CN104266769B - Phase recovering method - Google Patents
Phase recovering method Download PDFInfo
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- CN104266769B CN104266769B CN201410571350.3A CN201410571350A CN104266769B CN 104266769 B CN104266769 B CN 104266769B CN 201410571350 A CN201410571350 A CN 201410571350A CN 104266769 B CN104266769 B CN 104266769B
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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, more particularly 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 wavefront
Adjuster provides correction signal, finally makes optical system reach the resolution ratio for being close to diffraction limit.Can according to wavefront sensing principle
So that existing wavefront sensing technique is divided into two classes, a class is direct wavefront sensing, i.e. the wavefront distribution to pupil face is directly surveyed
Amount, includes Shack-Hartmann wavefront sensor, shearing interferometer etc. using the Wavefront sensor of sensing mode before ground wave.Directly
Connect wavefront sensing mode and have the advantages that simple principle, fast operation, Measurement bandwidth are high, disadvantage is that by photometry
Single optical path is added in system, the complexity of system is increased and is needed to eliminate non-co- path error in measurement.
Another kind of sensing mode is indirect wavefront sensing, i.e., by the light distribution in measurement focal plane or out of focus face, solve indirectly pupil face
Wave-front phase distribution.The advantage of indirect sensing mode is not need independent wavefront sensing light path, it is possible to use by light-metering
The imaging detector of system directly obtains required focal plane or out of focus face intensity signal, and simple system is reliable and does not exist non-
Common path error.Phase retrieval method is a kind of more conventional indirect wavefront sensing methods, the method using known image planes and
The phase distribution in pupil face light distribution inverting pupil face.Tradition is sensing accuracy based on the advantage of the phase recovery method of iteration
Height, shortcoming are to calculate complicated and restrain slow, it is difficult to for real-time wavefront sensing.
The content of the invention
In view of this, the invention provides a kind of phase recovery method, by the sectional type imaging detector positioned at out of focus face
The piece image of upper collection recovers pupil face phase distribution；The method need not introduce single optical path and Wavefront sensor enters
Row Wavefront detecting, system architecture are simple, and without the need for 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 include as
Lower step：
Step 1, tested imaging system is irradiated using spot light, and adopt imaging detector light spot received on out of focus face；
Wherein, by the circular test surface of the imaging detector radially equidistant from M region is divided into, as：Center
Border circular areas and M-1 circle ring area；Wherein, the maximum of the zernike polynomial of the value of M and sign pupil face wavefront error
Radial direction exponent number is consistent；
Outermost circle ring area is evenly dividing into into L sub- search coverage, wherein, the value of L is multinomial by the Ze Nike
The angular exponent number of maximum of formula is determined, and the value of sub- search coverage L is at least 2 times of the maximum angular exponent number；
M-2 circle ring area between outer annular region and central circular is evenly dividing into into some height respectively
Search coverage, the size of sub- search coverage are as far as possible equal with the size of the sub- search coverage in outermost circle ring area；
Step 2, according in the systematic parameter and imaging detector of tested imaging system each divide sub- search coverage,
Transfer matrix H is obtained using emulation mode；
Step 3, according in the systematic parameter and imaging detector of tested imaging system each divide sub- search coverage,
The normalization light intensity square of the normalization light intensity composition of imaging system each sub- search coverage in zero aberration is obtained using emulation mode
Battle array I0；
Step 4, in actual measurement, record the normalization light intensity magnitude that now each sub- search coverage is detected, obtain
The matrix I that the normalization light intensity detected by all sub- search coverages during aberration is constituted；By Δ I=I-I0, obtain normalization light
Strong transformation matrices Δ I；Wherein, the normalization light intensity in each sub- search coverage is the light that all pixels point is detected on respective region
Strong sum is normalized again；
It is step 5, many according to normalization light intensity the transformation matrices Δ I and transfer matrix H and Zernike on imaging detector
Linear relationship between binomial coefficient vector A：
Δ I=H × A
Obtain each rank Zernike multinomial coefficients：
A=H+ΔI
Wherein, H+It is the pseudo inverse matrix of transfer matrix H；
Step 6, the front N items that each rank Zernike multinomial coefficients that step 5 is obtained are updated to sign pupil face wavefront error
In the polynomial linear superposition formulas of Zernike：
Obtain pupil face phase distribution
Wherein, (x0,y0) it is position coordinates on pupil face, Zernike system of polynomials number vector A={ a2,a3,...,aN}T,
Zi(x0,y0) it is the i-th rank Zernike multinomials.
