CN100573065C - A kind of wavefront measurement method based on linear phase inversion - Google Patents

Abstract

A kind of wavefront measurement method based on linear phase inversion, according to the focal length of optical source wavelength, sensor, the known parameters such as pixel size of image device, the recovery matrix of corresponding relation between every zernike coefficient relative changing value in the far field light intensity relative changing value of the sensor that calibration obtains and the incident wavefront; Earlier with the light source calibration of aberrationless ideal plane, the far field image when obtaining aberrationless was as the calibration benchmark image before sensor used; Then the incident beam that comprises distorted wavefront to be measured is measured, obtained the far field image under the distorted wavefront condition, subtract each other the difference that obtains light distribution with benchmark image and according to being shaped as a light intensity difference vector in advance approximately.Recovery matrix and light intensity difference multiplication of vectors are obtained every zernike coefficient value of comprising in the wavefront distortion to be measured, thereby measure wavefront distortion.Capacity usage ratio height of the present invention, calculated amount are little, and computing velocity is fast, thereby can be applied to the application that real-times such as adaptive optics are had relatively high expectations.

Description

A kind of wavefront measurement method based on linear phase inversion

Technical field

The invention belongs to the optical information field of measuring technique, relate to a kind of method of measuring the incident beam wavefront, relate in particular to a kind of novel wavefront measurement method based on linear phase inversion.

Background technology

In applications such as adaptive optics, optical detections, need the wavefront of measuring beam.Especially in ADAPTIVE OPTICS SYSTEMS, need to measure fast wavefront information, be used for the real-time control of wavefront.Developed many kinds at present and measured the method for wavefront, as shearing interference method, Hartmann's method, the phase place method of inversion and curvature probe method etc.These methods respectively have relative merits, are suitable for application scenario separately, and wherein the phase place method of inversion and curvature probe method all are based on the wavefront measurement method of imaging, are particularly suitable for using in applications such as astronomical adaptive optics.

Usually the method that obtains the incident wavefront phase information according to light intensity distributed intelligence on the optical system image planes is called " phase place inverting (phase retrieval) " technology.In " measuring wavefront by the phase place inverting ", the paper of SPIE collection of thesis the 207th volume 32-39 page or leaf of publication in 1979 announced a kind of phase place inverting wavefront measurement method (R.A.Gonsalves andR.Chidlaw by R.A.Gonsalves and R.Chidlaw the earliest, " Wavefront sensing by phase retrieval " .Proc.of SPIE, Vol.207,32-39,1979).Fig. 1 is the principle schematic of the Wavefront sensor of phase place inverting wavefront measurement method.Utilize this method need write down the far field beam image on the width of cloth focal plane and the image of a width of cloth out of focus simultaneously, and continuous recording multiple image like this, utilize the difference between the multiple image, the method by iteration calculates Beam Wave-Front.

In the paper " curvature is surveyed: a kind of new wavefront measurement method " of SPIE collection of thesis the 976th volume 203-209 page or leaf of publication in 1988, announced a kind of curvature detection method (F.Roddier by F.Roddier the earliest, C.Roddier, N.Roddier, " Curvature sensing:a new wavefrontsensing method ", Proc.SPIE, vol.976,203-209,1988).Fig. 2 is the principle schematic of the Wavefront sensor of measuring method before the curvature probing wave.This method is different with above-mentioned phase place inversion method, utilize far field image on two equidistant before and after focus out of focus faces and the relation between Beam Wave-Front curvature, calculate beam curvature by specific method, wavefront curvature is the second derivative of Wave-front phase, can restore phase place before the efferent echo with specific method according to wavefront curvature.

The Wei Xueye of Beijing Institute of Technology and Yu's letter are at Chinese patent " based on polynomial Wavefront detecting of Zernike and the reconstructing method " (applying date 94.09.16 of application in 1994, application number 94115172, day for announcing 95.07.19, notification number 1105449), proposed a kind of based on polynomial Wavefront detecting of Ze Nike (Zernike) and reconstructing method.The zernike polynomial of this method utilization R.Noll suggestion characterizes the optical wavefront distortion through the entrance pupil place of atmospheric disturbance; Obtain the response matrix of normalization Ze Nike item on the detector of given shape by the light distribution decision of (front and back are equidistant) on two out of focus faces, by the light distribution of wavefront on two out of focus faces at response matrix and entrance pupil place, obtain the coefficient of incident wavefront Ze Nike item.

