Freeform surface characterization method based on CGH lens zero position compensation detection light path

Abstract

The present application relates to the technical field of optical aspheric surface, especially points to a kind of free curved surface characterization method based on CGH lens zero position compensation detection optical path, with the detection of free curved surface as the guide, based on zero position compensation detection principle, according to ray tracing method, Snell's law, diffraction principle and equal optical path principle, using the parameters required by interferometer incident wave front as plane wave, compensator as single CGH lens zero position compensation detection system indirectly characterizes free curved surface shape, by using XY polynomial and Zernike standard phase polynomial, the mathematical description of free curved surface is realized in design stage can determine its measurement scheme, and according to the characterization method self-defined a kind of aspheric surface type, called zero position free curved surface.The free curved surface characterization method improves the degree of freedom of free curved surface shape and the feasibility of zero position compensation method, reduces the detection difficulty of free curved surface shape, realizes the function of zero position free curved surface design can be detected.

Description

Technical Field

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

[0002] Optical freeform surfaces are advanced optical elements, typically composed of complex, non-rotationally symmetric surfaces. Unlike traditional spherical or aspherical lenses, they can be designed and manufactured in any shape to meet various application requirements.

[0003] Freeform surfaces can be effectively used in imaging optical systems to expand the field of view and reduce aberrations or add special effects, showing promising application prospects. However, due to the complex shape and high surface accuracy requirements of freeform surfaces in imaging optical systems, the final processing and inspection of optical manufacturing processes are difficult, which greatly limits their application.

[0004] In the detection of freeform surfaces, computational holograms (CGHs) can flexibly diffract wavefronts of arbitrary shapes, acting as phase compensators to replace complex refracting lens combinations. The null-compensation testing method is currently the most accurate method for measuring the surface shape of optical elements. By introducing various compensators, gradient compensation is performed on the measured object to achieve null-position interferometry. A CGH device is a binary optical diffraction element that can generate freeform wavefronts of arbitrary shapes, making it highly suitable for null-position interferometry of optical freeform surfaces.

[0005] However, the CGH method is a one-to-one detection method, and the design of the compensator is closely related to the shape of the freeform surface. Since the freeform lens is a common part of the system optical path and the zero-position compensation detection optical path, and in actual production, the design of the system optical path and the design of the zero-position compensation detection optical path are carried out sequentially and unidirectionally, the design of the zero-position compensation detection optical path cannot provide feedback for the design of the system optical path, and it is impossible to effectively utilize the tolerance of the system optical path to optimize the zero-position compensation detection optical path. This means that even a very small deviation in the shape of the freeform surface can make the compensator structure very complex, rendering the zero-position compensation method infeasible. Summary of the Invention

[0006] 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 freeform surfaces precedes processing and inspection, when using the zero-position compensation method for inspection, the inspection cannot provide feedback for the design, and the tolerance of the system optical path structure cannot be effectively utilized to fine-tune the inspection scheme, resulting in a very complex inspection scheme in some cases and reduced inspection accuracy.

[0007] To address the aforementioned technical problems, this invention provides a freeform surface characterization method based on a CGH lens null-compensation detection optical path, comprising:

[0008] In a zero-position compensation detection system where the incident wavefront of the interferometer is set to a plane wave and the compensator is a single CGH lens, the aperture of the interferometer standard mirror is D, the wavelength of the detection light is λ, the phase of the diffraction surface of the single CGH lens compensator is φ, the diffraction order is M, the radius of curvature of the refractive surface is r, the center thickness of the single CGH lens compensator is d, the refractive index of the material of the single CGH lens compensator is n, and the distance between the single CGH lens compensator and the freeform surface is L.

[0009] Based on the characterization parameters of the custom zero-position freeform surface, a zero-position compensation detection optical path is constructed. The detection light rays of the interferometer standard mirror are incident parallel to each other. Different heights and different diffraction orders correspond to different points on the freeform surface. This optical path follows the principle of equal optical path, the principle of diffraction, and Snell's law. Therefore, after the light rays are reflected by the freeform surface, they return along the original optical path. After passing through the single CGH lens compensator, they are re-formed into a plane wave, which interferes with the reference wave inside the interferometer, thereby reflecting the surface information of the measured freeform surface.

[0010] In the zero-position compensation detection system model, the phase function of the diffraction surface is either the binary optical surface 1 in the non-rotational symmetry form or the Zerinke standard phase. When the phase function of the diffraction surface is the binary optical surface 1 in the non-rotational symmetry form, the plane wave single CGH lens compensation detection optical path forms a zero-position freeform surface characterized by the XY polynomial. When the phase function of the diffraction surface is the Zerinke standard phase in the non-rotational symmetry form, the plane wave single CGH lens compensation detection optical path forms a zero-position freeform surface characterized by the Zernike polynomial.

[0011] The detection light is incident as a plane wave, and the single CGH lens compensator and the freeform surface form a zero spherical aberration system, which follows the principle of equal optical path length.

[0012] Based on the principle of equal optical path length, two detection rays are selected. One ray is the ray emitted from the center point of the diffraction surface, and the other ray is the parametric tracing ray, i.e., the off-axis ray. According to the parameters of the zero-position compensation detection system, the optical path length corresponding to the parametric tracing ray is determined, and the expressions of the two optical paths are combined to obtain the trajectory equation of the intersection point Q of the detection ray and the freeform surface, i.e., the custom zero-position freeform surface shape expression.

