CN101936780B - Wavefront sensor with two-sided cone mirror - Google Patents

Abstract

The invention relates to a wavefront sensor with two conical mirrors, which consists of four lenses, two conical mirrors, a beam splitter and two CCD image detectors; the incident distorted wavefront is firstly divided into two paths by a beam splitter, each path of light passes through a 4f beam-shrinking system consisting of two-sided cone mirrors and two lenses, ridge edges of the two-sided cone mirrors are mutually orthogonally arranged, and the ridge edges are respectively superposed with the focuses of the first lens or the third lens, one of the two-sided cone mirrors splits the front edge of the incident distorted wave in the horizontal direction, the other two-sided cone mirror splits the front edge of the incident distorted wave in the vertical direction, and then pupil conjugate images of the two-sided cone mirrors are imaged to respective CCD image detectors after passing through the second lens or the fourth lens; the CCD image detector is connected with a computer, the computer is used for reading pupil images, the light intensity distribution difference of the two pupil images in the horizontal direction or the vertical direction is compared to obtain measurement signals in the two directions, and then the wavefront phase is reconstructed by utilizing a wavefront restoration algorithm.

Description

A kind of Wavefront sensor with two sides axicon lens

Technical field

The present invention relates to a kind of Wavefront sensor, the Wavefront sensor of particularly a kind of two sides axicon lens belongs to the Primary Component of technical fields such as adaptive optics, Wavefront detecting.

Background technology

Wavefront sensor is an important devices of measuring wavefront distortion in the adaptive system; Can be divided into two types according to getting in touch between measuring-signal and the corrugated: one type is to obtain Wave-front phase through measuring wavefront slope (being the wavefront first order derivative); Hartmann wave front sensor is more typically arranged, shearing interferometer etc.; Another kind of is to measure wavefront curvature (being the wavefront second derivative) to obtain Wave-front phase, mainly contains the curvature Wavefront sensor.

The most frequently used Hartmann wave front sensor uses microlens array that entrance pupil is cut apart, and finds the solution wavefront slope through the center-of-mass coordinate of image patch on the measurement of Lens array focal plane and the difference of reference wavefront center-of-mass coordinate.A kind of in addition Wavefront sensor of pupil beam split utilizes the pyramid of the individual faceted pebble of N (N＞1) with the beam splitting of incident corrugated, and then measures wavefront distortion (U.S. Pat 4399356 " Optical wavefront sensing system " that nineteen eighty-three authorizes).

These two types of Wavefront sensors that Wavefront sensor all is an a kind of minute wavefront; Its spatial sampling rate is determined by sub-aperture number; Each sub-aperture needs several CCD pixels to survey spot center; To propose higher requirement to the pixel count of photoelectronic imaging element and increase sub-aperture number, and the efficiency of light energy utilization is lower.

The Australian Patent AU2003267457A1 " Pyramid sensorfor determing the wave aberration of the human eye " that authorized in 2002 utilizes the refracting telescope of Pyramid that the incident light of assembling is divided into 4 bundles in the focal plane; Then utilize relay lens to be imaged onto the ccd image detector; Difference through more same direction pupil image light intensity obtains measuring-signal; Utilize the linear reconstruction matrix to restore wavefront to be measured then, this sensor is called as rectangular pyramid Wavefront sensor (PWFS).It is compared with the Wavefront sensor of the two kinds of branch wavefront in front, and each pixel of CCD is equivalent to a sub-aperture, has the sampling rate height and is easy to change, efficiency of light energy utilization advantages of higher (A&A, 350, L23-L26,1999, Opt.Commun, 268,189-195,2006).

The core devices of PWFS is the refracting prisms of a Pyramid, is called for short rectangular pyramid, and its effect is at frequency plane incident wave to be carried out beam splitting; Therefore the berm width to its surfaceness and seamed edge has strict requirement (SPIE; Vol.4007,423-430,2000).Though the technology of processing rectangular pyramid is constantly improved; Still exist difficulty of processing big but produce qualified rectangular pyramid at present, be easy to produce the broad platform, thereby influence Wavefront detecting (Microelectronic Engineering67-68 at the tip of ridge seamed edge; 566-573,2003; PhD Thesis, Joana B ü chler costa.2005).In addition, when using unmodulated PWFS to measure wavefront difference, type method restores the used restructuring matrix of wavefront does not have analytic solution, needs the scene to measure (Appl.0pt, 47,79-87,2008).

