Optical System Relative Illuminance Calculation Method

Abstract

The present invention provides a method for calculating the relative illuminance of an optical system, comprising the following steps: S1. Uniformly sample at the entrance pupil of each field of view of the optical system, perform ray tracing, and record ray information; S2. Calculate the first average transmittance and the second average transmittance of the rays after removing emission loss and absorption loss in each field of view according to the ray information; S3. Calculate the image-side projected solid angle PSA, and calculate the relative illuminance RE of the optical system according to the projected solid angle. The present invention has the following advantages: on the premise of comprehensively considering various factors, it has high accuracy, fast calculation speed, is conducive to integration, and is more convenient to use.

Description

Technical Field

[0001] The present invention relates to the field of optical technologies, and particularly to a method for calculating the relative illuminance of an optical system. Background Art

[0002] Relative illuminance refers to the ratio of the illuminance at different coordinate points on the image plane to the illuminance at the center point, that is, the ratio of the illuminance in other fields of view to the illuminance in the central field of view, and is an important evaluation index of an imaging optical system. In an imaging optical system, if the relative illuminance of a certain field of view is small, it is easy to cause underexposure or overexposure problems at certain positions.

[0003] Currently, there are mainly two ways to calculate relative illuminance: One is to trace a large number of real rays. First, set the characteristics of the light source, simulate the light emission of the light source, and then trace a large number of real rays passing through the optical system. At the same time, the transmission and scattering conditions of each ray need to be considered. Finally, the illuminance map of the current field of view is generated by superimposing the light intensities on the image plane and compared with the central field of view. This method simulates the process of real light emission and light propagation, and considers various factors, so the calculation is relatively accurate. Currently, the method of tracing a large number of rays is widely used in stray light analysis software. This method belongs to the method of tracing a large number of rays. By tracing a large number of real rays, the result is accurate, but tracing a large number of rays takes a long time, and most of this method is integrated in stray light analysis software, and users cannot perform relative illuminance analysis in real time during the optical system design using imaging optical design software.

[0004] Another way is the cosine fourth power law. Assuming that the object point is a Lambert radiator, the off-axis illuminance formula can be obtained through a series of approximate derivations:

[0005] E′ = E′0cos 4 ω′ (1)

[0006]

[0007] Among them, E′ is the illuminance of the off-axis field of view, E′0 is the illuminance of the central field of view, ω′ is the off-axis exit angle, and RE is the relative illuminance. It can be seen that the relative illuminance of the off-axis field of view is proportional to the fourth power of the cosine of the off-axis exit angle. This method is simple to calculate and fast. It is adopted in textbooks at home and abroad and some imaging optical design software (such as CODE V and ZEMAX). This method belongs to the ideal model method, that is, the relative illuminance of each field of view is calculated through the cosine-fourth law. However, this method greatly simplifies the imaging process of the optical system. The simplified contents include: 1) It is considered that the transmittance of the off-axis field of view is the same as that of the central field of view. 2) It is considered that the image-side aperture angle of the off-axis field of view is very small. 3) The influence brought by factors such as vignetting and film layers is not considered. However, the actual optical system is complex, especially for wide-angle lenses or lenses with a large number of lenses. The relative illuminance obtained by the ideal model method often deviates greatly from the actual situation. Summary of the Invention

[0008] In view of the above problems, the purpose of the present invention is to propose a method for calculating the relative illuminance of an optical system. First, uniformly sample the entrance pupil and perform ray tracing, and then calculate the average transmittance of each field of view. This process needs to consider the losses caused by interface reflection and material absorption, as well as the light blocking of the element aperture. Finally, according to the exit pupil coordinates obtained by ray tracing, calculate the image-side projected solid angle, and multiply to obtain the illuminance, and then calculate the relative illuminance. The present invention can take into account factors such as transmittance difference, film layer, vignetting, etc., so as to simulate the light intensity change in the real imaging process as much as possible, and at the same time take into account the calculation speed. The method provided by the present invention can be applied to imaging design software for real-time analysis.

[0009] To achieve the above object, the present invention adopts the following specific technical solutions:

[0010] The present invention provides a method for calculating the relative illuminance of an optical system, including the following steps:

[0011] S1. Uniformly sample at the entrance pupil of each field of view of the optical system and perform ray tracing, and record the ray information;

[0012] S2. Calculate the first average transmittance after removing the emission loss and absorption loss of the ray in each field of view according to the ray information and the second average transmittance

[0013] S3. Calculate the image-side projected solid angle PSA, and calculate the relative illuminance RE of the optical system according to the projected solid angle:

[0014]

[0015] Among them,

[0016] τ ref0The first average transmittance of the central field of view;

[0017] τ abs0 The second average transmittance of the central field of view;

[0018] PSA0 is the image-side projected solid angle of the central field of view.