[0013] The zero-position freeform surface is a non-rotationally symmetric surface, and its maximum effective aperture is determined by the actual light-transmitting aperture of the interferometer's standard mirror.

[0014] In one embodiment of the present invention, taking the planar optical surface as a reference, when the phase function of the diffraction surface is a binary optical surface 1 in a non-rotationally symmetric form, only the change in its phase is considered, and the phase expression of the binary optical surface 1 is:

[0015]

[0016] Where M is the diffraction order, N is the number of polynomial terms, and C i Let x and y be the coefficient of the i-th term, and x and y be the coordinates under normalization.

[0017] In one embodiment of the present invention, when the diffraction surface of the single CGH lens compensator faces the incident plane wave, the detection ray is emitted parallel to the interferometer standard mirror, intersecting the binary optical surface 1 at point A. The M-order diffracted ray is emitted and intersects the refractive surface at point B, and the refracted ray intersects the freeform surface at point Q. The incident height h of the detection ray at the interferometer standard mirror is set. x h y and h x h y As a parameter of the freeform surface shape, h x h y Within the range of the standard mirror aperture of the interferometer The variables inside are continuous variables;

[0018] The trajectory equation formed by point Q at this point is the zero-position freeform surface formula characterized by the front surface of the single CGH lens compensator being a binary optical surface 1. The parametric expression based on the XY polynomial is:

[0019]

[0020] According to the principle of equal optical path, two detection rays are selected. One ray is the ray emitted from the center point O1 of the diffraction surface of the single CGH lens compensator, and the path is O1→O2→O. Among them, point O2 is the center vertex of the rear surface of the single CGH lens compensator, and point O is the center vertex of the freeform surface. The corresponding optical path is G0=n·d+L.

[0021] The other ray is the parametric tracing ray, i.e., the off-axis ray, with a path of A→B→Q. Based on the parameters of the zero-position compensation detection system, the optical path length of the parametric tracing ray is determined to be... Among them l AB Let l be the distance between point A and point B. BQ Let B be the distance between point B and point Q on the freeform surface;

[0022] According to the principle of equal optical path length, we have G0 = G1, so the distance between point B and point Q on the freeform surface is...

[0023] Based on the parameters of the zero-position compensation detection system, determine The direction vector of the light ray is represented as

[0024] With point O as the origin, and the front surface of the single CGH lens compensator in the zero-position compensation detection system being a binary optical surface 1, the trajectory equation of any point Q on the zero-position freeform surface, i.e., the expression for the surface shape of the zero-position freeform surface based on the XY polynomial characterization, is as follows:

[0025]

[0026] The zero-position freeform surface characterized by the XY polynomial is a non-rotationally symmetric surface, and its maximum effective aperture is determined by the actual light-transmitting aperture of the interferometer's standard spherical mirror.

[0027] In one embodiment of the present invention, when the diffraction surface of the single CGH lens compensator faces the zero-position freeform surface, the detection light is emitted parallel to the interferometer standard mirror, intersecting the refracting surface at point A, the refracted light intersects the diffraction surface at point B, the M-order diffracted light is emitted, and the emitted light intersects the freeform surface at point Q; the incident height h of the detection light at the interferometer standard mirror is set. x h y and h x h y As a parameter of the freeform surface shape, h x h y Within the range of the standard mirror aperture of the interferometer The variables inside are continuous variables;

[0028] The trajectory equation formed by point Q at this point is the zero-position freeform surface formula characterized by the rear surface of the single CGH lens compensator being a binary optical surface 1. The parametric expression based on the XY polynomial is:

[0029]

[0030] According to the principle of equal optical path, two detection rays are selected. One ray is the ray emitted from the center point O1 of the refractive surface of the single CGH lens compensator, and the path is O1→O2→O. Among them, point O2 is the center vertex of the rear surface of the single CGH lens compensator, and point O is the center vertex of the freeform surface. The corresponding optical path is G0=n·d+L.

[0031] The other ray is the parametric tracing ray, i.e., the off-axis ray, with a path of A→B→Q. Based on the parameters of the zero-position compensation detection system, the optical path length of the parametric tracing ray is determined to be... Among them l AB Let l be the distance between point A and point B. BQ Let B be the distance between point B and point Q on the freeform surface;

[0032] According to the principle of equal optical path length, we have G0 = G1, so the distance between point B and point Q on the freeform surface is...

[0033] Based on the parameters of the zero-position compensation detection system, determine The direction vector of the light ray is represented as

[0034] With point O as the origin, and the rear surface of the single CGH lens compensator in the zero-position compensation detection system being a binary optical surface 1, the trajectory equation of any point Q on the zero-position freeform surface, i.e., the expression for the surface shape of the zero-position freeform surface based on the XY polynomial characterization, is as follows:

[0035]

[0036] The zero-position freeform surface characterized by the XY polynomial is a non-rotationally symmetric surface, and its maximum effective aperture is determined by the actual light-transmitting aperture of the interferometer's standard spherical mirror.

[0037] In one embodiment of the present invention, when the phase function of the diffraction surface is the Zerinke standard phase in the non-rotationally symmetric form, its phase expression is:

[0038]

[0039] Where M is the diffraction order, N is the number of coefficient terms in the Zernike polynomial, and C i Zernike polynomial coefficients, Z i The expression is a Zernike polynomial, where ρ is the normalized radial coordinate. Let be the coordinates of the ray in the angular direction.

