CN105894127B - Segmentation variable step simulated annealing method applied to the different wavefront sensing of phase difference - Google Patents
Segmentation variable step simulated annealing method applied to the different wavefront sensing of phase difference Download PDFInfo
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Abstract
The invention belongs to optical fields, and in particular to a kind of segmentation variable step simulated annealing method applied to the different wavefront sensing of phase difference, comprising the following steps: 1] import the current solution x of objective function0, objective function is using system wavefront zernike coefficient as variable；2] initial annealing temperature, upper limit the number of iterations T are set and terminates residual values S；3] initial segment: between-δ and+δ, iteration is run to a times setting disturbance scale；4] interlude: between-Ф and+Ф, iteration is run to b times setting disturbance scale；5] final stage: setting disturbance scale is between-δ/10 and+δ/10, and iteration operation is until the termination residual values S or accumulative the number of iterations t that wavefront reconstruction residual error RMS is less than setting reach the upper limit the number of iterations T of setting；6] end simulation annealing process exports the solution x of objective function at this timet.Segmentation variable step simulated annealing method proposed by the present invention, which solves, restrained slow or precocious technical problem existing for traditional constant step size simulated annealing method.
Description
Technical field
The invention belongs to optical fields, and in particular to a kind of segmentation variable step simulation applied to the different wavefront sensing of phase difference
Method for annealing.
Background technique
Adaptive optics system is usually made of three parts: Wavefront sensor, wavefront correction device and wavefront controller.Its
In, Wavefront sensor bears the important task for obtaining system optics wavefront distortion, is the input terminal of entire adaptive optics system.When
To today, common wavefront sensing technique includes: shearing interferometer, curvature sensor, tetragonous axicon lens sensor and Shack-Kazakhstan
Special graceful sensor.These technologies with need to introduce special hardware, and some can only implement wavefront inverting for point light source
It calculates, therefore just receives certain limitation in terms of the range of application.Currently, a kind of novel wavefront based on image procossing passes
Sense technology becomes research hotspot both domestic and external, and here it is the different PD of famous phase difference (phase diversity) wavefront sensings
Technology.This technology only needs the positive burnt and defocus image of two width of Same Scene (target is unrelated), and is constructed accordingly with system wave
Preceding zernike coefficient is the objective function of variable, is carried out most with global optimization method such as simulated annealing or genetic method later
Smallization optimizing obtains the zernike coefficient of wavefront so as to inverting.Brief mathematical description is as follows:
The imaging process of any one noncoherence optics imaging system is represented by formula (1) in frequency domain,
G (u, v)=F (u, v) OTF (u, v) (1)
Wherein, u and v respectively represents the spatial frequency after normalization.F represents dreamboat image spectrum, and G then represents reality
The image spectrum that border receives.OTF indicates the optical transfer function of imaging system, can be by optical system generalized pupil functionIt is obtained by auto-correlation computation, wherein x and y difference
Indicate the normalized coordinate on pupil plane.φ is the unknown wave aberration in system, can be fitted by zernike polynomial, and
The coefficient of each rank zernike polynomial is exactly the direct characterization of system wave aberration and the physical quantity of the wanted inverting of PD method.Represent the defocus aberration introduced in positive burnt and defocus optical path.
By formula (1) it is found that positive coke optical path and the corresponding imaging process of defocus optical path respectively indicate it is as follows,
GI(u, v)=F (u, v) OTFI(u,v) (2)
GD(u, v)=F (u, v) OTFD(u,v) (3)
Wherein I represents in-focus, and D represents defocus.
If we will be by actual measured results to dreamboat image spectrum F, positive coke optical transfer function OTFIWith from
Burnt optical transfer function OTFDEstimated simultaneously, then following objective function can be constructed,
Wherein "~" represents estimation.
Formula (4) is enabled to seek local derviation to the frequency spectrum F of dreamboat image, and enabling it is zero, can obtain target image frequency spectrum
Estimator are as follows:
And formula (5) is substituted into formula (4) again, and we can obtain final objective function, and it is as follows,
Since optical transfer function OTF can be obtained by the auto-correlation computation of pupil function P, pupil function be again system not
Know the function of aberration φ, and φ can be fitted by zernike polynomial, so formula (6) is actually with system wavefront
Zernike coefficient is variable.Therefore, the estimation of system wavefront is equal to and carries out formula (6) minimum value in higher-dimension object space
It finds.By powerful global optimization method, we can obtain the pool of description system wavefront in limited iteration time
Buddhist nun gram coefficient, to realize wavefront sensing.
