A point spread function calculation method and system

Abstract

The point spread function calculation method and system provided in the present application construct an optical analysis model, obtain the image plane intersection point in the optical analysis model, obtain the intersection point of the lower edge light of the specified field of view of the optical analysis model and the last optical surface as the boundary of the tracing grid, establish ray tracing grid points, and perform reverse ray tracing based on the image plane intersection point and the grid point to obtain the pupil function. Compared with the traditional method that needs to find the entrance pupil boundary and involves complex logical processes, the present application will avoid the complex entrance pupil, exit pupil and their boundary determination process, and directly calculate the ray tracing boundary based on the surface aperture. The calculation process is closer to the real physical process, with low implementation complexity and good stability. Through reverse ray tracing, the calculation error introduced by Fourier grid distortion and the approximation error of the traditional Fraunhofer propagation method are avoided, and an accurate ideal point light source diffraction image, that is, the point spread function of the optical system, can be obtained in the image space.

Description

Technical Field

[0001] The present application relates to the technical field of optical system image quality analysis, and in particular to a point spread function calculation method and system. Background Art

[0002] The Point Spread Function (PSF) describes an optical system's ability to resolve a point light source. Because a point light source will form an enlarged image point after passing through any optical system due to aberrations and diffraction, calculating the system's PSF can accurately predict the system's imaging quality.

[0003] Currently, the traditional method for calculating the point spread function uses Fraunhofer diffraction theory. A beam of light is emitted from a light source, with each ray directed to a grid coordinate point on the entrance pupil plane of the optical system. This beam of light is then traced to the exit pupil sphere, and the optical path length as it passes through each surface is recorded in sequence. This is used to obtain an optical path difference matrix, forming a pupil function representing the light field distribution on the exit pupil sphere. Finally, the image formed by the pupil function after Fraunhofer diffraction onto the image plane is calculated, which is the point spread function that includes the effects of aberrations and aperture diffraction.

[0004] To accurately calculate the point spread function of general optical systems, the traditional method uses Fraunhofer diffraction theory. However, this method has the following problems:

[0005] Fraunhofer diffraction is calculated using the Fourier transform, which requires a uniform grid of data point coordinates. Traditional methods generally require uniform sampling at the entrance pupil. By the time light reaches the exit pupil, the sampling grid is no longer uniform due to pupil aberrations. Even if a uniform grid is restored through interpolation, fitting residuals cannot be avoided, and the resulting errors are particularly severe in systems with large aberrations. Fraunhofer diffraction is essentially a second-order approximation of the diffraction integral, generally applicable to systems with Fresnel numbers F < 1, but cannot accurately describe systems with large Fresnel numbers. The center of the exit pupil sphere is located at the ideal image point. When analyzing off-axis fields of view, the exit pupil sphere is tilted with respect to the optical axis, and the principal ray is not perpendicular to the image plane. The point spread function obtained by traditional methods is actually the projection of the true point spread function onto the xOy plane. Therefore, rigorous methods are needed to replace traditional methods and accurately calculate the point spread function. Summary of the Invention

[0006] In view of this, it is necessary to provide a point spread function calculation method and system for accurately calculating the point spread function to address the defects in the prior art.

[0007] To solve the above problems, this application adopts the following technical solutions:

[0008] One of the purposes of this application is to provide a method for calculating a point spread function, comprising the following steps:

[0009] Construct optical analysis models;

[0010] Obtaining an image plane intersection point in the optical analysis model;

[0011] Obtaining the intersection of the lower edge ray of the specified field of view of the optical analysis model and the last optical surface as the boundary of the tracing grid, and establishing the ray tracing grid points;

[0012] Perform reverse ray tracing according to the image plane intersection points and grid points to obtain a pupil function;

[0013] The point spread function is obtained according to the pupil function.

[0014] In some embodiments, the step of constructing an optical analysis model specifically includes the following steps: constructing an optical analysis model in imaging optical system analysis software based on the optical system, and defining surface properties of each optical component.