[0040] In one embodiment of the present invention, when the diffraction surface of the single CGH lens compensator faces the incident plane wave, the detection ray is emitted parallel to the interferometer standard mirror, intersecting the Zernike standard phase plane at point A. The M-order diffracted ray is emitted and intersects the refractive surface at point B. The refracted ray then intersects the freeform surface at point Q. The incident height h of the detection ray at the interferometer standard mirror is set. x h y and h x h y As a parameter of the freeform surface shape, h x h y Within the range of the standard mirror aperture of the interferometer The variables inside are continuous variables;

[0041] The trajectory equation formed by point Q at this point is the zero-position freeform surface formula characterized by the Zernike standard phase plane on the front surface of the single CGH lens compensator. The parametric expression based on the Zernike polynomial is:

[0042]

[0043] According to the principle of equal optical path, two detection rays are selected. One ray is the ray emitted from the center point O1 of the diffraction surface of the single CGH lens compensator, and the path is O1→O2→O. Among them, point O2 is the center vertex of the rear surface of the single CGH lens compensator, and point O is the center vertex of the freeform surface. The corresponding optical path is G0=n·d+L.

[0044] The other ray is the parametric tracing ray, i.e., the off-axis ray, with a path of A→B→Q. Based on the parameters of the zero-position compensation detection system, the optical path length of the parametric tracing ray is determined to be... Among them l AB Let l be the distance between point A and point B. BQ Let B be the distance between point B and point Q on the freeform surface;

[0045] According to the principle of equal optical path length, we have G0 = G1, so the distance between point B and point Q on the freeform surface is...

[0046] Based on the parameters of the zero-position compensation detection system, determine The direction vector of the light ray is represented as

[0047] With point O as the origin, and the front surface of the single CGH lens compensator in the zero-position compensation detection system being the Zernike standard phase plane, the trajectory equation of any point Q on the zero-position freeform surface, i.e., the expression for the surface shape of the zero-position freeform surface based on the Zernike polynomial, is as follows:

[0048]

[0049] The zero-position freeform surface characterized by Zernike polynomials is a non-rotationally symmetric surface, and its maximum effective aperture is determined by the actual light-transmitting aperture of the interferometer's standard spherical mirror.

[0050] In one embodiment of the present invention, when the diffraction surface of the single CGH lens compensator faces the zero-position freeform surface, the detection light is emitted parallel to the interferometer standard mirror, intersecting the refracting surface at point A, the refracted light intersects the diffraction surface at point B, the M-order diffracted light is emitted, and the emitted light intersects the freeform surface at point Q; the incident height h of the light at the interferometer standard mirror is set. x h y and h xh y As a parameter of the freeform surface shape, h x h y Within the range of the standard mirror aperture of the interferometer The variables inside are continuous variables;

[0051] The trajectory equation formed by point Q at this point is the zero-position freeform surface formula characterized by the Zernike standard phase plane on the rear surface of the single CGH lens compensator. The parametric expression based on the Zernike polynomial is:

[0052]

[0053] According to the principle of equal optical path, two detection rays are selected. One ray is the ray emitted from the center point O1 of the refractive surface of the single CGH lens compensator, and the path is O1→O2→O. Among them, point O2 is the center vertex of the rear surface of the single CGH lens compensator, and point O is the center vertex of the freeform surface. The corresponding optical path is G0=n·d+L.

[0054] The other ray is the parametric tracing ray, i.e., the off-axis ray, with a path of A→B→Q. Based on the parameters of the zero-position compensation detection system, the optical path length of the parametric tracing ray is determined to be... Among them l AB Let l be the distance between point A and point B. BQ Let B be the distance between point B and point Q on the freeform surface;

[0055] According to the principle of equal optical path length, we have G0 = G1, so the distance between point B and point Q on the freeform surface is...

[0056] Based on the parameters of the zero-position compensation detection system, determine The direction vector of the light ray is represented as

[0057] With point O as the origin, and the rear surface of the single CGH lens compensator in the zero-position compensation detection system being the Zernike standard phase plane, the trajectory equation of any point Q on the zero-position freeform surface, i.e., the expression for the surface shape of the zero-position freeform surface based on the Zernike polynomial, is as follows:

[0058]

[0059] The zero-position freeform surface characterized by Zernike polynomials is a non-rotationally symmetric surface, and its maximum effective aperture is determined by the actual light-transmitting aperture of the interferometer's standard spherical mirror.

[0060] The technical solution of the present invention has the following advantages over the prior art:

[0061] The present invention discloses a freeform surface characterization method based on a CGH lens zero-position compensation detection optical path. Guided by the detection method, the detection optical path is designed based on the zero-position compensation measurement principle and the diffraction optics principle. The freeform surface shape is indirectly characterized by the parameters required for a zero-position compensation detection system with an interferometer incident wavefront of a plane wave and a single CGH lens as the compensator. By using the XY polynomial and the Zernike standard phase polynomial, the mathematical description of the freeform surface can be determined at the design stage, and a custom zero-position freeform surface is proposed.