[0019] Preferably, the sampling method in step S1 includes: grid sampling, circular sampling or random sampling.

[0020] Preferably, the ray information includes:

[0021] The exit pupil coordinates (X i , Y i ) of each ray at any field of view of the optical system;

[0022] The incident angle θ i of each ray at the incident interface and the exit angle θ i ';

[0023] The path P i .

[0024] Preferably, in step S2, the calculation process of the first average transmittance is as follows:

[0025] Use the Fresnel formula to calculate the reflection loss REF i of any single ray on the incident interface in the optical system:

[0026]

[0027]

[0028]

[0029] Then the average reflection loss is:

[0030]

[0031] where N is the total number of ray samples;

[0032] The first average transmittance is:

[0033]

[0034] Preferably, in step S2, the calculation process of the second average transmittance is as follows:

[0035] The transmittance of any single ray after absorption loss in the medium is:

[0036]

[0037] Among them, τ0 is the transmittance of a single ray passing through a unit length of material;

[0038] The second average transmittance is:

[0039]

[0040] Preferably, in step S3, the image-side projection solid angle PSA is:

[0041]

[0042] Among them, R is the radius of the exit pupil sphere, and A is the area of the exit pupil.

[0043] Compared with the existing technologies, the present invention has the following advantages:

[0044] (1) Under the premise of comprehensively considering various factors, the accuracy is improved

[0045] Compared with the cosine fourth-power law commonly used in textbooks and commercial optical design software, the present invention comprehensively considers various factors. Although the cosine fourth-power law has a fast calculation speed, its limitations are also obvious. It ignores the difference in beam transmittance between the central field of view and the off-axis field of view, ignores the light-blocking difference of the aperture stop for beams in different fields of view, and ignores the difference in the shape of the exit pupil caused by aberration. Therefore, when facing a relatively large system, especially a fish-eye lens, or an objective lens with a large number of lenses and requiring coating, its calculation method becomes unreliable. In the calculation process of this algorithm, factors such as interface reflection, material absorption, and aperture stop light-blocking are considered, which is closer to the actual imaging process. Therefore, the calculation accuracy is higher.

[0046] (2) Fast calculation speed

[0047] The calculation method of tracing a large number of rays used in the stray light analysis software often needs to trace tens of thousands or hundreds of thousands of rays each time to obtain accurate results. The present invention has a lower requirement for the number of traced rays, and only needs to ensure obtaining approximate average transmittance and approximate exit pupil area.

[0048] (3) Facilitates integration and is more convenient to use

[0049] The illuminance calculation method of tracing a large number of rays in the stray light analysis software can only trace one field of view angle each time, and cannot obtain the trend of relative illuminance changing with the field of view at one time. In addition, the illuminance analysis is separated from the optical system design process and cannot analyze the optical system while designing. This algorithm can be integrated into the imaging optical design software for real-time analysis, which is very friendly to designers. Brief description of the drawings

[0050] Figure 1 It is a schematic flowchart of the method for calculating the relative illuminance of an optical system provided by an embodiment of the present invention.

[0051] Figure 2 It is a program block diagram of the method for calculating the relative illuminance of an optical system provided by an embodiment of the present invention.

[0052] Figure 3 It is a schematic structural diagram of a wide-angle lens provided by an embodiment of the present invention.

[0053] Figure 4 It is a schematic diagram of the relative illuminance curves of the method for calculating the relative illuminance of an optical system provided by an embodiment of the present invention and other methods. Detailed implementation manners

[0054] In the following, embodiments of the present invention will be described with reference to the accompanying drawings. In the following description, the same modules are denoted by the same reference numerals. In the case of the same reference numerals, their names and functions are also the same. Therefore, their detailed descriptions will not be repeated.

[0055] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

[0056] Figure 1 It shows a schematic flowchart of the method for calculating the relative illuminance of an optical system provided by an embodiment of the present invention.

[0057] Figure 2 It shows a program block diagram of the method for calculating the relative illuminance of an optical system provided by an embodiment of the present invention.

[0058] As Figure 1-2 shown, the method for calculating the relative illuminance of an optical system provided by an embodiment of the present invention includes the following steps:

[0059] S1. Uniformly sample at the entrance pupil of each field of view of the optical system, and perform ray tracing to record ray information.