The phase place method of inversion needs the multiple image iterative computation, and the calculated amount of algorithm is big, thereby real-time is not high, only is fit to image and the application scenario such as handles afterwards.The computing method of curvature probe method are simple relatively, and speed is very fast, be suitable for the demanding occasions of real-time such as adaptive optics, but the curvature probe method do not calculate wavefront at last.The basis of the wavefront measurement method of propositions such as Wei Xueye also is the curvature detection method, the Wavefront sensor optical layout of this method is identical with the curvature detection method, but the method for propositions such as Wei Xueye is not purpose with the wavefront curvature, but far field image and zernike polynomial on two directly that front and back are equidistant out of focus faces connect, and succinctly makes things convenient for than curvature probe method.

More than these several wavefront measurement methods all utilized at least two width of cloth images, need be to respectively imaging and detection after the incident beam beam split.In applications such as astronomical adaptive optics, the incident light energy of stellar target is very faint, any beam split all will reduce the efficiency of light energy utilization, if there are differences (for example the performance of two imaging systems is inconsistent) between two imaging systems after the beam split, can bring additive error to the Wavefront detecting result again.

Summary of the invention

Technology of the present invention is dealt with problems: overcome the deficiencies in the prior art, a kind of wavefront measurement method based on linear phase inversion is provided, this method only utilizes the linear phase inversion commercial measurement to go out the incident beam wavefront according to the single width far field image, efficiency of light energy utilization height, can not bring additive error to the Wavefront detecting result, and calculated amount is little, and is quick, practical.

Technical solution of the present invention: based on the wavefront measurement method of linear phase inversion, its characteristics are to realize by following technical measures:

(1) in advance according to the focal length of optical source wavelength, sensor, the known parameters such as pixel size of image device, the recovery matrix of corresponding relation between every zernike coefficient relative changing value in the far field light intensity relative changing value of the sensor that calibration obtains and the incident wavefront;

(2) before sensor used, with the light source calibration of aberrationless ideal plane, the far field image when obtaining aberrationless was measured the incident beam that comprises distorted wavefront to be measured then as the calibration benchmark image, obtains the far field image under the distorted wavefront condition earlier;

(3) the above-mentioned far field image that obtains and benchmark image are subtracted each other the difference that obtains light distribution and according to being shaped as a light intensity difference vector in advance approximately;

(4) recovery matrix and light intensity difference multiplication of vectors are obtained every zernike coefficient value of comprising in the wavefront distortion to be measured, thereby measure wavefront distortion.

Because the present invention a kind ofly obtains the method for incident wavefront phase information according to light intensity distributed intelligence on the optical system image planes, so belong to " phase place inverting " technology category; Because the phase place refutation process in this method is finished by the multiplication between a vector matrix, this is a kind of typical linear operation process simultaneously, so this phase place inversion algorithm is called " linear phase inversion algorithm ", this is an original creation part of the present invention.

Principle of the present invention: Ze Nike (Zernike) polynomial expression that adopt usually in utilization wave-front optical aberration measurement field characterizes the optical wavefront distortion through the entrance pupil place of atmospheric disturbance, and each rank zernike coefficient of aberration to be measured is arranged as a vectorial a according to prior about definite sequence (general according to spatial frequency order from low to high).The purpose of wavefront measurement is exactly the value that obtains the coefficient vector a of aberration correspondence to be measured; In an imaging optical system, utilize the far field image of a focal plane imaging device (as the CCD camera) record distorted wavefront and utilize image pick-up card with the bidimensional light distribution information acquisition of far field image in computing machine; In advance an ideal plane light source is measured, noted the bidimensional light distribution of far field image of the imaging optical system of ideal plane light source correspondence, expand into column vector according to prior agreement, and be designated as I ₀Utilize same imaging optical system, image device, image pick-up card etc. to note the bidimensional light distribution of the far field image of distorted wavefront correspondence to be measured, expand into column vector according to prior agreement equally, and be designated as I; Obtain the relative variation that has the far field image light distribution of aberration front and back, be designated as column vector Δ I=I-I ₀(perhaps Δ I=I ₀-I also can, according to prior agreement); According to the focal length of optical source wavelength, sensor, the known parameters such as pixel size of image device, the response matrix of corresponding relation between every zernike coefficient relative changing value Δ a in the far field light intensity relative changing value Δ I of the sensor that calibration in advance obtains and the incident wavefront, response matrix inverted obtains recovery matrix R; According to relationship delta a=R Δ I, utilize the linear operation of vector-matrix multiplication to obtain Δ a.Because the zernike coefficient a of ideal plane ripple correspondence ₀=0, so the every zernike coefficient a=Δ a that comprises in Here it is the wavefront distortion to be measured.Usually obtain zernike coefficient and promptly think and measured wavefront distortion, because, can obtain the occurrence of wavefront distortion to be measured easily according to restoring the every zernike coefficient that and the definition of each rank zernike polynomial.

