Method and device for manufacturing a curved substrate blazed grating based on swing etching
Patent Information
- Application Number
- CN202611486543.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-09-23
- Publication Date
- 2026-10-30
AI Technical Summary
[0006]针对现有技术所存在的上述缺点，本发明提供了基于摆动刻蚀的曲面基底闪耀光栅制作方法及装置，能够有效克服现有技术所存在的无法适应不同类型曲面基底、不能对闪耀角进行动态调整的缺陷
[0081]与现有技术相比，本发明所提供的基于摆动刻蚀的曲面基底闪耀光栅制作方法及装置，具有以下有益效果：
Smart Images
Figure CN123010160A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fabrication of blazed gratings, and more specifically to a method and apparatus for fabricating blazed gratings on curved substrates based on oscillating etching. Background Technology
[0002] Convex and concave gratings have unique curved surface structures (such as...) Figure 3 and Figure 4 As shown, convex gratings exhibit irreplaceable functional advantages in optical systems. In concentric optical structures such as Offner's, convex gratings, in conjunction with concave mirrors and other components, form aberration correction systems. Their compact structure and correctable aberrations make them suitable for a wide spectral range and have important applications in hyperspectral imaging. Concave gratings, combining dispersion and focusing functions, eliminate the need for collimating and focusing mirrors, offering advantages such as high luminous throughput, simple structure, and relatively controllable aberrations. They are of significant value in high-end fields such as spectrometers and extreme ultraviolet lithography. Building upon this, combining asymmetric blazed grooves with curved substrates has led to the development of higher-performance curved substrate blazed gratings. Through groove design, these gratings concentrate energy to specific diffraction orders, significantly improving the system's diffraction efficiency and signal-to-noise ratio, providing a more compact and efficient solution for applications such as precision spectral analysis and hyperspectral imaging. As optical systems become increasingly complex, for example, in broadband spectrometers, it is necessary to use gradient blaze angles to compensate for the diffraction efficiency of different wavelengths, and in multi-channel imaging systems, it is necessary to use partitioned blaze angles to achieve parallel acquisition of multiple spectral bands. The need to distribute blaze angles according to a gradient or to configure them according to regional partitions on the same curved substrate is gradually emerging, in order to further expand the degree of freedom of spectral control. This places higher demands on the manufacturing technology of curved substrate blazed gratings.
[0003] Currently, blazed grating fabrication processes employ holographic interference lithography and reactive ion beam etching. While these technologies are relatively mature on planar substrates, they struggle to meet the high-precision processing requirements of curved substrates. Because the ion beam incident direction is fixed, variations in the local tangent direction at different points on the curved substrate can lead to groove distortion and uneven depth, consequently affecting the accuracy of the blaze angle and the consistency of diffraction efficiency. Traditional oscillating etching for fabricating blazed gratings on curved substrates involves circular reciprocating oscillations with the substrate's radius of curvature as the oscillation radius. If the radius of curvature of the substrate to be processed is large, the oscillation radius will also increase accordingly. Due to the limited internal space of the etching machine, traditional methods can only fabricate blazed gratings on spherical substrates, making it difficult to process blazed gratings on substrates with large radii of curvature, and even more difficult to achieve gradual or zoned control of the blaze angle on the same curved substrate.
[0004] Therefore, there is an urgent need for a method and apparatus for fabricating blazed gratings on curved substrates that can adapt to different curved substrates and achieve dynamic adjustment of the blaze angle. Summary of the Invention
[0005] (a) Technical problems to be solved
[0006] In view of the above-mentioned shortcomings of the prior art, the present invention provides a method and apparatus for fabricating blazed gratings on curved substrates based on oscillating etching, which can effectively overcome the defects of the prior art that cannot adapt to different types of curved substrates and cannot dynamically adjust the blaze angle.
[0007] (II) Technical Solution
[0008] To achieve the above objectives, the present invention provides the following technical solution:
[0009] The method for fabricating blazed gratings on curved substrates based on oscillating etching includes the following steps:
[0010] S1. Prepare a grating mask on the surface of the curved substrate to be processed. Place the grating mask with the grating line direction perpendicular to the rotating disk on a liftable platform. Adjust the height so that the initial section to be etched is on the same horizontal line as the square slit.
[0011] S2. Fit each segment of the area to be etched on the curved substrate into a curve.
