CN104266769A - Phase recovering method - Google Patents
Phase recovering method Download PDFInfo
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- CN104266769A CN104266769A CN201410571350.3A CN201410571350A CN104266769A CN 104266769 A CN104266769 A CN 104266769A CN 201410571350 A CN201410571350 A CN 201410571350A CN 104266769 A CN104266769 A CN 104266769A
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Abstract
The invention discloses a phase recovering method. The method comprises the following steps: dividing the circular detecting surface of an image detector into M areas, namely a center circular area and surrounding annulus areas, in the radial direction in an equidistance manner; uniformly dividing the annulus area at the most outer side into L sub detecting areas; uniformly dividing the annulus area between the outer annulus area and the center circular area into a plurality of sub detecting areas, and using each sub detecting area as the minimum detecting unit to measure the phase error. The arithmetic speed is improved, a wave front sensor is not required to measure the wave front error, the complexity of the system is reduced, the cost is reduced, and the structure is relatively simple. The method disclosed by the invention only requires one image of the defocused surface, a plurality of images are not required to be collected, the steps are simplified, and besides, repeated iteration is not required, and the method has the characteristic of good real-time property.
Description
Technical field
The present invention relates to field of photoelectric technology, particularly relate to a kind of phase recovery method.
Background technology
Wavefront sensor is the important component part of ADAPTIVE OPTICS SYSTEMS, and its sensing outcome is utilized for follow-up wave-front corrector and provides correction signal, finally makes optical system reach resolution close to diffraction limit.Existing wavefront sensing technique can be divided into two classes according to wavefront sensing principle, one class is direct wavefront sensing, namely directly measure the wavefront distribution in pupil face, before adopting ground wave, the Wavefront sensor of sensing mode comprises Shack-Hartmann wavefront sensor, shearing interferometer etc.Before ground wave, sensing mode has the advantage that principle is simple, fast operation, Measurement bandwidth are high, and shortcoming is to need to add independent optical path in tested optical system, adds the complicacy of system and needs when measuring to eliminate non-co-path error.Another kind of sensing mode is indirect wavefront sensing, namely by measuring the light distribution of focal plane or out of focus face, indirectly solves the Wave-front phase distribution in pupil face.The advantage of indirect sensing mode is not need independently wavefront sensing light path, and the imaging detector of tested optical system can be utilized directly to obtain required focal plane or out of focus face intensity signal, and system is simple and reliable and there is not non-co-path error.Phase retrieval method is a kind of comparatively conventional indirect wavefront sensing methods, and the method utilizes the PHASE DISTRIBUTION in known image planes and light distribution inverting pupil face, pupil face.Based on the advantage of the phase recovery method of iteration, tradition is that sensing accuracy is high, shortcoming is calculation of complex and convergence is slow, is difficult to use in real-time wavefront sensing.
Summary of the invention
In view of this, the invention provides a kind of phase recovery method, recovering pupil face PHASE DISTRIBUTION by being positioned at the piece image that the sectional type imaging detector in out of focus face gathers; The method does not need the independent optical path of introducing and Wavefront sensor to carry out Wavefront detecting, and system architecture is simple, and without the need to successive ignition, real-time is good.
