CN102749143A - Wavefront reconstruction method for improving measuring precision of Shack-Hartmann wavefront sensor - Google Patents

Abstract

The invention provides a wavefront reconstruction method for improving the measuring precision of a Shack-Hartmann wavefront sensor. The method comprises the steps of taking the wavefront detection aberration obtained by a conventional Shack-Hartmann wavefront sensor as an initial point, repeatedly recycling between the wavefront aberration and a sub-aperture light spot by utilizing an iterative algorithm, and judging whether iteration is in place or not by comparing the form between the iterated sub-aperture light spot and an initial sub-aperture light spot so as to finally obtain the high-precision wavefront aberration distribution. According to the method, the weakness of the insufficient sampling ratio of the space of the Shack-Hartmann wavefront sensor can be overcome, the detection precision and the detection capability can be improved further, and the requirement on the Shack-Hartmann wavefront sensor can be lowered.

Description

A kind of wavefront reconstruction method that improves Shack-Hartmann wave front sensor measuring accuracy

Technical field

The present invention relates to Shack-Hartmann wave front sensor technical field of measuring; Be particularly related to a kind of wavefront reconstruction method that improves Shack-Hartmann wave front sensor measuring accuracy, can reduce of the influence of spatial sampling rate deficiency for Shack-Hartmann wave front sensor detection accuracy.

Background technology

Shack-Hartmann wave front sensor is the wavefront measurement instrument that on the basis of classical Hart Shack-Hartmann's measuring method, grows up.But that it and traditional digital interferometer relatively have is simple in structure, do not have moving-member, the anti-vibration ability is strong, to not required, need not when using reference light real time record wavefront variation process by the coherence of photometry, and be applicable to the advantages such as measurement of continuous light and pulsed light simultaneously, be widely used at present ADAPTIVE OPTICS SYSTEMS real-time Wavefront detecting, laser beam quality diagnosis, large-aperture optical spare face shape is detected and the continuous change procedure of record minute surface in.

Shack-Hartmann sensor is a kind of wavefront testing tool that is measured as the basis with wavefront slope.It can provide the dynamic space-time of light beam phase place and amplitude (light intensity) to distribute with high temporal resolution and spatial resolution.Shown in Figure 1 like patent accompanying drawing; In sensor with aperture segmentation element (microlens array); The input aperture is divided into many sub-apertures; Incident wavefront is focused at respectively and forms sub-aperture spot array on the focus of sub-aperture; The side-play amount of surveying the sub-aperture hot spot relative Calibration light of tested wavefront goes out on the pupil plane the average two-dimensional slope of wavefront (being the local wavefront slope) in each sub-aperture with regard to energy measurement, promptly can reconstruct tested near-field beam PHASE DISTRIBUTION and far-field focus information according to these slope datas through wave front restoration algorithms.

The maximum shortcoming of Shack-Hartmann wave front sensor is that sub-array of apertures number is limited, causes the spatial sampling rate lower, and this weakness is then more obvious when wave front aberration to be measured contains more high-order composition.For the aberration of a point on the detection analysis plane needs, need to use CCD to go up dozens of point and participate in calculating.To cause the pixel in the single sub-aperture to reduce again if increase sub-array of apertures number (exchanging more high spatial resolution for), influence the dynamic range of whole sensor.More disadvantageous is that the pixel count that reduces in the sub-aperture can make the diffraction pattern in sub-aperture get in the adjacent sub-aperture, influences the precision of centroid calculation.

On the other hand, the wave front restoration algorithm of existing Shack-Hartmann wave front sensor has utilized just that hot spot carries out the calculating (inclination) of first moment in sub-the aperture in, and the hot spot shape informations do not use in a large number.This is actually great waste, if can make full use of the measuring accuracy that the morphological feature of hot spot then might further improve Shack-Hartmann wave front sensor.

Summary of the invention

The objective of the invention is: overcome the deficiency of existing Shack-Hartmann sensor, propose a kind of wave front restoration method based on iterative algorithm, realize improving the purpose of Shack-Hartmann sensor detection accuracy to overcome the not enough problem of spatial resolution.This invention makes full use of the facula information of Shack-Hartmann wave front sensor, need not do any change to the hardware of Shack-Hartmann sensor, as long as sensor can operate as normal, can both improve measuring accuracy.

