Aspheric surface characterization method based on spherical single lens zero position compensation detection light path

Abstract

The application relates to the technical field of optical aspheric surfaces, in particular to an aspheric surface characterization method based on a zero-position compensation detection light path of a spherical single lens, which is oriented to aspheric surface detection, based on a zero-position compensation detection principle, according to a light ray tracing method, Snell's law and an equal optical path principle, and characterized by various parameters of a zero-position compensation detection system required by an interferometer incident wave front being a spherical wave and a compensator being a single lens, and according to an aspheric surface type defined by the characterization method, the aspheric surface type is called a zero-position aspheric surface. The aspheric surface characterization method can obtain detection-related data in the stage of designing an optical system, and can modulate and constrain characterization parameters of the zero-position aspheric surface according to imaging requirements, so as to balance factors such as system imaging quality, aspheric surface structure, compensator and detection light path rationality, and realize the function of aspheric surface design and detection.

Description

Technical Field

[0001] This invention relates to the field of optical aspherical technology, and in particular to an aspherical characterization method based on a spherical wave single-lens zero-position compensation detection optical path. Background Technology

[0002] Aspherical surfaces are an important type of optical surface shape. Compared to spherical lenses, aspherical lenses can more precisely control the direction and focusing effect of light, thereby achieving higher optical performance and less imaging distortion, and are therefore used in a wide range of fields.

[0003] The manufacturing process of aspherical lenses typically includes three stages: design, fabrication, and inspection. In the design stage, aspherical representation is mostly design-oriented, aiming to modify the surface shape through mathematical description to increase the degrees of freedom for optimization, correct various aberrations in the system, and obtain the optimal design. After design and fabrication, aspherical inspection is used to verify whether the optical performance of the aspherical lens meets the design requirements and to determine its surface shape and errors. Among these methods, the zero-position compensation method is an effective method for inspecting the entire surface of aspherical lenses. The compensator required for this method generally needs to have a simple structure; otherwise, errors in the fabrication and assembly of the compensator will cause the zero-position compensation method to lose its inspection accuracy.

[0004] When using the zero-position compensation method as a detection method, the design of the compensator is closely related to the aspherical surface shape. However, since the aspherical lens is a common part of both the system optical path and the zero-position compensation detection optical path, and in actual production, the system optical path design and the zero-position compensation detection optical path design are carried out sequentially and unidirectionally, the zero-position compensation detection optical path design cannot provide feedback for the system optical path design, and the tolerance of the system optical path cannot be effectively utilized to optimize the zero-position compensation detection optical path. This means that even a tiny deviation in the aspherical surface shape can make the compensator structure extremely complex, rendering the zero-position compensation method infeasible. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the problem that in the prior art, since the design of aspherical surfaces precedes processing and testing, when using the zero-position compensation method for testing, the testing cannot provide feedback for the design, and the tolerance of the system's optical path structure cannot be effectively utilized to fine-tune the testing scheme, resulting in a very complex testing scheme in some cases and reduced testing accuracy.

[0006] To address the aforementioned technical problems, this invention provides an aspherical characterization method based on a spherical wave single-lens null-position compensation detection optical path, comprising:

[0007] In a zero-position compensation detection system where the incident wavefront of the interferometer is set to a spherical wave and the compensator is a single lens, the F-number of the standard spherical mirror of the interferometer is R / D, where R is the back focal length of the standard spherical mirror and D is the aperture of the standard spherical mirror. The radii of curvature of the front and back surfaces of the single lens compensator are r1 and r2, the center thickness of the single lens compensator is d, the refractive index of the material of the single lens compensator is n, the distance between the standard spherical mirror of the interferometer and the single lens compensator is L1, and the distance between the single lens compensator and the aspherical surface is L2.

[0008] In the zero-position compensation detection system, the detection light is emitted from any point A on the standard spherical mirror of the interferometer, intersecting the front and rear surfaces of the single lens at points B and C respectively, and after refraction by the single lens, intersecting the aspherical surface at point Q; the emission height of the detection light on the standard spherical mirror of the interferometer is set as h, which is used as a parameter in the shape of the aspherical surface. h is a continuous variable in the aperture range of the standard spherical mirror of the interferometer [-D / 2, D / 2].