A kind of phase recovery method of the present invention, for measuring the phase error of tested imaging system, the method comprises the steps:
Step 1, employing pointolite irradiate tested imaging system, and adopt imaging detector light spot received on out of focus face;
Wherein, be divided into M region by radially equidistant for the circular test surface of described imaging detector, be: central circular and M-1 circle ring area; Wherein, the value of M is consistent with the maximum radial exponent number of the zernike polynomial characterizing pupil face wavefront error;
Outermost circle ring area is evenly divided into L sub-search coverage, wherein, the value of L is determined to exponent number by the maximum angular of described zernike polynomial, and the value of sub-search coverage L is at least described maximum angular to 2 times of exponent number;
M-2 between an outer annular region and central circular circle ring area is evenly divided into respectively some sub-search coverages, the size of sub-search coverage is as far as possible equal with the size of the sub-search coverage in outermost circle ring area;
Step 2, sub-search coverage according to each division in the systematic parameter of tested imaging system and imaging detector, adopt emulation mode to obtain transfer matrix H;
Step 3, sub-search coverage according to each division in the systematic parameter of tested imaging system and imaging detector, adopt emulation mode to obtain the normalization light intensity matrix I of the normalization light intensity composition of imaging system each sub-search coverage when zero aberration
0;
Step 4, when actual measurement, record is the normalization light intensity magnitude that detects of each sub-search coverage now, the matrix I that the normalization light intensity obtaining being detected by sub-search coverages all during aberration forms; By Δ I=I-I
0, obtain normalization light intensity transformation matrices Δ I; Wherein, the normalization light intensity in each sub-search coverage is that the light intensity sum that on respective region, all pixels detect is normalized again;
Step 5, according to the linear relationship between the normalization light intensity transformation matrices Δ I on imaging detector and transfer matrix H and Zernike system of polynomials number vector A:
ΔI＝H×A
Obtain each rank Zernike multinomial coefficient:
A＝H
+ΔI
Wherein, H
+it is the pseudo inverse matrix of transfer matrix H;
Step 6, each rank Zernike multinomial coefficient step 5 obtained are updated to and characterize before pupil face wavefront error in the polynomial linear superposition formula of N item Zernike:
Obtain pupil face PHASE DISTRIBUTION
Wherein, (x
0, y
0) be position coordinates on pupil face, Zernike system of polynomials number vector A={a
2, a
3..., a
n}
t, Z
i(x
0, y
0) be the i-th rank Zernike polynomial expression.
Further, normalization light intensity matrix I is obtained in described step 3
0detailed process be:
By emulation, the N rank polynomial coefficient of Zernike before the wavefront error of formation pupil face is all set to zero, record the light intensity of now each sub-search coverage, then by total light intensity that the light intensity of each sub-search coverage detects divided by whole test surface, normalization light intensity matrix I is namely formed
0.
Further, the detailed process adopting emulation mode to obtain transfer matrix H in described step 2 is:
The polynomial coefficient a of the i-th rank Zernike before pupil ground roll will be formed
ichange a small quantity δ a
i, calculate by δ a
ithe each described sub-search coverage caused corresponding normalization light intensity change δ I
i=I
i-I
0, wherein I
ibe the normalization light intensity magnitude of every sub-search coverage detection after the polynomial index variation of the i-th rank Zernike, calculate by δ a
ievery the corresponding δ I of sub-search coverage caused
i/ δ a
i, then δ I
i/ δ a
iform i-th row of transfer matrix H.
The present invention has following beneficial effect:
1. the present invention utilizes the image of imaging detector collection to carry out phase recovery, does not need to utilize independent Wavefront sensor to measure wavefront error, and reduce system complexity, reduce cost, structure is relatively simple.
2. the present invention only need gather a width out of focus face image, without the need to gathering multiple image, simplifies step, and without the need to successive ignition, has the advantages that real-time is good.
3. the present invention proposes the new method of sectional type detector, compared with the non-sectional type detector of tradition, improves algorithm speed.Meanwhile, can according to the piecemeal number of the calibration capability change detector of the wavefront error form of reality and different distortion mirror, implementation algorithm coordinates with actual conditions.
Accompanying drawing explanation
Fig. 1 is optical system illustraton of model of the present invention.
Fig. 2 is the zoning schematic diagram of detector of the present invention.
Embodiment
To develop simultaneously embodiment below in conjunction with accompanying drawing, describe the present invention.
A kind of phase recovery method of the present invention, comprises the steps:
1, the wavefront error polynomial linear superposition of front N item Zernike in pupil face is expressed as:
Wherein, (x
0, y
0) be position coordinates on pupil face, a
ithe polynomial coefficient of the i-th rank Zernike, Z
i(x
0, y
0) be the i-th rank Zernike polynomial expression.
2, as shown in Figure 1, the optical system model that the present invention uses, comprises pointolite, imaging system and imaging detector.Wherein, imaging detector is positioned at Jiao Nei or afocal range imaging system back focal plane is the position of d.According to the size of the Zernike polynomial expression exponent number N of institute's sensing, detector search coverage is divided into some sub-search coverages, the light intensity of every sub-search coverage equals the light intensity sum of all pixels in this subregion.Wherein, the exponent number N of zernike polynomial can go according to different applied environments to select.Required aberration of measuring, mainly based on low order aberration, can select the Zernike polynomial expression of fewer exponent numbers.When measurement aberration is high-order, the exponent number value that corresponding selection is larger.
