CN112903121B - Wavefront detection method based on cross iterative automatic focusing - Google Patents
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Abstract
The invention discloses a wavefront detection method based on cross iterative automatic focusing. The method optimizes the defocus distance by using an analytic gradient formula to automatically determine the defocus position, overcomes the problems of inaccurate defocus position determination caused by inaccurate wavefront and inaccurate wavefront reconstruction caused by uncertain defocus position by using a cross iteration method, and optimizes the defocus distance, wavefront amplitude and phase of the same target function to accurately reconstruct the defocus position and wavefront error. The method realizes the accurate determination of the large defocus errors of the multiple images, and realizes the accurate reconstruction of the wavefront under the condition of uncertain defocus positions without additionally constructing a target function.
Description
Technical Field
The invention relates to the technical field of optical measurement and imaging, in particular to a wavefront detection method based on cross iterative automatic focusing.
Background
The computed imaging greatly changes the mode seen in the traditional imaging, overcomes the defect of incomplete imaging of the traditional imaging system through the post-processing of a computer, and reduces the size and the weight of the imaging system. Coherent diffraction imaging is one implementation of computational imaging. Coherent diffraction imaging is a quantitative phase imaging mode based on an iterative method; collecting a diffraction image on a focal plane or a defocusing plane by using an image sensor; repeatedly and iteratively calculating by using Fourier transform and inverse Fourier transform to obtain the amplitude and the phase of the wavefront or the image to be detected; the processing of the amplitude or the support domain in the iteration process is similar to the mapping to the acquisition surface or the surface to be detected, and when the condition of the intensity acquisition surface and the condition of the surface to be detected are both satisfied, the wave front reconstruction is completed. Coherent diffraction imaging is further generally referred to as phase recovery. The phase recovery is a method for realizing wavefront phase reconstruction by using diffraction intensity based on Fourier transform and inverse Fourier transform, the device is very simple, and under the simplest condition, the phase recovery wavefront detection device based on the phase recovery can realize the wavefront reconstruction only by a light source, an element to be detected and an image sensor. The phase recovery can be divided into a transverse phase difference method (sub-aperture splicing) and an axial phase difference method according to different positions of the used diffraction spot, and the axial phase difference method is simple to operate and can meet the requirements of a common imaging system, so that the method is widely applied to the aspects of optical imaging, detection, adaptive optics and the like. The axial phase difference method is to collect a plurality of images on a focal plane and a defocusing plane, then sequentially use light intensity images collected at different positions in a phase recovery algorithm, and iterate repeatedly until the algorithm converges to realize wavefront reconstruction.
However, the axial phase difference method is very sensitive to the determination of the defocus position, especially to the relative position between different defocus planes, and generally a precise guide rail with high precision is selected to move the image sensor to collect diffraction spots, which causes the whole device to be very expensive, and in some application situations, such as in-situ detection, it is difficult to place the precise guide rail, which causes the defocus position to be very difficult to determine.
Disclosure of Invention
The invention aims to provide a wavefront detection method based on cross iterative auto-focusing aiming at the defects of the prior art, so as to solve the wavefront reconstruction error caused by the inaccuracy of the defocusing position in the axial phase difference method, reduce the cost of the whole set of device and replace an expensive precision displacement device with an algorithm.
