CN113686546B - Measuring method and modeling method for point spread function of off-axis imaging system - Google Patents
Measuring method and modeling method for point spread function of off-axis imaging system Download PDFInfo
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- CN113686546B CN113686546B CN202010424675.4A CN202010424675A CN113686546B CN 113686546 B CN113686546 B CN 113686546B CN 202010424675 A CN202010424675 A CN 202010424675A CN 113686546 B CN113686546 B CN 113686546B
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Abstract
The invention relates to the field of optical engineering, in particular to a measuring method and a modeling method of a point spread function of an off-axis imaging system. The measuring method adopts a screen as a standard substance to display circular spot characteristics, judges the contour line of a central area according to the light intensity gradient of spots acquired by a camera, shrinks the light intensity gradient outside the contour line to the center to obtain point spread function diffuse spots, adopts an oblique normal distribution function to carry out fitting, and then fits each parameter of a function expression into a continuous function of the pixel coordinate of the center of the spot, thereby realizing the analytical modeling of the asymmetric point spread function of the off-axis imaging system. The measuring method and the modeling method can better overcome the limitation that the traditional double Gaussian function can not accurately describe off-axis imaging, and improve the reliability of modeling the complex asymmetric point spread function.
Description
Technical Field
The invention relates to the field of optical engineering, in particular to a measuring method and a modeling method of a point spread function of an off-axis imaging system.
Background
In optical detection methods such as deflection, Hartmann inspection and the like, markers such as screen patterns, circular hole arrays and the like cannot be focused accurately in camera patterns, and a space-variant point spread function of a complex off-axis system is an important factor influencing measurement precision and reliability. The traditional geometrical optics theory generally considers that a point spread function is Fourier transform of an optical transfer function, and a line spread function is measured through edge imaging and is rotated into the point spread function. However, the method assumes that the point spread function is fixed and invariant in the whole field of view and is rotationally symmetric, and the constraint condition is not satisfied for a complex off-axis imaging system. Researchers also put forward a star point method, and by adopting dot array imaging, the change rule of the actual point spread function along with the position of a view field can be obtained. However, the method needs to process a special circular hole template, and the size of the standard object point cannot be changed, so that the detection error caused by factors such as off-axis imaging and environmental interference is difficult to correct.
In order to obtain a point spread function of any field position of the point, a continuous function model needs to be established for the point spread function. The paraxial imaging theory generally adopts Seidel polynomial, divides the primary aberration into different terms such as spherical aberration, coma aberration, astigmatism and the like, and determines the quantitative relation between a point spread function and a pupil and a field of view according to the coefficients of the terms. But this relationship is difficult to use for complex off-axis optical systems and aspheric imaging systems, and later researchers have used functions for modeling descriptions. And calculating the Hu integral moment of the point spread function, and modeling by using a double Gaussian function. However, the off-axis imaging system has serious comatic aberration, astigmatism and other components, so that the point spread function has no mirror image or rotational symmetry and cannot be described by a double Gaussian function. Therefore, for an optical system including a complex optical element such as a free-form surface or a severe off-axis, a point spread function model with stronger description capability needs to be established.
Disclosure of Invention
Aiming at the defects, the invention provides a measuring method and a modeling method of a point spread function of an off-axis imaging system, which can overcome the limitation that the traditional double Gaussian function cannot accurately describe off-axis imaging and improve the reliability of modeling of a complex asymmetric point spread function.
The technical scheme of the invention is as follows:
a method for measuring a point spread function of an off-axis imaging system adopts a projection screen as a standard object to display a circular spot array, and realizes reliable measurement of the point spread function of each view field position, and specifically comprises the following steps:
s1: a screen is adopted to display a binary circular spot array, a camera collects a pattern after passing through an off-axis imaging system, the gradient of each pixel of the spot pattern is calculated by using the following formula, and the intensity I (I, j) of each point is replaced by the light intensity gradient;
s2: fitting the pixel with the maximum light intensity gradient to an ellipse, wherein the ellipse curve is the contour line of the central area of the spot and the central point (u) of the ellipse0,v0) As the center of the entire blob, the points (u, v) outside the contour line to the closest point (u) on the contour line are calculatedn,vn) The point spread function diffuse spot corresponding to the ideal object point with radius 0 is obtained by moving (u, v) to a new point by the following formula.
(u',v')＝(u,v)-(un,vn)+(u0,v0)
The diameter of the spot is smaller than the array period and larger than the width of the diffuse spot.
A modeling method for realizing the point spread function of an off-axis imaging system by using the measuring method comprises the following steps:
s1: fitting each point diffusion function by adopting an oblique normal function,
wherein σ, κ1,κ2,α1,α2Where ω is a parameter determining the shape of the point spread function, where (i, j) — (u ', v') - (u)0,v0) Relative coordinates of each pixel in the diffuse spot;
s2: in each spot center pixel coordinate (u)0,v0) For independent variables, six parameters σ, κ1,κ2,α1,α2And omega is respectively fitted to a cubic function, and the distribution rule of the point spread function p along with the space change can be obtained.
The method adopts a screen as a standard substance to display the circular spot characteristics, judges the contour line of a central area according to the light intensity gradient of the spots acquired by a camera, shrinks the light intensity gradient outside the contour line to the center to obtain a point spread function diffuse spot, adopts an oblique normal distribution function to perform fitting, and then fits each parameter of a function expression into a continuous function of the center pixel coordinate of the spot, thereby realizing the analytical modeling of the asymmetric point spread function of the off-axis imaging system. The method can better overcome the limitation that the traditional double Gaussian function can not accurately describe off-axis imaging, and improve the modeling reliability of the complex asymmetric point spread function.