[0062] The freeform surface characterization method based on the zero-position compensation detection optical path of the CGH lens can determine its measurement scheme in the design stage through the mathematical description of the freeform surface, which improves the degree of freedom of the freeform surface shape and the feasibility of the zero-position compensation method, simplifies the detection structure of the optical system and improves its efficiency and accuracy, reduces the detection difficulty of the freeform surface shape, and realizes the function of zero-position freeform surface design for detection.

[0063] Therefore, the freeform surface characterization method based on the CGH lens zero-position compensation detection optical path can be tested based on the zero-position freeform surface design. By considering the limitations of detection during the design process, production efficiency can be improved. By meeting the detection requirements, the time spent on repeated trials and adjustments is reduced, and ineffective designs are avoided, thereby improving production efficiency. Attached Figure Description

[0064] 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...

[0065] Figure 1 The present invention provides a three-dimensional optical path diagram of the zero-position compensation detection system model when the incident wavefront of the interferometer is a plane wave and the front surface of the single CGH lens compensator is a binary optical surface 1.

[0066] Figure 2 The present invention provides a three-dimensional optical path diagram of the zero-position compensation detection system model when the incident wavefront of the interferometer is a plane wave and the rear surface of the single CGH lens compensator is a binary optical surface 1.

[0067] Figure 3 This invention provides a three-dimensional optical path diagram of a zero-position compensation detection system model when the incident wavefront of the interferometer is a plane wave and the front surface of the single CGH lens compensator is the Zernike standard phase plane.

[0068] Figure 4 The present invention provides a three-dimensional optical path diagram of a zero-position compensation detection system model when the incident wavefront of the interferometer is a plane wave and the rear surface of the single CGH lens compensator is the Zernike standard phase plane. Detailed Implementation

[0069] 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.

[0070] This invention provides a freeform surface characterization method based on a detection method and a single CGH lens zero-position compensation detection optical path with a plane wave and a binary optical surface 1 or the Zernike standard phase surface as the diffraction surface. It also defines a freeform surface type, which is called a zero-position freeform surface.

[0071] In a zero-position compensation detection system where the incident wave in the interferometer is a plane wave and the compensator is a single CGH lens, the aperture of the interferometer standard mirror is set to D, the wavelength of the detection light is λ, the phase of the diffraction surface of the single CGH lens compensator is φ, the diffraction order is M, the radius of curvature of the refractive surface is r, the center thickness of the single CGH lens compensator is d, the refractive index of the material of the single CGH lens compensator is n, and the distance between the single CGH lens compensator and the freeform surface is L.

[0072] Based on the characterization parameters of the aforementioned custom zero-position freeform surface, a zero-position compensation detection optical path is constructed. The detection light rays of the interferometer standard mirror are incident parallel to each other. Different heights and different diffraction orders correspond to different points on the freeform surface. This optical path follows the principle of equal optical path, the principle of diffraction, and Snell's law. Therefore, after the light rays are reflected by the freeform surface, they return along the original optical path and are re-formed into a plane wave after passing through a single CGH lens compensator. Inside the interferometer, the plane wave interferes with the reference wave, thereby reflecting the surface information of the measured freeform surface.

[0073] In the zero-position compensation detection system model, the phase function of the diffraction surface is either the binary optical surface 1 in the non-rotational symmetry form or the Zerinke standard phase. When the phase function of the diffraction surface is the binary optical surface 1 in the non-rotational symmetry form, the plane wave single CGH lens compensation detection optical path forms a zero-position freeform surface characterized by the XY polynomial. When the phase function of the diffraction surface is the Zerinke standard phase in the non-rotational symmetry form, the plane wave single CGH lens compensation detection optical path forms a zero-position freeform surface characterized by the Zernike polynomial.

[0074] When the phase function of the diffraction surface is the binary optical surface 1 in the non-rotationally symmetric form, the derivation process of the surface shape characterization of the zero-position freeform surface is as follows.

[0075] This invention uses a planar optical surface as a reference. When the phase function of the diffraction surface is a binary optical surface 1 in a non-rotationally symmetric form, only the phase change is considered. The phase expression of the binary optical surface 1 is:

[0076]

[0077] Where M is the diffraction order, N is the number of polynomial terms, and C i Let x and y be the coefficient of the i-th term, and x and y be the coordinates under normalization.

[0078] The binary optical surface 1 is not limited to two steps, but can be made into two steps. n The diffraction efficiency of a binary optical surface 2 is related to the number of steps; the more steps, the higher the efficiency. For example, a binary optical surface 2 with two steps has a first-order diffraction efficiency of 40.5%, while a binary optical surface 2 with four steps has a first-order diffraction efficiency of 81.1%. However, as the number of steps increases, the manufacturing process becomes more complex. Therefore, the number of steps in the design should be determined based on specific requirements.

[0079] The following section categorizes the cases where the diffraction surface of a single CGH lens compensator faces the incident plane wave and where the diffraction surface of a single CGH lens compensator faces the zero-position freeform surface. The surface shape of the zero-position freeform surface based on the XY polynomial characterization is then derived and calculated.