The present invention has two original committed steps: committed step is to utilize an ideal plane light source that the far-field intensity distribution of self aberration correspondence of sensor optics system is calibrated.This process can be got off demarcation such as sensor optics imaging system self aberration, CCD image device photoelectric response characteristic, image pick-up card propagation and transformation characteristic.Computing is afterwards all used and is existed the relative value of aberration front and back far field image light distribution to carry out.As long as the above characterisitic parameter of sensor etc. are constant, light intensity is changed the influence that unfavorable factors such as sensor imaging optical system self aberration can be effectively eliminated in computing that relative value carries out.Calibrating used ideal plane light source is easy to obtain in various Measurement Laboratory.The using method of this process and Hartmann wave front sensor is similar.Hartmann wave front sensor all needs to calibrate with the ideal plane light source before use.Certainly, ideal is relative, and the quality good or not of planar light source will determine the accuracy of wavefront sensor measurements.

Another committed step of the present invention is to determine in the far field light intensity relative changing value Δ I of sensor and the incident wavefront process of recovery matrix R between every zernike coefficient relative changing value Δ a.

Definite method of recovery matrix has the branch of one-pole method and bipolar process, and wherein the recovery matrix calibration process of one-pole method is as follows:

(1) at first according to the focal length of optical source wavelength, sensor, the known parameters such as pixel size of image device, obtain considering self aberration of sensor, but the light distribution of far field image when not having wavefront distortion to be measured, and expand into column vector according to prior agreement, be designated as I ₀

(2), obtain in the wavefront distortion to be measured only j item zernike polynomial coefficient a according to the focal length of optical source wavelength, sensor, the known parameters such as pixel size of image device _jNon-vanishing, other every zernike polynomial coefficients are under zero the situation, corresponding far field image bidimensional light distribution, and expand into column vector according to prior agreement, be designated as I _jJ=1 wherein, 2,3 ..., P.P is the zernike polynomial total item that desire is restored.In order to guarantee the linear relationship establishment, need the setting value of each rank zernike coefficient less, for example a _i＜0.5 is proper.

(3) far field image light distribution I when not having wavefront distortion ₀Compare, obtain the relative variation of far field image light distribution and carry out normalized, i.e. the relative variation of the far field image light distribution that causes of the unit's of obtaining zernike polynomial index variation is designated as column vector Δ I _j=(I _j-I ₀)/a _j(perhaps Δ I _j=(I ₀-I _j)/a _jAlso can, according to prior agreement).

(4) column vector that each light distribution is changed relatively is combined as a response matrix D=[Δ I ₁, Δ I ₂..., Δ I _P].

(5) column vector a=[a who forms by every zernike coefficient of definition ₁, a ₂..., a _P].Far field image light distribution I ideally when not having wavefront distortion ₀Compare, the wavefront distortion that these zernike coefficients are combined into will cause the relative variation of far field image light distribution, and expand into column vector Δ I according to prior agreement.With above procedural representation is a matrix equation Δ I=D * a;

(6) find the solution this matrix equation, will obtain from the matrix algorithms a=R * Δ I of the corresponding every zernike coefficient of relative change calculations of light distribution, wherein R is a recovery matrix.The zernike coefficient of corresponding incident wavefront is zero when noting not having aberration to be measured, i.e. light distribution I ₀Corresponding zernike coefficient is zero, so a is the every zernike coefficient that comprises in the wavefront distortion to be measured.The solving result of the least square method of recovery matrix R is R=(D ^T* D) ^-1D ^T, subscript T representing matrix transposition.But reliable and stable for numerical solution, adopt the method for matrix pseudoinverse to find the solution R=D usually ⁺, D wherein ⁺It is the pseudo inverse matrix of D.

Bipolar process recovery matrix calibration process is as follows:

(1) at first according to the focal length of optical source wavelength, sensor, the known parameters such as pixel size of image device, obtain considering self aberration of sensor, but the light distribution of far field image when not having wavefront distortion to be measured, and expand into column vector according to prior agreement, be designated as I ₀

(2) according to the focal length of optical source wavelength, sensor, the known parameters such as pixel size of image device, obtain in the wavefront distortion other every zernike polynomial coefficients respectively and be zero, only j item zernike polynomial coefficient is a _jWith-a _jUnder non-vanishing two kinds of situations, corresponding far field image bidimensional light distribution, and expand into column vector I respectively according to prior agreement _J1And I _J2J=1 wherein, 2,3 ..., P.P is the zernike polynomial total item that desire is restored.In order to guarantee the linear relationship establishment, need the setting value of each rank zernike coefficient less, for example a _i＜0.5 is proper.

