CN102818640A - Method for determining number of Hartmann arrays by image spectrum containing 4f system error - Google Patents
Method for determining number of Hartmann arrays by image spectrum containing 4f system error Download PDFInfo
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Abstract
The invention relates to a method for determining number of Shack-Hartmann sub-apertures in a system by adopting an image spectrum containing a 4f system error. The key steps are as follows: loading an image on an input interface of a 4f system, obtaining an image spectrum containing the system error by a Fourier lens, converting the spectrum of the image into the spectrum which takes a diffraction limit as a coordinate, and determining a front end sampling frequency of a Shack-Hartmann wave-front sensor through a distribution limit of the image spectrum containing the system error according to a sampling theorem. The invention provides an effective method for determining the rational number of arrays of the Shack-Hartmann wave-front sensor in wave-front measurement in the 4f system.
Description
Technical field
The present invention relates to the adaptive optics field, confirm the effective ways of its rational Shack Hartmann wave front sensor number of arrays when being particularly related to a kind of wavefront measurement of the 4f of comprising systematic error.
Background technology
Full light two-dimension optical degeneration factor, different with traditional ADAPTIVE OPTICS SYSTEMS, its optics closed-loop system is prerequisite to the control of phase place and the design of correction link with the optics closed loop of not cutting off physically physically realizing.In full light two dimension degeneration factor
,Message form is an optical imagery, on the basis that the optical wavefront phase place is accurately controlled, introduces degenerative notion.Therefore, in whole process, the accurate detection of optical wavefront phase place is one of sport technique segment of core.When the full light two dimension of structure degeneration factor, adopted self-adaptation wavefront sensing technology.In ADAPTIVE OPTICS SYSTEMS, detection before the random wave and correction are the emphasis of research.
The 4f optical system of this patent receives the influence of experiment condition possibly comprise higher order aberratons, and the dynamic range that the Shack Hartmann wave front sensor is proofreaied and correct is big, makes full use of advantages such as luminous energy, relatively is applicable to the system in the patent.Therefore, in conjunction with the different characteristics of various sensors, for system selectes the Shack Hartmann sensor as the Wavefront detecting system.In the present Shack Hartmann Wavefront detecting instrument; It is means that great majority have all adopted the Zernike polynomial expression; Before converting the wavefront raw data that detects the image wave of reconstruct into, to the playback accuracy of wavefront, the resolution that its front end is surveyed is an important index.With regard to Effect on Detecting, the precision of detection is high more good more, but the higher instrument of front end resolution often has higher price, and a large amount of sampled datas also is unfavorable for computing, simultaneously, also can introduce the error of calculating etc.Therefore, when measuring wavefront to be measured, confirm that its rational Shack Hartmann sub-lens number becomes exigence.
The present invention is at first from the count angle of influence of counterweight structure precision of sampling; Find through simulation analysis; When carrying out the match of Zernike wavefront, sampling is counted and is wanted strict spectrum distribution according to the wavefront function, and promptly the sampling interval should be greater than wavefront spectrum distribution scope.Therefore, the wavefront frequency range of optical imagery has determined the front end sampling of Wavefront sensor to count.On this basis; Through load image on the spatial light modulator on the input face of 4f system; Obtain the frequency spectrum of fault image through fourier lense; There are certain corresponding relationship in the frequency spectrum of combining image and far-field spot, can determine the front-end sampling frequency of Shack Hartmann wave front sensor according to the limit of distribution of the far-field spot of the image of sampling thheorem through comprising distortion information, thereby just can confirm to satisfy the Hartmann wave front sensor of the lens arra of system requirements.
Summary of the invention
Confirm that its rational Shack Hartmann sensor number of arrays provides a kind of effective ways when the objective of the invention is under the situation of considering actual systematic error the wavefront measurement for the 4f system; The outstanding feature of the scheme that is proposed is to confirm the spectral range of system according to the frequency spectrum of the image of 4f system; In follow-up full light two dimension degeneration factor; Through adding lens, can be system's equivalence the 4f system, confirm the spectral range of system and even each device; Thereby confirm the lens arra of the Wavefront sensor in the system, and then can method be provided for the Hartmann wave front sensor of the lens arra of confirming to satisfy the real system requirement.