Summary of the invention

The objective of the invention is to utilize the Wavefront sensor with two sides axicon lens to overcome that traditional Hartmann wave front sensor spatial sampling rate is low, the efficiency of light energy utilization is low, the rectangular pyramid Wavefront sensor is made the shortcoming that difficulty and linear reconstruction matrix need be measured in actual light path.

For reaching said purpose; Technical solution with Wavefront sensor of two sides axicon lens provided by the invention is: have two two sides axicon lens, a beam splitter BS, four lens and two ccd image detectors; The incident distorted wavefront is divided into the two-beam line through beam splitter BS; The 4f that each road light is all formed through a two sides axicon lens and two lens beam system that contracts, two mutually orthogonal putting of ridge seamed edge of two two sides axicon lens, and their ridge seamed edge overlaps with the focus of first lens or the 3rd lens respectively; One of them two sides axicon lens is with the beam split of incident distorted wavefront along continuous straight runs; Another two sides axicon lens is with the beam split vertically of incident distorted wavefront, and behind second lens or the 4th lens, its pupil conjugate image is imaged onto ccd image detector separately then; The 4f shared focal plane of two lens of beam system of contracting wherein, and the focal length of two lens does not wait; The ccd image detector links to each other with computing machine, utilizes computing machine to read pupil image, and the light distribution difference of comparison level direction or two pupil image of vertical direction can obtain the measuring-signal of both direction, utilizes wave front restoration algorithm reconstruct Wave-front phase again.

The present invention compared with prior art has following advantage:

(1) Wavefront sensor with two sides axicon lens of the present invention is compared with Hartmann wave front sensor, has sampling rate height (identical CCD target surface), the advantage that the efficiency of light energy utilization is high.

(2) Wavefront sensor of two sides of the present invention axicon lens, used two sides axicon lens has easy processing, and seamed edge is only formed by two planes, is difficult for producing platform.

(3) Wavefront sensor of two sides of the present invention axicon lens is compared with the rectangular pyramid Wavefront sensor, and when adopting type method to restore wavefront, restructuring matrix can be calculated by analytic expression need not in-site measurement, has the wave front restoration precision higher than rectangular pyramid Wavefront sensor.

Description of drawings

Fig. 1 is the schematic diagram of the Wavefront sensor of two sides of the present invention axicon lens;

Fig. 2 a is the pupil image light intensity synoptic diagram after the along continuous straight runs beam split of obtaining of the first ccd image detector;

Fig. 2 b is the pupil image distribution plan on the first ccd image detector after the beam split of coma along continuous straight runs;

Fig. 3 a is the pupil image light intensity synoptic diagram after the along continuous straight runs beam split of obtaining of the second ccd image detector;

Fig. 3 b is the pupil image distribution plan on the second ccd image detector after the beam split of coma along continuous straight runs;

Fig. 4 a to Fig. 4 c adopts the simulation result of type method to the coma wave front restoration for the Wavefront sensor of two sides of the present invention axicon lens.

Embodiment

For making the object of the invention, technical scheme and advantage clearer, below in conjunction with specific embodiment, and with reference to accompanying drawing, to further explain of the present invention.