[0009] When all parameters in the zero-position compensation detection optical path are fixed, the detection ray incident at any height h has the same optical path from point A to point Q. In this case, the trajectory function of point Q is the aspherical formula characterized by the single-lens compensator, and its general parametric expression is:

[0010]

[0011] The single-lens compensator and the aspherical surface form a zero-spherical-aberration system. The system follows the principle of equal optical path length. Two detection rays are selected. One detection ray is an on-axis ray passing through the center point O1 of the standard spherical mirror of the interferometer. The path is: O1→O2→O3→O, where O2 is the vertex of the front surface of the single-lens compensator, O3 is the vertex of the rear surface of the single-lens compensator, and O is the center vertex of the aspherical surface. The corresponding optical path length of the on-axis ray is G0=L1+nd+L2.

[0012] The other detection ray is a parametric tracing ray, an off-axis ray, with a path of A→B→C→Q. Based on the parameters of the zero-position compensation detection system, the optical path of the parametric tracing ray is determined to be G1 = l. AB +nl BC +l CM +l MQ ; where l AB Let l be the distance between point A and point B. BC Let l be the distance between points B and C. CM Let l be the distance between point M and point C, the intersection points of the refracted ray CQ on the optical axis. MQ Let M be the distance between the intersection point M and point Q of the refracted ray CQ on the optical axis;

[0013] According to the principle of equal optical path length, we have G0 = G1, and the distance between point Q and point Q on the aspherical surface is l. MQ=L1+nd+L2-l AB -nl BC -l CM ;

[0014] With point O as the origin, the equation of the locus of any point Q on the aspherical surface, i.e., the surface shape expression of the zero-position aspherical surface, is:

[0015]

[0016] Where u'2 is the angle between the refracted ray from the rear surface of the single-lens compensator and the optical axis, and l'2 is the distance from the intersection of the refracted ray from the rear surface of the single-lens compensator and the optical axis to the vertex O3 of the rear surface of the single-lens compensator; the zero-position aspherical surface is a rotationally symmetric surface, and the maximum effective aperture is determined by the actual light-transmitting aperture of the standard spherical mirror of the interferometer.

[0017] In one embodiment of the present invention, determining the optical path length corresponding to the parameter tracing ray based on the parameters of the zero-position compensation detection system includes:

[0018] The detection light is incident from the standard spherical mirror of the interferometer at a height h. The object distance l1 and the angle u1 between the incident ray and the optical axis are obtained according to the detection light path. Given the angle u1 between the incident ray and the optical axis, the angle i1 between the detection ray and the normal to the front surface of the single lens compensator is obtained according to the sine theorem. According to Snell's law, the angle i'1 of refraction of the ray on the front surface of the single lens compensator is obtained.

[0019] Thus, we obtain the angle u'1 between the refracted ray from the front surface of the single-lens compensator and the optical axis, and the distance l'1 from the intersection point of the refracted ray from the front surface of the single-lens compensator on the optical axis to the vertex O2 of the front surface of the single-lens compensator; according to the transition formula of the conjugate spherical system, we obtain the distance l2 between the intersection point of the incident ray from the rear surface of the single-lens compensator on the optical axis and the vertex of the rear surface of the single-lens compensator, and the angle u2 between the incident ray from the rear surface of the single-lens compensator and the optical axis.

[0020] Given the angle u2 between the incident ray on the rear surface of the single-lens compensator and the optical axis, we can obtain the angle i2 between the incident ray on the rear surface of the single-lens compensator and the normal to the rear surface of the single-lens compensator according to the sine theorem; and obtain the angle i'2 of refraction of the ray on the rear surface of the single-lens compensator according to Snell's law.

[0021] Thus, we obtain the angle u'2 between the refracted ray from the rear surface of the single lens compensator and the optical axis, and the distance l'2 from the intersection of the refracted ray from the rear surface of the single lens compensator and the optical axis to the vertex O3 of the rear surface of the single lens compensator.