To achieve these goals, the present invention is from the count angle of influence of counterweight structure precision of sampling, and the 4f system in conjunction with classical may further comprise the steps:
Step 1, generate optical wavefront and the wavefront frequency spectrum treat reconstruct
In numerical simulation, adopt one group of random number as preceding 35 polynomial coefficients of Zernike, the optical wavefront of generation and spectrum distribution thereof are used for simulating the various equivalent errors in the 4f system.
The design sketch of wavefront reconstruction can be found out when being counted with different sampling by the spectrogram of treating the reconstruct Wave-front phase, the frequency range that the frequency spectrum of wavefront roughly distributes; Corresponding corresponding reconstruct design sketch can find out that the effect of reconstruct can obviously reduce after the sampling step-length is greater than certain unit.For from this conclusion of numerical value proof, done the analysis of consistent situation of fitting coefficient and error variance distribution in the subsequent simulation and verified.
The noise model of actual 4f system and system transter are very complicated.For simplified system, all separate the various sum of errors phase perturbations of system, embody a concentrated reflection of on the image; Transport function is the wave filter with certain low-pass characteristic, and theoretical simulation is equivalent to input picture on the input face P1 of 4f system, and each item error of system is used the Zernike fitting of a polynomial; Be added on the input picture; Through the L1 Fourier transform, through the ideal low-pass filter on the P2, convert the frequency spectrum that diffraction limit is a coordinate at last into again.
In proof procedure, to observe principle according to the method for mentioning in the step 2:
(1) for an incident wavefront that is made up of N rank Zernike polynomial expression, the m sub-aperture will be set up 2m equation, is only the overdetermined equation group in the time of must satisfying N≤2m, and promptly sub-aperture number must satisfy m>=N/2;
(2) simultaneously through the number of varitron lens, observe the relation of Zernike original coefficient and reconstruction coefficients, i.e. recovery accuracy and number of lenses purpose relation.
System simulation model in 3 obtains the frequency spectrum of system set by step, and the energy of intercepting certain limit is converted into the diffraction coordinate limit, and then the method in the integrating step 2 is confirmed the array number of lens.
Beneficial effect of the present invention is:
1, the proof said method is feasible when confirming the number of the Shack Hartmann lens arra that system is required in theory, before studying the image wave in the full light two dimension degeneration factor, lays a good foundation;
The outstanding feature of the scheme that 2, this patent proposed is to confirm the spectral range of system according to the frequency spectrum of the image of 4f system; In follow-up full light two dimension degeneration factor; Through adding lens, can be system's equivalence the 4f system, confirm the spectral range of system and even each device; Thereby confirm the lens arra of the Wavefront sensor in the system, and then study wavefront in the full light two dimension degeneration factor and become next step research contents.
Description of drawings
Description of drawings of the present invention is following:
Fig. 1 is a wavefront frequency spectrum of treating reconstruct;
Fig. 2 sampling step length is zernike coefficient and the contrast of original coefficient of 3,18,24 o'clock reconstruct;
Fig. 3 sampling step length is the contrast sampling of zernike coefficient and original coefficient of 3,18,24 o'clock reconstruct;
Fig. 4 step-length is zernike coefficient and the contrast of original coefficient of 3,18,24 o'clock reconstruct;
The typical 4f of Fig. 5 system;
Fig. 6 system emulation process flow diagram;
Fig. 7 system image spectrum;
The relation of preceding 10 Zernike aberration aperture numbers of Fig. 8 and wavefront residual mean square (RMS) root;
The relation of preceding 20 Zernike aberration aperture numbers of Fig. 9 and wavefront residual mean square (RMS) root;
Index contrast figure before and after preceding 10 Zernike12 of Figure 10 * 12 lens wavefront reconstructions;
Index contrast figure before and after the heavy wavefront reconstruction of preceding 20 Zernike24 of Figure 11 * 24 lens.
Embodiment
Below in conjunction with specific embodiment and Figure of description the present invention is described further.Specific embodiment described herein is only in order to explaining the present invention, and is not used in qualification the present invention.
In an embodiment, the 4f system of this project is mainly used in the lens arra of confirming the Shack Hartmann wave front sensor in the system.
