CN113686546B - An off-axis imaging system point spread function measurement method and modeling method - Google Patents

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

An off-axis imaging system point spread function measurement method and modeling method

technical field

The invention relates to the field of optical engineering, in particular to a method for measuring and modeling a point spread function of an off-axis imaging system.

Background technique

In optical detection methods such as deflectometry and Hartmann test, markers such as screen patterns and circular hole arrays cannot be accurately focused in the camera pattern. The spatially variable point spread function of the complex off-axis system affects the measurement accuracy and reliability. important factor. The traditional geometrical optics theory generally considers that the point spread function is the Fourier transform of the optical transfer function, and the line spread function is measured by edge imaging and rotated into a point spread function. However, this method assumes that the point spread function is fixed in the entire field of view and is rotationally symmetric, and this constraint does not hold for complex off-axis imaging systems. The researchers also proposed the star point method, which uses a dot array imaging to obtain the variation law of the actual point spread function with the position of the field of view. However, this method needs to process a special round hole template, and the size of the standard point cannot be changed, so it is difficult to correct the detection error caused by factors such as off-axis imaging and environmental interference.

In order to obtain the point spread function at any position of the field of view, it is necessary to establish a continuous function model for it. The paraxial imaging theory generally uses Seidel polynomials, which divide the primary aberration into different terms such as spherical aberration, coma, and astigmatism, and determine the quantitative relationship between the point spread function, the pupil and the field of view according to the coefficients of the terms. However, this relationship is difficult to use for complex off-axis optical systems and aspheric imaging systems. Later, researchers used functions to model and describe them. Computes the integral Huo moments of the point spread function, modeled with a double Gaussian function. However, the off-axis imaging system has serious components such as coma and astigmatism, which cause the point spread function to have no mirror image or rotational symmetry, which cannot be described by the double Gaussian function. Therefore, for complex optical components such as free-form surfaces, or optical systems that are seriously off-axis, it is necessary to establish a point spread function model with a stronger description ability.

SUMMARY OF THE INVENTION

In view of the above shortcomings, the present invention provides a measurement method and a modeling method for the point spread function of an off-axis imaging system, which can overcome the limitation that the traditional double Gaussian function cannot accurately describe the off-axis imaging, and improve the accuracy of complex asymmetric points. Modeling reliability of the spread function.

The technical scheme of the present invention is:

A method for measuring the point spread function of an off-axis imaging system, which uses a projection screen as a standard to display a circular spot array and realizes reliable measurement of the point spread function of each field of view position, which specifically includes the following steps:

S1: The screen is used to display the binarized circular spot array. After passing through the off-axis imaging system, the camera collects the pattern. The following formula is used to calculate the gradient at each pixel of the spot pattern, and the intensity I(i, j) of each point is replaced by its light intensity. gradient;

S2: Fit the pixel with the largest light intensity gradient as an ellipse, the ellipse curve is the contour line of the center area of the spot, and the center point of the ellipse (u ₀ , v ₀ ) is the center of the entire spot, and calculate the points outside the contour line (u, v 0 ) v) to the nearest point (u _n , v _n ) on the contour line, move (u, v) to a new point using the following formula, and obtain the point spread function diffuse speck corresponding to an ideal object point with a radius of 0.

(u',v')＝(u,v)-(u _n ,v _n )+(u ₀ ,v ₀ )

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 above measurement method, comprising the following steps:

S1: For each point spread function, a sloped normal function is used to fit,

where σ,κ ₁ ,κ ₂ ,α ₁ ,α ₂ ,ω are the parameters that determine the shape of the point spread function, and (i,j)=(u',v')-(u ₀ ,v ₀ ) is the inner speckle the relative coordinates of each pixel;

S2: Taking the pixel coordinates (u ₀ , v ₀ ) of the center of each spot as independent variables, the six parameters σ, κ ₁ , κ ₂ , α ₁ , α ₂ , ω are fitted to cubic functions respectively, and the point spread function can be obtained. The distribution law of p varies with space.