[0012] S3. By rotating, the tangent direction of the starting etching point is made parallel to the etching direction, and the angle between the ion beam incident direction and the tangent direction of the current etching point determines the blaze angle.
[0013] S4. The etching start point is moved to the ion beam etching area by translation.
[0014] S5. The curved base is moved along the fitted curve in S2 by translation, and the rotating disk is controlled in association according to the type of the curved base and the preset blaze angle to perform oscillating etching on the curved base.
[0015] S6. Repeat S3~S5 until the scanning etching of the entire surface of the curved substrate is completed.
[0016] Preferably, in step S1, a grating mask is prepared on the surface of the curved substrate to be processed. The grating mask is placed on a liftable stage with the grating lines perpendicular to the rotating disk. The initial section to be etched is aligned with the square slit by raising and lowering the stage. This includes:
[0017] Holographic interference lithography is used to prepare a grating mask with a preset period and aspect ratio on the surface of the curved substrate to be processed. The grating mask is placed on a liftable stage with the grating line direction perpendicular to the rotating disk. The curved substrate is raised and lowered by the liftable stage so that the initial etchable section is on the same horizontal line as the square slit.
[0018] The width of the square slit determines the degree of segmentation of the blazed grating.
[0019] Preferably, in S2, each segment of the area to be etched on the curved substrate is fitted into a curve, including:
[0020] For a spherical substrate, each area to be etched can be fitted as a circular arc curve with a known radius.
[0021] Preferably, in S2, each segment of the area to be etched on the curved substrate is fitted into a curve, including:
[0022] For aspherical substrates, first determine the corresponding quadratic conic surface equation, and then fit each segment of the area to be etched into a conic curve by cutting:
[0023] 1) Aspherical surfaces are represented by the following formula:
[0024] ;
[0025] Where r is the radial distance, representing the perpendicular distance from a point on the aspherical surface to the Z-axis, Z(r) is the surface sag of the aspherical surface, representing the offset height of a point on the aspherical surface relative to the vertex along the Z-axis at a radial distance r, c is the vertex curvature, k is the conic coefficient, and A4, A6, and A8 are all even-order higher-order aspherical coefficients.
[0026] 2) On an aspherical surface, the aspherical cross-sectional curve obtained by cutting it with the XZ plane of y=y0 is expressed by the following formula:
[0027] ;
[0028] Where (x,y,z) are spatial coordinates, and Z'(x) is the sag at position (x,y0) on the aspherical cross-section curve;
[0029] 3) The angle between the tangent line at a point on the aspherical section curve and the Z-axis is expressed by the following formula:
[0030] ;
[0031] Where γ(x) is the angle between the tangent line at the point (x,y0,z) on the aspherical cross-section curve and the Z-axis, then z = Z'(x), and z' is the first derivative of the vertical coordinate z with respect to the horizontal coordinate x, representing the slope of the tangent line at the point (x,y0,z) on the aspherical cross-section curve. ;
[0032] 4) The rate of change of the angle between the tangent line at a point on the aspherical section curve and the Z-axis as a function of the x-coordinate. Expressed as follows:
[0033] ;
[0034] Where z'' is the second derivative of the vertical coordinate z with respect to the horizontal coordinate x, representing the curvature of the tangent line at the point (x, y0, z) on the aspherical cross-section curve. sgn(·) represents the symbolic function.
[0035] Preferably, in S3, rotation is used to make the tangent direction of the starting etching point parallel to the etching direction, while the angle between the ion beam incident direction and the tangent direction of the current etching point determines the blaze angle, including:
[0036] By controlling the rotating disk, the tangent direction of the starting etching point is made parallel to the etching direction. At the same time, the angle θ between the ion beam incident direction and the tangent direction of the current etching point determines the blaze angle. The required blaze angle is adjusted by controlling the angle θ.
[0037] Preferably, in step S4, the starting etching point is moved to the ion beam etching region by translation, including:
[0038] By controlling the first and second strip tracks in tandem, the etching start point is moved to the ion beam etching area.