When carrying out " piecemeal " to detector, the number of turns of detector piecemeal is determined by the polynomial maximum radial exponent number of used Zernike, and the piecemeal number of detector outmost turns is determined to exponent number by the polynomial maximum angular of used Zernike.When the Zernike polynomial expression that exponent number used is more, when namely the radio-frequency component of wavefront to be measured is more, the block count of detector can be increased.When such as adopting front 10 Zernike polynomial expression sensing wavefront, maximum radial exponent number is 3, therefore detector is evenly divided into 3 circles.Again because its maximum angular is 3 to exponent number, and comprise sinusoidal and cosine both direction, therefore according to sampling thheorem, need outmost turns to be divided into 12 pieces, now detector one is divided into 21 unit, as shown in Figure 2, solid line radius of circle is from inside to outside respectively r/3,2r/3 and r.From frequency domain, hot spot center section is based on low frequency, and structure is uncomplicated, and therefore the central circular of detector surface need not continue piecemeal again.
According to simulation result, now continue the block count increasing detector again, effectively can't improve the precision of this algorithm.
3, I is used
0the normalization light intensity magnitude of each sub-search coverage when representing that optical system error is zero, its computing method are: be all set to zero by emulation by forming the N rank polynomial coefficient of Zernike before before pupil ground roll, there is not aberration in the optical system now simulated, record the light intensity of now each sub-search coverage, and it is normalized, method for normalizing is: the total light intensity light intensity of each sub-search coverage detected divided by whole test surface.
4, the transfer matrix H of imaging system is demarcated.After optical system is determined, H can be drawn by simulation calculation, and its computation process is: the polynomial coefficient of the i-th rank Zernike before forming pupil ground roll is changed a small quantity δ a
i, calculate by δ a
ievery the sub-search coverage corresponding normalization light intensity change δ I caused
i=I
i-I
0, wherein I
ithe normalization light intensity magnitude of every sub-search coverage detection after the polynomial index variation of the i-th rank Zernike, δ I
i/ δ a
iform i-th row of transfer matrix H.N rank Zernike polynomial expression just has N column element, then a sub-search coverage is to there being N column element, and what make sub-search coverage adds up to Z, and namely transfer matrix H has Z capable.Element conveniently in sub-search coverage and H in correspondence with each other, can be numbered the sub-search coverage of detector, as shown in Figure 2, its numbering is from detector center open numbering, outside successively, each annulus is according to counterclockwise carrying out from little size number consecutively.But be not limited to this numbering in the present invention, as long as the element of certain row corresponds to the δ I of this sub-search coverage in transfer matrix H
i/ δ a
i.
5, when when actual measurement, record the light intensity magnitude that now each sub-search coverage detects, obtain normalization light intensity matrix I during aberration.By Δ I=I-I
0, obtain the normalization light intensity transformation matrices Δ I of every sub-search coverage.
6, Zernike system of polynomials number vector A={a is established
2, a
3..., a
n}
t, then according to the linear relationship between the normalization light intensity transformation matrices Δ I on the imaging detector in out of focus face and transfer matrix H and A:
ΔI＝H×A (2)
Try to achieve each rank Zernike multinomial coefficient:
A＝H
+ΔI (3)
Wherein H
+it is the pseudo inverse matrix of transfer matrix H.
7, pupil face PHASE DISTRIBUTION is obtained according to formula (1).
In sum, these are only preferred embodiment of the present invention, be not intended to limit protection scope of the present invention.Within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.