[0015] In some embodiments, the surface properties include the shape, position, material, eccentricity / tilt, and refraction of each surface.

[0016] In some embodiments, the step of obtaining the image plane intersection point in the optical analysis model specifically includes the following steps:

[0017] In the optical analysis model, the main ray is traced forward in a specified object field of view, the coordinates of the intersection of the ray and the image plane are calculated, and the image plane intersection point is obtained, and the angle between the main ray and the z-axis is recorded as β.

[0018] In some embodiments, in the step of obtaining the intersection position of the edge ray of the optical analysis model and the last optical surface of the optical system as the boundary of the tracing grid and establishing the ray tracing grid points, specifically:

[0019] By forward tracing the edge ray in the specified object field of view, the intersection of the ray and the last surface of the optical analysis model is calculated, and the intersection is used as the grid point, and the grid point is used as the boundary of the tracing grid, where the boundary width in the meridian direction is D T+ , the width of the lower boundary in the meridian direction is -D T- , the boundary width in the sagittal direction is D S+ , the width of the lower boundary in the sagittal direction is -D S- , take max(D T+ ,D T- ,D S+ ,D S- ) is the height of the semi-tracing grid boundary.

[0020] In some embodiments, the + axis is taken as the positive direction, the maximum value of the vector height of the last surface of the optical system is taken as the origin of the tracing grid, a plane perpendicular to the z axis is established, and the tracing grid is set, and the distance between the z coordinate of the tracing grid and the image plane is d.

[0021] In some embodiments, the tracing grid is set to (2N+1)×(2N+1) squares, where N is a positive integer not less than 16.

[0022] In some embodiments, the step of obtaining the pupil function according to the image point and the intersection point is specifically as follows:

[0023] The image plane intersection point is taken as the starting point, and the direction of the line connecting the image plane intersection point and the grid point is taken as the direction vector (k x ,k y ,k z ), perform reverse ray tracing;

[0024] In the reverse ray tracing process, the distance OPL(i,j) traveled by each surface is recorded in turn. k , where: i is the horizontal coordinate of the tracing grid, j is the vertical coordinate of the tracing grid, k is the tracing surface number and the corresponding refractive index n k , used to calculate the wavefront aberration OPL(i,j) of the optical system,

[0025]

[0026] After the reverse ray traces to the first surface and enters the object space, if the angle between the direction of the edge ray of the tracing grid and the main ray is less than a threshold Δ, it can be considered to be parallel and can be traced for any distance; if the angle is greater than the threshold Δ, it should be traced to an object point at a finite distance;

[0027] During the reverse ray tracing process, for the light rays that are blocked by the aperture of the optical system and cannot be traced further, the coordinates of the blocked light rays in the tracing grid are recorded and recorded as Mask(i,j);

[0028] The central ray (N+1, N+1) of the tracing grid is taken as the principal ray, and the wavefront aberration OPD(i, j) of the other rays of the grid relative to the principal ray is calculated as follows: OPD(i, j) = PL(i, j) - PL(N+1, N+1);

[0029] The pupil function is obtained from the wave aberration, and the pupil function PF(x,y) is expressed as: Wherein, without considering polarization, A(x,y)≡1, λ is the wavelength of light.

[0030] In some embodiments, the step of obtaining the point spread function according to the pupil function specifically includes the following steps:

[0031] By changing the main ray angle β of the tracing grid direction vector, the propagation factor γ(x,y) is obtained, γ(x,y)=(k z cosβ-k x sinβ);

[0032] The light field propagating from the pupil light field to the image plane is calculated by the angular spectrum method. in, is the Fourier transform, is the inverse Fourier transform;

[0033] According to the optical transfer function OTF of the optical system calculated by PSF, And modulation transfer function MTF, MTF = |OTF|.