Technical solution of the present invention is: scheme 1, a kind of wavefront reconstruction method that improves Shack-Hartmann wave front sensor measuring accuracy, this method comprises the steps:

The initial wave front aberration that step (1), record Shack-Hartmann wave front sensor detect

P arranges in sub-aperture _i(x, y) and Hartmann's dot matrix S ₀(x, y), i≤M wherein, M is sub-aperture number;

Step (2), with initial wave front aberration

According to the sub-aperture p that arranges _i(x, y) right on computers Do Region Segmentation and carry out secondary imaging, obtain Hartmann's dot matrix S _Est(x, y);

Step (3), according to the sub-aperture p that arranges _i(x y) calculates the center-of-mass coordinate (g of each sub-aperture _{X, i}, g _{Y, i}) and obtain the slope of each sub-aperture;

Step (4), the slope slope of each sub-aperture restored be wave front aberration

Step (5), the wave front aberration that estimates

Arrange according to sub-aperture and to do Region Segmentation on computers again and to carry out secondary imaging, obtain new Hartmann's dot matrix S' _Est(x, y); For keeping the iterative process symbol consistent, make:

S _est(x,y)＝S′ _est(x,y)；

Step (6), tolerance S ₀(x, y) and S _Est(x, similarity y), and with this as the iteration stopping condition, if wave front aberration is then exported in the requirement of satisfying the iteration stopping condition

Otherwise turn to step (3) to continue iteration.

In scheme 2, the said step (1)

Calculate by Shack-Hartmann wave front sensor; And S ₀(x y) is then provided by the CCD element of Shack-Hartmann wave front sensor; p _i(x, y) arrange by the lenticule of Shack-Hartmann wave front sensor and obtain:

$p_i(x,y)=\left\{\begin{array}{c}1,x\∈[a_i,a_i+c_x],y\∈[b_i,b_i+c_y]\\ 0,\mathrm{else}\end{array}\right.$

In the formula, (a _i, b _i) refer to the coordinate points in the i sub-aperture lower left corner, a _i, b _iBe (a _i, b _i) coordinate figure, c _xWith c _yRefer to the length of sub-aperture on x and y direction respectively.

Use p in scheme 3, the said step (2) _i(x, y) right The method of cutting apart is:

Corresponding i sub-aperture, i≤M wherein has:

Cut apart by this, finally can obtain M

Obtain Hartmann's dot matrix S in scheme 4, the said step (2) _Est(x, method y) is:

According to the method described in Scenario 3 would

divided into M

then substituting into the following equation is calculated for each sub-aperture of the light intensity distribution:

In the formula $j=\sqrt{-1};$

With M S _{Est, i}(x y) combines and promptly obtains Hartmann's dot matrix S _Est(x, y):

$S_{\mathrm{est}}(x,y)=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{S}_{\mathrm{est},i}(x,y)p_i(x,y).$

Scheme 5, said step (3) the operator aperture hot spot center-of-mass coordinate (g that falls into a trap _{X, i}, g _{Y, i}) method be:

For each sub-aperture S _{Est, i}(x, the center-of-mass coordinate (g that y) calculates _{X, i}, g _{Y, i}) be respectively:

$g_{x,i}=\frac{\underset{l,m}{\mathrm{\Σ}}{x}_{l,m}{I}_{l,m}}{\underset{l,m}{\mathrm{\Σ}}{I}_{l,m}},1\≤i\≤M$

$g_{y,i}=\frac{\underset{l,m}{\mathrm{\Σ}}{y}_{l,m}{I}_{l,m}}{\underset{l,m}{\mathrm{\Σ}}{I}_{l,m}},1\≤i\≤M$

In the formula, x _{L, m}Finger is at sub-aperture S _{Est, i}(x, the y) coordinate of interior x direction, y _{L, m}Then refer to the coordinate on the y direction; I _{L, m}The gray-scale value that refers to each pixel.