Further, normalization light intensity matrix I is obtained in the step 30Detailed process be：
The polynomial coefficients of front N ranks Zernike for constituting pupil face wavefront error are all set to into zero by emulation, this is recorded
When each sub- search coverage light intensity, the total light intensity that then light intensity of each sub- search coverage is detected divided by whole test surface,
That is composition normalization light intensity matrix I0。
Further, adopt emulation mode to obtain the detailed process of transfer matrix H in the step 2 for：
The polynomial coefficient a of the i-th rank Zernike of pupil face wavefront will be constitutediChange a small quantity δ ai, calculate by δ ai
Each the described sub- search coverage for causing normalizes light intensity change δ I accordinglyi=Ii-I0, wherein IiIt is that the i-th rank Zernike is more
Normalization light intensity magnitude after the index variation of item formula per individual sub- search coverage detection, calculates by δ aiThe every height detection for causing
The corresponding δ I in regioni/δai, then δ Ii/δaiConstitute i-th row of transfer matrix H.
The present invention has the advantages that：
1. the present invention carries out phase recovery using the image of imaging detector collection, it is not necessary to using single wavefront sensing
Device measures wavefront error, reduces system complexity, reduces cost, and structure is relatively easy.
2. the present invention only need to gather a width out of focus face image, need not gather multiple image, simplify step, and without the need for many
Secondary iteration, with real-time it is good the characteristics of.
3. the present invention proposes the new method of sectional type detector, compared with traditional non-sectional type detector, improves algorithm
Speed.Meanwhile, the piecemeal of detector can be changed according to the calibration capability of actual wavefront error form and different distortion mirror
Number, realizes the cooperation of algorithm and actual conditions.
Description of the drawings
Fig. 1 is optical system illustraton of model of the present invention.
Fig. 2 is the zoning schematic diagram of the detector of the present invention.
Specific embodiment
Develop simultaneously embodiment below in conjunction with the accompanying drawings, describes the present invention.
A kind of phase recovery method of the present invention, comprises the steps：
1st, pupil face wavefront error is expressed as with the polynomial linear superpositions of front N items Zernike：
Wherein, (x0,y0) it is position coordinates on pupil face, aiIt is the polynomial coefficients of the i-th rank Zernike, Zi(x0,y0) be
I-th rank Zernike multinomials.
2nd, as shown in figure 1, the optical system model that uses of the present invention, including spot light, imaging system and imaging detector.
Wherein, at position of the imaging detector positioned at Jiao Nei or afocal range imaging system back focal plane for d.According to what is sensed
Detector search coverage is divided into some sub- search coverages, per individual sub- search coverage by the size of Zernike polynomial order N
Light intensity be equal to the subregion in all pixels light intensity sum.Wherein, the exponent number N of zernike polynomial can be according to different
Applied environment goes to select.Required measurement aberration mainly, based on low order aberration, can select the Zernike of few some exponent numbers multinomial
Formula.When it is high-order to measure aberration, larger exponent number value is selected accordingly.
When carrying out " piecemeal " to detector, the number of turns of detector piecemeal is by the polynomial maximum diameters of the Zernike for being used
Determine to exponent number, the piecemeal number of detector outmost turns is determined by the polynomial maximum angular exponent numbers of the Zernike for being used.When
The more Zernike multinomials of exponent number used, i.e., when the radio-frequency component of wavefront to be measured is more, can increase the piecemeal of detector
Number.Such as using front 10 Zernike multinomials sense wavefront when, maximum radial exponent number be 3, therefore by detector be evenly dividing for
3 circles.Again because its maximum angular exponent number is 3, and comprising sinusoidal and cosine both direction, therefore according to sampling thheorem, need by
Outmost turns are divided into 12 pieces, and now detector one is divided into 21 units, as shown in Fig. 2 solid line radius of circle difference from inside to outside
For r/3,2r/3 and r.From from frequency domain, based on low frequency, structure is uncomplicated for hot spot mid portion, therefore in detector surface
Heart border circular areas are without being further continued for piecemeal.