The purpose of the invention is realized by the following technical scheme:
a wavefront detection method based on cross iterative auto-focusing is provided, wherein a beam expander, a flat plate to be detected, a convergent lens and an image sensor are sequentially arranged on an emergent light path of a laser, and the method comprises the following steps:
s1: moving the image sensor, and collecting n defocused light spots containing the wavefront error of the flat plate to be detected at different defocused distances;
s2: respectively setting the focal length s, the caliber D and the nominal defocusing position z of each defocusing light spot of the converging lenskStep for optimizing defocusing positionzStep of phase optimizationphaseAmplitude optimization stepampThe total iteration number N of wave-front detection, the total defocusing optimization iteration number N _ z, an iteration judgment threshold value M and the initial iteration number of wave-front detection1 as a generation count i and g as an initial estimation value of the wavefront to be measured1(x, y), wherein (x, y) is the coordinate of the flat plate to be detected;
s3: using the diffraction propagation calculation value U of the defocused light spot and the estimated value of the wavefront to be measuredkConstructing an optimized objective function
Where u, v are the coordinates at the off-focus spot position, IkIs at an out-of-focus position zkOut-of-focus spot, U, of the spotkIs the wavefront to be measured at the out-of-focus position zkThe integral of diffraction at (d); wk(u, v) is weight distribution, which is used to remove pixel points and dead pixels with low signal-to-noise ratio on the image sensor;
s4, when i is equal to 1, optimizing the out-of-focus position for the diffraction spots at all positions by using an out-of-focus position optimization algorithm, and when i is equal to 1, optimizing the out-of-focus position for the kth diffraction spot by using an out-of-focus position optimization algorithm; the defocus position optimization algorithm is realized by the following substeps:
s4.1: setting the initial iteration count j of the defocusing position to be 1, and inputting the defocusing position zk;
S4.2: calculating the optimized gradient of the defocus position
Wherein the content of the first and second substances,andrespectively representing a diffraction calculation operator and an inverse diffraction calculation operator,representing the complex amplitude of the diffraction calculation from the plane to be measured to the image acquisition plane,representing the complex amplitude calculated from the image acquisition surface inverse diffraction to the surface to be measured, representing taking complex conjugate, k 2 pi/lambda is wave number, Im () represents taking imaginary part, delta zkRepresenting the gradient of defocus positions;
s4.3: updating the defocus position using the following equation
zk=zk+stepzΔzk
S4.4: if j is less than N _ z, j is made to be j +1, and S4.2 is returned, otherwise, the iteration is ended, and the optimal out-of-focus position z is obtainedk;
S5: calculating wavefront optimized phase and amplitude gradients using the following equations
Where Re () stands for imaginary part, deltaa for amplitude gradient,representing the phase gradient.
S6: updating the amplitude and the phase of the wavefront to be detected, and obtaining the complex amplitude distribution of the flat plate to be detected by using a gradient optimization method;
s7: if mod ((i +1)/M) ═ k, return to S4;
s8: if i is less than N _ iter, let k be mod ((i +1)/N), i be i +1, and return to S5, otherwise end iteration, obtain the wavefront to be measured that satisfies all out-of-focus light spot constraints;
s9: and removing noise influence on the wavefront to be detected obtained in the step S8 by using polynomial fitting, so as to obtain real wavefront error distribution.
Further, to facilitate flexible sampling, the diffraction calculation operators in S4.2 and S5 preferentially use two-step fresnel diffraction.
Further, the gradient optimization method in S6 adopts a gradient descent method, and the calculation formula is as follows:
The invention has the following beneficial effects:
the method optimizes the defocusing position by using an analytic gradient method, and realizes the accurate determination of high-speed large defocusing errors. The nonlinear optimization method is utilized to realize the accurate reconstruction of the amplitude and the phase of the surface to be detected, the application range is expanded, and the axial phase difference method can be used for not only wavefront detection but also image reconstruction. The cross iterative optimization solves the problem of inaccurate reconstruction of the defocus error and the wavefront error caused by mutual influence.
Drawings
FIG. 1 is a schematic diagram of an apparatus for wavefront measurement based on cross-iterative auto-focusing according to the present invention.
FIG. 2 is a flow chart of a wavefront sensing method based on cross-iterative auto-focusing of the present invention.
FIG. 3 is a flow chart of the auto-focus optimization method of the present invention.
FIG. 4 is a diagram of the results of the wavefront sensing method based on cross-iterative auto-focusing of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and preferred embodiments, and the objects and effects of the present invention will become more apparent, it being understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.