It can be seen that the key of the different wavefront sensing of phase difference is to obtain using global optimization method to characterize distortional wave
Preceding zernike coefficient vector.When being distorted using zernike polynomial matching wavefront, the item number of used zernike polynomial
Determine the fitting precision of wavefront distortion.For example, wavefront distortion is mainly led by optical-mechanical system deformation for space camera system
It causes, belongs to that low order is gradual, and usual 13~21 rank can accurately describe；And for ground telescopic system, by atmosphere
Influence of the turbulent flow to wavefront reflects, it usually needs ranks up to a hundred can accurately describe.It means that being directed to objective function
(6) search of minimum will carry out in ten the apteryxs even higher dimensional space of dimensions up to a hundred, therefore easily fall into local optimum.
Simulated annealing method be it is a kind of be proved to can convergence with probability 1 in the optimization method of global optimum, object
It is clear to manage meaning, it is very widely used using simple.The feature of simulated annealing method maximum is, allows to calculate with dynamic
Probability come receive intermediate iteration process generation inferior solution, so that helping method is jumped out from local extremum.In addition to this, for working as
The preceding solution obtained introduces one ring of key that local disturbance and driving method converge to global optimum.Firstly, in routine
Simulated annealing method in, the disturbance quantity in iterative process is all according to identical scale and identical general each time from the beginning to the end
Rate distribution generates.When disturbance quantity is excessive, it may cause annealing process and be obstructed, the characteristic of the monotone decreasing of annealing curve will receive
It destroys；And disturbance quantity it is too small when, then can greatly increase the time for converging to global optimum again.Secondly, optimization method is starting rank
Section, the functional value of objective function greatly deviate from global optimum, and disturbance quantity wants sufficiently large, and method could approach attached to minimum as early as possible
Closely, later if also continued using identical disturbance quantity, method may fall into precocious and restrain in advance.
Summary of the invention
In order to solve to restrain slow or precocious technical problem existing for traditional constant step size simulated annealing method, this
Invention provides a kind of segmentation variable step simulated annealing method for the different wavefront distortion inverting customization of phase difference.
The technical solution of the invention is as follows: a kind of segmentation variable step simulated annealing applied to the different wavefront sensing of phase difference
Method, be characterized in that the following steps are included:
1] the current solution x of objective function is imported0, the objective function is using system wavefront zernike coefficient as variable；
2] initial annealing temperature, upper limit the number of iterations T are set and terminates residual values S
3] initial segment: setting disturbance scale is between-δ and+δ:
xt+1=xt+((-δ)+2*δ*rand)
Wherein, t is accumulative the number of iterations；xtFor the current solution of iteration operation；xt+1It is by xtDisturbance generates to be assessed new
Solution；δ is any number as unit of wavelength X, and the order of magnitude of δ is less than the quantity of maximum value in distorted wavefront zernike coefficient
Grade；Rand is the tandom number generator that value range is 0~1；
Using linear cooling strategy, iteration runs n times under each annealing temperature, until accumulative the number of iterations t be greater than or
Person is equal to initial segment the number of iterations a, and a is greater than 0 and is less than the constant of T；
4] interlude: setting disturbance scale is between-Ф and+Ф:
xt+1=xt+((-Ф)+2*Ф*rand)
Wherein, Ф is the constant between δ/10 and δ；
Using linear cooling strategy, iteration runs n times under each annealing temperature, until accumulative the number of iterations t be greater than or
Person is equal to interlude the number of iterations b, and b is greater than a and is less than the constant of T；
5] final stage: setting disturbance scale is between-δ/10 and+δ/10:
xt+1=xt+((-δ/10)+2*(δ/10)*rand)
Using linear cooling strategy, iteration runs n times under each annealing temperature, until wavefront reconstruction residual error RMS is less than
The termination residual values S of setting or accumulative the number of iterations t reaches the upper limit the number of iterations T of setting；
6] end simulation annealing process exports the solution x of objective function at this timet。
Above-mentioned initial segment the number of iterations a is a0+Δ；The interlude the number of iterations b is b0+Δ；Wherein Δ, which represents, divides not
With uncertainty when annealing stage.
Above-mentioned initial segment the number of iterations a is 80+ Δ；The interlude the number of iterations b is 350+ Δ；Δ is -30 to 30
Between constant.