[0022] Therefore, the radial coordinates of the intersection points B and C of the detection ray and the front and rear surfaces of the single-lens compensator are ρ. B =r1sin(u'1+i'1),ρ C =r2sin(u'2+i'2);

[0023] The distance between point A and point B is The distance between point B and point C is The distance between the intersection point M and point C of the refracted ray CQ on the optical axis is

[0024] In one embodiment of the present invention, the detection light is incident from the standard spherical mirror of the interferometer at a height h, and the object distance l1 = R - L1 and the angle between the incident ray and the optical axis are obtained according to the detection optical path.

[0025] In one embodiment of the present invention, the known angle u1 between the incident ray and the optical axis, according to the law of sines, is: The angle between the detected ray and the normal to the front surface of the single-lens compensator

[0026] In one embodiment of the present invention, the refraction angle of the detection ray on the front surface of the single-lens compensator is obtained according to Snell's law.

[0027] In one embodiment of the present invention, the angle u'1 between the refracted ray from the front surface of the single-lens compensator and the optical axis is u'1 = u1 + i1 - i'1, and the distance from the intersection point of the refracted ray from the front surface of the single-lens compensator on the optical axis to the vertex O2 of the front surface of the single-lens compensator is...

[0028] In one embodiment of the present invention, the distance l2 = l'1 - d between the intersection point of the incident light rays on the rear surface of the single lens compensator on the optical axis and the vertex of the rear surface of the single lens compensator is obtained according to the transition formula of the conjugate spherical system, and the angle u2 = u'1 between the incident light rays on the rear surface of the single lens compensator and the optical axis is obtained.

[0029] In one embodiment of the present invention, the angle u2 between the incident ray from the rear surface of the known single-lens compensator and the optical axis is given by the sine theorem: The angle between the incident ray on the rear surface of the single-lens compensator and the normal to the rear surface of the single-lens compensator.

[0030] In one embodiment of the present invention, according to Snell's law, the refraction angle i'2 of the detection ray on the rear surface of the single lens compensator is obtained as arcsin(n sin i2).

[0031] In one embodiment of the present invention, the angle u'2 between the refracted ray from the rear surface of the single-lens compensator and the optical axis is u'2 = u2 + i2 - i'2, and the distance from the intersection of the refracted ray from the rear surface of the single-lens compensator and the optical axis to the vertex O3 of the rear surface of the single-lens compensator is...

[0032] The technical solution of the present invention has the following advantages compared with the prior art:

[0033] This invention discloses an aspherical characterization method based on a spherical wave single-lens zero-position compensation detection optical path. Guided by the detection method and based on the zero-position compensation detection principle, it utilizes the parameters required for a zero-position compensation detection system with an interferometer incident wavefront of a spherical wave and a single-lens compensator to characterize the aspherical surface shape. This allows for the acquisition of relevant detection data during the optical system design phase and enables the modulation and constraint of the characterization parameters of the zero-position aspherical surface—that is, the parameters required for the zero-position compensator optical path—according to imaging requirements. This achieves a balance between system imaging quality, aspherical surface structure, and the rationality of the compensator and detection optical path. This aspherical characterization method not only verifies the role of the zero-position aspherical surface in the optical system but also effectively improves the feasibility of the zero-position compensation method and reduces the difficulty of aspherical surface shape detection.

[0034] Therefore, the aspherical characterization method achieves the function of detecting aspherical designs under the condition that the incident wave in the interferometer is a spherical wave and the compensator is a single lens with zero-position compensation detection optical path. Attached Figure Description

[0035] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein...

[0036] Figure 1 This is the meridional cross-section optical path diagram of the zero-position compensation detection system provided by the present invention, which uses the interferometer incident wavefront as a spherical wave and the compensator as a single lens.

[0037] Figure 2 This is a layout diagram of the zero-position aspherical surface in ZEMAX provided in an embodiment of the present invention;

[0038] Figure 3 This is an optical layout diagram of the zero-position aspherical surface established in ZEMAX according to an embodiment of the present invention;

[0039] Figure 4 This is the detection result of the zero-position aspherical surface provided in the embodiment of the present invention. Detailed Implementation

[0040] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0041] This invention provides an aspherical characterization method based on a spherical wave single-lens zero-position compensation detection optical path, guided by detection methods, and defines a type of aspherical surface called zero-position aspherical surface.