According to simulation result, now it is further continued for increasing the block count of detector, the essence of this algorithm can't be effectively improved
Degree.
3rd, use I0The normalization light intensity magnitude of each sub- search coverage, its computational methods when representing that optical system error is zero
For：The polynomial coefficients of front N ranks Zernike for constituting pupil face wavefront are all set to into zero by emulation, the optics now simulated
There is no aberration in system, record the light intensity of now each sub- search coverage, and which is normalized, method for normalizing
For：The total light intensity that the light intensity of each sub- search coverage is detected divided by whole test surface.
4th, demarcate the transfer matrix H of imaging system.After optical system determines, H can be drawn by simulation calculation, its meter
Calculation process is：The polynomial coefficients of the i-th rank Zernike for constituting pupil face wavefront are changed into a small quantity δ ai, calculate by δ aiDraw
That what is risen normalizes light intensity change δ I accordingly per individual sub- search coveragei=Ii-I0, wherein IiIt is that the i-th rank Zernike is polynomial
Normalization light intensity magnitude after index variation per individual sub- search coverage detection, δ Ii/δaiConstitute i-th row of transfer matrix H.N ranks
Zernike multinomials just have N column elements, then to there is N column elements, the sum for making sub- search coverage is Z to a sub- search coverage,
Transfer matrix H has Z rows.Element in sub- search coverage and H in correspondence with each other, can be to the sub- detecting area of detector for convenience
Domain is numbered, as shown in Figure 2, its numbering be from detector center open numbering, successively outwards, each annulus according to
Counterclockwise carry out from little size number consecutively.But this numbering is not limited in the present invention, as long as in transfer matrix H
δ I of the element of certain row corresponding to the sub- search coveragei/δai.
5th, when in actual measurement, the light intensity magnitude that now each sub- search coverage is detected is recorded, when having obtained aberration
Normalization light intensity matrix I.By Δ I=I-I0, obtain the normalization light intensity transformation matrices Δ I per individual sub- search coverage.
6th, Zernike system of polynomials number vector A={ a are set2,a3,...,aN}T, then on the imaging detector according to out of focus face
Normalization light intensity transformation matrices Δ I and the linear relationship between transfer matrix H and A：
Δ I=H × A (2)
Try to achieve each rank Zernike multinomial coefficients：
A=H+ΔI (3)
Wherein H+It is the pseudo inverse matrix of transfer matrix H.
7th, pupil face phase distribution is obtained according to formula (1).
In sum, presently preferred embodiments of the present invention is these are only, is not intended to limit protection scope of the present invention.
All any modification, equivalent substitution and improvements within the spirit and principles in the present invention, made etc., should be included in the present invention's
Within protection domain.