(3) obtain the relative variation of above two far field image light distribution and carry out normalized, i.e. the relative variation of the far field image light distribution that causes of the unit's of obtaining zernike polynomial index variation is designated as column vector Δ I _j=(I _J1-I _J2)/(2a _j);

(4) column vector that each light distribution is changed relatively is combined as a response matrix D=[Δ I ₁, Δ I ₂..., Δ I _P].

(5) column vector a=[a who forms by every zernike coefficient of definition ₁, a ₂..., a _P]; The wavefront distortion that is combined into by these zernike coefficients will cause the relative variation of far field image light distribution, and expand into column vector Δ I according to prior agreement.With above procedural representation is a matrix equation Δ I=D * a;

(6) find the solution this matrix equation, will obtain from the method a=R * Δ I of the corresponding every zernike coefficient of relative change calculations of light distribution, wherein R is a recovery matrix.The zernike coefficient of corresponding incident wavefront is zero when noting not having aberration to be measured, i.e. light distribution I ₀Corresponding zernike coefficient is zero, so a is the every zernike coefficient that comprises in the wavefront distortion to be measured.The solving result of the least square method of recovery matrix R is R=(D ^T* D) ^-1D ^T, subscript T representing matrix transposition.But reliable and stable for numerical solution, adopt the method for matrix pseudoinverse to find the solution R=D usually ⁺, D wherein ⁺It is the pseudo inverse matrix of D;

Because bipolar process has considered that simultaneously aberration coefficients is the situation of positive number or negative, more near actual scene, so the recovery matrix that common bipolar process obtains is more accurate.

The basic theories principle of institute of the present invention foundation is derived as follows: theoretical foundation of the present invention derives from the incident beam focal plane physical principle and the mathematical relation between COMPLEX AMPLITUDE on the COMPLEX AMPLITUDE and input aperture.

Order $\stackrel{\→}{x}=(x,y)$ Represent omnidirectional distribution on the input aperture (Cartesian) net point, (ξ η) represents orthogonal grid point on the focal plane.A (x, y) exp[i φ (x, y)] represent the complex amplitude on the input aperture, wherein (x y) is distribution of amplitudes to A, and (x y) is PHASE DISTRIBUTION to φ.According to Fourier optical principle, the COMPLEX AMPLITUDE w on the focal plane (ξ, η) and the pass between the complex amplitude on the input aperture be:

$w(\mathrm{\ξ},\mathrm{\η})=\frac{\exp [\mathrm{i\π}({\mathrm{\ξ}}^2+{\mathrm{\η}}^2)/\mathrm{\λf}]}{\mathrm{i\λf}}{\∫}_{-\∞}^{\∞}{\∫}_{-\∞}^{\∞}A(x,y)\exp \left[\mathrm{i\φ}(x,y)\right]\exp [-\frac{i2\mathrm{\π}(\mathrm{x\ξ}+\mathrm{y\η})}{\mathrm{\λf}}]\mathrm{dxdy}---\left(1\right)$

Wherein λ is a wavelength, and f is an imaging focal length.In normal circumstances, the light distribution on the input aperture is more uniform, and promptly (x y) is constant to distribution of amplitudes A, and its influence to imaging can be ignored.If we define $\stackrel{\→}{u}=(u,v)=(\mathrm{\ξ},\mathrm{\η})/\mathrm{\λf},$ And ignore the item before the integration in (1) formula, the COMPLEX AMPLITUDE on input aperture and the imaging focal plane can be used the expression of two-dimensional Fourier transform (Fourier transform) relation:

w(u，v)＝F[Aexp[iφ(x，y)]](2)

Wherein Fourier transform is closed and is $F\left[f(x,y)\right]={\∫}_{-\∞}^{\∞}{\∫}_{-\∞}^{\∞}f(x,y)\exp [-i2\mathrm{\π}(\mathrm{xu}+\mathrm{yv})]\mathrm{dxdy}.$ Under discrete state, replace the continuous domain Fourier transform with two dimensional discrete Fourier transform (Discrete Fourier transform):

