Design method of standard spherical lens and standard spherical lens

By constructing an optical interference cavity model and calculating the numerical relationship between cavity error and angular aberration, a seven-piece standard spherical lens was designed. This solved the problem of the connection between the design indicators of the large relative aperture standard spherical lens and the interferometer measurement accuracy, achieving cost reduction and performance balance.

CN119644543BActive Publication Date: 2025-10-10江淮前沿技术协同创新中心 +1
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Patent Information

Application Number
CN202411814554.5
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-12-11
Publication Date
2025-10-10
Estimated Expiration
2044-12-11

AI Technical Summary

Technical Problem

In the existing technology, the design indicators of large relative aperture standard spherical lenses cannot be linked to the interferometer measurement accuracy, and it is difficult to predict the impact of their actual optical performance on the interferometer measurement accuracy, resulting in high processing and assembly costs and difficulty in balancing performance and R&D difficulty.

Method used

An optical interferometer cavity model is constructed, and the cavity error of light in the optical interferometer cavity is calculated. The numerical relationship between the cavity error and angular aberration is obtained through small-angle approximation. The conversion relationship between wavefront aberration is obtained using aberration theory, and a seven-piece standard spherical lens is designed to meet certain interferometer measurement accuracy requirements.

Benefits of technology

The standard spherical lens index parameters are decomposed according to the interferometer measurement accuracy. The angular aberration is used as a design and evaluation indicator to predict its impact on the interferometer measurement accuracy, reducing the processing and assembly costs while maintaining the lens performance.

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Abstract

The application provides a design method of a standard spherical lens and the standard spherical lens, and relates to the field of optical lens design. The design method is designed to solve the problem that the design index of the existing standard spherical lens with a large relative aperture cannot be connected with the interferometer measurement accuracy, so that the actual optical performance of the standard spherical lens is difficult to predict the influence on the interferometer measurement accuracy. The design method of the standard spherical lens comprises the following steps: constructing an optical interference cavity model composed of a reference spherical surface of the standard spherical lens and a measured spherical surface; calculating the cavity error of the light in the optical interference cavity model; based on the accuracy of the standard spherical lens, the small-angle approximation of the angular aberration is carried out to obtain the numerical relationship between the cavity error and the angular aberration. According to the interferometer measurement accuracy, the index parameters of the standard spherical lens are decomposed, the design process of the standard spherical lens is connected with the actual detection process, and the influence of the actual optical performance of the standard spherical lens on the interferometer measurement accuracy can be predicted.
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Description

Technical Field

[0001] The present invention relates to the field of optical lens design, and in particular to a design method for a standard spherical lens and the standard spherical lens. Background Art

[0002] The standard spherical lens is a key component of the Fizeau interferometer for surface shape detection and wavefront aberration measurement of spherical and aspheric optical components. It provides a stable, high-precision spherical reference datum. The uniformity of the converging light at the reference surface ensures the common optical path characteristics of the Fizeau interferometer. Spherical interferometry, in principle, requires that the F-number of the standard spherical lens be smaller than the R-number of the lens being measured or the F-number of the lens being measured. The F-number is defined as the ratio of the focal length of the lens to the entrance pupil diameter, while the R-number is defined as the ratio of the radius of curvature of the optical lens to the effective aperture.

[0003] With the development of the optical industry, the demand for extreme detection such as nearly hemispherical lenses (R number is about 0.6), large numerical aperture microscope lenses, and high-steepness aspherical optical lenses has emerged. Therefore, there is an urgent need for small F-number standard spherical lenses. However, as the F-number decreases, the difficulty of lens optical design and the number of lenses will increase sharply. For example, for a standard spherical lens with an aperture of 101.6mm and an F-number of 0.56, its processing and assembly costs will also increase rapidly, and a balance needs to be struck between performance and R&D difficulty. In the existing technology, only the peak-to-valley value (PV) of the lens transmitted wavefront ≤λ / 10 is used as an evaluation standard, and this indicator is not linked to the interferometer measurement accuracy, making it difficult to predict the impact of its actual optical performance on the interferometric measurement accuracy. Summary of the Invention

[0004] The first object of the present invention is to provide a design method for a standard spherical lens to solve the technical problem that the design indicators of existing large relative aperture standard spherical lenses cannot be linked to the interferometer measurement accuracy, making it difficult to predict the impact of their actual optical performance on the interferometer measurement accuracy.