[0080] Reference Figure 1 As shown, when the diffraction surface of the single CGH lens compensator faces the incident plane wave, the detection ray is emitted parallel to the interferometer standard mirror, intersecting the binary optical surface 1 at point A. The M-order diffracted ray is emitted and intersects the refractive surface at point B, and the refracted ray intersects the freeform surface at point Q. The incident height h of the detection ray at the interferometer standard mirror is set. x h y and h x h y As a parameter of the freeform surface shape, h x h y Within the range of the standard mirror aperture of the interferometer The variables inside are continuous variables;

[0081] The trajectory equation formed by point Q at this point is the zero-position freeform surface formula characterized by the front surface of the single CGH lens compensator being a binary optical surface 1. The parametric expression based on the XY polynomial is:

[0082]

[0083] Based on the principle of equal optical path length, two detection rays are selected. One ray is the ray emitted from the center point O1 of the diffraction surface of the single CGH lens compensator, with the path O1→O2→O. Among them, point O2 is the center vertex of the rear surface of the single CGH lens compensator, and point O is the center vertex of the freeform surface. The corresponding optical path length is G0=n·d+L.

[0084] The other ray is the parametric tracing ray, i.e., the off-axis ray, with a path of A→B→Q. Based on the parameters of the zero-position compensation detection system, the optical path length of the parametric tracing ray is determined to be... Among them l ABLet l be the distance between point A and point B. BQ Let B be the distance between point B and point Q on the freeform surface.

[0085] According to the principle of equal optical path length, we have G0 = G1, so the distance between point B and point Q on the freeform surface is...

[0086] Based on the parameters of the zero-position compensation detection system, determine The direction vector of the light ray is represented as

[0087] With point O as the origin, and the front surface of the single CGH lens compensator in the zero-position compensation detection system being a binary optical surface 1, the trajectory equation of any point Q on the zero-position freeform surface, i.e., the expression for the surface shape of the zero-position freeform surface based on the XY polynomial characterization, is as follows:

[0088]

[0089] The zero-position freeform surface characterized by the XY polynomial is a non-rotationally symmetric surface, and its maximum effective aperture is determined by the actual light-transmitting aperture of the interferometer's standard spherical mirror.

[0090] Reference Figure 2 As shown, when the diffraction surface of the single CGH lens compensator faces the zero-position freeform surface, the detection ray is emitted parallel to the interferometer standard mirror, intersecting the refractive surface at point A. The refracted ray intersects the diffraction surface at point B, and the M-order diffracted ray is emitted, intersecting the freeform surface at point Q. The incident height h of the detection ray at the interferometer standard mirror is set. x h y and h x h y As a parameter of the freeform surface shape, h x h y Within the range of the standard mirror aperture of the interferometer The variables inside are continuous variables.

[0091] The trajectory equation formed by point Q at this point is the zero-position freeform surface formula characterized by the rear surface of the single CGH lens compensator being a binary optical surface 1. The parametric expression based on the XY polynomial is:

[0092]

[0093] Based on the principle of equal optical path length, two detection rays are selected. One ray is the ray emitted from the center point O1 of the refractive surface of the single CGH lens compensator, with the path O1→O2→O. Among them, point O2 is the center vertex of the rear surface of the single CGH lens compensator, and point O is the center vertex of the freeform surface. The corresponding optical path length is G0=n·d+L.

[0094] The other ray is the parametric tracing ray, i.e., the off-axis ray, with a path of A→B→Q. Based on the parameters of the zero-position compensation detection system, the optical path length of the parametric tracing ray is determined to be... Among them l AB Let l be the distance between point A and point B. BQ Let B be the distance between point B and point Q on the freeform surface.

[0095] According to the principle of equal optical path length, we have G0 = G1, so the distance between point B and point Q on the freeform surface is...

[0096] Based on the parameters of the zero-position compensation detection system, determine The direction vector of the light ray is represented as

[0097] With point O as the origin, and the rear surface of the single CGH lens compensator in the zero-position compensation detection system being a binary optical surface 1, the trajectory equation of any point Q on the zero-position freeform surface, i.e., the expression for the surface shape of the zero-position freeform surface based on the XY polynomial characterization, is as follows:

[0098]

[0099] The zero-position freeform surface characterized by the XY polynomial is a non-rotationally symmetric surface, and its maximum effective aperture is determined by the actual light-transmitting aperture of the interferometer's standard spherical mirror.

[0100] When the phase function of the diffraction surface is the Zerinke standard phase surface in the non-rotationally symmetric form, the derivation process of the surface shape characterization of the zero-position freeform surface is as follows.

[0101] When the phase function of the diffraction surface is the Zerinke standard phase in the non-rotationally symmetric form, its phase expression is:

[0102]

[0103] Where M is the diffraction order, N is the number of coefficient terms in the Zernike polynomial, and C i Zernike polynomial coefficients, Z i The expression is a Zernike polynomial, where ρ is the normalized radial coordinate. Let be the coordinates of the ray in the angular direction.

[0104] The following section categorizes the cases where the diffraction surface of a single CGH lens compensator faces the incident plane wave and where the diffraction surface of a single CGH lens compensator faces the zero-position freeform surface. The surface shape of the zero-position freeform surface based on the Zernike polynomial characterization is then derived and calculated.

[0105] Reference Figure 3As shown, when the diffraction surface of the single CGH lens compensator faces the incident plane wave, the detection ray exits parallel to the interferometer standard mirror, intersecting the Zernike standard phase plane at point A. The M-order diffracted ray exits, intersecting the refractive surface at point B, and the refracted ray intersects the freeform surface at point Q. The incident height h of the detection ray at the interferometer standard mirror is set. x h y and h x h y As a parameter of the freeform surface shape, h x h y Within the range of the standard mirror aperture of the interferometer The variables inside are continuous variables.