As shown in fig. 1 to 3, in the wavefront detection method based on cross iterative auto-focusing of the present invention, a beam expander 2, a flat plate 3 to be measured, a converging lens 4, and an image sensor 5 are sequentially arranged on an emergent light path of a laser 1, and the method includes the following steps:
s1: moving the image sensor 5, and acquiring n defocused light spots containing the wavefront error of the flat plate to be detected at different defocused distances;
s2: respectively setting the focal length s, the caliber D and the nominal defocusing position z of each defocusing light spot of the convergent lenskStep for optimizing defocusing positionzStep of phase optimizationphaseAmplitude optimization stepampThe total iteration number N of wavefront detection, the total defocusing optimization iteration number N _ z, an iteration judgment threshold value M, the initial iteration count i of wavefront detection being 1, and the initial estimated value g of wavefront to be detected1(x, y), wherein (x, y) is the coordinate of the flat plate to be detected;
s3: calculating value U of diffraction propagation by using estimated values of defocused light spots and wavefront to be measuredkConstructing an optimized objective function
Where u, v are the coordinates at the off-focus spot position, IkIs at an out-of-focus position zkOut-of-focus spot, U, of the spotkIs the wavefront to be measured at the out-of-focus position zkThe integral of diffraction at (d); wk(u, v) is a weight distribution for removing the imagePixel points and dead pixels on the sensor with low signal-to-noise ratio;
s4, when i is equal to 1, optimizing the out-of-focus position for the diffraction spots at all positions by using an out-of-focus position optimization algorithm, and when i is equal to 1, optimizing the out-of-focus position for the kth diffraction spot by using an out-of-focus position optimization algorithm; the defocus position optimization algorithm is realized by the following substeps:
s4.1: setting the initial iteration count j of the defocusing position to be 1, and inputting the defocusing position zk;
S4.2: calculating the optimized gradient of the defocus position
Wherein the content of the first and second substances,andrespectively representing a diffraction calculation operator and an inverse diffraction calculation operator,representing the complex amplitude of the diffraction calculation from the plane to be measured to the image acquisition plane,representing the complex amplitude calculated from the image acquisition surface inverse diffraction to the surface to be measured, representing taking complex conjugate, k 2 pi/lambda is wave number, Im () represents taking imaginary part, delta zkRepresenting the gradient of defocus positions.
S4.3: updating the defocus position using the following equation
zk=zk+stepzΔzk
S4.4: if j is less than N _ z, j is made to be j +1, and S4.2 is returned, otherwise, the iteration is ended, and the optimal out-of-focus position z is obtainedk;
S5: calculating wavefront optimized phase and amplitude gradients using the following equations
Where Re () stands for imaginary part, deltaa for amplitude gradient,representing the phase gradient.
S6: updating the amplitude and the phase of the wavefront to be detected, and obtaining the complex amplitude distribution of the flat plate to be detected by using a gradient optimization method;
s7: if mod ((i +1)/M) ═ k, return to S4;
s8: if i is less than N _ iter, let k be mod ((i +1)/N), i be i +1, and return to S5, otherwise end iteration, obtain the wavefront to be measured that satisfies all out-of-focus light spot constraints;
s9: and removing noise influence on the wavefront to be detected obtained in the step S8 by using polynomial fitting, so as to obtain real wavefront error distribution.
To facilitate flexible sampling, the diffraction calculation operators in S4.2 and S5 preferably use two-step fresnel diffraction.
The gradient optimization method in S6 adopts a gradient descent method, and the calculation formula is as follows:
A specific example of the method of the present invention is given below to illustrate the technical effect of the method
Here, s is 1079.41mm, z is selected as the focal length1,z2,z3=[-10,-15,20]mm, the caliber D is 22.9mm, and the defocusing position optimization step lengthz-0.00004, step of phase optimizationphaseAmplitude optimization step-0.4 ═ 0.4ampThe total iteration number N of wavefront detection is 5000, the total defocus optimization iteration number N _ z is 300, and the iteration judgment threshold M is 50.