[0005] The design method of the standard spherical lens provided by the present invention includes:

[0006] Construct an optical interference cavity model consisting of a reference spherical surface of a standard spherical lens and a spherical surface to be measured;

[0007] Calculate the cavity error of the light in the optical interferometer cavity model, where the cavity error is the deviation of the optical path difference between the reference light and the measurement light caused by the actual light angular aberration from the optical path difference between the reference light and the measurement light caused by the theoretical light angular aberration.

[0008] Based on the accuracy of the standard spherical lens, the angular aberration of the actual light is approximated at a small angle, and the numerical relationship between the cavity error and the angular aberration is obtained.

[0009] Furthermore, the optical path difference between the reference light and the measurement light caused by the theoretical light angular aberration satisfies the formula:

[0010]

[0011] The actual light angular aberration causes the optical path difference between the reference light and the measurement light to satisfy the formula:

[0012]

[0013] The cavity error satisfies the formula:

[0014]

[0015] Among them, A and B are any points on the reference sphere, and P is any point on the measured sphere. are the ideal incident light and the ideal outgoing light, is the actual incident light, R1 is the curvature radius of the reference sphere, R2 is the curvature radius of the measured sphere, α is the angular aberration, and ΔOPD is the cavity error.

[0016] Furthermore, after the angular aberration is approximated at a small angle, the formula is satisfied:

[0017] sinα=α

[0018] The numerical relationship between cavity error and angular aberration satisfies the formula:

[0019] ΔOPD=α 2 R1(1+1 / ρ)

[0020] Where, ρ = -R2 / R1.

[0021] Furthermore, the design method further includes: obtaining a conversion relationship between angular aberration and wavefront aberration through aberration theory, wherein the conversion relationship between the angular aberration and the wavefront aberration is:

[0022]

[0023] Wherein, n is the refractive index of the medium in the optical interference cavity model, and ΔW(x, y) is the wavefront aberration.

[0024] Furthermore, the cavity error does not exceed λ / 30, and the curvature radius of the reference spherical surface of the standard spherical lens is less than or equal to 56.9 mm.

[0025] The beneficial effects of the design method of the standard spherical lens of the present invention are:

[0026] In the design method of this standard spherical lens, an optical interference model consisting of a reference sphere and a measured sphere is constructed. The optical path difference between the reference light and the measured light under theoretical angular aberration is calculated through theoretical calculation. The optical path difference between the reference light and the measured light caused by actual angular aberration is further calculated. By comparing and calculating these two optical path differences, the cavity error of the light in the optical interference cavity model can be obtained. During the design process, the cavity error is ensured to meet a certain value range, that is, by ensuring that the interferometer meets a certain measurement accuracy, and utilizing the numerical relationship between the cavity error and angular aberration, the range of angular aberration can be determined.

[0027] It can be seen that the design method of the standard spherical lens can decompose the index parameters of the standard spherical lens according to the interferometer measurement accuracy, and use the angular aberration that has a greater impact on the accuracy as the design and evaluation index, so as to link the design process of the standard spherical lens with the actual detection process, so that the influence of the actual optical performance of the standard spherical lens on the interferometer measurement accuracy can be predicted, thereby effectively balancing the performance and manufacturing difficulty of the standard spherical lens.

[0028] A second object of the present invention is to provide a standard spherical lens to solve the technical problem that the design indicators of existing large relative aperture standard spherical lenses cannot be linked to the interferometer measurement accuracy, making it difficult to predict the impact of their actual optical performance on the interferometer measurement accuracy.