The method of calculating each sub-aperture slope in scheme 6, the said step (3) is

$t_{x,i}=g_{x,i}-{\stackrel{\‾}{g}}_{x,i}$

$t_{y,i}=g_{y,i}-{\stackrel{\‾}{g}}_{y,i}$

In the formula,

With

Refer to the centroid position of nominal light in each sub-aperture respectively, provide by Shack-Hartmann wave front sensor; With all t _{X, i}With t _{Y, i}Combine, obtain slope vector (t _x, t _y).

The method that reverts to wave front aberration

from slope in scheme 7, the said step (4) is:

In the formula, f is Shack-Hartmann wave front sensor lenticule focal length, and λ is a lambda1-wavelength; Solve this partial differential equations and can obtain wave front aberration

Scheme 8, said step are passed through in (5)

Obtain new Hartmann's dot matrix S' _Est(x, method y) is:

Will according to the method in the scheme 3 According to p _i(x y) is divided into M

I≤M wherein, again with its substitution following formula:

In the formula $j=\sqrt{-1};$

With M S' _{Est, i}(x y) combines and promptly obtains Hartmann's dot matrix S' _Est(x, y);

${S^{\′}}_{\mathrm{est}}(x,y)=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{S^{\′}}_{\mathrm{est},i}{p}_i(x,y);$

For keeping the iterative process symbol consistent, make:

S _est(x,y)＝S' _est(x,y)。

Scheme 9, said step (6) metrics S _EstWith S ₀The method of similarity is:

The size in each sub-aperture is c _x* c _y, calculate correspondence position S _{Est, i}(x, y) and S _{0, i}(x, simple crosscorrelation y):

$C_i(p,q)=\underset{m=0}{\overset{c_x-1}{\mathrm{\Σ}}}\underset{n=0}{\overset{c_y-1}{\mathrm{\Σ}}}{S}_{\mathrm{est},i}(m,n)S_{0,i}^{*}(m+p,n+q),$

In the formula, " * " represents complex conjugate, and

0≤p≤2Ma-1，0≤q≤2Na-1；

Get C _i(p, maximal value q) is as the criterion of iteration stopping condition:

r _i＝max(C _i(p,q))

Set a constant ε, if the N (r of N≤M) is arranged in the M sub-aperture _iAll satisfy:

r _i≥ε

Iteration stopping then, output

otherwise turn to step (3) to continue iteration.

Principle of the present invention is:

The Wavefront detecting aberration that obtains with traditional Shack-Hartmann wave front sensor is as starting point; Utilize iterative algorithm between wave front aberration and sub-aperture hot spot, to circulate repeatedly; Sub-aperture hot spot through iteration relatively goes out judges with the form between the hot spot of initial sub-aperture whether iteration puts in place, obtains high-precision wave front aberration distribution at last.

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

(1), the present invention made full use of the facula information of Shack-Hartmann wave front sensor through the means of iteration, be of value to and replenish the low sampling error of bringing of spatial sampling rate;

(2), the present invention need not increase the additional hardware expense, pure computed in software;

(3), adaptive faculty of the present invention is strong, possibly be applied on arbitrary Shack-Hartmann wave front sensor.

Description of drawings

Fig. 1 is the measuring principle figure of Shack-Hartmann wave front sensor;

Fig. 2 is a process flow diagram of the present invention

Embodiment

Elaborate in the face of the present invention down.Be subject to limited spatial resolution to existing Shack-Hartmann wave front sensor measuring accuracy; The present invention proposes to utilize iterative algorithm to improve the wave front restoration method of Shack-Hartmann wave front sensor detection accuracy: the wave front aberration that promptly obtains with Shack-Hartmann wave front sensor is as starting point; Measuring principle according to Shack-Hartmann wave front sensor; Wave front aberration arranged by sub-aperture again generates new Shack-Hartmann's dot matrix, restores the wave front aberration that obtains estimating after calculating the slope of each sub-aperture, converts it into dot matrix again; So go round and begin again, finish to obtain high-precision wave front aberration until iteration.Whole algorithm is accomplished by software fully, need not increase or change the light path layout of Shack-Hartmann wave front sensor.The process flow diagram of this algorithm is explained respectively by shown in Figure 2 below:

(1) Shack-Hartmann wave front sensor is measured wave front aberration to be measured, and aberration measured in record P arranges in sub-aperture _i(x, y) (i≤M, M are sub-aperture number) and Hartmann's dot matrix S ₀(x, y); Wherein, arrange and can be expressed as in sub-aperture:

$p_i(x,y)=\left\{\begin{array}{c}1,x\∈[a_i,a_i+c_x],y\∈[b_i,b_i+c_y]\\ 0,\mathrm{else}\end{array}\right.---\left(1\right)$

In the formula, (a _i, b _i) refer to the coordinate points in the i sub-aperture upper left corner, c _xWith c _yRefer to the length of sub-aperture on x and y direction respectively;

(2) use p _i(x, y) right

Cut apart, so that obtain new Hartmann's dot matrix.

Corresponding i sub-aperture (i≤M) have:

Cut apart by this, finally can obtain M

again with the light distribution in its each sub-aperture of substitution computes:

In the formula $j=\sqrt{-1}.$

With M S _{Est, i}(x y) combines and promptly obtains Hartmann's dot matrix S _Est(x, y)

$S_{\mathrm{est}}(x,y)=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{S}_{\mathrm{est},i}{p}_i(x,y)---\left(4\right)$

(3) for each sub-aperture S _{Est, i}Center-of-mass coordinate (the g that calculates _{X, i}, g _{Y, i}) be respectively

$g_{x,i}=\frac{\underset{l,m}{\mathrm{\Σ}}{x}_{l,m}{I}_{l,m}}{\underset{l,m}{\mathrm{\Σ}}{I}_{l,m}},1\≤i\≤M---\left(5\right)$

$g_{y,i}=\frac{\underset{l,m}{\mathrm{\Σ}}{y}_{l,m}{I}_{l,m}}{\underset{l,m}{\mathrm{\Σ}}{I}_{l,m}},1\≤i\≤M---\left(6\right)$

In the formula, x _{L, m}Finger is at sub-aperture S _{Est, i}(x, the y) coordinate of interior x direction, y _{L, m}Then refer to the coordinate on the y direction; I _{L, m}The gray-scale value that refers to each pixel.

Further, can calculate each sub-aperture slope, promptly

$t_{x,i}=g_{x,i}-{\stackrel{\‾}{g}}_{x,i}---\left(7\right)$

$t_{y,i}=g_{y,i}-{\stackrel{\‾}{g}}_{y,i}---\left(8\right)$

In the formula;

and refer to the centroid position of nominal light in each sub-aperture respectively, are provided by Shack-Hartmann wave front sensor.With all t _{X, i}With t _{Y, i}Combine, obtain slope vector (t _x, t _y);

(4) obtain slope after, by following formula it is returned to wave front aberration:

In the formula, f is Shack-Hartmann wave front sensor lenticule focal length, and λ is a lambda1-wavelength.Solve this partial differential equations and can obtain wave front aberration

(5) for realizing iteration; The Hartmann's dot matrix that need the wave front aberration of estimating

derived and to be made new advances; Similar in method and the step (2), unique difference is

replaced with

Will According to p _i(x y) is divided into M

(i≤M), again with its substitution following formula

In the formula $j=\sqrt{-1}.$

With M S' _{Est, i}(x y) combines and promptly obtains new Hartmann's dot matrix S' _Est(x, y)

${S^{\′}}_{\mathrm{est}}(x,y)=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{S^{\′}}_{\mathrm{est},i}{(x,y)p}_i(x,y)---\left(11\right)$

For keeping the iterative process symbol consistent, make

S _est(x,y)＝S′ _est(x,y) （12）

(6) the present invention is with S _Est(x, y) and S ₀(x, similarity y) is an iteration stopping criterion, measures the similarity of the two with cross correlation function.