Claims (3)
1. a kind of phase recovery method, for measuring the phase error of tested imaging system, it is characterised in that including following step
Suddenly：
Step 1, tested imaging system is irradiated using spot light, and adopt imaging detector light spot received on out of focus face；
Wherein, by the circular test surface of the imaging detector radially equidistant from M region is divided into, as：Central circular
Region and M-1 circle ring area；Wherein, the maximum radial of the zernike polynomial of the value of M and sign pupil face wavefront error
Exponent number is consistent；
Outermost circle ring area is evenly dividing into into L sub- search coverage, wherein, the value of L is by the zernike polynomial
Maximum angular exponent number is determined, and the value of sub- search coverage L is at least 2 times of the maximum angular exponent number；
M-2 circle ring area between outermost circle ring area and central circular is evenly dividing into some height respectively to visit
Region is surveyed, 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, according in the systematic parameter and imaging detector of tested imaging system each divide sub- search coverage, adopt
Emulation mode obtains transfer matrix H；
Step 3, according in the systematic parameter and imaging detector of tested imaging system each divide sub- search coverage, adopt
Emulation mode obtains the normalization light intensity matrix I of the normalization light intensity composition of imaging system each sub- search coverage in zero aberration0；
Step 4, in actual measurement, record the normalization light intensity magnitude that now each sub- search coverage is detected, obtained picture
The matrix I of the normalization light intensity composition that all sub- search coverages are detected during difference；By Δ I=I-I0, obtain normalizing light intensity change
Change matrix Δ I；Wherein, the normalization light intensity in each sub- search coverage be all pixels point is detected on respective region light intensity it
It is normalized again；
Step 5, according to the normalization light intensity transformation matrices Δ I and transfer matrix H and Zernike multinomial on imaging detector
Linear relationship between coefficient vector A：
Δ I=H × A
Obtain each rank Zernike multinomial coefficients：
A=H+ΔI
Wherein, H+It is the pseudo inverse matrix of transfer matrix H；
Step 6, the front N items that each rank Zernike multinomial coefficients that step 5 is obtained are updated to sign pupil face wavefront error
In the polynomial linear superposition formulas of Zernike：
Obtain pupil face phase distribution
Wherein, (x0,y0) it is position coordinates on pupil face, Zernike system of polynomials number vector A={ a2,a3,...,aN}T, Zi
(x0,y0) it is the i-th rank Zernike multinomials.
2. a kind of phase recovery method as claimed in claim 1, it is characterised in that normalization light intensity is obtained in the step 3
Matrix I0Detailed process be：
The polynomial coefficients of front N ranks Zernike for constituting pupil face wavefront error are all set to into zero by emulation, are recorded now each
The light intensity of individual sub- search coverage, the total light intensity that then light intensity of each sub- search coverage is detected divided by whole test surface, i.e. group
Into normalization light intensity matrix I0。
3. a kind of phase recovery method as claimed in claim 1, it is characterised in that obtained using emulation mode in the step 2
Detailed process to transfer matrix H is：
The polynomial coefficient a of the i-th rank Zernike of pupil face wavefront will be constitutediChange a small quantity δ ai, calculate by δ aiCause
Each described sub- search coverage normalize accordingly light intensity change δ Ii=Ii-I0, wherein IiIt is the i-th rank Zernike multinomials
Index variation after normalization light intensity magnitude per individual sub- search coverage detection, calculate by δ aiCause per individual sub- search coverage
Corresponding δ Ii/δai, then δ Ii/δaiConstitute i-th row of transfer matrix H.
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| 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 |
| CN117745551B (en) * | 2024-02-19 | 2024-04-26 | 电子科技大学 | Method for recovering phase of image signal |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1904569A (en) * | 2006-08-07 | 2007-01-31 | 中国科学院光电技术研究所 | Preware measuring method based on linear phase position reversal development |
| CN101013195A (en) * | 2007-01-10 | 2007-08-08 | 中国科学院光电技术研究所 | Self-adaptive optical system based on linear phase inversion restoration technology |
| CN102735348A (en) * | 2012-06-15 | 2012-10-17 | 中国科学院光电技术研究所 | Wavefront measuring method based on Hartmann wavefront sensor |
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| JP2009121951A (en) * | 2007-11-15 | 2009-06-04 | Nikon Corp | Evaluation method for aberration distribution of imaging optical system, adjusting method for imaging optical system, exposure device, and method for manufacturing device |
| EP2478407A1 (en) * | 2009-09-15 | 2012-07-25 | The University Of Sheffield | Method and apparatus for retrieving a phase of a wavefield |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN1904569A (en) * | 2006-08-07 | 2007-01-31 | 中国科学院光电技术研究所 | Preware measuring method based on linear phase position reversal development |
| CN101013195A (en) * | 2007-01-10 | 2007-08-08 | 中国科学院光电技术研究所 | Self-adaptive optical system based on linear phase inversion restoration technology |
| CN102735348A (en) * | 2012-06-15 | 2012-10-17 | 中国科学院光电技术研究所 | Wavefront measuring method based on Hartmann wavefront sensor |
Non-Patent Citations (1)
| Title |
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| Small-phase solution to the phase-retrieval problem;Robert A. Gonsalves;《OPTICS LETTERS》;20010515;第26卷(第10期);第684-685页 * |
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