Above-mentioned termination residual values S is 1/50 λ；The upper limit the number of iterations T is 8000.
Above-mentioned steps 1] in initial annealing temperature be 9000；The step 3]-step 5] under each annealing temperature
Iteration number of run be 1 time.
The beneficial effects of the present invention are: segmentation variable step simulated annealing method proposed by the present invention is moved back in analytic routines
It is proposed on the basis of fiery process and bound site facial difference wavefront sensing feature, brought benefit has two o'clock: first, can be with
It quickly locates near global minimum, the convergent process of accelerated method；Second, it is capable of the termination in advance of prevention method,
It is more conducive to find global optimum.By the way that annealing process is decomposed into initial segment, interlude and final stage, each stage use is controlled
Different disturbance scales, is not only applicable to the wavefront distortion of small scale, and is also applied for the wavefront distortion of large scale.
Detailed description of the invention
Fig. 1 is the method flow diagram of present pre-ferred embodiments；
Fig. 2 is short wave length front-distortion traditional analog method for annealing iterative inversion objective function extremal with constant disturbance
Amount variation situation schematic diagram；
Fig. 3 is large-scale wavefront aberration traditional analog method for annealing iterative inversion objective function extremal with constant disturbance
Amount variation situation schematic diagram；
Specific embodiment
Simulated annealing is the simulation to true annealing (quenching) physical process.Originally, the state metal that burns of extreme temperatures exists
After being put into the liquid water of room temperature suddenly, the physical state of interior atoms will generate cataclysm within the extremely short time；
Later, with the extension of time, physical state will gradually tend to balance.It can be seen that this has inherently reflected a problem:
Annealing is the nonlinear function of time variable.Corresponding with optimization, for iteration optimization in the incipient stage, the functional value of objective function is big
Global optimum is deviated from greatly, and disturbance quantity will could be approached near minimum as early as possible to enough to big (cataclysm), later if also
Identical disturbance quantity is continued to use, then simulated annealing may fall into precocious and restrain in advance.Therefore, the present invention proposes segmentation
Set different scale disturbance quantity this strategy, using with traditional analog anneal similar frame carry out segmentation variable step simulation move back
Fire.
Referring to Fig. 1, the method and step of present pre-ferred embodiments specifically: import the current solution x of objective function0, target
Function is using system wavefront zernike coefficient as variable.Initial annealing temperature is set as 9000, using linear cooling strategy, every
Iteration is run 1 time under one annealing temperature.Introduced part micro disturbance is currently solved for iteration each time is corresponding
Scale reduces as the process of annealing is segmented.Particularly, entire annealing process is divided into 3 stages, each stage and wherein
It is determined for the micro disturbance in introduced part is currently solved according to following rule, wherein xtIt represents and currently solves, and xt+1It represents by xt
Local dip and the new explanation to be assessed generated.
In initial segment, the number of iterations is less than 80+ Δ, and the micro disturbance in part is maximum, disturbs scale between-δ and+δ,
That is xt+1=xt+((-δ)+2*δ*rand)；
In interlude, the number of iterations is greater than 80+ Δ time and is less than 350+ Δ, and disturbance scale Ф is less than initial segment and is greater than
Ending segment, i.e. xt+1=xt+ ((- Ф)+2* Ф * rand), and Ф meets δ/10 < Ф < δ；
In ending segment, the number of iterations is greater than 350+ Δ, and the micro disturbance in part is minimum, disturbance scale be located at-δ/10 and+δ/
Between 10, i.e. xt+1=xt+((-δ/10)+2*(δ/10)*rand)。
Wherein, Δ is uncertainty when dividing different annealing stages, is taken ± 30 times；
Rand represents tandom number generator, and value range is 0~1；
δ is the numerical value arbitrarily as unit of wavelength X, as long as its order of magnitude is less than maximum value in distorted wavefront zernike coefficient
The order of magnitude.
Using wave-front reconstruction residual mean square (RMS) root error RMS (Root-Mean-Squares) less than 1/50 λ as standard, small scale
Distorted wavefront reconstruction can be completed within 100~300 iteration, and the reconstruction of medium and large scale distorted wavefront can be 1000
It is completed within~3000 times.End simulation annealing process after the completion of iteration exports the globally optimal solution x of objective function at this timet。
In disturbance quantity this optimisation strategy that segmentation applies different scale, entire annealing process is divided into several sections, it is each
It is two key problems to be determined when specific implementation that how the disturbance quantity of section, which should set,.