The size in each sub-aperture is c _x* c _y, calculate correspondence position (i sub-aperture) S _{Est, i}With S _{0, i}Simple crosscorrelation:

$C_i(p,q)=\underset{m=0}{\overset{c_x-1}{\mathrm{\Σ}}}\underset{n=0}{\overset{c_y-1}{\mathrm{\Σ}}}{S}_{\mathrm{est},i}(m,n)S_{0,i}^{*}(m+p,n+q),---\left(13\right)$

In the formula, " * " represents complex conjugate, and

0≤p≤2Ma-1，0≤q≤2Na-1

Get C _i(p, maximal value q) is as the criterion of iteration stopping condition:

r _i＝max(C _i(p,q)) （14）

Set constant ε, if the N (r of N≤M) arranged in the M sub-aperture _iAll satisfy

r _i≥ε

Iteration stopping then, output

otherwise turn to step (3) to continue iteration.

The technology contents that the present invention does not set forth in detail belongs to those skilled in the art's known technology.

Although above the illustrative embodiment of the present invention is described; So that the technician of present technique neck understands the present invention, but should be clear, the invention is not restricted to the scope of embodiment; To those skilled in the art; As long as various variations appended claim limit and the spirit and scope of the present invention confirmed in, these variations are conspicuous, all utilize innovation and creation that the present invention conceives all at the row of protection.

Claims (9)

1. wavefront reconstruction method that improves Shack-Hartmann wave front sensor measuring accuracy, it is characterized in that: this method comprises the steps:

The initial wave front aberration that step (1), record Shack-Hartmann wave front sensor detect P arranges in sub-aperture _i(x, y) and Hartmann's dot matrix S ₀(x, y), i≤M wherein, M is sub-aperture number;

Step (2), with initial wave front aberration

According to the sub-aperture p that arranges _i(x, y) right on computers

Do Region Segmentation and carry out secondary imaging, obtain Hartmann's dot matrix S _Est(x, y);

Step (3), according to the sub-aperture p that arranges _i(x y) calculates the center-of-mass coordinate (g of each sub-aperture _{X, i}, g _{Y, i}) and obtain the slope of each sub-aperture;

Step (4), the slope slope of each sub-aperture restored be wave front aberration

Step (5), the wave front aberration that estimates

Arrange according to sub-aperture and to do Region Segmentation on computers again and to carry out secondary imaging, obtain new Hartmann's dot matrix S' _Est(x, y); For keeping the iterative process symbol consistent, make:

S _est(x,y)＝S _est(x,y)；

Step (6), tolerance S ₀(x, y) and S _Est(x, similarity y), and with this as the iteration stopping condition, if wave front aberration is then exported in the requirement of satisfying the iteration stopping condition

Otherwise turn to step (3) to continue iteration.

2. a kind of wavefront reconstruction method that improves Shack-Hartmann wave front sensor measuring accuracy according to claim 1 is characterized in that: in the said step (1)

Calculate by Shack-Hartmann wave front sensor; And S ₀(x y) is then provided by the CCD element of Shack-Hartmann wave front sensor; p _i(x, y) arrange by the lenticule of Shack-Hartmann wave front sensor and obtain:

$p_i(x,y)=\left\{\begin{array}{c}1,x\∈[a_i,a_i+c_x],y\∈[b_i,b_i+c_y]\\ 0,\mathrm{else}\end{array}\right.$

In the formula, (a _i, b _i) refer to the coordinate points in the i sub-aperture lower left corner, a _i, b _iBe (a _i, b _i) coordinate figure, c _xWith c _yRefer to the length of sub-aperture on x and y direction respectively.

3. a kind of wavefront reconstruction method that improves Shack-Hartmann wave front sensor measuring accuracy according to claim 1 is characterized in that: use p in the said step (2) _i(x, y) right

The method of cutting apart is:

Corresponding i sub-aperture, i≤M wherein has:

Cut apart by this, finally can obtain M

4. a kind of wavefront reconstruction method that improves Shack-Hartmann wave front sensor measuring accuracy according to claim 1 is characterized in that: obtain Hartmann's dot matrix S in the said step (2) _Est(x, method y) is:

According to claim 3, wherein the method divided into M

then substituted into the following formula for each sub-aperture intensity distribution:

In the formula $j=\sqrt{-1};$

With M S _{Est, i}(x y) combines and promptly obtains Hartmann's dot matrix S _Est(x, y):

$S_{\mathrm{est}}(x,y)=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{S}_{\mathrm{est},i}(x,y)p_i(x,y).$