Drawings
FIG. 1 is a flow chart of point spread function measurement and fitting according to the present invention;
FIG. 2 is a circular spot array of a screen display according to the present invention;
FIG. 3 illustrates a circle spot pattern measured according to the present invention;
FIG. 4 is a measurement and fitting process of a circular spot according to the present invention;
FIG. 5 is a comparison graph of measured spots, projected spots and intensity gradient curves of the present invention.
Detailed Description
The conception, specific structure and technical effects of the present invention will be further described in conjunction with the accompanying drawings to fully understand the purpose, characteristics and effects of the present invention.
The invention aims to provide an accurate point spread function measuring and modeling method for a large aberration off-axis imaging system, and the rule that the point spread function changes along with the position of a field of view is defined. The method comprises the following specific steps:
1) in a large aberration off-axis imaging system, a projection screen is used as a standard substance to display a binary circular spot characteristic array pattern. The spot diameter is less than 1/3 of the array period, but greater than the width of the diffuse spot. The pattern is collected by the camera after passing through the off-axis imaging system, and the gradient of each pixel of the speckle pattern is calculated:
and the intensity I (I, j) of each spot is replaced by its intensity gradient g (I, j).
2) The pixel with the greatest intensity gradient is fitted to an ellipse:
a(u-u0)2+b(u-u0)(v-v0)+c(v-v0)2＝1
the elliptic curve is regarded as the contour line of the central region of the spot, the elliptic central point (u)0,v0) As the center of the entire blob, the contour lines shrink to the center point (u)0,v0) Calculating the closest point (u) on the contour line for each point (u, v) outside the contourn,vn) Move (u, v) to a new point:
(u',v')＝(u,v)-(un,vn)+(u0,v0)
thereby obtaining the point spread function diffuse spot corresponding to the ideal object point with the radius of 0.
3) And (3) fitting the point spread function obtained by each spot by respectively adopting an oblique normal function:
wherein σ, κ1,κ2,α1,α2Where ω is a parameter determining the shape of the point spread function, where (i, j) — (u ', v') - (u)0,v0) Is the relative coordinates of each pixel within the diffuse spot.
2) With each spot center pixel coordinate (u)0,v0) For independent variables, six parameters σ, κ1,κ2,α1,α2Omega being fitted to cubic functions respectively
The distribution rule of the point spread function p along with the space change can be obtained, and therefore modeling of the space-variant asymmetric point spread function of the off-axis imaging system is achieved.
Example (b): the measurement and modeling flow of the point spread function is shown in fig. 1. First, a 6 × 6 circular spot array is displayed in the middle area of a screen with the number of pixels 1920 × 1080, wherein the circular spot has a period of 150 pixels and a diameter of 30 pixels. The pattern captured by the camera is shown in fig. 3. Fitting modeling is carried out by adopting the method of the invention, and one of the spots is taken to display the processing process, as shown in FIG. 4. In FIG. 4, (a) shows the circular spot, (b) measures the circular spot, (c) shows the intensity gradient, (d) shows the elliptical profile, (e) shows the shrinkage as the diffuse spot, and (f) shows the fitted point spread function. The light intensity gradient at each pixel of the circular spot is calculated, and an elliptical profile is obtained from the position where the gradient is maximum, as shown in fig. 4 (d). The point spread function is obtained by contracting the point spread function towards the middle, and then fitting is carried out by adopting the proposed oblique normal function, as shown in fig. 4 (f). The results show that this function is suitable for asymmetric point spread function modeling of such large aberration systems.
The above disclosure is only an embodiment of the present invention, but the present invention is not limited thereto, and any variations that can be considered by those skilled in the art are within the scope of the present invention.
Claims (1)
1. A measuring method of a point spread function of an off-axis imaging system is characterized in that a projection screen is used as a standard object to display a circular spot array, and reliable measurement of the spread function of each position is realized, and the method specifically comprises the following steps:
s1: displaying a binary circular spot array by using a screen, wherein the diameter of the circular spot is less than 1/3 of the array period;
s2, collecting the pattern by the camera after the off-axis imaging system, wherein each round spot is correspondingly a fuzzy image spot, calculating the light intensity gradient of each pixel of the pattern by using the following formula, wherein I (u, v) is the light intensity of each pixel, and (u, v) is the pixel coordinate:
s3: according to the light intensity gradient distribution of each image spot, fitting the pixel with the maximum light intensity gradient value into an ellipse, wherein the ellipse curve is the contour line of the central area of the image spot and the central coordinate (u) of the ellipse0,v0) As the center of the entire image patch, the coordinates (u, v) of each pixel (u, v) outside the contour line to the nearest pixel on the contour line are calculatedn,vn) Moving each pixel (u, v) outside the contour line to the center of the image spot by using the following formula to obtain a point spread function diffuse spot (u ', v') corresponding to an ideal screen object point with the radius of 0:
(u',v')＝(u,v)-(un,vn)+(u0,v0)
s4, fitting each point diffusion function diffuse spot by adopting a skewed normal function:
wherein σ, κ1,κ2,α1,α2Where ω is a parameter determining the shape of the point spread function, where (i, j) — (u ', v') - (u)0,v0) Relative coordinates of each pixel in the diffuse spot;
s5: with all the acquired diffuse spot center coordinates (u)0,v0) As independent variable, six parameters σ, κ for fitting the diffuse speckle1,κ2,α1,α2ω is regarded as a dependent variable, and is fitted to (u) respectively0,v0) And obtaining a distribution rule of the point spread function p (i, j) along with the change of the space by a cubic function.
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