[0039] Preferably, in S5, the curved substrate is moved along the fitted curve in S2 by translation, and the rotating disk is correlated with the type of the curved substrate and the preset blaze angle to perform oscillating etching on the curved substrate, including:
[0040] For a spherical base:
[0041] 1) When the required scintillation angle is a uniform scintillation angle, through the coordinated control of the first and second strip tracks, each segment of the spherical substrate to be etched moves at a uniform speed v1 along the arc curve fitted in S2. Simultaneously, the attitude of the spherical substrate is adjusted by controlling the first angular velocity ω1 of the rotating disk, ensuring that the first angle θ1 between the ion beam incident direction and the tangent direction of the current etching point remains constant, satisfying the following:
[0042] ;
[0043] ;
[0044] Where t1 is the time for each segment of the etched area on the spherical substrate to undergo uniform curvilinear motion, c is the length of the fitted arc curve corresponding to each segment of the etched area on the spherical substrate, and α is the central angle of the fitted arc curve corresponding to each segment of the etched area on the spherical substrate.
[0045] 2) When the required scorch angle is the partitioned scorch angle, through the linkage control of the first strip track and the second strip track, each segment of the area to be etched on the spherical substrate moves at a constant speed v1 along the arc curve fitted in S2, while simultaneously performing segmented uniform etching on each segment of the area to be etched on the spherical substrate.
[0046] 3) When the required scorch angle is a gradual scorch angle, through the coordinated control of the first and second strip tracks, each segment of the spherical substrate to be etched moves at a uniform speed v1 along the arc curve fitted in S2. Simultaneously, by controlling the second angular velocity ω2 of the rotating disk, the attitude of the spherical substrate is adjusted so that the angle between the ion beam incident direction and the tangent direction of the current etching point gradually changes from the second angle θ2 to the third angle θ3, which must satisfy:
[0047] ;
[0048] .
[0049] Preferably, in S5, the curved substrate is moved along the fitted curve in S2 by translation, and the rotating disk is correlated with the type of the curved substrate and the preset blaze angle to perform oscillating etching on the curved substrate, including:
[0050] For aspherical substrates:
[0051] 1) When the required scintillation angle is a uniform scintillation angle, through the linkage control of the first and second strip tracks, each segment of the area to be etched on the aspherical substrate moves at a uniform speed v2 along the conic curve fitted in S2, while simultaneously rotating the disk by the first rotation amount. The angle between the tangent line at a point on the aspherical section curve in S2 and the Z-axis changes with the x-coordinate in the same way:
[0052] ;
[0053] Where △x represents the change in the x-coordinate;
[0054] 2) When the required scorch angle is the partitioned scorch angle, through the linkage control of the first strip track and the second strip track, each segment of the area to be etched on the aspherical substrate moves at a constant speed along the conic curve fitted in S2 at the second speed v2, while simultaneously performing segmented uniform etching on each segment of the area to be etched on the aspherical substrate.
[0055] 3) When the required scintillation angle is a gradient scintillation angle, through the coordinated control of the first and second strip tracks, each segment of the aspherical substrate to be etched moves at a constant speed v2 along the fitted conic curve in S2. Simultaneously, the fitted conic curve corresponding to each segment of the aspherical substrate to be etched is divided into n conic sub-curves of length Δc. The angle between the ion beam incident direction and the tangent direction of the current etching point starts from the fourth angle θ4. The angle corresponding to each segment of the conic curve increases by Δθ, thus increasing the second momentum of the rotating disk. for:
[0056] .
[0057] An apparatus for fabricating blazed gratings on curved substrates based on oscillating etching includes the following components:
[0058] A liftable platform is fixedly installed on a rotating disk and used to drive the curved base to move up and down.
[0059] A rotating disk, mounted on the first and second strip tracks, is used to drive the curved base to rotate.
[0060] The first and second strip tracks are used to drive the curved base to move horizontally;
[0061] An ion source is used to etch a curved substrate through a square slit.
[0062] The controller, through the coordinated control of the liftable stage, rotating disk, first strip track and second strip track, dynamically adjusts the angle between the ion beam incident direction and the tangent direction of the current etching point according to a preset rule, thereby realizing the fabrication of uniform, partitioned and gradient blazed angle gratings on spherical and aspherical substrates with known shape equations.