[0106] The trajectory equation formed by point Q at this point is the zero-position freeform surface formula characterized by the Zernike standard phase plane on the front surface of the single CGH lens compensator. The parametric expression based on the Zernike polynomial is:

[0107]

[0108] Based on the principle of equal optical path length, two detection rays are selected. One ray is the ray emitted from the center point O1 of the diffraction surface of the single CGH lens compensator, with the path O1→O2→O. Among them, point O2 is the center vertex of the rear surface of the single CGH lens compensator, and point O is the center vertex of the freeform surface. The corresponding optical path length is G0=n·d+L.

[0109] The other ray is the parametric tracing ray, i.e., the off-axis ray, with a path of A→B→Q. Based on the parameters of the zero-position compensation detection system, the optical path length of the parametric tracing ray is determined to be... Among them l AB Let l be the distance between point A and point B. BQ Let B be the distance between point B and point Q on the freeform surface.

[0110] According to the principle of equal optical path length, we have G0 = G1, so the distance between point B and point Q on the freeform surface is...

[0111] Based on the parameters of the zero-position compensation detection system, determine The direction vector of the light ray is represented as

[0112] With point O as the origin, and the front surface of the single CGH lens compensator in the zero-position compensation detection system being the Zernike standard phase plane, the trajectory equation of any point Q on the zero-position freeform surface, i.e., the expression for the surface shape of the zero-position freeform surface based on the Zernike polynomial, is as follows:

[0113]

[0114] The zero-position freeform surface characterized by Zernike polynomials is a non-rotationally symmetric surface, and its maximum effective aperture is determined by the actual light-transmitting aperture of the interferometer's standard spherical mirror.

[0115] Reference Figure 4 As shown, when the diffraction surface of the single CGH lens compensator faces the zero-position freeform surface, the detection light is emitted parallel to the interferometer standard mirror, intersecting the refraction surface at point A, the refracted light intersects the diffraction surface at point B, the M-order diffracted light is emitted, and the emitted light intersects the freeform surface at point Q; the incident height h of the light at the interferometer standard mirror is set. x h y and h x h y As a parameter of the freeform surface shape, h x h y Within the range of the standard mirror aperture of the interferometer The variables inside are continuous variables.

[0116] The trajectory equation formed by point Q at this point is the zero-position freeform surface formula characterized by the Zernike standard phase plane on the front surface of the single CGH lens compensator. The parametric expression based on the Zernike polynomial is:

[0117]

[0118] Based on the principle of equal optical path length, two detection rays are selected. One ray is the ray emitted from the center point O1 of the refractive surface of the single CGH lens compensator, with the path O1→O2→O. Among them, point O2 is the center vertex of the rear surface of the single CGH lens compensator, and point O is the center vertex of the freeform surface. The corresponding optical path length is G0=n·d+L.

[0119] The other ray is the parametric tracing ray, i.e., the off-axis ray, with a path of A→B→Q. Based on the parameters of the zero-position compensation detection system, the optical path length of the parametric tracing ray is determined to be... Among them l AB Let l be the distance between point A and point B. BQ Let B be the distance between point B and point Q on the freeform surface;

[0120] According to the principle of equal optical path length, we have G0 = G1, so the distance between point B and point Q on the freeform surface is...

[0121] Based on the parameters of the zero-position compensation detection system, determine The direction vector of the light ray is represented as

[0122] With point O as the origin, and the rear surface of the single CGH lens compensator in the zero-position compensation detection system being the Zernike standard phase plane, the trajectory equation of any point Q on the zero-position freeform surface, i.e., the expression for the surface shape of the zero-position freeform surface based on the Zernike polynomial, is as follows:

[0123]

[0124] The zero-position freeform surface characterized by Zernike polynomials is a non-rotationally symmetric surface, and its maximum effective aperture is determined by the actual light-transmitting aperture of the interferometer's standard spherical mirror.

[0125] The freeform surface characterization method based on the zero-position compensation detection optical path of the CGH lens described above is guided by the detection method. It realizes the detection optical path design based on the zero-position compensation measurement principle and the diffraction optics principle. It indirectly characterizes the freeform surface shape by using the parameters required for the zero-position compensation detection system with the interferometer incident wavefront being a plane wave and the compensator being a single CGH lens. By using the XY polynomial and the Zernike standard phase polynomial, the mathematical description of the freeform surface can be determined at the design stage, and a custom zero-position freeform surface is proposed.

[0126] The freeform surface characterization method based on the zero-position compensation detection optical path of the CGH lens improves the degree of freedom of the freeform surface shape and the feasibility of the zero-position compensation method, simplifies the detection structure of the optical system and improves its efficiency and accuracy, reduces the detection difficulty of the freeform surface shape, and realizes the function of zero-position freeform surface design for detection.

[0127] Therefore, the freeform surface characterization method described above can improve production efficiency by taking into account the limitations of testing during the design process. By meeting testing requirements, it reduces the time spent on repeated trials and adjustments, avoids ineffective designs, and thus improves production efficiency.

[0128] 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.

[0129] 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.

[0130] 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.

[0131] 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.