[0029] The standard spherical lens provided by the present invention is obtained using the above-mentioned design method for a standard spherical lens. The standard spherical lens includes a first spherical lens with negative optical power, a second spherical lens with negative optical power, a third spherical lens with positive optical power, a fourth spherical lens with positive optical power, a fifth spherical lens with positive optical power, a sixth spherical lens with positive optical power, and a spherical reference mirror with negative optical power, which are arranged in sequence along the optical axis. The first spherical lens is a meniscus negative lens, which is used to expand a collimated light beam; the second spherical lens is a biconcave negative lens; the third spherical lens is a biconvex positive lens; the fourth spherical lens is a biconvex positive lens; the fifth spherical lens is a meniscus positive lens; the sixth spherical lens is a meniscus positive lens; and the spherical reference mirror is a meniscus negative lens. The aperture of the standard spherical lens is 101.6 mm, and the F-number of the standard spherical lens is 0.56.

[0030] Further, the focal length of the first spherical lens is FL1, 310mm<|FL1|<360mm; the focal length of the second spherical lens is FL2, 230mm<|FL2|<290mm; the focal length of the third spherical lens is FL3, 300mm<|FL3|<350mm; the focal length of the fourth spherical lens is FL4, 240mm<|FL4|<280mm; the focal length of the fifth spherical lens is FL5, 220mm<|FL5|<260mm; the focal length of the sixth spherical lens is FL6, 240mm<|FL6|<300mm; and the focal length of the spherical reference mirror is FL7, 400mm<|FL7|<450mm.

[0031] Further, the thickness of the first spherical lens is B1, 15mm<B1<25mm; the thickness of the second spherical lens is A2, 15mm<A2<25mm; the thickness of the third spherical lens is A3, 25mm<A3<35mm; the thickness of the fourth spherical lens is A4, 25mm<A4<35mm; the thickness of the fifth spherical lens is A5, 20mm<A5<30mm; the thickness of the sixth spherical lens is A6, 20mm<A6<30mm; and the thickness of the spherical reference mirror is A7, 13mm<A7<23mm.

[0032] Further, the air interval between the first spherical lens and the second spherical lens is B1, 30mm<B1<50mm; the air interval between the second spherical lens and the third spherical lens is B2, 10mm<B2<20mm; the air interval between the third spherical lens and the fourth spherical lens is B3, 1mm<B3<10mm; the air interval between the fourth spherical lens and the fifth spherical lens is B4, 1mm<B4<10mm; the air interval between the fifth spherical lens and the sixth spherical lens is B5, 1mm<B5<10mm; and the air interval between the sixth spherical lens and the spherical reference mirror is B6, 1mm<B6<10mm.

[0033] Further, the material of the first spherical lens, the third spherical lens, the fourth spherical lens, the fifth spherical lens and the sixth spherical lens is heavy flint glass, the material of the second spherical lens is light crown glass, and the material of the spherical reference mirror is fused quartz.

[0034] The standard spherical lens brings the beneficial effects of the present application:

[0035] The standard spherical lens is obtained by adopting the above-mentioned design method of the standard spherical lens, so that the influence of the actual optical performance of the standard spherical lens on the interference measurement accuracy can be predicted. On this basis, by setting the standard spherical lens as a seven-piece structure mainly consisting of a first spherical lens, a second spherical lens, a third spherical lens, a fourth spherical lens, a fifth spherical lens, a sixth spherical lens and a spherical reference mirror, and by setting the aperture of the standard spherical lens to 101.6 mm and the F-number to 0.56, the processing, manufacturing and assembly costs are greatly reduced without affecting the final performance of the lens. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0037] Figure 1 A diagram of an optical interference cavity model constructed using the design method for a standard spherical lens provided by an embodiment of the present invention;

[0038] Figure 2 A schematic structural diagram of a standard spherical lens provided by an embodiment of the present invention;

[0039] Figure 3 Wavefront diagram of the standard spherical lens provided by an embodiment of the present invention at a wavelength of 632.8 mm;

[0040] Figure 4 The spot diagram of the standard spherical lens provided by an embodiment of the present invention at a wavelength of 632.8 mm;

[0041] Figure 5 This is a diagram showing the angular aberration distribution of a standard spherical lens provided by an embodiment of the present invention.