[0042] In a zero-position compensation detection system where the incident wave of the interferometer is a spherical wave and the compensator is a single lens, the F-number of the standard spherical mirror of the interferometer is set to R / D (R is the back focal length of the standard spherical mirror and D is the aperture of the standard spherical mirror), the radii of curvature of the front and back surfaces of the single lens compensator are r1 and r2, the center thickness of the single lens compensator is d, the refractive index of the material of the single lens compensator is n, the distance between the standard spherical mirror of the interferometer and the single lens compensator is L1, and the distance between the single lens compensator and the aspherical surface is L2.

[0043] Reference Figure 1 As shown, the detection ray exits from any point A on the standard spherical mirror of the interferometer, intersecting the front and rear surfaces of the single lens at points B and C, respectively. After refraction by the single lens, it intersects the aspherical surface at point Q. The exit height of the detection ray on the standard spherical mirror of the interferometer is set to h, which is used as a parameter in the derivation of the aspherical surface shape. h is a continuous variable within the aperture range of the standard spherical mirror [-D / 2, D / 2].

[0044] The coordinates of any point Q(z) on the aspherical surface Q ,ρ Q The aspherical surface can be calculated using ray tracing methods using the radius of curvature R of the interferometer's standard spherical mirror, the radii of curvature r1 and r2 of the front and rear surfaces of the single-lens compensator, the center thickness d of the single-lens compensator, the refractive index n of the lens material, the distance L1 between the interferometer's standard spherical mirror and the single-lens compensator, and the distance L2 between the single-lens compensator and the aspherical surface. When all parameters in the zero-position compensation detection optical path are fixed, the detection ray incident at any height h has the same optical path from point A to point Q. The trajectory function at point Q is then the zero-position aspherical surface formula represented by the single-lens compensator, and its general parametric expression is as follows:

[0045]

[0046] The symbols for the parameters used in ray tracing are defined as follows: along the axial segments such as l, l', and r, with the vertex O of the refraction surface as the origin, positive from left to right; the angles u and u' between the ray and the optical axis, positive when the optical axis rotates clockwise and negative when it rotates counterclockwise; the angles i and i' between the ray and the normal, positive when the ray rotates clockwise and negative when it rotates counterclockwise; and the distances d, L1, and L2, calculated from the vertex of the previous surface to the vertex of the next surface, positive from left to right.

[0047] The detection light is incident from the standard spherical mirror of the interferometer at a height h, with an object distance of l1. Based on the detection light path:

[0048] l1=R-L1

[0049] The angle u1 between the incident ray and the optical axis is:

[0050]

[0051] Given u1, according to the Law of Sines:

[0052]

[0053] The angle i1 between the detection ray and the normal to the front surface of the single-lens compensator is:

[0054]

[0055] According to Snell's law, the refraction angle i'1 of the detection ray at the front surface of the single-lens compensator is obtained as:

[0056]

[0057] Therefore, the angle u'1 between the refracted ray BC and the optical axis on the front surface of the single lens compensator is:

[0058] u'1=u1+i1-i'1

[0059] The distance l'1 from the point where the refracted rays BC intersect on the optical axis at the front surface of the single-lens compensator to the vertex O2 of the front surface of the single-lens compensator is:

[0060]

[0061] According to the transition formula for the conjugate spherical system, the distance between the intersection point of the incident light rays on the rear surface of the single-lens compensator and the vertex of the rear surface of the single-lens compensator is l2 = l'1 - d, and the angle between the incident light rays on the rear surface of the single-lens compensator and the optical axis is u2 = u'1.

[0062] Given u2, according to the Law of Sines:

[0063]

[0064] The angle i2 between the incident ray BC (i.e., the refracted ray BC) on the rear surface of the single-lens compensator and the normal to the rear surface of the single-lens compensator is:

[0065]

[0066] According to Snell's law, the angle of refraction i'2 of the detected ray at the rear surface of the single-lens compensator is:

[0067] i'2 = arcsin(n sin i2)

[0068] Therefore, the angle u'2 between the refracted ray CQ and the optical axis at the rear surface of the single-lens compensator is:

[0069] u'2=u2+i2-i'2

[0070] The distance l'2 from the point where the refracted ray CQ intersects the optical axis at the rear surface of the single-lens compensator to the vertex O3 of the rear surface of the single-lens compensator is:

[0071]

[0072] Therefore, the radial coordinates of the intersection points B and C of the detection ray and the front and rear surfaces of the single-lens compensator are obtained as follows:

[0073] ρ B =r1sin(u'1+i'1)

[0074] ρ C =r2sin(u'2+i'2)

[0075] The distance between point A and point B is:

[0076]

[0077] The distance between point B and point C is:

[0078]

[0079] The distance between point M and point C, where the refracted ray CQ intersects on the optical axis, is:

[0080]

[0081] A single-lens compensator and an aspherical surface form a zero-spherical-aberration system, which follows the principle of equal optical path length. Two detection rays are selected. One detection ray is an on-axis ray passing through the center point O1 of the standard spherical mirror of the interferometer, with the path: O1→O2→O3→O. Point O is the center vertex of the zero-spherical-aberration aspherical surface, and the corresponding optical path length is:

[0082] G0 = L1 + nd + L2

[0083] The other detection ray is a parametric tracing ray, an off-axis ray, with a path of A→B→C→Q, and the corresponding optical path length is:

[0084] G1 = l AB +nl BC +l CM +l MQ

[0085] According to the principle of equal optical path length, G0 = G1, from which the distance between point M and point W on the aspherical surface is obtained as:

[0086] lMQ =L1+nd+L2-l AB -nl BC -l CM

[0087] With point O as the origin, the coordinates of point Q are expressed as follows:

[0088]

[0089] This equation represents the trajectory equation of any point Q on the zero-position aspherical surface, i.e., the surface shape expression of the zero-position aspherical surface. The zero-position aspherical surface is a rotationally symmetric surface, and its maximum effective aperture is determined by the actual light-transmitting aperture of the interferometer's standard spherical mirror.

[0090] Based on the characterization parameters of the zero-position aspherical surface, a zero-position compensation detection optical path is constructed. The detection rays emitted from the interferometer standard mirror at different heights correspond to different points on the zero-position aspherical surface. The optical path follows the principle of equal optical path. Therefore, after the light is reflected by the aspherical surface, it returns along the original optical path and is re-formed into a spherical wave after passing through the single lens compensator. It then interferes with the reference wave inside the interferometer, reflecting the surface information of the aspherical surface being measured.

[0091] In this embodiment, the custom zero-position aspherical surface is completed in the optical software ZEMAX using dynamic link libraries, and the surface is drawn according to the surface shape equation of the zero-position aspherical surface. The aperture of the zero-position aspherical surface is set to 60mm, and the surface shape parameters are R = 90mm, r1 = 95mm, r2 = -72.5mm, d = 10mm, L1 = 50mm, L2 = 150mm, and n = 1.515089. The layout diagram of the obtained zero-position aspherical surface in ZEMAX is shown below. Figure 2 As shown.

[0092] In this embodiment, to verify whether the detection results meet the requirements for zero-position detection, a zero-position compensation detection system is constructed using the optical software ZEMAX, with the interferometer incident wavefront as a spherical wave and the compensator as a single lens. The single-lens compensator is used to detect the zero-position aspherical surface whose corresponding system parameters are used as surface shape parameters. That is, the surface shape parameters of the detected zero-position aspherical surface are the same as the parameters of the constructed zero-position compensation detection system.

[0093] The surface shape parameters of the zero-position aspherical surface in the zero-position compensation detection system are set as follows: R = 90 mm, r1 = 75 mm, r2 = -62.5 mm, d = 5 mm, L1 = 18 mm, L2 = 125 mm, and n = 1.515089.

[0094] The parameters of the zero-position compensation detection system are set as follows: entrance pupil diameter is 30mm, back focal length of the interferometer standard spherical mirror is 90mm, front surface curvature radius of curvature of the single lens compensator is 75mm, back surface curvature radius of curvature of the single lens is -62.5mm, single lens thickness is 5mm, single lens material is N-BK7 glass, distance between the interferometer standard spherical mirror and the compensator is 18mm, and distance between the compensator and the aspherical surface is 125mm.

[0095] The optical layout diagram of the zero-position aspherical surface established in ZEMAX is shown below. Figure 3 As shown, the detection of zero-position aspherical surfaces can be completed directly without optimizing the detection system.