Firstly, according to the corresponding physical significance of simulated annealing process, initial stage of the iteration optimization process in execution, target
Functional value should decline rapidly under the traction of larger disturbance quantity, relatively good situation several times, poor situation most tens
It is secondary to be just stabilized to the lesser position of target function value.Therefore, the setting of initial annealing stage, which is no more than tens times, is
Compare reasonably, specific to the present embodiment, sets initial annealing stage no more than 80+ Δ.Research shows that: simulated annealing is passing through
It has gone through after the sharp fall of the objective function of initial period, the variation of target function value after iteration proceeds to several hundred times
Just not significant, it is exactly suitable for being excavated at this time using lesser disturbance quantity closer to the position of global optimum, so generally will
Final stage after several hundred times as annealing, the last rank specific to the present embodiment, after setting 350+ Δ is secondary as annealing
Section.Therefore, according to such a division mode, entire annealing process is divided into 3 stages.Wherein, different annealing stages are divided
When probabilistic characterization parameter Δ for introducing impart the present invention and dividing the flexibility in annealing process.
Secondly, in simulated annealing process, for the disturbance quantity currently solved setting usually according to xt+1=xt+((-δ)+
2* δ * rand) mode carry out, wherein xtAnd xt+1It respectively represents current solution and is obtained via current solution disturbance to be assessed new
Solution.In conventional simulated annealing method, δ is to maintain constant in entire annealing process.δ acquirement is too small, and convergence rate will
Become very slow, and if δ acquirement is excessive, it will soon be restrained in advance after it experienced initial annealing stage.Fig. 2 be
When wavefront distortion scale is smaller, feelings that objective function extremal when conventional algorithm iterative inversion changes with constant disturbance quantity
Condition.Wherein, about 0.1 λ of wavefront distortion scale, abscissa are the number of iterations, and ordinate is target function value.Fig. 3 is abnormal in wavefront
When mutative scale is larger, the case where objective function extremal when conventional algorithm iterative inversion changes with constant disturbance quantity.Wherein,
About 1.1 λ of wavefront distortion scale, abscissa are the number of iterations, and ordinate is target function value.Fig. 2 and Fig. 3 is set forth two kinds
The feelings of dimensional distortion wavefront condition objective function extreme value variation when the execution of simulation degeneration method when keeping δ invariable
Condition.It can be seen that either short wave length front-distortion (about 1/10 λ of RMS) still large scale wavefront distortion (about 1.1 λ of RMS),
The situation of change of objective function extremal is similar.When δ is smaller, curve is from start to finish smoothly drilled with approaching constant slope
Change, convergence rate is inevitable slower at this time；And when δ is larger, there are suddenly decline and two kinds of situations of slow gradual change in curve, and deposit
In many platform effects, this means that Optimization Progress has been restrained in advance locally.When obtaining Fig. 2 and Fig. 3, iteration
Maximum number of iterations is subject in the termination of process, without setting the wavefront reconstruction residual error RMS upper limit.
Therefore, δ should carry out different settings according to the different phase of annealing process, and its value has with concrete application
It closes, corresponds to the different wavefront sensing of phase difference, value of the δ in different annealing processes and the distortion scale phase to inverting distorted wavefront
It closes.Any one optical camera system, gets into smooth, links experienced all can be to final therebetween from designing, being assembled to
Wavefront affect, rule of thumb the magnitude of its scale substantially can be estimated, and this just provides ginseng for the value of δ
It examines.It is found through exploratory development, in the δ of initial annealing stage, value should be in zernike coefficient more corresponding than distorted wavefront most
It is worth a small magnitude greatly, for example distorted wavefront, after Ze Nike is fitted, maximum coefficient is 0.2 λ, then δ should just take at this time
With a great deal of grade of value of 0.02 λ.In the final stage of annealing, δ should then choose again the value of small an order of magnitude.For annealing
Intermediate stage for, the value of δ is relatively free, as long as smaller than the value of initial stage, the value than final stage greatly can
With.