[0042] Description of reference numerals:

[0043] 1-first spherical lens; 2-second spherical lens; 3-third spherical lens; 4-fourth spherical lens; 5-fifth spherical lens; 6-sixth spherical lens; 7-spherical reference mirror; D-entrance pupil diameter; f-focal length. DETAILED DESCRIPTION

[0044] In order to make the above-mentioned objects, features and advantages of the present invention more clearly understood, the following detailed description of the specific embodiments of the present invention is given in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0045] Figure 1 This is a diagram of an optical interference cavity model constructed using the design method of a standard spherical lens provided in this embodiment. This embodiment provides a design method of a standard spherical lens, including: constructing an optical interference cavity model consisting of a reference spherical surface of a standard spherical lens and a spherical surface to be measured, such as Figure 1 As shown in the figure, the cavity error of the light in the optical interference cavity model is calculated, where the cavity error is: the optical path difference between the reference light and the measurement light caused by the angular aberration of the actual light, which is the deviation from the optical path difference between the reference light and the measurement light caused by the angular aberration of the theoretical light; based on the accuracy of the standard spherical lens, the angular aberration is approximated at a small angle to obtain the numerical relationship between the cavity error and the angular aberration.

[0046] In the design method of this standard spherical lens, an optical interference model consisting of a reference sphere and a measured sphere is constructed. The optical path difference between the reference light and the measured light under theoretical angular aberration is calculated through theoretical calculation. The optical path difference between the reference light and the measured light caused by actual angular aberration is further calculated. By comparing and calculating these two optical path differences, the cavity error of the light in the optical interference cavity model can be obtained. During the design process, the cavity error is ensured to meet a certain value range, that is, by ensuring that the interferometer meets a certain measurement accuracy, and utilizing the numerical relationship between the cavity error and angular aberration, the range of angular aberration can be determined.

[0047] It can be seen that the design method of the standard spherical lens can decompose the index parameters of the standard spherical lens according to the interferometer measurement accuracy, and use the angular aberration that has a greater impact on the accuracy as the design and evaluation index, so as to link the design process of the standard spherical lens with the actual detection process, so that the influence of the actual optical performance of the standard spherical lens on the interferometer measurement accuracy can be predicted, thereby effectively balancing the performance and manufacturing difficulty of the standard spherical lens.

[0048] Please continue to refer to Figure 1 In this embodiment, A and B are arbitrary points on the reference sphere, and P is an arbitrary point on the measured sphere. are the ideal incident light and the ideal outgoing light, is the actual incident light, R1 is the radius of curvature of the reference sphere, R2 is the radius of curvature of the measured sphere, α is the angular aberration, and ΔOPD is the cavity error. In the figure, C represents the center of the reference sphere, and F' represents the focus of the reference sphere. According to this optical interference cavity model, assuming that there is no surface error between the reference sphere and the measured sphere, and when the standard spherical lens does not have aberration, the focus F' of the reference sphere coincides with the center C of the reference sphere. At this time, for any object point P on the measured sphere, the light is incident vertically from point A of the reference sphere (ie: angular aberration α = 0°), part of the light will return along the original path to form the reference light path, and part of the light will be transmitted through point C and incident vertically at point P, forming the measurement light path after reflection. Therefore, in theory, the optical path difference between the reference light and the measurement light is The refractive index of the optical interferometer cavity is 1, and both the reference sphere and the measured sphere are concave spheres with negative curvature radii.

[0049] However, for a standard spherical lens with large relative aperture, its aberration cannot be ignored. Figure 1 In the example, the light actually incident on point P fails to pass through the center C of the reference sphere, but intersects the reference sphere at point B. The incident angle is α. At this time, the optical path difference between the reference light and the measurement light is In ΔBCP, According to the sine theorem, we can get:

[0050]

[0051] According to the triangular relationship, we can get:

[0052]

[0053] Combining (1) and (2) above, we can get:

[0054]

[0055] Therefore, the cavity error can be obtained as:

[0056]

[0057] Since the standard spherical lens has high precision, its angular aberration α can be approximated by a small angle. Combined with Taylor's formula, we can get:

[0058] sinα=α (4)

[0059] cosα=1-α 2 / 2 (5)

[0060]

[0061] Where, ρ = -R2 / R1.

