i^{,}(x,y)}{\∂x}\mathrm{dxdy}}{A_j}\\ {\mathrm{IM}}_{\_\mathrm{real}}{(j+\mathrm{Nsub},i)}_{2\mathrm{NsubXNact}}=-\frac{\underset{S_j}{\∫\∫}\frac{\∂V_i^{,}(x,y)}{\∂y}\mathrm{dxdy}}{A_j}\end{array},\begin{array}{c}i=\mathrm{1,2},...,\mathrm{Nact},\\ j=\mathrm{1,2},...,\mathrm{Nsub}\end{array}$

To IM _{_ real}generalized inverse matrix is asked namely to obtain the result of calculation R of adaptive optics system reset matrix _{_ real}.

4. a kind of method improving ADAPTIVE OPTICS SYSTEMS transfer matrix measuring accuracy according to claim 3, is characterized in that: obtain the detailed process of the measurement result of transfer matrix according to measuring voltage and wavefront slope in described step (5) as follows:

(1) R is utilized _{_ real}make ADAPTIVE OPTICS SYSTEMS work, each sub-aperture slope that closed-loop corrected Hartman wavefront detector records, after record closed-loop stabilization, the voltage of each driver obtains static aberration compensation voltage vector V _c;

(2) to i=1,2 ..., Nact driver successively carries out following operation: apply bucking voltage vector V to distorting lens _c, then keep other actuator voltages constant, change No. i-th actuator voltage into V _c(i)+V _s, be recorded in the slope vector that Hartman wavefront detector records change No. i-th actuator voltage into V again _c(i)-V _s, be recorded in the slope vector that Hartman wavefront detector records wherein, V _sfor signal voltage, utilize formula:

${\mathrm{IM}}_m=\frac{\left[\begin{array}{cccc}\stackrel{\→}{g_{m1\_1}}-\stackrel{\→}{g_{m2\_1}}& \stackrel{\→}{g_{m1\_2}}-\stackrel{\→}{g_{m2\_2}}& ...& \stackrel{\→}{g_{m1\_595}}-\stackrel{\→}{g_{m2\_595}}\end{array}\right]}{2V_s}$

The measurement result IM of the ADAPTIVE OPTICS SYSTEMS transfer matrix after static aberration correction can be obtained _m.