[0034] A second object of this application is to provide a point spread function calculation system, comprising:

[0035] A model building unit, used for building an optical analysis model;

[0036] An image plane intersection point acquisition unit, configured to acquire image plane intersection points in the optical analysis model;

[0037] A grid point acquisition unit, configured to acquire the intersection of the lower edge ray of the specified field of view of the optical analysis model and the last optical surface as the boundary of the tracing grid, and establish a ray tracing grid point;

[0038] A pupil function acquisition unit, configured to perform reverse ray tracing based on the image plane intersection points and the grid points to obtain a pupil function;

[0039] A point spread function calculation unit is configured to obtain the point spread function according to the pupil function.

[0040] This application adopts the above technical solution, and its beneficial effects are as follows:

[0041] The point spread function calculation method and system provided in the present application construct an optical analysis model, obtain the image plane intersection point in the optical analysis model, obtain the intersection point of the lower edge light of the specified field of view of the optical analysis model and the last optical surface as the boundary of the tracing grid, establish ray tracing grid points, perform reverse ray tracing based on the image plane intersection point and the grid point to obtain the pupil function, and obtain the point spread function based on the pupil function. Compared with the traditional method that needs to find the entrance pupil boundary and involves complex logical processes, the present application will avoid the complex entrance pupil, exit pupil and their boundary determination process, and directly calculate the ray tracing boundary based on the surface aperture. The calculation process is closer to the real physical process, with low implementation complexity and good stability. Through reverse ray tracing, the calculation error introduced by Fourier grid distortion and the approximation error of the traditional Fraunhofer propagation method are avoided, and an accurate ideal point light source diffraction image, that is, the point spread function of the optical system, can be obtained in the image space. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following briefly introduces the drawings required for use in the embodiments of the present application or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0043] Figure 1 This is a flowchart of the steps of the point spread function calculation method provided in Example 1 of the present application.

[0044] Figure 2 A schematic structural diagram of the COOKE three-piece optical system provided in Application Example 1;

[0045] Figure 3 A schematic diagram of the diffraction propagation process from the last surface of the optical system to the image plane in the image space provided in Application Example 1;

[0046] Figure 4 This is a schematic diagram of the structure of the point spread function calculation system provided in application embodiment 2. DETAILED DESCRIPTION

[0047] The following describes in detail embodiments of the present application, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present application, and should not be construed as limiting the present application.

[0048] In the description of this application, it should be understood that the terms "upper", "lower", "horizontal", "inside", "outside", etc., indicating orientations or positional relationships, are based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on this application.

[0049] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features. Throughout the description of this application, "plurality" means two or more, unless otherwise specifically defined.

[0050] In order to make the purpose, technical solutions and advantages of this application more clear, this application is further described in detail below with reference to the accompanying drawings and embodiments.

[0051] Example 1

[0052] See also Figure 1 , which is a flowchart of a point spread function calculation method provided in this embodiment 1, including the following steps S110 to S150. The implementation method of each step is described in detail below.

[0053] Step S110: constructing an optical analysis model.

[0054] In some embodiments, the step of constructing an optical analysis model specifically includes the following steps: constructing an optical analysis model in imaging optical system analysis software based on the optical system, and defining surface properties of each optical component. The surface properties include the surface shape, position, material, eccentricity / tilt, and refraction of each surface.

[0055] See also Figure 2 , is a structural diagram of the COOKE three-piece optical system provided in this embodiment. The COOKE optical system consists of three lenses with optical power and two air spacers. The optical power of the three lenses is positive, negative, and positive, respectively.

[0056] Step S120: obtaining image plane intersection points in the optical analysis model.

[0057] In this embodiment, the step of obtaining the image plane intersection in the optical analysis model specifically includes the following steps: forward tracing the main ray under the specified object field of view, calculating the coordinates of the intersection between the ray and the image plane, and recording the angle between the main ray and the z-axis as β.

[0058] It should be noted that the angle β here takes into account the situation where the global x-axis and y-axis do not coincide. Using such a setting can reduce the amount of calculation by 50% when performing the subsequent Fourier transform.

[0059] Step S130: obtaining the intersection of the lower edge ray of the field of view specified by the optical analysis model and the last optical surface as the boundary of the tracing grid, and establishing the ray tracing grid points.