[0062] It can be seen from formula (6) that the greater the difference between the curvature radius of the measured sphere and the curvature radius of the reference sphere, the greater the cavity error ΔOPD; when R1 and R2 (the geometric structure of the optical interference cavity) are determined, the cavity error ΔOPD will increase with the increase of the angular aberration of the standard spherical lens.

[0063] Angular aberration α, as a process variable of ray tracing, can effectively constrain the optimization process of optical design. In practice, according to aberration theory, it can also be converted into a physical quantity that can be detected by interferometer, that is, the gradient of the transmitted wavefront ΔW(x, y), where in the x direction,

[0064]

[0065] In the y direction,

[0066]

[0067] Therefore, for angular aberration, we have,

[0068]

[0069] Wherein, n is the refractive index of the medium in the optical interference cavity model.

[0070] The angular aberration α can be obtained by using the above conversion relationship, so that the simulation design process and the actual lens assembly process can be evaluated using a unified standard, ensuring that the final standard spherical lens achieves the expected performance.

[0071] As a specific embodiment of the present invention, the above-mentioned design method requires that the cavity error introduced by the standard spherical lens does not exceed λ / 30. For a standard spherical lens with an aperture of 101.6 mm and an F-number of 0.56, the curvature radius R1 of its reference sphere is ≤ 56.9 mm. When the value of ρ is 0.2, the angular aberration (i.e., the transmitted wavefront gradient) of the standard spherical lens is less than 250 μrad.

[0072] Figure 2 This is a schematic diagram of the structure of the standard spherical lens provided in this embodiment. Figure 2As shown, this embodiment also provides a standard spherical lens, which is obtained by the above-mentioned design method. Specifically, the standard spherical lens includes a first spherical lens with negative optical focal length, a second spherical lens with negative optical focal length, a third spherical lens with positive optical focal length, a fourth spherical lens with positive optical focal length, a fifth spherical lens with positive optical focal length, a sixth spherical lens with positive optical focal length, and a spherical reference mirror with negative optical focal length, which are arranged in sequence along the optical axis. The first spherical lens is a meniscus negative lens, which is used to expand the collimated light beam; the second spherical lens is a biconcave negative lens; the third spherical lens is a biconvex positive lens; the fourth spherical lens is a biconvex positive lens; the fifth spherical lens is a meniscus positive lens; the sixth spherical lens is a meniscus positive lens; and the spherical reference mirror is a meniscus negative lens. The aperture of the standard spherical lens is 101.6 mm, and the F number of the standard spherical lens is 0.56. That is to say, the overall optical power of the standard spherical lens is: negative-negative-positive-positive-positive-positive-negative.

[0073] The standard spherical lens is obtained by adopting the above-mentioned design method of the standard spherical lens, so that the influence of the actual optical performance of the standard spherical lens on the interference measurement accuracy can be predicted. On this basis, by setting the standard spherical lens as a seven-piece structure mainly consisting of a first spherical lens, a second spherical lens, a third spherical lens, a fourth spherical lens, a fifth spherical lens, a sixth spherical lens and a spherical reference mirror, and by setting the aperture of the standard spherical lens to 101.6 mm and the F-number to 0.56, the processing, manufacturing and assembly costs are greatly reduced without affecting the final performance of the lens.

[0074] Specifically, in this embodiment, the focal length of the first spherical lens is FL1, 310 mm < |FL1| < 360 mm; the focal length of the second spherical lens is FL2, 230 mm < |FL2| < 290 mm; the focal length of the third spherical lens is FL3, 300 mm < |FL3| < 350 mm; the focal length of the fourth spherical lens is FL4, 240 mm < |FL4| < 280 mm; the focal length of the fifth spherical lens is FL5, 220 mm < |FL5| < 260 mm; the focal length of the sixth spherical lens is FL6, 240 mm < |FL6| < 300 mm; and the focal length of the spherical reference mirror is FL7, 400 mm < |FL7| < 450 mm.