[0132] 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. A freeform surface characterization method based on a CGH lens zero-position compensation detection optical path, characterized in that, include: In a zero-position compensation detection system where the incident wavefront of the interferometer is set to a plane wave and the compensator is a single CGH lens compensator, the aperture of the standard mirror of the interferometer is [missing information]. The detection wavelength is The phase of the diffraction surface of the single CGH lens compensator is Diffraction order is The radius of curvature of the refractive surface is The center thickness of the single CGH lens compensator is The refractive index of the material of the single CGH lens compensator is The distance between the single CGH lens compensator and the freeform surface is ; A zero-point compensation detection system is constructed based on the characterization parameters of the freeform surface of the CGH lens zero-point compensation detection optical path. The detection light rays of the interferometer standard mirror are incident parallel to each other. Different heights and different diffraction orders correspond to different points on the freeform surface. This optical path follows the principle of equal optical path, the principle of diffraction, and Snell's law. Therefore, after the light rays are reflected by the freeform surface, they return along the original optical path and are re-formed into a plane wave after passing through the single CGH lens compensator. Inside the interferometer, the plane wave interferes with the reference wave, thereby reflecting the surface information of the measured freeform surface. In the zero-position compensation detection system, the phase function of the diffraction surface is either the binary optical surface 1 in the non-rotational symmetry form or the Zernike standard phase. When the phase function of the diffraction surface is the binary optical surface 1 in the non-rotational symmetry form, the plane wave single CGH lens compensation detection optical path forms a zero-position freeform surface characterized by the XY polynomial. When the phase function of the diffraction surface is the Zernike standard phase in the non-rotational symmetry form, the plane wave single CGH lens compensation detection optical path forms a zero-position freeform surface characterized by the Zernike polynomial. The detection light is incident as a plane wave, and the single CGH lens compensator and the freeform surface form a zero spherical aberration system, which follows the principle of equal optical path length. Based on the principle of equal optical path length, two detection rays are selected. One ray is the ray emitted from the center point of the diffraction surface, and the other ray is the parametric tracing ray, i.e., the off-axis ray. According to the parameters of the zero-position compensation detection system, the optical path length corresponding to the parametric tracing ray is determined. By simultaneously establishing the expressions for the two optical path lengths, the intersection point of the detection ray and the freeform surface is obtained. The trajectory equation of a point, i.e., the custom zero-position freeform surface shape expression; The zero-position freeform surface is a non-rotationally symmetric surface, and its maximum effective aperture is determined by the actual light-transmitting aperture of the interferometer's standard mirror. Taking the planar optical surface as a reference, when the phase function of the diffraction surface is a binary optical surface 1 in a non-rotationally symmetric form, considering only the change in its phase, the phase expression of the binary optical surface 1 is: ,in, For diffraction orders, Let be the number of terms in the polynomial. For the first Term coefficient, , The coordinates are normalized. When the phase function of the diffraction surface is the Zernike standard phase in the non-rotationally symmetric form, its phase expression is: ,in For diffraction orders, Let be the number of terms in the polynomial. For the first Term coefficient, ( , ) is the first Zernike polynomials, For normalized radial coordinates, Let be the coordinates of the ray in the angular direction.

2. The freeform surface characterization method based on the CGH lens zero-position compensation detection optical path according to claim 1, characterized in that, When the diffraction surface of the single CGH lens compensator faces the incident plane wave, the detection light is emitted parallel to the standard mirror of the interferometer and intersects the binary optical surface 1. point, The diffracted rays are emitted and intersect the refracting surface at... The point, after which the refracted ray intersects the freeform surface at... Point; set the incident height of the detection ray at the interferometer's standard mirror. , and will , As a parameter of the shape of a freeform surface, , Within the range of the standard mirror aperture of the interferometer , The variables inside are continuous variables; at this time The trajectory equation formed by the points is the zero-position freeform surface formula characterized by the front surface of a single CGH lens compensator being a binary optical surface 1. The parametric expression based on the XY polynomial is: Based on the principle of equal optical path length, two detection rays are selected, one of which is the center point of the diffraction surface of the single CGH lens compensator. The emitted ray has the following path: ;in, The point is the center vertex of the rear surface of the single CGH lens compensator. The point is the center vertex of the freeform surface; the corresponding optical path is ; The other ray is a parametric tracing ray, i.e., 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 Points on freeform surfaces Distance between points; According to the principle of equal optical path length, we have ,get Points on freeform surfaces The distance between the points is ; Based on the parameters of the zero-position compensation detection system, determine The direction vector of the light ray is represented as ; by Point 1 is the origin of the coordinate system. In the zero-position compensation detection system, when the front surface of the single CGH lens compensator is a binary optical surface 1, any point on the zero-position freeform surface... The trajectory equation, i.e., the expression for the zero-position freeform surface shape based on the XY polynomial representation, is: The zero-position freeform surface characterized by the XY polynomial is a non-rotationally symmetric surface, and its maximum effective aperture is determined by the actual light-transmitting aperture of the interferometer standard mirror.

