CN106596056B - A kind of detection method of sparse aperture optical system Piston error - Google Patents
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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 invention relates to a method for Piston error detection, in particular to a method for Piston error detection of a sparse aperture optical system.
Background
The sparse aperture optical system is an array formed by a plurality of small aperture optical systems, and the small aperture optical systems realize coherent superposition of light fields on a focal plane through phase matching and light path adjustment of light beams passing through each sub-aperture. Compared with a single large-aperture system with the same clear aperture, the sparse aperture has the same diffraction limit resolution, and has the advantages of simplicity in processing, easiness in detection, low cost and the like. In order to obtain high-quality images, when a sparse aperture optical system (usually a reflective type) is adjusted, the relative position error among the sub apertures, especially the Piston error, must be strictly controlled (usually less than lambda/20 rms), which is difficult for the current detection and adjustment technology; in addition, in practical applications, the subaperture Piston error is also caused by factors such as temperature and gravity of the environment surrounding the system, so that an accurate and efficient wavefront detection method is needed to detect and correct such error.
For an optical system with a discontinuous surface such as a sparse aperture, the method for detecting the Piston error mainly comprises the methods of phase recovery, phase difference and the like based on post-image processing. Compared with a phase recovery method, the phase difference method is more widely applied because the phase difference method can be suitable for expanding a target object, and the basic principle is that a focal plane image and a defocusing image with known defocusing amount of the target object are collected through a system, an objective function is constructed according to the two images, and then an optimization algorithm is adopted to solve an extreme value of the objective function. However, since the image, which is the object of calculation processing by methods such as phase recovery and phase difference, is susceptible to gaussian noise in the acquisition process, the calculated value of the Piston error tends to deviate from the actual value, and the larger the intensity of the gaussian noise is, the larger the deviation is;
document 'detection of Piston error of synthetic aperture telescope based on phase difference method of genetic algorithm' ([ J ] astronomical research and technology, 2011,8 (4): 369-. In fact, at present, no good solution exists for the influence of Gaussian noise on the Piston error detection of the sparse aperture optical system.
Disclosure of Invention
Aiming at the defects existing in the prior art when the Piston error of the sparse aperture optical system is detected, the invention provides the method which is simple to operate and can effectively improve the detection precision of the Piston error of the sparse aperture optical system under the influence of Gaussian noise.
The technical scheme for realizing the aim of the invention is to provide a method for detecting the Piston error of a sparse aperture optical system, which comprises the following steps:
(1) imaging the target through a sparse aperture optical system, obtaining an image g at the focal plane1(ii) a Moving a certain sub-aperture distance z along the optical axis direction, imaging the same target again through the sparse aperture optical system, and obtaining an image g at the focal plane2；
(2) Respectively obtaining images g according to Fourier transform relation1And g2Corresponding system optical transfer function S1And S2；
(3) According to the image g1And g2And an optical transfer function S1And S2Establishing an objective function E by adopting a phase difference method;
(4) obtaining an extreme value of the objective function E by using an optimization algorithm to obtain the Piston error of each sub-aperture of the sparse aperture optical system
Wherein N is the number of sub-apertures of the sparse aperture optical system.
The range of the distance z of the sub-aperture moving along the optical axis direction is 0.1 lambda-1 lambda, and lambda is the wavelength. A certain sub-aperture that moves in the optical axis direction is any one of the sub-apertures in the sparse aperture optical system.
The optimization algorithm in the technical scheme of the invention comprises a genetic algorithm, a conjugate gradient method, a Newton method or a quasi-Newton method.
The invention is based on the principle that: the sparse aperture optical system can be regarded as a space-invariant linear system, and then the system imaging equation can be expressed as formula (1):
gd＝f*sd+noised (1)
wherein g is imaged by a sparse aperture optical system; subscript d may take 1 and 2, respectively, to represent image g1And g2(ii) a f is an imaging target object; symbol is convolution operator; s1And s2Are respectively an image g1And g2A corresponding system point spread function; noise1And noise2Is an image g1And g2Random Gaussian noise which is generated in the collection process; s1And s2Can be expressed as formula (2) and formula (3), respectively:
(3) in the formula, FT is a Fourier transform operator; a. thenA binary pupil function of the nth sub-aperture in the sparse aperture optical system;the Piston phase difference generated for the sub-aperture m moving the distance z along the optical axis,in relation to z isNamely, it isWith a period of lambda, for the other sub-apertures,is 0. Phi is anThe error of the nth sub-aperture is expressed by a zernike polynomial as formula (4):
in the formula, ZjRepresenting the j-th Zernike polynomial, αnjThe j-th terms of the Zernike polynomials which represent the nth sub-aperture, i.e. the errors to be detected for the sub-apertures, and j 1, i.e. the Piston error.