[0063] Preferably, the controller dynamically adjusts the angle between the incident direction of the ion beam and the tangent direction of the current etching point according to a preset rule by linking the liftable stage, the rotating disk, the first strip track, and the second strip track, thereby realizing the fabrication of uniform, partitioned, and gradient blaze angle gratings on spherical and aspherical substrates with known shape equations, including:
[0064] For a spherical base:
[0065] 1) When the required scintillation angle is a uniform scintillation angle, through the coordinated control of the first and second strip tracks, each segment of the spherical substrate to be etched moves at a uniform speed v1 along the arc curve fitted in S2. Simultaneously, the attitude of the spherical substrate is adjusted by controlling the first angular velocity ω1 of the rotating disk, ensuring that the first angle θ1 between the ion beam incident direction and the tangent direction of the current etching point remains constant, satisfying the following:
[0066] ;
[0067] ;
[0068] Where t1 is the time for each segment of the etched area on the spherical substrate to undergo uniform curvilinear motion, c is the length of the fitted arc curve corresponding to each segment of the etched area on the spherical substrate, and α is the central angle of the fitted arc curve corresponding to each segment of the etched area on the spherical substrate.
[0069] 2) When the required scorch angle is the partitioned scorch angle, through the linkage control of the first strip track and the second strip track, each segment of the area to be etched on the spherical substrate moves at a constant speed v1 along the arc curve fitted in S2, while simultaneously performing segmented uniform etching on each segment of the area to be etched on the spherical substrate.
[0070] 3) When the required scorch angle is a gradual scorch angle, through the coordinated control of the first and second strip tracks, each segment of the spherical substrate to be etched moves at a uniform speed v1 along the arc curve fitted in S2. Simultaneously, by controlling the second angular velocity ω2 of the rotating disk, the attitude of the spherical substrate is adjusted so that the angle between the ion beam incident direction and the tangent direction of the current etching point gradually changes from the second angle θ2 to the third angle θ3, which must satisfy:
[0071] ;
[0072] ;
[0073] For aspherical substrates:
[0074] 1) When the required scintillation angle is a uniform scintillation angle, through the linkage control of the first and second strip tracks, each segment of the area to be etched on the aspherical substrate moves at a uniform speed v2 along the conic curve fitted in S2, while simultaneously rotating the disk by the first rotation amount. The angle between the tangent line at a point on the aspherical section curve in S2 and the Z-axis changes with the x-coordinate in the same way:
[0075] ;
[0076] Where △x represents the change in the x-coordinate;
[0077] 2) When the required scorch angle is the partitioned scorch angle, through the linkage control of the first strip track and the second strip track, each segment of the area to be etched on the aspherical substrate moves at a constant speed along the conic curve fitted in S2 at the second speed v2, while simultaneously performing segmented uniform etching on each segment of the area to be etched on the aspherical substrate.
[0078] 3) When the required scintillation angle is a gradient scintillation angle, through the coordinated control of the first and second strip tracks, each segment of the aspherical substrate to be etched moves at a constant speed v2 along the fitted conic curve in S2. Simultaneously, the fitted conic curve corresponding to each segment of the aspherical substrate to be etched is divided into n conic sub-curves of length Δc. The angle between the ion beam incident direction and the tangent direction of the current etching point starts from the fourth angle θ4. The angle corresponding to each segment of the conic curve increases by Δθ, thus increasing the second momentum of the rotating disk. for:
[0079] .
[0080] (III) Beneficial Effects
[0081] Compared with the prior art, the method and apparatus for fabricating blazed gratings on curved substrates based on oscillating etching provided by the present invention have the following advantages:
[0082] 1) Adaptive etching of curved substrates: Supports substrate processing with any known analytical shape such as concave spherical surfaces, convex spherical surfaces and freeform surfaces, effectively suppressing groove distortion caused by curvature changes;
[0083] 2) Dynamic angle compensation: Through multi-axis linkage control of the liftable stage, rotating disk and strip track, dynamic matching between the ion beam incident direction and the local tangential direction of the substrate can be achieved. When the preset angle is constant, the consistency of the blaze angle during the etching process can be ensured. When the preset angle changes according to the gradual or partitioned pattern, flexible control of the gradual or partitioned blaze angle can be achieved.
[0084] 3) Etching depth uniformity control: By combining the coordinated control of oscillation frequency and scanning speed, the bombardment flux of the ion beam in different regions is adjusted, which effectively solves the problem of uneven etching depth and improves the consistency of diffraction efficiency of the blazed grating on the curved substrate across the entire aperture range.
[0085] 4) Reduced etching space requirements: Compared with the traditional oscillating etching technology that uses the substrate curvature radius as the oscillation radius, the present invention achieves dynamic adjustment of the blaze angle through multi-axis linkage control. The motion stroke is freed from dependence on the substrate curvature radius, thereby effectively reducing the internal space required for etching equipment. It is especially suitable for processing blaze gratings with large curvature radius and aspherical substrates. Attached Figure Description
[0086] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.