In the embodiments of the invention, confirm to may further comprise the steps the method for Shack Hartmann lens arra based on the image spectrum of the systematic error that comprises the 4f system:
Step 1, generate optical wavefront and the wavefront frequency spectrum treat reconstruct
Count to the influence of wavefront reconstruction precision to sampling, use the covariance matrix method having carried out numerical simulation based on the polynomial wavefront reconstruction of Zernike.In simulation process, the optical imagery wavefront that generates is at random carried out different step-length sampling and carries out Zernike reconstruct.Adopt one group of random number as preceding 35 polynomial coefficients of Zernike, the optical wavefront spectrum distribution of generation, as shown in Figure 1.
The design sketch of wavefront reconstruction can be found out when being counted with different sampling by the spectrogram of treating the reconstruct Wave-front phase, and the frequency spectrum of wavefront roughly is distributed in 80 to 120 frequency ranges; Correspondence can seen in corresponding reconstruct design sketch, obviously reduction of the effect of reconstruct after the sampling step-length is greater than 20 units.
Having done the analysis of the consistent situation of fitting coefficient in the subsequent simulation verifies; In fit procedure; The Zernike multinomial coefficient that original Zernike multinomial coefficient and match obtain is respectively 3,18,24 o'clock distribution situation like Fig. 2,3, shown in 4 in step-length, error matrix is carried out the variance statistical study, and to obtain the result as shown in table 1.
Table 1
| The sampling step- |
3 | 6 | 9 | 12 | 15 | 18 | 24 |
| The error mean square value | 1.5552 | 1.5557 | 1.5546 | 1.5550 | 1.5539 | 1.5542 | 16.3541 |
Above numerical value shows the surface, and when the sampling step-length surpassed its spectrum distribution, match was that error is significantly improved.
Typical 4f system is as shown in Figure 4 in the information optics.F is the focal length of lens, and S is the coherent point light source, L
0Be collimation lens, P
1Be input plane, placement space photomodulator (SLM) loads input picture on it.This input is through fourier lense L
1Do Fourier transform, at P
2Face obtains its frequency spectrum.At P
2Face is placed another SLM, loads required frequency domain filter on it, after filtering, passes through second fourier lense L again
2Do inverse Fourier transform, at P
3Obtain output image on the face.
The noise model and the system transter complicacy very of actual 4f system.For simplified system, all separate the various sum of errors phase perturbations of system, embody a concentrated reflection of on the image, transport function is the wave filter with certain low-pass characteristic.Theoretical simulation is equivalent to input picture on the input face p1 of 4f system; Each item error of system is used the Zernike fitting of a polynomial, on the input picture that is added to, through the L1 Fourier transform; Again through the ideal low-pass filter on the P2; Convert the frequency spectrum that diffraction limit is a coordinate at last into, carry out theoretical model emulation with Matlab, the system emulation flow process is as shown in Figure 5.
Fig. 6 is the image spectrum that obtains by Fig. 5 method, 85% of intercepting image energy, and its scope is 302 ~ 313; The scope of far-field spot is 11 times a diffraction limit; Want complete recovery wavefront, required sub-lens number is at least 11 * 11, and the scope of intercepting energy is decided according to the precision that will restore.
Experiment effect of the present invention
For proving that the correctness of the present invention in embodiment is in follow-up emulation; The aberration equivalence is systematic error to adopt preceding 20 Zernike polynomial expressions to generate at random; The number of (1) so needed sub-lens is at least 10 * 10 on principle, for the aberration at random that adopts 20 Zernike polynomial expression reconstruct to generate on principle; (2) when the lens arra that adopts 12 * 12,16 * 16,20 * 20,24 * 24,28 * 28,32 * 32 respectively; The root-mean-square error of reconstruct is along with the increase of lens arra reduces gradually; As shown in Figure 8; Reach at 32 * 32 o'clock at lens arra, the root-mean-square error of reconstruct is 0.006, and reconstruction accuracy has reached through very high.In like manner, adopt preceding 10 Zernike polynomial expressions that the aberration at random that generates is carried out reconstruct, the lens arra that comprehensive (1), (2) need to adopt is respectively 8 * 8,12 * 12,16 * 16,20 * 20,24 * 24,28 * 28,32 * 32; As shown in Figure 9; The root-mean-square error of reconstruct does not reduce along with the increase of lens arra, and when 12 * 12 lens arras, the root-mean-square error of reconstruct is 0.02; Increase lens arra again, the error of reconstruct increases on the contrary.Ordinate among Fig. 8,9 is the root mean square of wavefront residual error.