[0096] The detection results of the zero-position aspherical surface are as follows: Figure 4 As shown, the maximum radius of the circle of confusion on the ideal focal plane is 0.023 μm, the residual wavefront difference (PV) is 0.0005λ, and the RMS value is 0.0001λ, which meets the zero-point compensation test standard.

[0097] In summary, the null-position aspherical surface can be customized in the optical software ZEMAX and meets the testing requirements, achieving the function of design-based testing. During the design phase, the parameters of the null-position compensation testing system can be directly obtained simultaneously with the surface shape design of the null-position aspherical surface. Furthermore, the characterization parameters of the null-position aspherical surface, i.e., the parameters required by the optical path of the null-position compensator, can be modulated and constrained according to imaging needs, achieving a balance between system imaging quality, aspherical surface shape structure, compensator, and the rationality of the detection optical path. During the testing phase, the surface shape testing of the null-position aspherical surface is simpler, eliminating the need for surface shape verifiability assessment, effectively improving the feasibility of the null-position compensation method and reducing the difficulty of aspherical surface shape testing.

[0098] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0099] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0100] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0101] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0102] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. An aspherical characterization method based on a spherical wave single-lens null-position compensation detection optical path, characterized in that, include: In a zero-position compensation detection system where the incident wavefront of the interferometer is a spherical wave and the compensator is a single-lens compensator, the standard spherical mirror of the interferometer... Number of ,in For the back focal length of the standard spherical mirror of the interferometer, The aperture of the standard spherical mirror of the interferometer is given, and the radii of curvature of the front and rear surfaces of the single-lens compensator are given. and The center thickness of the single-lens compensator is The refractive index of the material of the single lens compensator is The distance between the standard spherical mirror of the interferometer and the single-lens compensator is The distance between the single-lens compensator and the aspherical surface is ; In a zero-position compensation detection system, the detection light beam originates from any point on the standard spherical mirror of the interferometer. Point emission, intersecting the front and rear surfaces of the single lens respectively. Point and The point, after refraction by a single lens, intersects the aspherical surface at... Point; set the exit height of the detection ray at the standard spherical mirror of the interferometer as... It is used as a parameter in the aspherical shape. Within the range of the standard spherical mirror aperture of the interferometer The variables inside are continuous variables; When all parameters in the zero-position compensation detection system are fixed, the detection light beam travels at any height. Incident, by Click The optical path lengths are all the same at this point. The trajectory function of a point is the aspherical formula represented by a single-lens compensator, and its general parametric expression is as follows: ； The single-lens compensator and the aspherical surface form a zero-spherical-aberration system. The system follows the principle of equal optical path length and selects two detection rays, one of which passes through the center point of the standard spherical mirror of the interferometer. The path of the on-axis ray from the point is: ,in, The point is the vertex of the front surface of the single-lens compensator. The point is the vertex of the rear surface of the single-lens compensator. The point is the center vertex of the aspherical surface; the optical path length of the ray on the axis is... ; The other detection ray is a parametric tracing ray, an off-axis ray, with the following path: Based on the parameters of the zero-position compensation detection system, the optical path length corresponding to the parameter tracing ray is determined to be... ;in for Point and Distance between points for Point and Distance between points To refract light Intersection on the optical axis Point and Distance between points To refract light Intersection on the optical axis Point and Distance between points; According to the principle of equal optical path length, we have ,get Points and non-spherical surfaces The distance between the points is ; by The point is the origin of the coordinate system, and is any point on the non-spherical surface. The trajectory equation, that is, the surface shape expression of the zero-position aspherical surface, is: ； in The angle between the refracted ray from the rear surface of the single-lens compensator and the optical axis. The point where the refracted ray from the rear surface of the single-lens compensator intersects the optical axis and reaches the vertex of the rear surface of the single-lens compensator. The distance; the zero-position aspherical surface is a rotationally symmetric surface, and the maximum effective aperture is determined by the actual light-transmitting aperture of the interferometer's standard spherical mirror.