The schematic diagram of the Wavefront sensor of two sides of the present invention as shown in Figure 1 axicon lens, the present invention is made up of two two sides axicon lens, a beam splitter BS, four lens and two ccd image detectors.The incident distorted wavefront is divided into the two-beam line through beam splitter BS, and each road light is all through a two sides axicon lens and two lens L ₁, L ₂(or two lens L ₃, L ₄) 4f that the forms beam system that contracts, two mutually orthogonal putting of ridge seamed edge of two two sides axicon lens, and their ridge seamed edge respectively with the first lens L ₁Or the 3rd lens L ₃Focus overlap, one of them two sides axicon lens is with the beam split of incident distorted wavefront along continuous straight runs, then through the second lens L ₂, another two sides axicon lens is with the beam split vertically of incident distorted wavefront, then through the 4th lens L ₄After, its pupil conjugate image is imaged onto ccd image detector separately.The 4f shared focal plane of two lens of beam system of contracting wherein, and the focal length of two lens does not wait; Two ccd image detectors link to each other with computing machine respectively; Utilize computing machine to read pupil image; And the light distribution difference of comparison level direction or two pupil image of vertical direction can obtain the measuring-signal of both direction, utilizes wave front restoration algorithm reconstruct Wave-front phase again.

Said beam splitter BS has any splitting ratio.

Said two two sides axicon lens comprise the first two sides axicon lens 1 and the second two sides axicon lens 2; Said ridge seamed edge is that the first two sides axicon lens 1 has the first ridge seamed edge 11 and the second two sides axicon lens 2 has the second ridge seamed edge 21; The said first ridge rib 11 and the said second ridge rib, 21 mutually orthogonal putting is placed on the first lens L respectively ₁With the 3rd lens L ₃The focal plane, and the first ridge seamed edge 11 and the second ridge seamed edge 21 are over against the first lens L ₁With the 3rd lens L ₃Focus.

The first lens L in said four lens ₁With the 3rd lens L ₃Focal length be respectively f ₁, the second lens L ₂With the 4th lens L ₄Focal length is respectively f ₂,

Decision pupil image size, wherein, D is the incident wavefront aperture.

The refractive two sides axicon lens that described two sides axicon lens is made for the traditional optical device manufacturing process; The base angle of two sides axicon lens M is the adjacent pupil image centre distance and the ratio of pupil image, f ₁Be the first lens L ₁With the 3rd lens L ₃Focal length, n is the refractive index of material.

The said adjacent pupil image centre distance and the ratio of pupil image are M＞2.

The bottom surface of said two sides axicon lens and ridge face plating anti-reflection film; The wide drift angle less than said two sides axicon lens of rib in the middle of the face shape

is near 180 °, and λ is a wavelength.

The pixel size of said two ccd image detectors equates that the shortest length of the target surface of each ccd image detector is greater than

When adopting type method to carry out wave front restoration, distorted wavefront to be measured can be described as

Z wherein _m(x y) is the Zernike polynomial expression on m rank, a _mBe corresponding coefficient, N representes the Zernike exponent number got, and (x y) is the coordinate of distorted wavefront to be measured.Used response matrix is made up of N column vector; The m column vector is provided by two analytic expressions of

; Wherein, P (x) and P (y) represented respectively sensing point (x, y) perpendicular to the straight line of coordinate axis y and x and the intersection point on pupil function P border, λ is a wavelength; (x '; Y ') denotation coordination is that (x, the y) coordinate of middle arbitrfary point is so need not in-site measurement.

If the light field at the entrance pupil place of two sides axicon lens Wavefront sensor is:

$E_1(x,y)=u_0\exp \left[\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HSA00000229685000011.png"\; state="\{\{state\}\}">i</figure-callout>}\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}\mathrm{\&phi;}(x,y)\right]P,---\left(1\right)$

