CN106596056B - A kind of detection method of sparse aperture optical system Piston error - Google Patents
A kind of detection method of sparse aperture optical system Piston error Download PDFInfo
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Abstract
The invention discloses a kind of detection methods of sparse aperture optical system Piston error.It is detected based on Piston error of the phase difference method to sparse aperture.Image focal plane and out-of-focus image is used to carry out processing from traditional phase difference method different, there are the images of known Piston phase difference for some sub-aperture in sparse aperture for one of two width image focal planes that technical solution of the present invention uses, objective function is constructed with this two images, then carries out calculating Piston error by optimization algorithm.Compared with traditional Piston error detection method, this method improves the Piston error-detecting precision under the influence of Gaussian noise under the premise of not increasing any hardware cost and operation difficulty.
Description
Technical field
The present invention relates to a kind of methods of Piston error-detecting, and in particular to a kind of sparse aperture optical system
Piston error detection method.
Background technique
Sparse aperture optical system refers to the array being made of multiple small-bore optical systems, these small-bore optical systems
It is adjusted by phase matched and optical path, so that realizing the coherent superposition of light field on focal plane by the light beam of each sub-aperture.
Sparse aperture is compared with the comparable single heavy caliber system of clear aperture, not only resolution of diffraction having the same, and
Also have many advantages, such as that the processing is simple, be easy detection and it is at low cost.In order to obtain the image of high-quality, sparse aperture optical system
(usually reflective) in adjustment, the relative position error especially Piston error between each sub-aperture has to obtain tight
Lattice control (usually less than λ/20rms), this difficulty for current detection and integration techno logy is larger；In addition, actual
In application process, the factors such as environment such as temperature and gravity around system also result in the generation of sub-aperture Piston error, because
This needs accurate, the efficient wave-front detection method of one kind to detect such error and corrected.
The optical system of noncontinuous surface this kind of for sparse aperture, Piston error detection method are predominantly based on the later period
The methods of the phase recovery of image procossing, phase difference.And phase difference method is opened up compared to phase retrieval method due to can be suitably used for
Object is opened up, therefore application is more extensive, the basic principle is that passing through a width image focal plane and one for system acquisition object
Out-of-focus image known to width defocusing amount constructs objective function according to this two images, then using optimization algorithm to objective function
Seek extreme value.But due to object-image of the methods of phase recovery, phase difference calculation processing, vulnerable to height in acquisition process
The influence of this noise, therefore, the calculated value of Piston error often deviate actual value, and Gaussian noise intensity is bigger, this inclined
Difference is also bigger；
Document " detects " ([J] based on Piston error of the phase difference method of genetic algorithm to synthesis telescope
Astronomical research and technology, 2011,8 (4): 369-373) disclose a kind of utilization defocus phase difference method measurement sparse aperture sub-aperture
The method of Piston error, the defocusing amount of out-of-focus image is chosen for 1 wavelength in this method, and document finally all adds two images
When the gaussian random white Gauss noise that upside deviation is 1%, the computational accuracy of Piston error is significantly affected, and in document not
The method for proposing to solve the problems, such as this.Influence of the actually current Gaussian noise to sparse aperture optical system Piston error-detecting
There has been no good solutions.
Summary of the invention
The present invention is the deficiency existing when detecting the Piston error of sparse aperture optical system for the prior art,
It is easy to operate to provide one kind, and can effectively improve under the influence of Gaussian noise to sparse aperture optical system Piston error-detecting
The method of precision.
Realize that the technical solution of the object of the invention is to provide a kind of detection side of sparse aperture optical system Piston error
Method includes the following steps:
(1) object is imaged by sparse aperture optical system, obtains image g in focal plane1；Along optical axis direction
Mobile some sub-aperture distance z obtains image in focal plane again by sparse aperture optical system to same target imaging
g2；
(2) image g is respectively obtained according to Fourier transformation relationship1And g2Corresponding system optics transmission function S1And S2；
(3) according to image g1And g2And optical transfer function S1And S2, using phase difference method, establish objective function E；
(4) extreme value is asked to objective function E using optimization algorithm, obtains each sub-aperture of sparse aperture optical system
Piston error
Wherein, N is the sub-aperture number of sparse aperture optical system.