[0060] In some embodiments, in the step of obtaining the intersection of the edge ray of the field of view specified by the optical analysis model and the last optical surface as the boundary of the tracing grid and establishing the ray tracing grid points, specifically:

[0061] By forward tracing the edge ray in the specified object field of view, the intersection of the ray and the last surface of the optical analysis model is calculated, and the intersection is used as the grid point, and the grid point is used as the boundary of the tracing grid, where the boundary width in the meridian direction is D T+ , the width of the lower boundary in the meridian direction is -D T- , the boundary width in the sagittal direction is D S+ , the width of the lower boundary in the sagittal direction is -D S- , take max(D T+ ,D T- ,D S+ ,D S- ) is the height of the semi-tracing grid boundary.

[0062] Furthermore, with the + axis as the positive direction and the maximum value of the vector height of the last surface of the optical system as the origin of the tracing grid, a plane perpendicular to the z axis is established, and the tracing grid is set, and the distance between the z coordinate of the tracing grid and the image plane is d.

[0063] Furthermore, the tracing grid is set to (2N+1)×(2N+1) squares, where N is preferably a positive integer not less than 16.

[0064] Step S140: performing reverse ray tracing according to the image plane intersection points and grid points to obtain a pupil function.

[0065] In some embodiments, the step of performing reverse ray tracing according to the image plane intersection points and the grid points to obtain the pupil function specifically includes the following steps:

[0066] Step S141: Taking the image plane intersection point as the starting point and the direction of the line connecting the image plane intersection point and the grid point as the direction vector (k x ,k y ,k z ), perform reverse ray tracing;

[0067] Step S142: During the reverse ray tracing process, the distance oPL(i,j)k traveled by each surface is recorded in sequence, where: i is the horizontal coordinate of the tracing grid, j is the vertical coordinate of the tracing grid, and k is the number of the traced surface and the corresponding refractive index n k , used to calculate the wavefront aberration oPL(i,j) of the optical system,

[0068]

[0069] Step S143: After the reverse ray traces to the first surface, it enters the object space. If the angle between the edge ray of the tracing grid and the direction of the main ray is less than the threshold Δ, it can be considered to be parallel and can be traced for any distance. If the angle is greater than the threshold Δ, it should be traced to an object point at a finite distance.

[0070] In this embodiment, the threshold Δ can be set to a smaller number, preferably, it can be set to 10 -8 , the unit is the system length unit.

[0071] See also Figure 3 , which is a schematic diagram of the diffraction propagation process from the last surface of the optical system to the image plane in the image space provided by the embodiment.

[0072] It is understood that in this embodiment, the directions of the outgoing light rays are substantially parallel, so it is only necessary to trace them to a plane perpendicular to the principal light ray. Preferably, the plane can be set to be tangential to the first surface and perpendicular to the principal light ray.

[0073] Step S144: During the reverse ray tracing process, for light rays that are blocked by the aperture of the optical system and cannot be traced further, the coordinates of the blocked light rays in the tracing grid are recorded as Mask(i, j);

[0074] Step S145: Taking the central ray (N+1, N+1) of the tracing grid as the principal ray, the wavefront aberration OPD(i, j) of the other rays of the grid relative to the principal ray is calculated as: OPD(i, j) = OPL(i, j) - OPL(N+1, N+1);

[0075] Step S146: Obtaining a pupil function from the wavefront aberration. The pupil function PF(x, t) is expressed as: Wherein, without considering polarization, A(x,y)≡1, λ is the wavelength of light.

[0076] It can be understood that the pupil function is obtained from the wave aberration. The pupil function calculated by the traditional method is the light field at the exit pupil spherical surface, which is essentially equivalent to the exit pupil plane light field plus the spherical wavefront phase.

[0077] Step S150: performing reverse ray tracing according to the image plane intersection points and grid points to obtain a pupil function.