U wherein ₀And φ (x y) representes the amplitude and the phase place of incident field respectively, and x and y represent the coordinate of distortion to be measured; I representes imaginary part unit, and P is a pupil function, and λ is a wavelength; Incident field is divided into two-way by beam splitter BS, and its transmissivity equals a/b with the ratio of reflectivity, and two-way light is respectively through after two sides axicon lens and the 4f system; The pupil image that on the target surface of ccd image detector, forms, wherein I ₁, I ₂Be the pupil image light intensity that forms after the distorted wavefront along continuous straight runs to be measured beam split of obtaining of the first ccd image detector, Fig. 2 a is seen in its distribution; Fig. 2 b is coma (the 7th rank Zernike pattern, Z ₇) pupil image distribution plan after the beam split of along continuous straight runs on the first ccd image detector; I ₃And I ₄Be the pupil image light intensity that forms after the distorted wavefront to be measured beam split vertically of obtaining of the second ccd image detector, Fig. 3 a is seen in its distribution; Fig. 3 b is coma (the 7th rank Zernike pattern, Z ₇) pupil image distribution plan after the beam split of along continuous straight runs on the second ccd image detector.Light-intensity difference through between two pupil image of more same direction can obtain measuring-signal S _xAnd S _y, the relational expression between measuring-signal and the distorted wavefront is:

Range of integration P (x) and P (y) represented respectively that (x, y) perpendicular to the straight line of coordinate axis y and x and the intersection point on pupil function P border, (x ', y ') denotation coordination was (x, y) coordinate of middle arbitrfary point to sensing point in formula (2) and (3).f ₁And f ₂The focal length of representing two lens in the 4f system respectively, said two lens are the first lens L ₁With the 3rd lens L ₃, the second lens L ₂With the 4th lens L ₄

Use Zernike modal representation distorted wavefront aberration to be measured:

Z _m(x y) is the Zernike polynomial expression on m rank, a _mBe corresponding coefficient, N representes the Zernike exponent number got.As

hour; Sine function in formula (2) and (3) can come approximate representation with first in its Taylor expansion, so top two formulas can be write as:

$S_x=\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}{a}_m\underset{-P\left(y\right)}{\overset{P\left(y\right)}{\&Integral;}}\frac{2}{\mathrm{\&lambda;}}\frac{Z_m(x,y)-Z_m(x^{\&prime;},y)}{(x-x^{\&prime;})}d{x}^{\&prime;}---\left(4\right)$

$S_y=\underset{m=1}{\overset{N}{\mathrm{\&Sigma;}}}{a}_m\underset{-P\left(x\right)}{\overset{P\left(x\right)}{\&Integral;}}\frac{2}{\mathrm{\&lambda;}}\frac{Z_m(x,y)-Z_m(x^{\&prime;},y)}{(y-y^{\&prime;})}d{y}^{\&prime;}---\left(5\right)$

$G_{\mathrm{xm}}=\underset{-P\left(y\right)}{\overset{P\left(y\right)}{\&Integral;}}\frac{2}{\mathrm{\&lambda;}}\frac{Z_m(x,y)-Z_m(x^{\&prime;},y)}{(x-x^{\&prime;})}d{x}^{\&prime;}---\left(6\right)$

$G_{\mathrm{ym}}=\underset{-P\left(x\right)}{\overset{P\left(x\right)}{\&Integral;}}\frac{2}{\mathrm{\&lambda;}}\frac{Z_m(x,y)-Z_m(x^{\&prime;},y)}{(y-y^{\&prime;})}d{y}^{\&prime;}---\left(7\right)$

S _xAnd S _yBe preceding N rank Zernike item at coefficient hour each rank signal G _XmAnd G _YmLinear superposition.When aberration to be measured is big; Formula (2) and (3) will produce bigger error to the approximation of formula (4) and (5), thereby measurement result can only embody the direction of distorted wavefront to be measured.At this moment can use distorting lens that incident field is carried out negative feedback and proofread and correct, correction back irreducible phase errors is reduced gradually, till reaching the correction accuracy that needs, thereby can obtain distorted wavefront to be measured through this close loop maneuver.