[0060] The sampling methods include: grid sampling, annular sampling, random sampling, etc., as long as uniformity is ensured.

[0061] Perform ray tracing until the image plane. The ray information includes: recording the exit pupil coordinates (X i , Y i ) of each ray in this field of view, the incident angle θ i of each ray at the interface and the exit angle θ i’, the path P of each ray propagating in the medium i (which is different from the optical path here).

[0062] At the same time, the rays that cannot pass through the aperture should also be marked for subsequent calculations.

[0063] S2. Calculate the first average transmittance and the second average transmittance of the rays after removing the emission loss and absorption loss in each field of view according to the ray information.

[0064] When a ray passes through a piece of glass, there are generally three energy loss processes: reflection loss at the air-glass interface, absorption loss of the glass material, and reflection loss at the glass-air interface. If there is a film layer, the antireflection or other effects brought by the film layer should also be considered.

[0065] S21. Calculate the average reflection loss of the rays at the mirror surface in the optical system and the first average transmittance

[0066] Use the Fresnel formula to calculate the reflection loss REF of a single ray at the interface i :

[0067]

[0068]

[0069]

[0070] Sum up the reflectivities REF of the single rays that can pass through the surface i and divide by the total number of samples to obtain the average reflection loss of this interface

[0071]

[0072] where N is the total number of samples.

[0073] 1 - average reflection loss is the surface average transmittance after considering the interface reflection. The product of the interface average transmittances of each surface is the first average transmittance of the system in this field of view after considering the interface reflection

[0074]

[0075] S22. Calculate the second average transmittance of the rays propagating in the medium of the optical system

[0076] Generally, the transmittance τ0 of the rays passing through the unit length of the material is directly given in the material library.

[0077] For example:

[0078] The transmittance of SBSM81_OHARA material at a wavelength of 587.56 nm is 0.9964 / 5 mm;

[0079] The transmittance of STIH6_OHARA material at a wavelength of 587.56 nm is 0.9972 / 5 mm;

[0080] The transmittance of SLAL18_OHARA material at a wavelength of 587.56 nm is 0.9991 / 5 mm;

[0081] Therefore, the transmittance of a single ray after medium absorption loss can be directly calculated here.

[0082]

[0083] Using the same method, the second average transmittance of the system considering medium absorption in this field of view can be calculated.

[0084]

[0085] S3. Calculate the image-side projected solid angle PSA, and calculate the relative illuminance RE of the optical system based on the projected solid angle.

[0086] For the image-side projected solid angle PSA, the shape of the exit pupil is not always circular. Due to the existence of aberrations, the exit pupil is often irregular. Here, the method of ray tracing is also used. For the same bundle of rays filling the entrance pupil, trace them to the exit pupil spherical surface, record their coordinates, and obtain the approximate spherical cap-shaped exit pupil area A. Then the projected solid angle PSA is:

[0087]

[0088]

[0089] where R is the radius of the exit pupil spherical surface and A is the exit pupil area.

[0090] Due to the existence of aberrations, the shape of the exit pupil is often irregular, and the accurate calculation of the exit pupil area A is rather troublesome. Therefore, it is necessary to simply fit the shape of the exit pupil. In the above ray tracing process, the exit pupil coordinates (X i , Y i ) of each ray are obtained, and they are fitted into an ellipse by the least squares method to reduce the calculation difficulty.

[0091] Assume that the object point is a Lambert radiator, and the luminous flux Φ emitted into the solid angle range with a plane aperture angle of U is:

[0092]

[0093] The image-space luminous flux Φ′ is as follows:

[0094] Φ′ = L′dA * PSA

[0095] where L′ is the image-space luminance;

[0096] PSA is the image-space projected solid angle;

[0097] A is the exit pupil area.

[0098] Therefore, the image-space illuminance E′ is:

[0099]

[0100] Then the image-space illuminance E′ is the product of the image-space luminance L′ and the image-space projected solid angle PSA.

[0101] When light passes through a lens, it generally undergoes three losses: reflection loss at the air-glass interface, transmission loss during propagation in the glass, and reflection loss at the glass-air interface. If there is a film layer at the air interface, the influence brought by the film layer also needs to be considered, and all these are related to the incident angle of the light. Therefore, the incident angle will affect the image-space luminance L′. Due to the presence of the aperture stop and vignetting, when the light beams with different field angles are traced to the image plane, their image-space projected solid angles may also have large differences.

[0102] For the image-space luminance L′, it is mainly affected by the transmittance τ, and there is the following relationship

[0103] L′ = Lτ

[0104] where L is the luminance of the object point.