Sub-aperture of the present invention along the distance z that optical axis direction moves range between the λ of 0.1 λ~1, λ is wavelength.
Along any sub-aperture that some sub-aperture that optical axis direction moves is in sparse aperture optical system.
Optimization algorithm described in technical solution of the present invention includes genetic algorithm, conjugate gradient method, Newton method or quasi- ox
The method of pausing.
The principle of foundation of the present invention is: sparse aperture optical system can be regarded as space invariance linear system, then system
Imaging equation is represented by formula (1):
gd=f*sd+noised (1)
Wherein, g is sparse aperture optical system imaging；Subscript d desirable 1 and 2, respectively image g1And g2；F is imaging
Object；Symbol * is convolution algorithm operator；s1And s2Respectively image g1And g2Corresponding system point spread function；noise1With
noise2For image g1And g2The randomness Gaussian noise supervened in collection process；s1And s2Can be expressed as formula (2) and
Formula (3):
(3) in formula, FT is Fourier transform operator；AnFor the two-value light of n-th of sub-aperture in sparse aperture optical system
Pupil function；For the Piston phase difference that sub-aperture m is generated along optical axis moving distance z,Relationship with z isI.e.Period be λ, for other sub-apertures,It is 0.φnIndicate n-th of sub-aperture
The error of diameter is expressed as formula (4) with zernike polynomial:
In formula, ZjIndicate jth item zernike polynomial, αnjIndicate the jth item zernike polynomial of n-th of sub-aperture is
Number, i.e. the sub-aperture error to be detected, j=1 indicate Piston error.
Carrying out Fourier transformation to (1) formula can be obtained formula (5):
Gd(u)=F (u) Sd(u)+NOISEd(u) (5)
The Fourier that wherein G (u), F (u), S (u) and NOISE (u) are respectively g (x), f (x), s (x) and noise (x) becomes
It changes, S (u) is also referred to as the optical transfer function of system；U is frequency domain coordinates.
Target function type (6) E is derived according to phase difference method；
Wherein, u is frequency domain coordinates；χ1To make denominator | S1(u)|2+|S2(u)|2It is not 0 spatial frequency set.
Extreme value is asked to objective function E using optimization algorithm, so that the Piston for calculating each sub-aperture of sparse aperture is missed
Difference
Sparse aperture Piston error is calculated using the phase difference method of traditional image focal plane and focal plane image
Would generally face a problem, i.e., the defocusing amount of focal plane image on earth this take what value that could make computational accuracy highest, about
Document has no too many elaboration before this, and widespread practice is that defocusing amount is chosen for 0.5 λ or 1.0 λ, typically not greater than 2.0 λ；And
Its period of sub-aperture moving distance is λ, and therefore, value range is 0.1 λ between 1.0 λ.
By adopting the above-described technical solution, the invention has the advantages that by changing some in sparse aperture optical system
Position of the sub-aperture on optical axis thus provides a kind of method for calculating sparse aperture Piston error, and improves when height
Error-detecting precision in the presence of this noise.
Detailed description of the invention
Fig. 1 is the process that a kind of pair of sparse aperture optical system Piston error provided in an embodiment of the present invention is detected
Figure；
Fig. 2 is the sparse aperture optical system of Golay3 structure provided in an embodiment of the present invention；
Fig. 3 is object provided in an embodiment of the present invention；
When Fig. 4 is that Gaussian noise variance provided in an embodiment of the present invention is respectively 0,0.1%, 0.5% and 1%, Golay3
Focal plane imaging figure of the sparse aperture optical system to object；
Fig. 5 is the distance provided in an embodiment of the present invention that sub-aperture 1 is moved to 0.3 wavelength along optical axis, and Gaussian noise side
Difference is other 0, when being 0.1%, 0.5% and 1%, focal plane imaging figure of the Golay3 sparse aperture optical system to object；
Fig. 6~9 are provided in an embodiment of the present invention respectively with sub-aperture Piston phase difference and defocus phase difference method
To the comparison figure of each sub-aperture Piston error detection result of Golay3 sparse aperture.