[0078] In some embodiments, the step of obtaining the point spread function according to the pupil function specifically includes the following steps:

[0079] Step S151: By changing the tracing grid direction vector by the main ray angle β, a propagation factor γ(x,y) is obtained, γ(x,y)=(k z cosβ-k x sinβ);

[0080] Step S152: Calculate the light field propagating from the pupil light field to the image plane using the angular spectrum method. in, is the Fourier transform, is the inverse Fourier transform;

[0081] Step S153: Obtain the optical transfer function (OTF) of the optical system according to the PSF calculation. And modulation transfer function MTF, MTF = |OTF|.

[0082] Compared with the traditional method that needs to find the entrance pupil boundary and involves complex logical processes, the point spread function calculation method provided in this application will avoid the complex entrance pupil, exit pupil and their boundary determination process, and directly calculate the ray tracing boundary based on the surface aperture. The calculation process is closer to the real physical process, with low implementation complexity and good stability. By reverse ray tracing, the calculation error introduced by Fourier grid distortion and the approximate error of the traditional Fraunhofer propagation method are avoided, and an accurate ideal point light source diffraction image, that is, the point spread function of the optical system, can be obtained in the image space.

[0083] The point spread function calculation method provided in this application can be further applied to the calculation of image quality evaluation methods such as optical system modulation transfer function, enclosure energy distribution, and two-dimensional image simulation.

[0084] Example 2

[0085] See also Figure 4, which is a structural diagram of the point spread function calculation system provided in this embodiment, including: a model construction unit 110, used to construct an optical analysis model; an image plane intersection acquisition unit 120, used to obtain image plane intersection points in the optical analysis model; a grid point acquisition unit 130, used to obtain the intersection points of the lower edge rays of the specified field of view of the optical analysis model and the last optical surface as the boundaries of the tracing grid, and establish ray tracing grid points; a pupil function acquisition unit 140, used to perform reverse ray tracing based on the image plane intersection points and grid points to obtain a pupil function; and a point spread function calculation unit 150, used to obtain the point spread function based on the pupil function.

[0086] The point spread function calculation system provided in Example 2 of the present application can be implemented in detail by referring to Example 1 and will not be described in detail here.

[0087] The point spread function calculation system provided in Example 2 of the present application, compared with the traditional method that needs to find the entrance pupil boundary and involves complex logical processes, the present application will avoid the complex entrance pupil, exit pupil and their boundary determination process, and directly calculate the ray tracing boundary based on the surface aperture. The calculation process is closer to the real physical process, with low implementation complexity and good stability. By reverse ray tracing, the calculation error introduced by Fourier grid distortion and the approximate error of the traditional Fraunhofer propagation method are avoided, and an accurate ideal point light source diffraction image, that is, the point spread function of the optical system, can be obtained in the image space.

[0088] It can be understood that the various technical features of the above-described embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the various technical features in the above-described embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0089] The above are merely preferred embodiments of the present application and only specifically describe the technical principles of the present application. These descriptions are intended only to explain the principles of the present application and should not be construed in any way as limiting the scope of protection of the present application. Based on the explanations herein, any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present application, as well as other specific implementations of the present application that can be conceived by those skilled in the art without inventive effort, shall be included within the scope of protection of the present application.

Claims

1. A method for calculating a point spread function, characterized in that: The steps include: Construct optical analysis models; Obtaining an image plane intersection point in the optical analysis model; Obtaining the intersection of the lower edge ray of the specified field of view of the optical analysis model and the last optical surface as the boundary of the tracing grid, and establishing the ray tracing grid points; Perform reverse ray tracing according to the image plane intersection points and grid points to obtain a pupil function; obtaining the point spread function according to the pupil function; The step of constructing an optical analysis model specifically includes the following steps: constructing an optical analysis model in imaging optical system analysis software based on the optical system, and defining surface properties of each optical component; The step of obtaining the image plane intersection point in the optical analysis model specifically includes the following steps: In the optical analysis model, the main ray is traced forward in a specified object field of view, the coordinates of the intersection of the ray and the image plane are calculated, and the image plane intersection point is obtained, and the angle between the main ray and the z-axis is recorded as β.