[0087] Figure 1 This is a schematic diagram of the process of the present invention;
[0088] Figure 2 This is a schematic diagram of the device structure of the present invention;
[0089] Figure 3 A schematic diagram of the substrate for an existing convex grating;
[0090] Figure 4 A schematic diagram of the substrate for an existing concave grating;
[0091] Figure 5 This is a schematic diagram of fitting each segment of the area to be etched on the concave spherical surface into a circular arc curve in this invention;
[0092] Figure 6 This is a schematic diagram of fitting a conic curve to each segment of the convex aspherical surface to be etched in this invention;
[0093] Figure 7 For the present invention Figure 5 A schematic diagram of the cross-sectional curve of a concave spherical surface;
[0094] Figure 8 For the present invention Figure 6 A schematic diagram of the cross-sectional curve of a convex aspherical surface;
[0095] Figure 9 This is a schematic diagram illustrating how rotation makes the tangent direction of the starting etching point parallel to the etching direction in this invention;
[0096] Figure 10 This is a schematic diagram illustrating how the starting etching point is moved to the ion beam etching region by translation in this invention. Detailed Implementation
[0097] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.
[0098] The following describes the specific process of the method for fabricating a blazed grating on a curved substrate based on oscillating etching provided by this invention, using specific examples (e.g.) Figure 1 (as shown) and technical effects.
[0099] S1. Prepare a grating mask on the surface of the curved substrate to be processed. Place the grating mask with the grating line direction perpendicular to the rotating disk on a liftable stage. Adjust the height so that the initial section to be etched is on the same horizontal line as the square slit. This includes:
[0100] Holographic interference lithography is used to prepare a grating mask with a preset period and aspect ratio on the surface of the curved substrate to be processed. The grating mask is placed on a liftable stage with the grating line direction perpendicular to the rotating disk. The curved substrate is raised and lowered by the liftable stage so that the initial etchable section is on the same horizontal line as the square slit.
[0101] The width of the square slit determines the degree of segmentation of the blazed grating.
[0102] S2. Fit each segment of the area to be etched on the curved substrate into a curve, including:
[0103] For a spherical substrate, each segment of the area to be etched can be fitted as a circular arc curve with a known radius;
[0104] For aspherical substrates, first determine the corresponding quadratic conic surface equation, and then fit each segment of the area to be etched into a conic curve by cutting:
[0105] 1) Aspherical surfaces are represented by the following formula:
[0106] ;
[0107] Where r is the radial distance, representing the perpendicular distance from a point on the aspherical surface to the Z-axis, Z(r) is the surface sag of the aspherical surface, representing the offset height of a point on the aspherical surface relative to the vertex along the Z-axis at a radial distance r, c is the vertex curvature, k is the conic coefficient, and A4, A6, and A8 are all even-order higher-order aspherical coefficients.
[0108] 2) On an aspherical surface, the aspherical cross-sectional curve obtained by cutting it with the XZ plane of y=y0 is expressed by the following formula:
[0109] ;
[0110] Where (x,y,z) are spatial coordinates, and Z'(x) is the sag at position (x,y0) on the aspherical cross-section curve;
[0111] 3) The angle between the tangent line at a point on the aspherical section curve and the Z-axis is expressed by the following formula:
[0112] ;
[0113] Where γ(x) is the angle between the tangent line at the point (x,y0,z) on the aspherical cross-section curve and the Z-axis, then z = Z'(x), and z' is the first derivative of the vertical coordinate z with respect to the horizontal coordinate x, representing the slope of the tangent line at the point (x,y0,z) on the aspherical cross-section curve. ;
[0114] 4) The rate of change of the angle between the tangent line at a point on the aspherical section curve and the Z-axis as a function of the x-coordinate. Expressed as follows:
[0115] ;
[0116] Where z'' is the second derivative of the vertical coordinate z with respect to the horizontal coordinate x, representing the curvature of the tangent line at the point (x, y0, z) on the aspherical cross-section curve. sgn(·) represents the symbolic function.