The invention uses the screen as a standard to display the characteristics of the circular spot, judges the contour line of the central area according to the gradient of the light intensity of the spot acquired by the camera, and shrinks the light intensity gradient outside the contour line to the center to obtain the point spread function diffused spot. Then, each parameter of the function expression is fitted as a continuous function of the pixel coordinates of the spot center, thereby realizing the analytical modeling of the asymmetric point spread function of the off-axis imaging system. It can better overcome the limitation that the traditional double Gaussian function cannot accurately describe off-axis imaging, and improve the modeling reliability of complex asymmetric point spread functions.

Description of drawings

Fig. 1 is the flow chart of point spread function measurement and fitting of the present invention;

Fig. 2 is the circular spot array of the screen display of the present invention;

Fig. 3 is the circular spot pattern that the present invention measures;

Fig. 4 is the measurement and fitting process of a circular spot of the present invention;

FIG. 5 is a comparison diagram of actual measured spots, projected spots and light intensity gradient curves of the present invention.

Detailed ways

The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings, so as to fully understand the purpose, characteristics and effects of the present invention.

The purpose of the present invention is to provide an accurate point spread function measurement and modeling method for a large aberration off-axis imaging system, and to clarify the law of the point spread function changing with the position of the field of view. The specific steps of its realization are:

1) In the large aberration off-axis imaging system, the projection screen is used as the standard to display the pattern of the binarized circular spot feature array. The diameter of the spot is smaller than 1/3 of the array period, but larger than the width of the diffuse spot. After passing through the off-axis imaging system, the camera collects the pattern, and calculates the gradient of each pixel of the speckle pattern:

And replace the intensity I(i,j) of each point with its light intensity gradient g(i,j).

2) Fit the pixel with the largest light intensity gradient as an ellipse:

a(uu ₀ ) ² +b(uu ₀ )(vv ₀ )+c(vv ₀ ) ² =1

The elliptic curve is regarded as the contour line of the central area of the spot, the center point of the ellipse (u ₀ , v ₀ ) is taken as the center of the entire spot, and the contour line shrinks to the center point (u ₀ , v ₀ ), and each point outside the contour (u, v 0 ) v) Calculate the closest point (u _n , v _n ) on the contour line, move (u, v) to the new point:

(u',v')＝(u,v)-(u _n ,v _n )+(u ₀ ,v ₀ )

Thus, the point spread function speckle corresponding to an ideal object point with a radius of 0 is obtained.

3) The point spread function obtained for each spot is fitted with a sloped normal function:

where σ,κ ₁ ,κ ₂ ,α ₁ ,α ₂ ,ω are the parameters that determine the shape of the point spread function, and (i,j)=(u',v')-(u ₀ ,v ₀ ) is the inner speckle The relative coordinates of each pixel.

2) Taking the pixel coordinates (u ₀ , v ₀ ) of the center of each spot as independent variables, fit the six parameters σ, κ ₁ , κ ₂ , α ₁ , α ₂ , ω as cubic functions respectively

The distribution law of the point spread function p with the change in space can be obtained, thereby realizing the modeling of the space-varying asymmetric point spread function of the off-axis imaging system.

Example: The measurement and modeling process of the point spread function is shown in Figure 1 . First, a 6×6 circular spot array is displayed in the middle area of the screen with a pixel count of 1920×1080, where the period of the circular spot is 150 pixels and the diameter is 30 pixels. The pattern captured by the camera is shown in Figure 3. The method in the present invention is used for fitting modeling, and one of the spots is selected to display the processing process, as shown in FIG. 4 . In Figure 4, (a) is the display spot, (b) is the measurement spot, (c) is the light intensity gradient, (d) is the elliptical outline, (e) is the shrinking to the diffuse spot, and (f) is the fitting point spread function. The light intensity gradient at each pixel of the circular spot is calculated, and the ellipse outline is obtained according to the maximum gradient, as shown in Figure 4(d). Shrink it to the middle to get the diffuse speckle of the point spread function, which is then fitted with the proposed oblique normal function, as shown in Fig. 4(f). The results show that the 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, however, the present invention is not limited thereto, and any changes that can be conceived by those skilled in the art should fall within the protection 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 calculated_n,v_n) 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)-(u_n,v_n)+(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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