[0075] Specifically, in the embodiment, the thickness of the first spherical lens is B1, 15mm < B1 < 25mm; the thickness of the second spherical lens is A2, 15mm < A2 < 25mm; the thickness of the third spherical lens is A3, 25mm < A3 < 35mm; the thickness of the fourth spherical lens is A4, 25mm < A4 < 35mm; the thickness of the fifth spherical lens is A5, 20mm < A5 < 30mm; the thickness of the sixth spherical lens is A6, 20mm < A6 < 30mm; and the thickness of the spherical reference mirror is A7, 13mm < A7 < 23mm.

[0076] The thickness of each lens refers to the size of each lens in the position and extending direction of the optical axis.

[0077] Specifically, in the embodiment, the air gap between the first spherical lens and the second spherical lens is B1, 30mm < B1 < 50mm; the air gap between the second spherical lens and the third spherical lens is B2, 10mm < B2 < 20mm; the air gap between the third spherical lens and the fourth spherical lens is B3, 1mm < B3 < 10mm; the air gap between the fourth spherical lens and the fifth spherical lens is B4, 1mm < B4 < 10mm; the air gap between the fifth spherical lens and the sixth spherical lens is B5, 1mm < B5 < 10mm; and the air gap between the sixth spherical lens and the spherical reference mirror is B6, 1mm < B6 < 10mm.

[0078] The air gap between any two adjacent lenses refers to the distance between any two adjacent lenses in the position and extending direction of the optical axis.

[0079] It should be noted that, in the embodiment, the last surface of the spherical reference mirror is a parallel surface, and the back intercept is equal to the radius of curvature of the last surface.

[0080] Specifically, in the embodiment, the materials of the first spherical lens, the third spherical lens, the fourth spherical lens, the fifth spherical lens and the sixth spherical lens are heavy flint glass, the material of the second spherical lens is light crown glass, and the material of the spherical reference mirror is fused quartz.

[0081] By manufacturing one lens in the standard spherical lens with light crown glass at a low price, the cost is reduced without affecting the final performance.

[0082] Figure 3 The standard spherical lens provided in the embodiment is provided with a wavefront diagram at a wavelength of 632.8mm. As shown in Figure 3 the axial wavefront of the standard spherical lens at a wavelength of 632.8nm is 0.06λ, which meets the actual use requirements.

[0083] Figure 4The point diagram of the standard spherical lens provided in this embodiment at a wavelength of 632.8 mm. Figure 4 As shown in FIG, the on-axis point diagram geometric radius of the standard spherical lens is 0.182 μm, which is much smaller than the Airy disk radius and is at the diffraction limit.

[0084] Figure 5 This is the angular aberration distribution diagram of the standard spherical lens provided in this embodiment. Figure 5 As shown in the figure, the maximum angular aberration of the standard spherical lens at full aperture is 70μrad, which meets the design index requirements.

[0085] Although the present invention is disclosed as above, the present invention is not limited thereto. Any person skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, the scope of protection of the present invention should be based on the scope defined by the claims.

[0086] Finally, it should be noted that, in this document, relational terms such as first and second, etc., are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprises" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article, or device that includes a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further limitations, an element defined by the phrase "comprises a ..." does not exclude the presence of other identical elements in the process, method, article, or device that includes the element.

[0087] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A design method for a standard spherical lens, characterized in that: include: Construct an optical interference cavity model consisting of a reference spherical surface of a standard spherical lens and a spherical surface to be measured; Calculate the cavity error of the light in the optical interferometer cavity model, where the cavity error is: the deviation of the optical path difference between the reference light and the measurement light caused by the actual light angular aberration relative to the optical path difference between the reference light and the measurement light caused by the theoretical light angular aberration; the optical path difference between the reference light and the measurement light caused by the theoretical light angular aberration satisfies the formula: The actual light angular aberration causes the optical path difference between the reference light and the measurement light to satisfy the formula: The cavity error satisfies the formula: Among them, A and B are any points on the reference sphere, and P is any point on the measured sphere. are the ideal incident light and the ideal outgoing light, is the actual incident light, R1 is the curvature radius of the reference sphere, R2 is the curvature radius of the measured sphere, α is the angular aberration, ΔOPD is the cavity error, and the cavity error does not exceed λ / 30; Based on the accuracy of the standard spherical lens, the angular aberration of the actual light is approximated at a small angle to obtain the numerical relationship between the cavity error and the angular aberration. After the angular aberration is approximated at a small angle, the formula is satisfied: sinα=α The numerical relationship between cavity error and angular aberration satisfies the formula: ΔOPD=α 2 R1(1+1 / ρ) Where, ρ = -R2 / R1.