[0117] Figure 5 This is a schematic diagram of fitting each segment of the etchable area on the concave spherical surface to a circular arc curve in this invention. It shows the spatial morphology of the concave spherical surface in the X, Y, and Z axes and the red cutting plane (XZ plane with y=0), which is used to establish a three-dimensional mathematical model of the concave spherical substrate to be processed. Figure 7 For the present invention Figure 5 The schematic diagram of the cross-sectional curve of a concave sphere shows the arc curve obtained by mathematical fitting of the concave sphere at a specific cross-sectional position. It is used to reduce the dimension of the three-dimensional concave trajectory and provide a two-dimensional curve path for precise oscillation that is actually needed.
[0118] Figure 6 This is a schematic diagram of fitting each segment of the convex aspherical surface to be etched as a conic curve in this invention. It shows the spatial morphology of the convex aspherical surface in the X, Y, and Z axes and the red cutting plane (XZ plane with y=0), which is used to establish the macroscopic equation of the convex aspherical substrate to be processed. Figure 8 For the present invention Figure 6 The schematic diagram of the cross-sectional curve of a convex aspherical surface shows the conic curve obtained by mathematical fitting of the convex aspherical surface at a specific cross-sectional position. It is used to reduce the dimension of the three-dimensional convex surface trajectory and provide a two-dimensional curve path for precise oscillation required in actual practice.
[0119] S3. By rotating the beam, the tangent direction of the starting etching point is made parallel to the etching direction. Simultaneously, the angle between the ion beam incident direction and the tangent direction of the current etching point determines the blaze angle. Figure 9 As shown, it includes:
[0120] By controlling the rotation of the disk, the tangent direction of the starting etching point is adjusted. Figure 9The green dashed line in the image is parallel to the etching direction, while the ion beam incident direction is ( Figure 9 The blaze angle is determined by the angle θ between the solid red line in the image and the tangent direction of the current etching point. The desired blaze angle can be adjusted by controlling the angle θ.
[0121] S4. The etching start point is moved to the ion beam etching area by translation, such as... Figure 10 As shown, it includes:
[0122] By controlling the first and second strip tracks in tandem, the etching start point is moved to the ion beam etching area.
[0123] S5. The curved substrate is moved along the fitted curve in S2 by translation, and the rotating disk is controlled in association according to the type of the curved substrate and the preset blaze angle to perform oscillating etching on the curved substrate, including:
[0124] For a spherical base:
[0125] 1) When the required scintillation angle is a uniform scintillation angle, through the coordinated control of the first and second strip tracks, each segment of the spherical substrate to be etched moves at a uniform speed v1 along the arc curve fitted in S2. Simultaneously, the attitude of the spherical substrate is adjusted by controlling the first angular velocity ω1 of the rotating disk, ensuring that the first angle θ1 between the ion beam incident direction and the tangent direction of the current etching point remains constant, satisfying the following:
[0126] ;
[0127] ;
[0128] Where t1 is the time for each segment of the etched area on the spherical substrate to undergo uniform curvilinear motion, c is the length of the fitted arc curve corresponding to each segment of the etched area on the spherical substrate, and α is the central angle of the fitted arc curve corresponding to each segment of the etched area on the spherical substrate.
[0129] 2) When the required scorch angle is the partitioned scorch angle, through the linkage control of the first strip track and the second strip track, each segment of the area to be etched on the spherical substrate moves at a constant speed v1 along the arc curve fitted in S2, while simultaneously performing segmented uniform etching on each segment of the area to be etched on the spherical substrate.
[0130] 3) When the required scorch angle is a gradual scorch angle, through the coordinated control of the first and second strip tracks, each segment of the spherical substrate to be etched moves at a uniform speed v1 along the arc curve fitted in S2. Simultaneously, by controlling the second angular velocity ω2 of the rotating disk, the attitude of the spherical substrate is adjusted so that the angle between the ion beam incident direction and the tangent direction of the current etching point gradually changes from the second angle θ2 to the third angle θ3, which must satisfy:
[0131] ;
[0132] ;
[0133] For aspherical substrates:
[0134] 1) When the required scintillation angle is a uniform scintillation angle, through the linkage control of the first and second strip tracks, each segment of the area to be etched on the aspherical substrate moves at a uniform speed v2 along the conic curve fitted in S2, while simultaneously rotating the disk by the first rotation amount. The angle between the tangent line at a point on the aspherical section curve in S2 and the Z-axis changes with the x-coordinate in the same way:
[0135] ;
[0136] Where △x represents the change in the x-coordinate;
[0137] 2) When the required scorch angle is the partitioned scorch angle, through the linkage control of the first strip track and the second strip track, each segment of the area to be etched on the aspherical substrate moves at a constant speed along the conic curve fitted in S2 at the second speed v2, while simultaneously performing segmented uniform etching on each segment of the area to be etched on the aspherical substrate.