When adopting the type method wave front restoration, can find the solution G in advance _XmWith G _YmAnalytic solution; Carry out numerical discretization according to the spatial sampling rate of actual optical system then; Set up linear response matrix G thus, at this moment, the matrix form of formula (4) and (5) can be expressed as S=GA; A is the Zernike coefficient vector, further adopts singular value decomposition method (SVD) to obtain the generalized inverse G of this response matrix ⁺M representes the spatial sampling rate of distorted wavefront to be measured, the Zernike pattern exponent number of getting when N representes the pattern recovery, and each rank Zernike coefficient of wavefront to be measured passes through computes:

A＝G ⁺S. (8)

Wherein, $A=\left[\begin{array}{c}{a}_1\\ a_2\\ \&CenterDot;\&CenterDot;\&CenterDot;\\ a_N\end{array}\right];$ $G=\left[\begin{array}{cccc}{G}_{x1}\left(1\right)& G_{x2}\left(1\right)& \&CenterDot;\&CenterDot;\&CenterDot;& G_{\mathrm{xN}}\left(1\right)\\ G_{y1}\left(1\right)& G_{y2}\left(1\right)& \&CenterDot;\&CenterDot;\&CenterDot;& G_{\mathrm{yN}}\left(1\right)\\ G_{x1}\left(2\right)& G_{x2}\left(2\right)& \&CenterDot;\&CenterDot;\&CenterDot;& G_{\mathrm{xN}}\left(2\right)\\ G_{y1}\left(2\right)& G_{y2}\left(2\right)& \&CenterDot;\&CenterDot;\&CenterDot;& G_{\mathrm{yN}}\left(2\right)\\ \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;\\ G_{x1}\left(M\right)& G_{x2}\left(M\right)& \&CenterDot;\&CenterDot;\&CenterDot;& G_{\mathrm{xN}}\left(M\right)\\ G_{y1}\left(M\right)& G_{y2}\left(M\right)& \&CenterDot;\&CenterDot;\&CenterDot;& G_{\mathrm{yN}}\left(M\right)\end{array}\right];$ $S=\left[\begin{array}{c}{S}_x\left(1\right)\\ S_y\left(1\right)\\ S_x\left(2\right)\\ S_y\left(2\right)\\ \&CenterDot;\&CenterDot;\&CenterDot;\\ S_x\left(M\right)\\ S_y\left(M\right)\end{array}\right]$

When adopting two face cone Wavefront sensors to measure the corrugated, each item of response matrix G can directly be calculated by analytic expression (6) and (7), and contains the cross term between the signal in the corresponding expression formula of rectangular pyramid, can not obtain with analytic expression.

Fig. 4 a to Fig. 4 c adopts type method to coma (the 7th rank Zernike pattern, Z for the Wavefront sensor of two sides of the present invention axicon lens ₇) simulation result of wave front restoration, wherein Fig. 4 a is an original wavefront, Fig. 4 b is for restoring wavefront, before Fig. 4 c is residual wave.

The above; Be merely the embodiment among the present invention, but protection scope of the present invention is not limited thereto, anyly is familiar with this technological people in the technical scope that the present invention disclosed; Can understand conversion or the replacement expected, all should be encompassed within the protection domain of claims of the present invention.

Claims (9)

1. Wavefront sensor with two sides axicon lens; It is characterized in that: have two two sides axicon lens, a beam splitter BS, four lens and two ccd image detectors; The incident distorted wavefront is divided into the orthogonal light of two bundles through beam splitter BS; Horizontal direction light through first lens, the first two sides axicon lens and the 3rd lens after; Its pupil conjugate image is imaged onto the first ccd image detector, vertical direction light through second lens, the second two sides axicon lens and the 4th lens after, its pupil conjugate image is imaged onto the second ccd image detector; The 4f that each road light is all formed through a two sides axicon lens and two lens beam system that contracts; Mutually orthogonal the putting of ridge seamed edge of the first and second two sides axicon lens; And the ridge seamed edge of the first two sides axicon lens overlaps with the focus of first lens; The ridge seamed edge of the second two sides axicon lens overlaps with the focus of the 3rd lens, the 4f shared focal plane of two lens of beam system of contracting wherein, and the focal length of two lens does not wait; The ccd image detector links to each other with computing machine; Utilize computing machine to read the pupil conjugate image; And the light distribution difference of comparison level direction and two pupil conjugate images of vertical direction can access the measuring-signal of both direction, utilizes wave front restoration algorithm reconstruct Wave-front phase again.