[0105] At each field, each ray corresponds to a transmittance τ. If processed separately, it will undoubtedly increase the computational amount and difficulty. Here, the method of average transmittance is adopted. For each field, a ray filling the entrance pupil is traced, and the average transmittance of these rays is calculated as the transmittance of the current field

[0106] The relative illuminance RE of the off-axis field is the product of the average transmittance and the ratio of the projected solid angle.

[0107] Then the relative illuminance RE of a certain off-axis field can be obtained:

[0108]

[0109] where

[0110] τ ref0 is the first average transmittance of the central field (generally 0°);

[0111] τ abs0 The second average transmittance of the central field of view;

[0112] PSA0 is the image-side projection solid angle of the central field of view (generally 0°).

[0113] Figure 3 The structural schematic diagram of the wide-angle lens provided by the embodiment of the present invention is shown.

[0114] As Figure 3 Shown, taking a wide-angle lens as an example, the maximum half field of view angle is 85°, the entrance pupil diameter is 1mm, there are a total of 3 lenses and 6 surfaces, and the relative illuminance of 11 fields of view from 0° to 85° is calculated. The present invention completes the simulation of a wide-angle lens on a PC with AMD Ryzen7 4800H, 2.90G, on the MATLAB 2020b platform, with a maximum half field of view angle of 85° and an entrance pupil diameter of 1mm. Through grid sampling, the number of sampled light rays is 20×20. The number of entrance pupil samples for each field of view is 400 points.

[0115] Figure 4 The schematic diagram of the relative illuminance curve of the optical system relative illuminance calculation method provided by the embodiment of the present invention and other methods is shown.

[0116] As Figure 4 Shown, using a large number of existing ray tracing methods, the cosine fourth power law method is compared with the method provided by the present invention. Among them, when simulating using the method of tracing a large number of rays, 25,000 rays are traced for each field of view; when simulating using the cosine fourth power law method, only one principal ray is traced for each field of view point.

[0117] The present invention aims at the wide-angle lens as Figure 3 Shown, with a half field of view angle from 0° to 85°, the relative illuminance at 11 field of view points is calculated, and the relative illuminance curve is drawn.

[0118] Through analysis, the relative illuminance curve obtained by the present invention is close to the illuminance curve result obtained by the method of tracing a large number of rays, with a maximum error of 4.98%. However, the result deviation between the cosine fourth power law method and the method of tracing a large number of rays is relatively large, with a maximum error of 17.35%.

[0119] Although the embodiments of the present invention have been shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention.

[0120] The above specific embodiments of the present invention do not constitute a limitation on the protection scope of the present invention. Any other corresponding changes and deformations made according to the technical concept of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A method for calculating the relative illuminance of an optical system, characterized in that, Including the following steps: S1. Uniformly sample at the entrance pupil of each field of view of the optical system, perform ray tracing, and record ray information; S2. Calculate the first average transmittance of light in each field of view after removing emission loss and absorption loss based on the light information and the second average transmittance ; S3. Calculate the image-side projected solid angle PSA, and calculate the relative illuminance RE of the optical system according to the projected solid angle: Image-side projection solid angle is as follows: where R is the radius of the exit pupil spherical surface, is the exit pupil area; Wherein, The first average transmittance for the central field of view; The second average transmittance for the central field of view; PSA0 is the image-side projected solid angle of the central field of view.

2. The method for calculating the relative illumination of an optical system according to claim 1, characterized in that, The sampling method in the step S1 includes: grid sampling, circular sampling or random sampling.

3. The method for calculating the relative illuminance of an optical system according to claim 2, wherein The ray information includes: The exit pupil coordinates (X i , Y i ) of each ray under any field of view of the optical system; The incident angle θ of each ray at the incident interface i and the exit angle θ i '; The path P of each ray during propagation in the medium i .

4. The method for calculating the relative illumination of an optical system according to claim 3, characterized in that, In the step S2, the calculation process of the first average transmittance is as follows: Use the Fresnel formula to calculate the reflection loss of any single ray at the incident interface in the optical system : The average reflection loss is as follows: Wherein, N is the total number of ray samplings; The first average transmittance is as follows: 。 5. A method for calculating the relative illuminance of an optical system according to claim 4, characterized in that, In the step S2, the second average transmittance is calculated as follows: The transmittance of any single ray after absorption loss by the medium is: Among them, is the transmittance of the single ray passing through the material per unit length; The second average transmittance is: 。

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