[0138] 3) When the required scintillation angle is a gradient scintillation angle, through the coordinated control of the first and second strip tracks, each segment of the aspherical substrate to be etched moves at a constant speed v2 along the fitted conic curve in S2. Simultaneously, the fitted conic curve corresponding to each segment of the aspherical substrate to be etched is divided into n conic sub-curves of length Δc. The angle between the ion beam incident direction and the tangent direction of the current etching point starts from the fourth angle θ4. The angle corresponding to each segment of the conic curve increases by Δθ, thus increasing the second momentum of the rotating disk. for:
[0139] .
[0140] S6. Repeat S3~S5 until the scanning etching of the entire surface of the curved substrate is completed.
[0141] Based on the above-described method for fabricating blazed gratings on curved substrates using oscillating etching, this invention also provides an apparatus for fabricating blazed gratings on curved substrates using oscillating etching, such as... Figure 2 As shown, it includes the following components:
[0142] A liftable platform is fixedly installed on a rotating disk and used to drive the curved base to move up and down.
[0143] A rotating disk, mounted on the first and second strip tracks (perpendicular to each other), is used to drive the curved base to rotate.
[0144] The first and second strip tracks are used to drive the curved base to move horizontally;
[0145] An ion source is used to etch a curved substrate through a square slit.
[0146] The controller, through the coordinated control of the liftable stage, rotating disk, first strip track and second strip track, dynamically adjusts the angle between the ion beam incident direction and the tangent direction of the current etching point according to a preset rule, thereby realizing the fabrication of uniform, partitioned and gradient blazed angle gratings on spherical and aspherical substrates with known shape equations.
[0147] Specifically, the controller dynamically adjusts the angle between the incident direction of the ion beam and the tangent direction of the current etching point according to a preset rule by coordinating the lifting stage, the rotating disk, the first strip track, and the second strip track. This enables the fabrication of uniform, partitioned, and gradient blazed angle gratings on spherical and aspherical substrates with known shape equations, including:
[0148] For a spherical base:
[0149] 1) When the required scintillation angle is a uniform scintillation angle, through the coordinated control of the first and second strip tracks, each segment of the spherical substrate to be etched moves at a uniform speed v1 along the arc curve fitted in S2. Simultaneously, the attitude of the spherical substrate is adjusted by controlling the first angular velocity ω1 of the rotating disk, ensuring that the first angle θ1 between the ion beam incident direction and the tangent direction of the current etching point remains constant, satisfying the following:
[0150] ;
[0151] ;
[0152] Where t1 is the time for each segment of the etched area on the spherical substrate to undergo uniform curvilinear motion, c is the length of the fitted arc curve corresponding to each segment of the etched area on the spherical substrate, and α is the central angle of the fitted arc curve corresponding to each segment of the etched area on the spherical substrate.
[0153] 2) When the required scorch angle is the partitioned scorch angle, through the linkage control of the first strip track and the second strip track, each segment of the area to be etched on the spherical substrate moves at a constant speed v1 along the arc curve fitted in S2, while simultaneously performing segmented uniform etching on each segment of the area to be etched on the spherical substrate.
[0154] 3) When the required scorch angle is a gradual scorch angle, through the coordinated control of the first and second strip tracks, each segment of the spherical substrate to be etched moves at a uniform speed v1 along the arc curve fitted in S2. Simultaneously, by controlling the second angular velocity ω2 of the rotating disk, the attitude of the spherical substrate is adjusted so that the angle between the ion beam incident direction and the tangent direction of the current etching point gradually changes from the second angle θ2 to the third angle θ3, which must satisfy:
[0155] ;
[0156] ;
[0157] For aspherical substrates:
[0158] 1) When the required scintillation angle is a uniform scintillation angle, through the linkage control of the first and second strip tracks, each segment of the area to be etched on the aspherical substrate moves at a uniform speed v2 along the conic curve fitted in S2, while simultaneously rotating the disk by the first rotation amount. The angle between the tangent line at a point on the aspherical section curve in S2 and the Z-axis changes with the x-coordinate in the same way:
[0159] ;
[0160] Where △x represents the change in the x-coordinate;
[0161] 2) When the required scorch angle is the partitioned scorch angle, through the linkage control of the first strip track and the second strip track, each segment of the area to be etched on the aspherical substrate moves at a constant speed along the conic curve fitted in S2 at the second speed v2, while simultaneously performing segmented uniform etching on each segment of the area to be etched on the aspherical substrate.