$w(u,v)=\frac{1}{N^2}\underset{x=0}{\overset{N-1}{\mathrm{\Σ}}}\underset{y=0}{\overset{N-1}{\mathrm{\Σ}}}\mathrm{Aexp}\left[\mathrm{i\φ}(x,y)\right]\exp [-i2\mathrm{\π}(\mathrm{xu}+\mathrm{yv})/N]---\left(3\right)$

Simultaneously, on the focal plane of incident beam, utilize an imaging detector record hot spot intensity distributions:

$I\left(\stackrel{\→}{u}\right)={\left|w\left(\stackrel{\→}{u}\right)\right|}^2---\left(4\right)$

If PHASE DISTRIBUTION in the input aperture

On apply an increment or variable quantity

The approximation relation of utilization index function, the COMPLEX AMPLITUDE on the imaging surface is by this:

$\hat{w}\left(\stackrel{\→}{u}\right)=F\left\{\mathrm{Aexp}\right[\mathrm{i\φ}\left(\stackrel{\→}{x}\right)+\mathrm{i\Δ\φ}\left(\stackrel{\→}{x}\right)\left]\right\}\≈F\left\{\mathrm{Aexp}\right[\mathrm{i\φ}\left(\stackrel{\→}{x}\right)]\·[1+\mathrm{i\Δ\φ}\left(\stackrel{\→}{x}\right)\left]\right\}---\left(5\right)$

The variable quantity of COMPLEX AMPLITUDE on the focal plane so

With the PHASE DISTRIBUTION variable quantity

Between have a linear relationship:

$\mathrm{\Δw}\left(\stackrel{\→}{u}\right)=\hat{w}\left(\stackrel{\→}{u}\right)-w\left(\stackrel{\→}{u}\right)=F\{\mathrm{i\Δ\φ}\left(\stackrel{\→}{x}\right)\·\mathrm{Aexp}[\mathrm{i\φ}\left(\stackrel{\→}{x}\right)\left]\right\}---\left(6\right)$

The light distribution that applies on the phase changing capacity back focal plane also exists a variable quantity to be:

$I\left(\stackrel{\→}{u}\right)+\mathrm{\ΔI}\left(\stackrel{\→}{u}\right)=[w\left(\stackrel{\→}{u}\right)+\mathrm{\Δw}\left(\stackrel{\→}{u}\right)]*\·[w\left(\stackrel{\→}{u}\right)+\mathrm{\Δw}\left(\stackrel{\→}{u}\right)]---\left(7\right)$

$\mathrm{\ΔI}\left(\stackrel{\→}{u}\right)=w\left(\stackrel{\→}{u}\right)*\·\mathrm{\Δw}\left(\stackrel{\→}{u}\right)+w\left(\stackrel{\→}{u}\right)\·\mathrm{\Δw}\left(\stackrel{\→}{u}\right)*+\mathrm{\Δw}\left(\stackrel{\→}{u}\right)*\·\mathrm{\Δw}\left(\stackrel{\→}{u}\right)\≈2\mathrm{Re}[w\left(\stackrel{\→}{u}\right)*\·\mathrm{\Δw}\left(\stackrel{\→}{u}\right)]---\left(8\right)$

Wherein asterisk represent the plural number conjugation, Re[.] expression complex item real part.Ignored second order in the following formula in a small amount ${\left|\mathrm{\Δw}\left(\stackrel{\→}{u}\right)\right|}^2\≈0.$ Comprehensive above various, obtain the result:

$\mathrm{\ΔI}\left(\stackrel{\→}{u}\right)\≈2\mathrm{Re}\left\{F\right\{\mathrm{Aexp}\left[\mathrm{i\φ}\left(\stackrel{\→}{x}\right)\right]\}*\·F\{\mathrm{i\Δ\φ}\left(\stackrel{\→}{x}\right)\·\mathrm{Aexp}\left[\mathrm{i\φ}\left(\stackrel{\→}{x}\right)\right]\left\}\right\}---\left(9\right)$

There is linear approximate relationship between the variable quantity of PHASE DISTRIBUTION on the variable quantity of light distribution and the input aperture on the following formula explanation focal plane.This linear relationship can be expressed as with matrix form:

ΔI＝H·ΔΦ(10)

Wherein light distribution variation delta I is (N ²* 1) Wei vector is (the focal plane pixel of N * N) expands into single-row vector and forms.PHASE DISTRIBUTION variable quantity ΔΦ is (M ²* 1) Wei vector is (the two-dimensional phase lattice array of M * M) expands into single-row vector and forms on the input aperture.H in the formula is (N ²* M ²) linear matrix.After the corresponding relation of input aperture and focal plane was determined, H entry of a matrix element can calculated in advance or is measured and determine.According to linear equation, when M=N, the process that known light distribution variable quantity is found the solution the PHASE DISTRIBUTION variable quantity is:

ΔΦ＝H ^-1·ΔI (11)

In solution procedure, two important constraint conditions are arranged.The summation of first phase changing capacity is zero:

${\mathrm{\Σ}}_{n=1}^{N^2}\mathrm{\Δ\Φ}\left(n\right)=0---\left(12\right)$

The phase average that this constraint condition also can be understood as on the aperture is zero, avoids the wavefront translation problem in the solution procedure.Another constraint condition is that the summation of light distribution variable quantity is zero, because the gross energy conservation of hot spot on the focal plane:

${\mathrm{\Σ}}_{n=1}^{N^2}\mathrm{\ΔI}\left(n\right)=0---\left(13\right)$

Just can carry out the wavefront inverting according to above (11) formula from the light distribution on the focal plane.But this algorithm is very unrealistic.At first, calculated amount and memory space are huge.If restore 100 * 100 PHASE DISTRIBUTION, just need to calculate and store 10 from 100 * 100 light distribution ⁴* 10 ⁴Huge matrix.Secondly, the phase value that directly restores each point there is no need.According to the principle of pattern wave front restoration, only need calculate the coefficient of a series of set wave premodes, can restore efferent echo before.Wavefront distortion can be represented with the linear superposition of a series of wavefront modes:

$\mathrm{\φ}(x,y)={\mathrm{\Σ}}_{i=1}^P{a}_i{M}_i(x,y)---\left(14\right)$

A wherein _iBe mode coefficient, M _i(x y) is wavefront modes.Here adopt zernike polynomial commonly used in the Wavefront sensor field, P is the pattern exponent number.The variable quantity that Wave-front phase distributes and the variation delta a of each rank wavefront modes coefficient _iBetween have a linear relationship:

$\mathrm{\Δ\φ}(x,y)={\mathrm{\Σ}}_{i=1}^P\mathrm{\Δ}{a}_i{M}_i(x,y)---\left(15\right)$

Following formula can be expressed as with matrix form:

ΔΦ＝A·Δa (16)

Wherein mode coefficient variation delta a is the vector of (P * 1) dimension, and A is (M ²* P) rectangular matrix.According to (10) formula, also there is linear relationship on the variable quantity of each rank wavefront modes coefficient that is easy to get and the focal plane between the light intensity distribution variable quantity:

ΔI＝H·A·Δa＝D·Δa (17)

Wherein D=HA is generally rectangular matrix, is called response matrix in the present invention.Process from light distribution variable quantity calculating wavefront zernike coefficient variable quantity is so:

Δa＝R·ΔI (18)

Wherein R is the Ze Nike pattern recovery matrix of this sensor.The solving result of least square method is R=(D ^T* D) ^-1D ^T, subscript T representing matrix transposition.But reliable and stable for numerical solution, adopt the method for svd (SVD) to find the solution matrix pseudoinverse R=D usually ⁺, D wherein ⁺It is the pseudo inverse matrix of D.

Because the zernike coefficient of corresponding incident wavefront is not zero when having aberration to be measured, so the every zernike coefficient a=Δ a that comprises in the wavefront distortion to be measured.Obtain restoring the Wave-front phase on any a plurality of points in the footpath, entrance port behind the zernike coefficient.Whole wavefront measurement process is reduced to a vector-matrix multiplication computing.This linear operation is particularly suitable for finishing real-time with modern DSP (digital signal processing) technology.

The present invention compared with prior art has following advantage:

(1) in the wavefront measurement method of the present invention, only need when calibration, obtain a width of cloth benchmark image, carry out in the measuring process at the incident beam that contains wavefront distortion then, only need to measure corresponding single width far field image and can finish the wavefront process, do not need incident beam is carried out unified beam split (as the curvature Wavefront sensor) or sub-aperture beam split (as Hartmann wave front sensor).This point is particularly useful to the very faint application of the incident intensities such as adaptive optics of stellar target astronomical sight, can save valuable incident light energy, improves the efficiency of light energy utilization.

(2) in the wavefront measurement method of the present invention, the influence of Wavefront sensor imaging optical system self aberration is considered and eliminated to the calibration process of benchmark image and recovery matrix, and sensor optics system self aberration is inevitably under practical application, so the present invention has advantages of high practicability.