In the embodiment, three defocusing diffraction images are collected to carry out wave front phase and amplitude reconstruction, the defocusing errors of the three defocusing light spots are respectively +3, + 3-3 mm, the selected diffraction calculation model is a two-step Fresnel diffraction model, and fig. 4 is a recovery result graph of the method provided by the invention. It can be seen from the figure that under the condition of defocusing error, the amplitude and the phase of the wavefront can be accurately recovered, and the recovery result is consistent with the morphology profile of the true value.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and although the invention has been described in detail with reference to the foregoing examples, it will be apparent to those skilled in the art that various changes in the form and details of the embodiments may be made and equivalents may be substituted for elements thereof. All modifications, equivalents and the like which come within the spirit and principle of the invention are intended to be included within the scope of the invention.
Claims (3)
1. A wave-front detection method based on cross iterative auto focusing is provided, a beam expander, a flat plate to be measured, a convergent lens and an image sensor are arranged on an emergent light path of a laser in sequence, and the method is characterized by comprising the following steps:
s1: moving the image sensor, and collecting n defocused light spots containing the wavefront error of the flat plate to be detected at different defocused distances;
s2: respectively setting the focal length s, the caliber D and the nominal defocusing position z of each defocusing light spot of the converging lenskStep for optimizing defocusing positionzStep of phase optimizationphaseAmplitude optimization stepampThe total iteration number N of wavefront detection, the total defocusing optimization iteration number N _ z, an iteration judgment threshold value M, the initial iteration count i of wavefront detection being 1, and the initial estimated value g of wavefront to be detected1(x, y), wherein (x, y) is the coordinate of the flat plate to be detected;
s3: using the diffraction propagation calculation value U of the defocused light spot and the estimated value of the wavefront to be measuredkConstructing an optimized objective function
Where u, v are the coordinates at the off-focus spot position, IkIs at an out-of-focus position zkOut-of-focus spot, U, of the spotkIs the wavefront to be measured at the out-of-focus position zkThe integral of diffraction at (d); wk(u, v) is weight distribution, which is used to remove pixel points and dead pixels with low signal-to-noise ratio on the image sensor;
s4, when i is equal to 1, optimizing the out-of-focus position for the diffraction spots at all positions by using an out-of-focus position optimization algorithm, and when i is equal to 1, optimizing the out-of-focus position for the kth diffraction spot by using an out-of-focus position optimization algorithm; the defocus position optimization algorithm is realized by the following substeps:
s4.1: setting the initial iteration count j of the defocusing position to be 1, and inputting the defocusing position zk;
S4.2: calculating the optimized gradient of the defocus position
Wherein the content of the first and second substances,andrespectively representing a diffraction calculation operator and an inverse diffraction calculation operator,representing the complex amplitude of the diffraction calculation from the plane to be measured to the image acquisition plane,representing the complex amplitude calculated from the image acquisition surface inverse diffraction to the surface to be measured, representing taking complex conjugate, k 2 pi/lambda is wave number, Im () represents taking imaginary part, delta zkRepresenting the gradient of defocus positions;
s4.3: updating the defocus position using the following equation
zk=zk+stepzΔzk
S4.4: if j is<N _ z, making j equal to j +1, and returning to S4.2, otherwise ending iteration to obtain the optimal out-of-focus position zk;
S5: calculating wavefront optimized phase and amplitude gradients using the following equations
s6: updating the amplitude and the phase of the wavefront to be detected, and obtaining the complex amplitude distribution of the flat plate to be detected by using a gradient optimization method;
s7: if mod ((i +1)/M) ═ k, return to S4;
s8: if i is less than N, making k equal to mod ((i +1)/N), i equal to i +1, and returning to S5, otherwise, ending iteration, and obtaining the wavefront to be measured which meets all the defocused light spot constraints;
s9: and removing noise influence on the wavefront to be detected obtained in the step S8 by using polynomial fitting, so as to obtain real wavefront error distribution.
2. The wavefront sensing method based on cross-iterative auto-focusing of claim 1, wherein for flexible sampling, the diffraction calculation operators in S4.2 and S5 use two-step fresnel diffraction preferentially.
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CN110375964A (en) * | 2019-07-18 | 2019-10-25 | 浙江大学 | It is a kind of based on extension how the wavefront error detection device and detection method of bohr-Zernike polynominal optimization phase recovery |
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