2. according to the said Wavefront sensor with two sides axicon lens of claim 1, it is characterized in that: said beam splitter has any splitting ratio.

3. according to the said Wavefront sensor of claim 1 with two sides axicon lens; It is characterized in that: said two two sides axicon lens comprise the first two sides axicon lens and the second two sides axicon lens; The first two sides axicon lens has one first ridge seamed edge; The second two sides axicon lens has one second ridge seamed edge; The said first ridge seamed edge and said second the ridge seamed edge is mutually orthogonal puts is placed on the focal plane of first lens and the 3rd lens respectively, and the first ridge seamed edge and the second ridge seamed edge are respectively over against first lens and the 3rd lens focus.

4. according to the said Wavefront sensor with two sides axicon lens of claim 1, it is characterized in that: the focal length of first lens and the 3rd lens is f in said four lens ₁, second lens and the 4th focal length of lens are f ₂,

Decision pupil conjugate image size, wherein, D is the incident wavefront aperture.

5. according to the said Wavefront sensor of claim 1, it is characterized in that: the refractive two sides axicon lens that the described first two sides axicon lens and the second two sides axicon lens are made for the traditional optical device manufacturing process with two sides axicon lens; The base angle of the first two sides axicon lens and the second two sides axicon lens

M is the ratio of adjacent pupil conjugate image centre distance and pupil conjugate image, f ₁Be the focal length of first lens and the 3rd lens, n is the refractive index of material, and D is the incident wavefront aperture.

6. according to the said Wavefront sensor with two sides axicon lens of claim 5, it is characterized in that: the said adjacent pupil conjugate image centre distance and the ratio of pupil conjugate image are M, M＞2.

7. according to the said Wavefront sensor of claim 1, it is characterized in that: the bottom surface of the first two sides axicon lens and the second two sides axicon lens and ridge face plating anti-reflection film, face shape error root-mean-square value with two sides axicon lens

Middle rib wide less than

The drift angle of the said first two sides axicon lens and the second two sides axicon lens is near 180 °, and λ is a wavelength, f ₁Be the focal length of first lens and the 3rd lens, D is the incident wavefront aperture.

8. according to the said Wavefront sensor with two sides axicon lens of claim 1, it is characterized in that: the pixel size of two ccd image detectors equates that the shortest length of the target surface of each ccd image detector is greater than

M is the ratio of adjacent pupil conjugate image centre distance and pupil conjugate image, f ₁Be the focal length of first lens and the 3rd lens, f ₂Be the focal length of second lens and the 4th lens, D is the incident wavefront aperture.

9. according to the said Wavefront sensor with two sides axicon lens of claim 1, it is characterized in that: when adopting type method to carry out wave front restoration, distorted wavefront to be measured can be described as

Z wherein _m(x y) is the Zernike polynomial expression on m rank, a _mBe corresponding coefficient, N representes the Zernike exponent number got, and (x y) is the coordinate of distorted wavefront to be measured; Used response matrix is made up of N column vector, the m column vector by $G_{\mathrm{xm}}=\underset{-P\left(y\right)}{\overset{P\left(y\right)}{\&Integral;}}\frac{2}{\mathrm{\&lambda;}}\frac{Z_m(x,y)-Z_m(x^{\&prime;},y)}{\left({x-x}^{\&prime;}\right)}{\mathrm{dx}}^{\&prime;};$ $G_{\mathrm{ym}}=\underset{-P\left(x\right)}{\overset{P\left(x\right)}{\&Integral;}}\frac{2}{\mathrm{\&lambda;}}\frac{Z_m(x,y)-Z_m(x,y^{\&prime;})}{\left({y-y}^{\&prime;}\right)}{\mathrm{dy}}^{\&prime;}$ Two analytic expressions provide, and wherein, P (x) and P (y) represented sensing point (x respectively; Y) perpendicular to the straight line of coordinate axis y and x and the intersection point on pupil function P border, λ is a wavelength, (x '; Y ') denotation coordination is that (x, the y) coordinate of middle arbitrfary point is so need not in-site measurement.

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