2. The point spread function calculation method according to claim 1, wherein: The surface properties include the shape, position, material, eccentricity / tilt, and refraction of each surface.

3. The point spread function calculation method according to claim 1, wherein: The step of obtaining the intersection position of the edge ray of the optical analysis model and the last optical surface of the optical system as the boundary of the tracing grid and establishing the ray tracing grid points is specifically as follows: By forward tracing the edge ray in the specified object field of view, the intersection of the ray and the last surface of the optical analysis model is calculated, and the intersection is used as the grid point, and the grid point is used as the boundary of the tracing grid, where the boundary width in the meridian direction is D T+ , the width of the lower boundary in the meridian direction is -D T- , the boundary width in the sagittal direction is D S+ , the width of the lower boundary in the sagittal direction is -D S- , take max(D T+ ,D T- ,D S+ ,D S- ) is the height of the semi-tracing grid boundary.

4. The point spread function calculation method according to claim 3, wherein: With the +z axis as the positive direction and the maximum value of the sag of the last surface of the optical system as the origin of the tracing grid, a plane perpendicular to the z axis is established, and the tracing grid is set. The distance between the z coordinate of the tracing grid and the image plane is d.

5. The point spread function calculation method according to claim 4, wherein: The tracing grid is set to a (2N+1)×(2N+1) grid, where N is a positive integer not less than 16.

6. The point spread function calculation method according to claim 1, wherein: The step of performing reverse ray tracing according to the image plane intersection points and the grid points to obtain the pupil function is specifically as follows: The image plane intersection point is taken as the starting point, and the direction of the line connecting the image plane intersection point and the grid point is taken as the direction vector (k x ,k y ,k z ), perform reverse ray tracing; In the reverse ray tracing process, the distance OPL(i,j) traveled by each surface is recorded in turn. k Where: i is the horizontal coordinate of the tracing grid, j is the vertical coordinate of the tracing grid, k is the number of the tracing surface and the corresponding refractive index n k To calculate the wavefront aberration OPL(i,j) of the optical system, After the reverse ray traces to the first surface and enters the object space, if the angle between the direction of the edge ray of the tracing grid and the main ray is less than a threshold Δ, it can be considered to be parallel and can be traced for any distance; if the angle is greater than the threshold Δ, it should be traced to an object point at a finite distance; During the reverse ray tracing process, for the light rays that are blocked by the aperture of the optical system and cannot be traced further, the coordinates of the blocked light rays in the tracing grid are recorded and recorded as Mask(i,j); The central ray (N+1, N+1) of the tracing grid is taken as the principal ray, and the wavefront aberration OPD(i, j) of the other rays of the grid relative to the principal ray is calculated as follows: OPD(i, j) = OPL(i, j) - OPL(N+1, N+1); The pupil function is obtained from the wave aberration, and the pupil function PF(x,y) is expressed as: Wherein, without considering polarization, A(x,y)≡1, λ is the wavelength of light.

7. The point spread function calculation method according to claim 1, wherein: The step of obtaining the point spread function according to the pupil function specifically includes the following steps: By changing the main ray angle β of the tracing grid direction vector, the propagation factor γ(x,y) is obtained, γ(x,y)=(k z cosβ-k x sinβ); The light field propagating from the pupil light field to the image plane is calculated by the angular spectrum method. in, is the Fourier transform, is the inverse Fourier transform; According to the optical transfer function OTF of the optical system calculated by PSF, And modulation transfer function MTF, MTF = |OTF|.

8. A point spread function calculation system, characterized in that: include: A model building unit, used for building an optical analysis model; An image plane intersection point acquisition unit, configured to acquire image plane intersection points in the optical analysis model; A grid point acquisition unit, which acquires the intersection of the edge ray of the field of view specified by the optical analysis model and the last optical surface as the boundary of the tracing grid, and establishes the ray tracing grid point; A pupil function acquisition unit, performing reverse ray tracing according to the image plane intersection points and grid points to obtain the pupil function; A point spread function calculation unit is configured to obtain the point spread function according to the pupil function.

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