Specific embodiment
With reference to the accompanying drawings and examples, technical solution of the present invention is further elaborated.
Embodiment 1
Referring to attached drawing 1, it is that a kind of pair of sparse aperture optical system Piston error provided in this embodiment detects
Flow chart；Referring to attached drawing 2, it is the sparse aperture optical system of Golay3 structure provided in this embodiment.In Fig. 2, sub-aperture
Diameter 1, sub-aperture 2 and sub-aperture 3 are circle, 120 ° of the center rotation pair of the centers of three sub-apertures respectively about circumscribed circle
Claim.
According to Fig. 1 step S101, it is 200mm that the parameter that sparse aperture optical system is arranged, which is respectively as follows: sub-aperture bore,；Outside
Connecing circular aperture is 600mm；Operation wavelength is 600nm；F/# is 5.
Referring to attached drawing 3, it is the object in the present embodiment, and resolution ratio is 100 × 100, according to Fig. 1 step S102, benefit
It is imaged with Golay3 sparse aperture optical system provided in this embodiment, obtains image focal plane g1, as a result referring to attached drawing
4, wherein Fig. 4 (a) is noise variance focal plane imaging figure when being 0, (b), (c) and (d) of Fig. 4 is respectively to work as the sparse hole Golay3
Diameter optical system is with Gaussian noise and when noise variance is respectively 0.1%, 0.5% and 1%, focal plane of the system to object
Image.
According to Fig. 1 step S103,1 distance z of sub-aperture (by taking 0.3 λ as an example, λ is wavelength) is moved along optical axis direction, again
By sparse aperture optical system to same target imaging, image g is obtained in focal plane2, Fig. 5 (a) is noise variance when being 0
Focal plane imaging figure, (b) of Fig. 5, (c) and (d) be respectively when Golay3 sparse aperture optical system have Gaussian noise and
When noise variance is respectively 0.1%, 0.5% and 1%, focal plane imaging figure of the system to object.
Image g1With image g2Corresponding optical transfer function is respectively formula (7) and (8):
Wherein φnIndicate the error of n-th of sub-aperture to be measured；AndIt is generated for 1 moving distance z of sub-aperture
Piston phase difference, the relationship of the two are
According to Fig. 1 step S104, objective function E such as formula (9) is derived using phase difference method；
Wherein, u is frequency domain coordinates；G1(u) and G2It (u) is respectively image g1With image g2Fourier transformation；χ1To make
Denominator | S1(u)|2+|S2(u)|2It is not 0 spatial frequency set.
According to Fig. 1 step S105, extreme value is asked to objective function using optimization algorithm, the present embodiment uses genetic algorithm meter
Calculate the Piston error of each sub-aperture of Golay3 sparse aperture optical system.Genetic algorithm is a kind of global probabilistic search calculation
Method, it only needs the information of target function value, does not need the gradient of calculating target function；Algorithm is easy to accomplish, and has fine
Global convergence.
Assuming that the error of each sub-aperture is as shown in table 1 in sparse aperture optical system, in order to simulate truth, so often
A sub-aperture has also assigned value to Tip the and Tilt error of each sub-aperture respectively, as it is assumed that sub-aperture in addition to Piston error
1 is, with reference to sub-aperture, so Piston, Tip and Tilt error of sub-aperture 1 are 0, i.e., the present embodiment is only to 2 He of sub-aperture
The Piston error of sub-aperture 3 is calculated.