Figure 10 representes with the index contrast figure before and after preceding 10 Zernike polynomial expressions, 12 * 12 lens arra wavefront reconstructions; Can find out through Figure 10; Wavefront with the reconstruct of preceding 10 Zernike polynomial expressions can only effectively reconstruct preceding 10 Zernike coefficient; 10 of the back can not be come out in reconstruct, and the wavefront that reconstructs has been lost radio-frequency component, the reason that does not therefore also reduce along with the increase of lens arra with regard to the reconstructed error of having explained Fig. 9.
Through with on preceding 20 the Zernike polynomial expressions simulation systematic error and the input picture that is added to, confirm spectral range according to the far-field spot of the image spectrum that comprises systematic error, thereby confirm Shack Hartmann's front-end sampling frequency.The number of confirming Hartmann's sub-lens according to the frequency spectrum of image is at least 11 * 11; Pass through simulating, verifying; With the error of 20 Zernike polynomial expressions simulation systems, the wavefront of reconstruct can only effectively reconstruct low order aberration during with preceding 10 Zernike polynomial expression reconfiguration system random distortion control informations, and is shown in figure 11; 10 of the back do not have reconstruct to come out; The wavefront that reconstructs has been lost radio-frequency component, so reconstruction accuracy do not increase along with the increase of lens, just can make the root mean square of wavefront residual error reach 0.02 in the lens permutation with 12 * 12.The array effect that continues the increase lens is undesirable.During with preceding 20 Zernike fitting of a polynomial random distortion control informations, along with the increase of lens arra, reconstruction accuracy improves gradually, and when lens arra reached 32 * 32, the root mean square of wavefront residual error was 0.006.Continuing increases lens arra again, and reconstruction accuracy does not have obvious variation.
Claims (1)
1. confirm the method for Hartmann's number of arrays with the image spectrum that comprises the 4f systematic error, it is characterized in that this method may further comprise the steps:
A, generate optical wavefront and the wavefront frequency spectrum treat reconstruct
In numerical simulation, adopt one group of random number as preceding 35 polynomial coefficients of Zernike, the optical wavefront of generation and spectrum distribution thereof are used for simulating the equivalent error in the 4f system;
B, adopt different step-length samplings
The design sketch of wavefront reconstruction can be found out when being counted with different sampling by the spectrogram of treating the reconstruct Wave-front phase; The roughly frequency range of the spectrum distribution of wavefront; Correspondence can be found out in the design sketch of reconstruct; The effect of reconstruct can obviously reduce after the sampling step-length is greater than certain unit, for from this conclusion of numerical value proof, has done consistent situation of fitting coefficient and error matrix in the subsequent simulation and has carried out the analysis of variance statistics;
C,Confirm the realistic model of 4f system
The noise model and the system transter complicacy very of actual 4f system for simplified system, are all separated the various sum of errors phase perturbations of system; Embody a concentrated reflection of on the image; Transport function is the wave filter with certain low-pass characteristic, and theoretical simulation is equivalent to input picture on the input face p1 of 4f system, and each item error of system is used the Zernike fitting of a polynomial; Be added on the input picture; Through the L1 Fourier transform, through the ideal low-pass filter on the P2, convert the frequency spectrum that diffraction limit is a coordinate at last into again;
D,Confirm the lens arra number in the 4f system
In proof procedure, to observe principle according to the method for mentioning in the step 2:
(1) for an incident wavefront that is made up of N rank Zernike polynomial expression, the m sub-aperture will be set up 2m equation, is only the overdetermined equation group in the time of must satisfying N≤2m, and promptly sub-aperture number must satisfy m>=N/2;
(2) simultaneously through the number of varitron lens, observe the relation of Zernike original coefficient and reconstruction coefficients, i.e. recovery accuracy and number of lenses purpose relation;
System model among the C obtains the frequency spectrum of system set by step, and the energy of intercepting certain limit is converted into the diffraction coordinate limit, thereby confirms the array number of lens.
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| CN107656143A (en) * | 2016-12-14 | 2018-02-02 | 中国电力科学研究院有限公司 | Positive-negative sequence impedance measurement module, the system and method for new-energy grid-connected current transformer |
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107656143A (en) * | 2016-12-14 | 2018-02-02 | 中国电力科学研究院有限公司 | Positive-negative sequence impedance measurement module, the system and method for new-energy grid-connected current transformer |
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