Performing fourier transform on equation (1) to obtain equation (5):
Gd(u)＝F(u)Sd(u)+NOISEd(u) (5)
wherein G (u), F (u), S (u) and NOISE (u) are the Fourier transforms of g (x), f (x), s (x) and noise (x), respectively, and S (u) is also known as the optical transfer function of the system; u is the frequency domain coordinate.
Deducing an object function formula (6) E according to a phase difference method;
wherein u is a frequency domain coordinate; chi shape1So that the denominator | S1(u)|2+|S2(u)|2A set of spatial frequencies other than 0.
Obtaining an extreme value of the objective function E by using an optimization algorithm, thereby calculating the Piston error of each sub-aperture of the sparse aperture
The method for calculating the sparse aperture Piston error by using the phase difference method of the traditional focal plane image and the defocused plane image generally faces a problem that the calculation accuracy can be highest only by which value the defocused amount of the defocused plane image is obtained, and the prior literature does not describe much, and the common method is to select the defocused amount to be 0.5 lambda or 1.0 lambda, and generally not to exceed 2.0 lambda; the sub-aperture is moved by a distance having a period λ, and thus, the range of values is from 0.1 λ to 1.0 λ.
Due to the adoption of the technical scheme, the invention has the advantages that: by changing the position of a certain sub-aperture along the optical axis in the sparse aperture optical system, the method for calculating the sparse aperture Piston error is provided, and the error detection precision when Gaussian noise exists is improved.
Drawings
Fig. 1 is a flowchart of detecting a Piston error of a sparse aperture optical system according to an embodiment of the present invention;
fig. 2 is a sparse aperture optical system of Golay3 structure provided by an embodiment of the present invention;
FIG. 3 is a target provided by an embodiment of the present invention;
fig. 4 is an imaging diagram of a Golay3 sparse aperture optical system at a focal plane to a target object when the variance of gaussian noise provided by an embodiment of the present invention is 0, 0.1%, 0.5% and 1%, respectively;
fig. 5 is a focal plane imaging diagram of the Golay3 sparse aperture optical system on a target object when the sub-aperture 1 is moved by a distance of 0.3 wavelength along the optical axis and the gaussian noise variances are 0, 0.1%, 0.5% and 1%, respectively, according to the embodiment of the present invention;
fig. 6-9 are comparison diagrams of sub-aperture Piston error detection results of Golay3 sparse apertures by using a sub-aperture Piston phase difference and defocus phase difference method provided by the embodiment of the invention.
Detailed Description
The technical scheme of the invention is further explained by combining the drawings and the embodiment.
Example 1
Referring to fig. 1, it is a flowchart for detecting a Piston error of a sparse aperture optical system according to this embodiment; referring to fig. 2, it is a sparse aperture optical system of Golay3 structure provided in this embodiment. In fig. 2, each of the sub-apertures 1, 2 and 3 is a circle, and the centers of the three sub-apertures are respectively rotationally symmetric about 120 ° with respect to the center of the circumscribed circle.
According to step S101 in fig. 1, the parameters of the sparse aperture optical system are set as follows: the aperture of the sub-aperture is 200 mm; the diameter of the circumscribed circle is 600 mm; the working wavelength is 600 nm; f/# is 5.
Referring to fig. 3, which is an object in the present embodiment, the resolution is 100 × 100, and according to step S102 in fig. 1, the Golay3 sparse aperture optical system provided in the present embodiment is used to perform imaging to obtain a focal plane image g1Referring to fig. 4, the results are shown in fig. 4, wherein fig. 4(a) is a focal plane imaging diagram when the noise variance is 0, and fig. 4 (b), (c) and (d) are focal plane imaging diagrams of the system on the target respectively when the Golay3 sparse aperture optical system has gaussian noise and the noise variances are 0.1%, 0.5% and 1%, respectively.
According to step S103 of fig. 1, the sub-aperture is moved by a distance z (λ is the wavelength, for example 0.3 λ) along the optical axis direction, the same target is imaged again by the sparse aperture optical system, and an image g is obtained at the focal plane2Fig. 5(a) is a focal plane imaging diagram when the noise variance is 0, and fig. 5 (b), (c) and (d) are focal plane imaging diagrams of the system for the target object when the Golay3 sparse aperture optical system has gaussian noise and the noise variances are 0.1%, 0.5% and 1%, respectively.
Image g1And image g2The corresponding optical transfer functions are respectively equations (7) and (8):
wherein phinRepresenting the error of the nth sub-aperture to be measured; whileThe Piston phase difference generated for the sub-aperture 1 moving the distance z is related to
According to step S104 in fig. 1, a phase difference method is used to derive an objective function E as formula (9);
wherein u is a frequency domain coordinate; g1(u) and G2(u) are each an image g1And image g2Fourier transform of (1); chi shape1So that the denominator | S1(u)|2+|S2(u)|2A set of spatial frequencies other than 0.