(3) in the wavefront measurement method of the present invention, the wave front restoration process is reduced to a simple vector sum matrix multiplication operation, and this linear operation is particularly suitable for finishing real-time with modern DSP (digital signal processing) technology.The iterative computation process of relative other wavefront measurement technology, calculated amount of the present invention is little, thereby computing velocity is fast.Wavefront measurement method of the present invention can be applied to the application that real-times such as adaptive optics are had relatively high expectations.

Description of drawings

The principle schematic of the Wavefront sensor of Fig. 1 conventional phase inverting wavefront measurement method;

The principle schematic of the Wavefront sensor of measuring method before the curvature probing wave of Fig. 2 prior art;

Fig. 3 is a Wavefront sensor principle schematic of carrying out the incident beam wavefront measurement according to the single width far field image with the linear phase inversion technology of the present invention.

Embodiment

As shown in Figure 3, realize that the Wavefront sensor that method of the present invention adopts is made up of diffraction imaging optical system, focal plane imaging device (as the CCD camera), image pick-up card, computing machine, the zernike polynomial that adopt usually in utilization wave-front optical aberration measurement field characterizes the optical wavefront distortion through the entrance pupil place of atmospheric disturbance, each rank zernike coefficient of aberration to be measured is arranged as a vectorial a according to prior about definite sequence (general according to spatial frequency order from low to high), and the purpose of wavefront measurement is exactly the value that obtains the coefficient vector a of aberration correspondence to be measured.

Wavefront distortion φ (x to be measured, y) through imaging on the focal plane after the diffraction imaging optical system, place the far field image of a CCD cameras record distorted wavefront near the focal plane, utilize image pick-up card with the bidimensional light distribution information acquisition of far field image in computing machine.(x y) is the aberration of this imaging system self to S.Modal optical imaging system aberration is the out of focus aberration, Be the wavefront distortion that is finally inversed by, the reference planes light source is used to demarcate Wavefront sensor self aberration.

Concrete measuring process of the present invention is as follows:

(1) sensor needs according to the focal length of optical source wavelength, sensor, the known parameters such as pixel size of image device before using, the response matrix D of corresponding relation between every zernike coefficient relative changing value Δ a in the far field light intensity relative changing value Δ I of the sensor that calibration in advance obtains and the incident wavefront, response matrix D inverted obtains recovery matrix R.In the process of measuring response matrix, the general bipolar process more accurately that adopts.

(2) also need before sensor uses self aberration, CCD camera target surface pixel size and the photoelectric response sensitivity of sensor, the parameters such as conversion characteristic of image pick-up card to be demarcated with a desirable reference planes light source, obtain the image of reference plane wave light source, expand into column vector according to prior agreement, and be designated as I ₀After having calibrated reference light source is removed.Utilize same imaging optical system, image device, image pick-up card etc. to note the bidimensional light distribution of the far field image of distorted wavefront correspondence to be measured, expand into column vector according to prior agreement equally, and be designated as I.

(3) obtain the relative variation that has the far field image light distribution of aberration front and back, be designated as column vector Δ I=I-I ₀(perhaps Δ I=I ₀-I also can, according to prior agreement).

(4), utilize the linear operation of vector-matrix multiplication to obtain Δ a according to relationship delta a=R Δ I.Because the zernike coefficient a of ideal plane ripple correspondence ₀=0, so the every zernike coefficient a=Δ a that comprises in Here it is the wavefront distortion to be measured obtains zernike coefficient usually and promptly thinks and measured wavefront distortion.Because, can obtain the occurrence of wavefront distortion to be measured easily according to restoring the every zernike coefficient that and the definition of each rank zernike polynomial.

In obtaining Ze Nike response matrix process, the aberration of sensor imaging system self is extremely important.Any one sensing system all has an intrinsic aberration, and needs to demarcate in advance.For example Hartmann sensor just needs the sub-aperture hot spot side-play amount that measurement in advance self aberration causes, and as the zero point of measuring in the future.Self aberration of imaging wavefront inverting sensor can freely be provided with, the size of the position that for example can be by freely being adjusted to image planes or the position change out of focus aberration (defocus) of lens.The imaging distribution I of reference plane wave noted earlier ₀In comprised sensor self aberration S (x, influence y).(x, size y) and form are very big to the influence of recovery matrix and wavefront inverting sensor performance for sensor self aberration S.After sensor self aberration changes, need remeasure recovery matrix.