2. The design method of a standard spherical lens according to claim 1, wherein: The design method further includes: obtaining a conversion relationship between angular aberration and wavefront aberration through aberration theory, wherein the conversion relationship between the angular aberration and the wavefront aberration is: Wherein, n is the refractive index of the medium in the optical interference cavity model, and ΔW(x, y) is the wavefront aberration.

3. The design method of a standard spherical lens according to claim 1, wherein: The curvature radius of the reference spherical surface of the standard spherical lens is less than or equal to 56.9 mm.

4. A standard spherical lens, characterized in that: The standard spherical lens is obtained by adopting the design method of any one of claims 1 to 3, wherein the standard spherical lens includes a first spherical lens with negative optical focal power, a second spherical lens with negative optical focal power, a third spherical lens with positive optical focal power, a fourth spherical lens with positive optical focal power, a fifth spherical lens with positive optical focal power, a sixth spherical lens with positive optical focal power, and a spherical reference mirror with negative optical focal power, which are arranged in sequence along the optical axis, wherein the first spherical lens is a meniscus negative lens, which is used to expand a collimated light beam; the second spherical lens is a biconcave negative lens; the third spherical lens is a biconvex positive lens; the fourth spherical lens is a biconvex positive lens; the fifth spherical lens is a meniscus positive lens; the sixth spherical lens is a meniscus positive lens; and the spherical reference mirror is a meniscus negative lens; the aperture of the standard spherical lens is 101.6 mm, and the F number of the standard spherical lens is 0.

56.

5. The standard spherical lens according to claim 4, characterized in that: The focal length of the first spherical lens is FL1, 310 mm < |FL1| < 360 mm; The focal length of the second spherical lens is FL2, 230 mm < |FL2| < 290 mm; The focal length of the third spherical lens is FL3, 300mm<|FL3|<350mm; The focal length of the fourth spherical lens is FL4, 240 mm < |FL4| < 280 mm; The focal length of the fifth spherical lens is FL5, 220 mm < |FL5| < 260 mm; The focal length of the sixth spherical lens is FL6, 240 mm < |FL6| < 300 mm; The focal length of the spherical reference mirror is FL7, 400mm<|FL7|<450mm.

6. The standard spherical lens according to claim 4, wherein: The thickness of the first spherical lens is B1, 15mm<B1<25mm; The thickness of the second spherical lens is A2, 15mm<A2<25mm; The thickness of the third spherical lens is A3, 25mm<A3<35mm; The thickness of the fourth spherical lens is A4, 25mm<A4<35mm; The thickness of the fifth spherical lens is A5, 20mm<A5<30mm; The thickness of the sixth spherical lens is A6, 20mm<A6<30mm; The thickness of the spherical reference mirror is A7, 13mm<A7<23mm.

7. The standard spherical lens according to claim 4, wherein: The air gap between the first spherical lens and the second spherical lens is B1, 30mm<B1<50mm; The air gap between the second spherical lens and the third spherical lens is B2, 10mm<B2<20mm; The air gap between the third spherical lens and the fourth spherical lens is B3, 1mm<B3<10mm; The air gap between the fourth spherical lens and the fifth spherical lens is B4, 1mm<B4<10mm; The air gap between the fifth spherical lens and the sixth spherical lens is B5, 1mm<B5<10mm; The air gap between the sixth spherical lens and the spherical reference mirror is B6, 1mm<B6<10mm.

8. The standard spherical lens according to claim 4, wherein: The first spherical lens, the third spherical lens, the fourth spherical lens, the fifth spherical lens and the sixth spherical lens are all made of heavy flint glass, the second spherical lens is made of light crown glass, and the spherical reference mirror is made of fused quartz.

Citation Information

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