According to step S105 in fig. 1, an optimization algorithm is used to obtain an extremum for the objective function, and in this embodiment, a genetic algorithm is used to calculate the Piston error of each sub-aperture of the Golay3 sparse aperture optical system. The genetic algorithm is a global probability search algorithm, only needs the information of a target function value, and does not need to calculate the gradient of a target function; the algorithm is easy to realize and has good global convergence.
Assuming that errors of sub-apertures in the sparse aperture optical system are shown in table 1, in order to simulate a real situation, each sub-aperture also assigns values to Tip and Tilt errors of each sub-aperture in addition to the Piston error, and since the sub-aperture 1 is assumed to be a reference sub-aperture, the Piston, Tip and Tilt errors of the sub-aperture 1 are all 0, that is, the embodiment only calculates the Piston errors of the sub-aperture 2 and the sub-aperture 3.
TABLE 1 assumed values of sub-aperture errors of Golay3 sparse aperture optical system
To illustrate the effect of the method of the present invention, the embodiment first uses the conventional phase difference method to acquire two images, i.e. one is the focal plane image and the other is the out-of-focus plane image to calculate the above-mentioned Piston error of the Golay3 sparse aperture sub-aperture, and the out-of-focus amount of the out-of-focus plane image changes from 0.1 λ to 2.0 λ. Correspondingly, in the subaperture Piston phase difference method, a focal plane image is collected firstly; the sub-aperture 1 is moved along the optical axis by a distance corresponding to 0.1 λ to 1.9 λ, and then a focal plane image is acquired (actually, since the moving distance z has periodicity, 0.1 λ -0.9 λ corresponds to 1.1 λ -1.9 λ), and the calculation results of the two methods are shown in fig. 5.
The abscissa of fig. 6 is the moving distance z and defocus of the sub-aperture 1 along the optical axis in the two methods for measuring the Piston error of the sub-apertures 2, 3, and the ordinate represents the average of the percentage deviation of the Piston error detection values of the sub-apertures 2, 3 from the preset values in table 1, and the coordinate settings of fig. 7, 8 and 9 are the same as fig. 6. Where figure 6 is the case of imaging without gaussian noise and figures 7, 8 and 9 are the cases of imaging when the system has variance of 0.1%, 0.5% and 1% gaussian noise, respectively.
As can be seen from fig. 6, when the system does not have gaussian noise, the accuracy of the defocused phase difference method for detecting the sparse aperture sub-aperture Piston error is generally higher than the detection accuracy of the sub-aperture Piston phase difference method. As can be seen from fig. 7, 8 and 9, as the gaussian noise intensity increases, the accuracy of the Piston error detection of the sub-aperture Piston phase difference method is obviously higher than that of the defocus phase difference method; and the higher the Gaussian noise intensity is, the higher the computational stability of the sub-aperture Piston phase difference method is.
Therefore, when the sparse aperture optical system has no gaussian noise, the conventional defocused phase difference method can be adopted to measure the Piston error of the sparse aperture sub-aperture, which is an ideal situation and does not exist actually. When Gaussian noise exists, a sub-aperture Piston phase difference method can be selected to calculate the Piston error of the sparse aperture sub-aperture, the error detection precision is higher, and the calculation result is more stable along with the increase of the Gaussian noise intensity.
Claims (4)
1. A method for detecting a Piston error of a sparse aperture optical system is characterized by comprising the following steps:
(1) imaging a target through a sparse aperture optical system, obtaining an image at a focal planeg 1(ii) a Moving a certain sub-aperture in the sparse aperture optical system by a distance z along the optical axis direction, imaging the same target through the sparse aperture optical system again, and obtaining an image at a focal planeg 2；
(2) Respectively obtaining images according to Fourier transform relationg 1Andg 2corresponding system optical transfer functionS 1AndS 2；
(3) according to the imageg 1Andg 2and optical transfer functionS 1AndS 2establishing an objective function by using a phase difference methodE；
(4) Using an optimization algorithm to target functionsEObtaining an extreme value to obtain the Piston error of each sub-aperture of the sparse aperture optical system：
；
Wherein,Nthe number of sub-apertures of the sparse aperture optical system.
2. The method for detecting the Piston error of the sparse aperture optical system according to claim 1, wherein the method comprises the following steps: distance of sub-aperture moving along optical axis directionIn the range of 0.1λ～1λIn the above-mentioned manner,λis the wavelength.
3. The method for detecting the Piston error of the sparse aperture optical system according to claim 1, wherein the method comprises the following steps: a certain sub-aperture that moves in the optical axis direction is any one of the sub-apertures in the sparse aperture optical system.
4. The method for detecting the Piston error of the sparse aperture optical system according to claim 1, wherein the method comprises the following steps: the optimization algorithm comprises a genetic algorithm, a conjugate gradient method, a Newton method or a quasi-Newton method.
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