2. The aspherical characterization method based on a spherical wave single-lens null-position compensation detection optical path according to claim 1, characterized in that, Determining the optical path length corresponding to the parameter tracing ray based on the parameters of the zero-position compensation detection system includes: Detection light at high The object distance is obtained by observing the light incident through the standard spherical mirror of the interferometer and the detection optical path. and the angle between the incident ray and the optical axis The angle between the incident ray and the optical axis is known. According to the law of sines, the angle between the detection ray and the normal to the front surface of the single-lens compensator is obtained. According to Snell's law, the angle of refraction of light on the front surface of the single-lens compensator is obtained. ; This yields the angle between the refracted ray from the front surface of the single-lens compensator and the optical axis. The intersection of the refracted rays from the front surface of the single-lens compensator on the optical axis and the vertex of the front surface of the single-lens compensator. distance Based on the transition formula for conjugate spherical systems, the distance between the intersection point of the incident rays on the rear surface of a single-lens compensator along the optical axis and the vertex of the rear surface of the single-lens compensator is obtained. and the angle between the incident ray from the rear surface of the single-lens compensator and the optical axis ; Given the angle between the incident ray from the rear surface of a single-lens compensator and the optical axis. According to the law of sines, the angle between the incident ray on the rear surface of the single-lens compensator and the normal to the rear surface of the single-lens compensator can be obtained. According to Snell's law, the angle of refraction of light at the rear surface of the single-lens compensator is obtained. ; This yields the angle between the refracted ray from the rear surface of the single-lens compensator and the optical axis. The point where the refracted ray from the rear surface of the single-lens compensator intersects the optical axis reaches the vertex of the rear surface of the single-lens compensator. distance ; Therefore, the intersection of the detection light rays with the front and rear surfaces of the single-lens compensator is... , The radial coordinates are , ; but Point and The distance between the points is ; Point and The distance between the points is Refracted light Intersection on the optical axis Point and The distance between points is .

3. The aspherical characterization method based on a spherical wave single-lens null-position compensation detection optical path according to claim 2, characterized in that, The detection light is at a high frequency The object distance is obtained by observing the light incident through the standard spherical mirror of the interferometer and the detection optical path. and the angle between the incident ray and the optical axis .

4. The aspherical characterization method based on the spherical wave single-lens null compensation detection optical path according to claim 2, characterized in that, The known angle between the incident ray and the optical axis According to the Law of Sines, we have The angle between the detected ray and the normal to the front surface of the single-lens compensator is... .

5. The aspherical characterization method based on a spherical wave single-lens null-position compensation detection optical path according to claim 2, characterized in that, According to Snell's law, the angle of refraction of the detected light at the front surface of the single-lens compensator is obtained. .

6. The aspherical characterization method based on the spherical wave single-lens null compensation detection optical path according to claim 2, characterized in that, The angle between the refracted light rays on the front surface of the single-lens compensator and the optical axis The intersection of the refracted rays from the front surface of the single-lens compensator on the optical axis and the vertex of the front surface of the single-lens compensator. distance .

7. The aspherical characterization method based on a spherical wave single-lens null-position compensation detection optical path according to claim 2, characterized in that, The distance between the intersection point of the incident rays on the optical axis of the rear surface of the single-lens compensator and the vertex of the rear surface of the single-lens compensator is obtained according to the transition formula of the conjugate spherical system. and the angle between the incident ray from the rear surface of the single-lens compensator and the optical axis .

8. The aspherical characterization method based on a spherical wave single-lens null-position compensation detection optical path according to claim 2, characterized in that, The angle between the incident ray from the rear surface of the known single-lens compensator and the optical axis According to the Law of Sines, we have The angle between the incident ray from the rear surface of the single-lens compensator and the normal to the rear surface of the single-lens compensator is... .

9. The aspherical characterization method based on a spherical wave single-lens null-position compensation detection optical path according to claim 2, characterized in that, According to Snell's law, the angle of refraction of the detected light at the rear surface of the single-lens compensator is obtained. .

10. The aspherical characterization method based on a spherical wave single-lens null-position compensation detection optical path according to claim 2, characterized in that, The angle between the refracted light rays from the rear surface of the single-lens compensator and the optical axis The point where the refracted ray from the rear surface of the single-lens compensator intersects the optical axis reaches the vertex of the rear surface of the single-lens compensator. distance .

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