5. a kind of wavefront reconstruction method that improves Shack-Hartmann wave front sensor measuring accuracy according to claim 1 is characterized in that: said step (3) the operator aperture hot spot center-of-mass coordinate (g that falls into a trap _{X, i}, g _Yi) method be:

For each sub-aperture S _{Est, i}(x, the center-of-mass coordinate (g that y) calculates _{X, i}, g _Yi) be respectively:

$g_{x,i}=\frac{\underset{l,m}{\mathrm{\Σ}}{x}_{l,m}{I}_{l,m}}{\underset{l,m}{\mathrm{\Σ}}{I}_{l,m}},1\≤i\≤M$

$g_{y,i}=\frac{\underset{l,m}{\mathrm{\Σ}}{y}_{l,m}{I}_{l,m}}{\underset{l,m}{\mathrm{\Σ}}{I}_{l,m}},1\≤i\≤M$

In the formula, x _{L, m}Finger is at sub-aperture S _{Est, i}(x, the y) coordinate of interior x direction, y _{L, m}Then refer to the coordinate on the y direction; I _{L, m}The gray-scale value that refers to each pixel.

6. a kind of wavefront reconstruction method that improves Shack-Hartmann wave front sensor measuring accuracy according to claim 1 is characterized in that: the method for calculating each sub-aperture slope in the said step (3) is

$t_{x,i}=g_{x,i}-{\stackrel{\‾}{g}}_{x,i}$

$t_{y,i}=g_{y,i}-{\stackrel{\‾}{g}}_{y,i}$

In the formula,

With

Refer to the centroid position of nominal light in each sub-aperture respectively, provide by Shack-Hartmann wave front sensor; With all t _{X, i}With t _{Y, i}Combine, obtain slope vector (t _x, t _y).

7. a kind of wavefront reconstruction method that improves Shack-Hartmann wave front sensor measuring accuracy according to claim 1 is characterized in that: the method that reverts to wave front aberration

from slope in the said step (4) is:

In the formula, f is Shack-Hartmann wave front sensor lenticule focal length, and λ is a lambda1-wavelength; Solve this partial differential equations and can obtain wave front aberration

8. a kind of wavefront reconstruction method that improves Shack-Hartmann wave front sensor measuring accuracy according to claim 1, it is characterized in that: said step is passed through in (5)

Obtain new Hartmann's dot matrix S' _Est(x, method y) is:

Will according to the method in the claim 3

According to p _i(x y) is divided into M

I≤M wherein, again with its substitution following formula:

In the formula $j=\sqrt{-1};$

With M S' _{Est, i}(x y) combines and promptly obtains Hartmann's dot matrix S' _Est(x, y);

${S^{\′}}_{\mathrm{est}}(x,y)=\underset{i=1}{\overset{M}{\mathrm{\Σ}}}{S^{\′}}_{\mathrm{est},i}{p}_i(x,y);$

For keeping the iterative process symbol consistent, make:

S _est(x,y)＝S′ _est(x,y)。

9. a kind of wavefront reconstruction method that improves Shack-Hartmann wave front sensor measuring accuracy according to claim 1 is characterized in that: said step (6) metrics S _EstWith S ₀The method of similarity is:

The size in each sub-aperture is c _x* c _y, calculate correspondence position S _{Est, i}(x, y) and S _{0, i}(x, simple crosscorrelation y):

$C_i(p,q)=\underset{m=0}{\overset{c_x-1}{\mathrm{\Σ}}}\underset{n=0}{\overset{c_y-1}{\mathrm{\Σ}}}{S}_{\mathrm{est},i}(m,n)S_{0,i}^{*}(m+p,n+q),$

In the formula, " * " represents complex conjugate, and

0≤p≤2Ma-1，0≤q≤2Na-1；

Get C _i(p, maximal value q) is as the criterion of iteration stopping condition:

r _i＝max(C _i(p,q))

Set a constant ε, if the N (r of N≤M) is arranged in the M sub-aperture _iAll satisfy:

r _i≥ε

Iteration stopping then, output

otherwise turn to step (3) to continue iteration.

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