3. The freeform surface characterization method based on the CGH lens zero-position compensation detection optical path according to claim 1, characterized in that, When the diffraction surface of the single CGH lens compensator faces the zero-position freeform surface, the detection light is emitted parallel to the standard mirror of the interferometer and intersects the refractive surface at... At the point where the refracted ray intersects the diffraction plane. point, The diffracted rays are emitted and intersect the freeform surface at... Point; set the incident height of the detection ray at the interferometer's standard mirror. , and will , As a parameter of the shape of a freeform surface, , Within the range of the standard mirror aperture of the interferometer , The variables inside are continuous variables; at this time The trajectory equation formed by the points is the zero-position freeform surface formula characterized by the rear surface of a single CGH lens compensator being a binary optical surface 1. The parametric expression based on the XY polynomial is as follows: Based on the principle of equal optical path length, two detection rays are selected, one of which is the center point of the refractive surface of the single CGH lens compensator. The emitted ray has the following path: ;in, The point is the center vertex of the rear surface of the single CGH lens compensator. The point is the center vertex of the freeform surface; the corresponding optical path is ; The other ray is a parametric tracing ray, i.e., 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 Points on freeform surfaces Distance between points; According to the principle of equal optical path length, we have ,get Points on freeform surfaces The distance between the points is ; Based on the parameters of the zero-position compensation detection system, determine The direction vector of the light ray is represented as ; by Point 1 is the origin of the coordinate system. In the zero-position compensation detection system, when the rear surface of the single CGH lens compensator is a binary optical surface 1, any point on the zero-position freeform surface... The trajectory equation, i.e., the expression for the zero-position freeform surface shape based on the XY polynomial representation, is: The zero-position freeform surface characterized by the XY polynomial is a non-rotationally symmetric surface, and its maximum effective aperture is determined by the actual light-transmitting aperture of the interferometer standard mirror.

4. The freeform surface characterization method based on the CGH lens zero-position compensation detection optical path according to claim 1, characterized in that, When the diffraction surface of the single CGH lens compensator faces the incident plane wave, the detection light is emitted parallel to the interferometer's standard mirror and intersects the Zernike standard phase plane. point, The diffracted rays are emitted and intersect the refracting surface at... The point, after which the refracted ray intersects the freeform surface at... Point; set the incident height of the detection ray at the interferometer's standard mirror. , and will , As a parameter of the shape of a freeform surface, , Within the range of the standard mirror aperture of the interferometer , The variables inside are continuous variables; at this time The trajectory equation formed by the points is the zero-position freeform surface formula characterized by the Zernike standard phase plane on the front surface of a single CGH lens compensator. The parametric expression based on the Zernike polynomial is as follows: Based on the principle of equal optical path length, two detection rays are selected, one of which is the center point of the diffraction surface of the single CGH lens compensator. The emitted ray has the following path: ;in, The point is the center vertex of the rear surface of the single CGH lens compensator. The point is the center vertex of the freeform surface; the corresponding optical path is ; The other ray is a parametric tracing ray, i.e., 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 Points on freeform surfaces Distance between points; According to the principle of equal optical path length, we have ,get Points on freeform surfaces The distance between the points is ; Based on the parameters of the zero-position compensation detection system, determine The direction vector of the light ray is represented as ; by Point 1 is the origin of the coordinate system. In a zero-position compensation detection system, when the front surface of the single CGH lens compensator is the Zernike standard phase plane, any point on the zero-position freeform surface... The trajectory equation, i.e., the expression for the zero-position freeform surface shape based on the Zernike polynomial representation, is: The zero-position freeform surface characterized by Zernike polynomials is a non-rotationally symmetric surface, and its maximum effective aperture is determined by the actual light-transmitting aperture of the interferometer standard mirror.

5. The freeform surface characterization method based on the CGH lens zero-position compensation detection optical path according to claim 1, characterized in that, When the diffraction surface of the single CGH lens compensator faces the zero-position freeform surface, the detection light is emitted parallel to the standard mirror of the interferometer and intersects the refractive surface at... At the point where the refracted ray intersects the diffraction plane. point, The diffracted rays are emitted and intersect the freeform surface at... Point; setting the incident height of the light ray at the standard mirror of the interferometer. , and will , As a parameter of the shape of a freeform surface, , Within the range of the standard mirror aperture of the interferometer , The variables inside are continuous variables; at this time The trajectory equation formed by the points is the zero-position freeform surface formula characterized by the Zernike standard phase plane on the back surface of a single CGH lens compensator. The parametric expression based on the Zernike polynomial is as follows: Based on the principle of equal optical path length, two detection rays are selected, one of which is the center point of the refractive surface of the single CGH lens compensator. The emitted ray has the following path: ;in, The point is the center vertex of the rear surface of the single CGH lens compensator. The point is the center vertex of the freeform surface; the corresponding optical path is ; The other ray is a parametric tracing ray, i.e., 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 Points on freeform surfaces Distance between points; According to the principle of equal optical path length, we have ,get Points on freeform surfaces The distance between the points is ; Based on the parameters of the zero-position compensation detection system, determine The direction vector of the light ray is represented as ; by Point 1 is the origin of the coordinate system. In a zero-position compensation detection system, when the rear surface of the single CGH lens compensator is the Zernike standard phase plane, any point on the zero-position freeform surface... The trajectory equation, i.e., the expression for the zero-position freeform surface shape based on the Zernike polynomial representation, is: The zero-position freeform surface characterized by Zernike polynomials is a non-rotationally symmetric surface, and its maximum effective aperture is determined by the actual light-transmitting aperture of the interferometer standard mirror.

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