Claims (3)

1, a kind of wavefront measurement method based on linear phase inversion is characterized in that passing through following steps

Realize:

(1) in advance according to the focal length of optical source wavelength, sensor, the pixel size known parameters of image device, the recovery matrix of corresponding relation between every zernike coefficient relative changing value in the far field light intensity relative changing value of the sensor that calibration obtains and the incident wavefront;

(2) before sensor used, with the light source calibration of aberrationless ideal plane, the far field image when obtaining aberrationless was measured the incident beam that comprises distorted wavefront to be measured then as the calibration benchmark image, obtains the far field image under the distorted wavefront condition earlier;

(3) the above-mentioned far field image that obtains and benchmark image are subtracted each other the difference that obtains light distribution and according to being shaped as a light intensity difference vector in advance approximately;

(4) recovery matrix and light intensity difference multiplication of vectors are obtained every zernike coefficient value of comprising in the wavefront distortion to be measured, thereby measure wavefront distortion.

2, the method based on the wavefront measurement of linear phase inversion according to claim 1, it is characterized in that: " one-pole method " adopted in the recovery matrix calibration in the described step (1), and its calibration process is as follows:

(1) according to the focal length of optical source wavelength, sensor, the pixel size known parameters of image device, obtain considering self aberration of sensor, but the light distribution of far field image when not having wavefront distortion to be measured, and expand into column vector according to prior agreement, be designated as I ₀

(2), obtain in the wavefront distortion to be measured only j item zernike polynomial coefficient a according to the focal length of optical source wavelength, sensor, the pixel size known parameters of image device _jNon-vanishing, other every zernike polynomial coefficients are under zero the situation, corresponding far field image bidimensional light distribution, and expand into column vector according to prior agreement, be designated as I _j, j=1 wherein, 2,3 ..., P, P are the zernike polynomial total items that desire is restored;

(3) far field image light distribution I when not having wavefront distortion ₀Compare, obtain the relative variation of far field image light distribution and carry out normalized, i.e. the relative variation of the far field image light distribution that causes of the unit's of obtaining zernike polynomial index variation is designated as column vector Δ I _j=(I _j-I ₀)/a _jPerhaps according to being decided to be Δ I in advance approximately _j=(I ₀-I _j)/a _j

(4) column vector that each light distribution is changed relatively is combined as a response matrix D=[Δ I ₁, Δ I ₂..., Δ I _P];

(5) column vector a=[a who forms by every zernike coefficient of definition ₁, a ₂..., a _P], far field image light distribution I ideally when not having wavefront distortion ₀Compare, the wavefront distortion that these zernike coefficients are combined into will cause the relative variation of far field image light distribution, and expand into column vector Δ I according to prior agreement, be a matrix equation Δ I=D * a with above procedural representation;

(6) find the solution this matrix equation, will obtain from the matrix algorithms a=R * Δ I of the corresponding every zernike coefficient of relative change calculations of light distribution, wherein R is a recovery matrix.

3, the method based on the wavefront measurement of linear phase inversion according to claim 1, it is characterized in that: " bipolar process " adopted in the recovery matrix calibration in the described step (1), and its calibration process is as follows:

(1) at first according to the focal length of optical source wavelength, sensor, the pixel size known parameters of image device, obtain considering self aberration of sensor, but the light distribution of far field image when not having wavefront distortion to be measured, and expand into column vector according to prior agreement, be designated as I ₀

(2) according to the focal length of optical source wavelength, sensor, the pixel size known parameters of image device, obtain in the wavefront distortion other every zernike polynomial coefficients respectively and be zero, only j item zernike polynomial coefficient is a _jWith-a _jUnder non-vanishing two kinds of situations, corresponding far field image bidimensional light distribution, and expand into column vector I respectively according to prior agreement _J1And I _J2, j=1 wherein, 2,3 ..., P, P are the zernike polynomial total item that desire is restored;

(3) obtain the relative variation of above two far field image light distribution and carry out normalized, i.e. the relative variation of the far field image light distribution that causes of the unit's of obtaining zernike polynomial index variation is designated as column vector Δ I _j=(I _J1-I _J2)/(2a _j);

(4) column vector that each light distribution is changed relatively is combined as a response matrix D=[Δ I ₁, Δ I ₂..., Δ I _P];

(5) column vector a=[a who forms by every zernike coefficient of definition ₁, a ₂..., a _P], the wavefront distortion that is combined into by these zernike coefficients will cause the relative variation of far field image light distribution, and expand into column vector Δ I according to prior agreement, be a matrix equation Δ I=D * a with above procedural representation;

(6) find the solution this matrix equation, will obtain from the method a=R * Δ I of the corresponding every zernike coefficient of relative change calculations of light distribution, wherein R is a recovery matrix.

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