To rebuild wavefront residual error RMS less than 1/10 λ as evaluation criterion, it is abnormal that two kinds of scale wavefront are set forth in Tables 1 and 2
Pair of improved simulated annealing method and traditional analog method for annealing the number of iterations when reaching optimizing index under the conditions of change
Than permitted upper limit the number of iterations is 8000 times.Wherein, in the method for the invention, it is initial segment less than 50 times, arrives for 51 times
300 times are interlude, and being greater than 300 times is ending segment.Corresponding to small dimensional distortion, 0.005 λ is taken in initial segment δ, in interlude
δ takes 0.0025 λ, takes 0.00025 λ in ending segment δ；It distorts corresponding to large scale, 0.05 λ is taken in initial segment δ, in interlude δ
0.025 λ is taken, takes 0.0025 λ in ending segment δ.For conventional method, the disturbance quantity of 4 kinds of different scales has been selected respectively (respectively
0.25 λ, 0.025 λ, 0.0025 λ and 0.00025 λ) it is compared.
Reach convergent the number of iterations when the small dimensional distortion wavefront of table 1 (0.1 λ of RMS) to compare
Reach convergent the number of iterations when 2 large scale distorted wavefront of table (1.1 λ of RMS) to compare
It can be seen that attempting different disturbance quantities by enumerating, traditional annealing methods can for different scale distortion
Find the disturbance quantity for being reached relatively quickly convergence state.Nevertheless, at this time required for the number of iterations still with than
Biggish probability is more than improved simulated annealing method.It should furthermore be noted that the distortion for medium large scale comes
Say, improved simulated annealing method is more outstanding in terms of fast convergence characteristic, be run multiple times show most situations its
Required the number of iterations is much smaller than traditional analog method for annealing.Thus illustrate that method for annealing provided by the invention can either be prevented
The only precocity of Optimization Progress can also achieve the purpose that fast convergence.
Claims (5)
1. a kind of segmentation variable step simulated annealing method applied to the different wavefront sensing of phase difference, it is characterised in that: including following
Step:
1] the current solution x of objective function is imported0, the objective function is using the wavefront zernike coefficient of optical imaging system as variable；
2] initial annealing temperature, upper limit the number of iterations T are set and terminates residual values S；
3] initial segment: setting disturbance scale is between-δ and+δ:
xt+1=xt+((-δ)+2*δ*rand)
Wherein, t is accumulative the number of iterations；xtFor the current solution of iteration operation；xt+1It is by xtDisturb the new explanation to be assessed generated；δ
It is any number as unit of wavelength X, the order of magnitude of δ is less than the order of magnitude of maximum value in distorted wavefront zernike coefficient；
Rand is the tandom number generator that value range is 0~1；
Using linear cooling strategy, iteration runs n times under each annealing temperature, until accumulative the number of iterations t is greater than or waits
0 is greater than in initial segment the number of iterations a, a and is less than the constant of T；
4] interlude: setting disturbance scale is between-Ф and+Ф:
xt+1=xt+((-Ф)+2*Ф*rand)
Wherein, Ф is the constant between δ/10 and δ；
Using linear cooling strategy, iteration runs n times under each annealing temperature, until accumulative the number of iterations t is greater than or waits
A is greater than in interlude the number of iterations b, b and is less than the constant of T；
5] final stage: setting disturbance scale is between-δ/10 and+δ/10:
xt+1=xt+((-δ/10)+2*(δ/10)*rand)
Using linear cooling strategy, iteration runs n times under each annealing temperature, until wavefront reconstruction residual error RMS is less than setting
Termination residual values S or accumulative the number of iterations t reach the upper limit the number of iterations T of setting；
6] end simulation annealing process exports the solution x of objective function at this timet；
7] pass through the solution x of output objective functiont, that is, the wavefront zernike coefficient of optical imaging system is obtained, to realize that wavefront passes
Sense.
2. the segmentation variable step simulated annealing method according to claim 1 applied to the different wavefront sensing of phase difference, special
Sign is: the initial segment the number of iterations a is a0+Δ；The interlude the number of iterations b is b0+Δ；Wherein Δ, which represents, divides not
With uncertainty when annealing stage.
3. the segmentation variable step simulated annealing method according to claim 2 applied to the different wavefront sensing of phase difference, special
Sign is: the initial segment the number of iterations a is 80+ Δ；The interlude the number of iterations b is 350+ Δ；Δ be -30 to 30 it
Between constant.
4. the segmentation variable step simulated annealing method according to claim 3 applied to the different wavefront sensing of phase difference, special
Sign is: the termination residual values S is 1/50 λ；The upper limit the number of iterations T is 8000.
5. the segmentation variable step simulated annealing method according to claim 4 applied to the different wavefront sensing of phase difference, special
Sign is: the step 1] in initial annealing temperature be 9000；The step 3]-step 5] under each annealing temperature
Iteration number of run is 1 time.
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