Claims (3)
1. a phase recovery method, for measuring the phase error of tested imaging system, is characterized in that, comprising the steps:
Step 1, employing pointolite irradiate tested imaging system, and adopt imaging detector light spot received on out of focus face;
Wherein, be divided into M region by radially equidistant for the circular test surface of described imaging detector, be: central circular and M-1 circle ring area; Wherein, the value of M is consistent with the maximum radial exponent number of the zernike polynomial characterizing pupil face wavefront error;
Outermost circle ring area is evenly divided into L sub-search coverage, wherein, the value of L is determined to exponent number by the maximum angular of described zernike polynomial, and the value of sub-search coverage L is at least described maximum angular to 2 times of exponent number;
M-2 between an outer annular region and central circular circle ring area is evenly divided into respectively some sub-search coverages, the size of sub-search coverage is as far as possible equal with the size of the sub-search coverage in outermost circle ring area;
Step 2, sub-search coverage according to each division in the systematic parameter of tested imaging system and imaging detector, adopt emulation mode to obtain transfer matrix H;
Step 3, sub-search coverage according to each division in the systematic parameter of tested imaging system and imaging detector, adopt emulation mode to obtain the normalization light intensity matrix I of the normalization light intensity composition of imaging system each sub-search coverage when zero aberration
0;
Step 4, when actual measurement, record is the normalization light intensity magnitude that detects of each sub-search coverage now, the matrix I that the normalization light intensity obtaining being detected by sub-search coverages all during aberration forms; By Δ I=I-I
0, obtain normalization light intensity transformation matrices Δ I; Wherein, the normalization light intensity in each sub-search coverage is that the light intensity sum that on respective region, all pixels detect is normalized again;
Step 5, according to the linear relationship between the normalization light intensity transformation matrices Δ I on imaging detector and transfer matrix H and Zernike system of polynomials number vector A:
ΔI＝H×A
Obtain each rank Zernike multinomial coefficient:
A＝H
+ΔI
Wherein, H
+it is the pseudo inverse matrix of transfer matrix H;
Step 6, each rank Zernike multinomial coefficient step 5 obtained are updated to and characterize before pupil face wavefront error in the polynomial linear superposition formula of N item Zernike:
Obtain pupil face PHASE DISTRIBUTION
Wherein, (x
0, y
0) be position coordinates on pupil face, Zernike system of polynomials number vector A={a
2, a
3..., a
n}
t, Z
i(x
0, y
0) be the i-th rank Zernike polynomial expression.
2. a kind of phase recovery method as claimed in claim 1, is characterized in that, obtains normalization light intensity matrix I in described step 3
0detailed process be:
By emulation, the N rank polynomial coefficient of Zernike before the wavefront error of formation pupil face is all set to zero, record the light intensity of now each sub-search coverage, then by total light intensity that the light intensity of each sub-search coverage detects divided by whole test surface, normalization light intensity matrix I is namely formed
0.
3. a kind of phase recovery method as claimed in claim 1, is characterized in that, the detailed process adopting emulation mode to obtain transfer matrix H in described step 2 is:
The polynomial coefficient a of the i-th rank Zernike before pupil ground roll will be formed
ichange a small quantity δ a
i, calculate by δ a
ithe each described sub-search coverage caused corresponding normalization light intensity change δ I
i=I
i-I
0, wherein I
ibe the normalization light intensity magnitude of every sub-search coverage detection after the polynomial index variation of the i-th rank Zernike, calculate by δ a
ievery the corresponding δ I of sub-search coverage caused
i/ δ a
i, then δ I
i/ δ a
iform i-th row of transfer matrix H.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113203485A (en) * | 2021-04-27 | 2021-08-03 | 浙江大学 | Device and method for realizing axial phase difference wavefront reconstruction through single exposure |
| CN117745551A (en) * | 2024-02-19 | 2024-03-22 | 电子科技大学 | Method for recovering phase of image signal |
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| US20120179425A1 (en) * | 2009-09-15 | 2012-07-12 | University Of Sheffield | Method and apparatus for retrieving a phase of a wavefield |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113203485A (en) * | 2021-04-27 | 2021-08-03 | 浙江大学 | Device and method for realizing axial phase difference wavefront reconstruction through single exposure |
| CN113203485B (en) * | 2021-04-27 | 2022-08-05 | 浙江大学 | Device and method for realizing axial phase difference wavefront reconstruction through single exposure |
| CN117745551A (en) * | 2024-02-19 | 2024-03-22 | 电子科技大学 | Method for recovering phase of image signal |
| CN117745551B (en) * | 2024-02-19 | 2024-04-26 | 电子科技大学 | Method for recovering phase of image signal |
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