1 each sub-aperture error assumption value of Golay3 sparse aperture optical system of table
In order to illustrate the effect of the method for the present invention, embodiment acquires two images first with the conventional phase method of difference, i.e.,
One width is image focal plane, the Piston that in addition a width is focal plane image to calculate above-mentioned Golay3 sparse aperture sub-aperture
The defocusing amount of error, focal plane image changes to 2.0 λ from 0.1 λ.It is corresponding to it in sub-aperture Piston phase of the invention
In the method for difference, a width image focal plane is first acquired；After sub-aperture 1 also accordingly changes to 1.9 λ from 0.1 λ along the distance that optical axis moves
A width image focal plane is acquired again (actually since moving distance z has periodical, 0.1 λ -0.9 λ phase corresponding with 1.1 λ -1.9 λ
Together), the calculated result of two methods is as shown in Figure 5.
The abscissa of Fig. 6 is that the two methods sub-aperture 1 when measuring the Piston error of sub-aperture 2,3 is moved along optical axis
Distance z and defocusing amount, ordinate indicate the percentage deviation of preset value in the Piston error detecting value and table 1 of sub-aperture 2,3
The coordinate setting of average value, Fig. 7,8 and 9 is identical as Fig. 6.Wherein, Fig. 6 is no Gaussian noise imaging contexts, and Fig. 7,8 and 9 are
System is respectively present imaging contexts when variance is 0.1%, 0.5% and 1% Gauss Gaussian noise.
As seen from Figure 6, when Gaussian noise is not present in system, defocus phase difference method is to sparse aperture sub-aperture
The precision of Piston error-detecting will be generally higher than the detection accuracy of sub-aperture Piston phase difference method.And it can by Fig. 7,8 and 9
To find out, with the increase of Gauss Gaussian noise intensity, the Piston error-detecting precision of sub-aperture Piston phase difference method
It is apparently higher than defocus phase difference method；And Gauss Gaussian noise intensity is higher, the meter of sub-aperture Piston phase difference method
It is higher to calculate stability.
Therefore when sparse aperture optical system is without Gauss Gaussian noise, can using traditional defocus phase difference method come
The Piston error of sparse aperture sub-aperture is measured, this is a kind of ideal situation certainly, and reality is simultaneously not present.And it is high when existing
When this noise, sub-aperture Piston phase difference method can choose at this time to calculate the Piston error of sparse aperture sub-aperture,
Not only error-detecting precision is higher, and as the increase calculated result of Gaussian noise intensity is more stable.
Claims (4)
1. a kind of detection method of sparse aperture optical system Piston error, it is characterised in that include the following steps:
(1) object is imaged by sparse aperture optical system, obtains image in focal planeg 1；By sparse aperture optical system
Some sub-aperture in system is along optical axis direction moving distance z, again by sparse aperture optical system to same target imaging,
Image is obtained in focal planeg 2；
(2) image is respectively obtained according to Fourier transformation relationshipg 1Withg 2Corresponding system optics transmission functionS 1WithS 2；
(3) according to imageg 1Withg 2And optical transfer functionS 1WithS 2, using phase difference method, establish objective functionE；
(4) using optimization algorithm to objective functionEExtreme value is sought, the Piston of each sub-aperture of sparse aperture optical system is obtained
Error:
；
Wherein,NFor the sub-aperture number of sparse aperture optical system.
2. a kind of detection method of sparse aperture optical system Piston error according to claim 1, it is characterised in that:
The distance that sub-aperture is moved along optical axis directionRange 0.1λ~1λBetween,λFor wavelength.
3. a kind of detection method of sparse aperture optical system Piston error according to claim 1, it is characterised in that:
Along any sub-aperture that some sub-aperture that optical axis direction moves is in sparse aperture optical system.
4. a kind of detection method of sparse aperture optical system Piston error according to claim 1, it is characterised in that:
The optimization algorithm includes genetic algorithm, conjugate gradient method, Newton method or quasi-Newton method.
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| CN111595559B (en) * | 2020-06-22 | 2021-05-25 | 中国科学院长春光学精密机械与物理研究所 | First-order wavefront error measuring system of non-continuous mirror telescope |
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