[0162] 3) When the required scintillation angle is a gradient scintillation angle, through the coordinated control of the first and second strip tracks, each segment of the aspherical substrate to be etched moves at a constant speed v2 along the fitted conic curve in S2. Simultaneously, the fitted conic curve corresponding to each segment of the aspherical substrate to be etched is divided into n conic sub-curves of length Δc. The angle between the ion beam incident direction and the tangent direction of the current etching point starts from the fourth angle θ4. The angle corresponding to each segment of the conic curve increases by Δθ, thus increasing the second momentum of the rotating disk. for:
[0163] .
[0164] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions will not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for fabricating a blazed grating on a curved substrate based on oscillating etching, characterized in that: Includes the following steps: S1. Prepare a grating mask on the surface of the curved substrate to be processed. Place the grating mask with the grating line direction perpendicular to the rotating disk on a liftable platform. Adjust the height so that the initial section to be etched is on the same horizontal line as the square slit. S2. Fit each segment of the area to be etched on the curved substrate into a curve. S3. By rotating, the tangent direction of the starting etching point is made parallel to the etching direction, and the angle between the ion beam incident direction and the tangent direction of the current etching point determines the blaze angle. S4. The etching start point is moved to the ion beam etching area by translation. S5. The curved base is moved along the fitted curve in S2 by translation, and the rotating disk is controlled in association according to the type of the curved base and the preset blaze angle to perform oscillating etching on the curved base. S6. Repeat S3~S5 until the scanning etching of the entire surface of the curved substrate is completed.
2. The method for fabricating a blazed grating on a curved substrate based on oscillating etching according to claim 1, characterized in that: In S1, a grating mask is prepared on the surface of the curved substrate to be processed. The grating line direction of the grating mask is perpendicular to the rotating disk and placed on a liftable stage. By raising and lowering the stage, the initial section to be etched is aligned with the square slit at the same horizontal line, including: Holographic interference lithography is used to prepare a grating mask with a preset period and aspect ratio on the surface of the curved substrate to be processed. The grating mask is placed on a liftable stage with the grating line direction perpendicular to the rotating disk. The curved substrate is raised and lowered by the liftable stage so that the initial etchable section is on the same horizontal line as the square slit. The width of the square slit determines the degree of segmentation of the blazed grating.
3. The method for fabricating a blazed grating on a curved substrate based on oscillating etching according to claim 2, characterized in that: In S2, each segment of the area to be etched on the curved substrate is fitted as a curve, including: For a spherical substrate, each area to be etched can be fitted as a circular arc curve with a known radius.
4. The method for fabricating a blazed grating on a curved substrate based on oscillating etching according to claim 3, characterized in that: In S2, each segment of the area to be etched on the curved substrate is fitted as a curve, including: For aspherical substrates, first determine the corresponding quadratic conic surface equation, and then fit each segment of the area to be etched into a conic curve by cutting: 1) Aspherical surfaces are represented by the following formula: ； Where r is the radial distance, representing the perpendicular distance from a point on the aspherical surface to the Z-axis, Z(r) is the surface sag of the aspherical surface, representing the offset height of a point on the aspherical surface relative to the vertex along the Z-axis at a radial distance r, c is the vertex curvature, k is the conic coefficient, and A4, A6, and A8 are all even-order higher-order aspherical coefficients. 2) On an aspherical surface, the aspherical cross-sectional curve obtained by cutting it with the XZ plane of y=y0 is expressed by the following formula: ； Where (x,y,z) are spatial coordinates, and Z'(x) is the sag at position (x,y0) on the aspherical cross-section curve; 3) The angle between the tangent line at a point on the aspherical section curve and the Z-axis is expressed by the following formula: ； Where γ(x) is the angle between the tangent line at the point (x,y0,z) on the aspherical cross-section curve and the Z-axis, then z = Z'(x), and z' is the first derivative of the vertical coordinate z with respect to the horizontal coordinate x, representing the slope of the tangent line at the point (x,y0,z) on the aspherical cross-section curve. ; 4) The rate of change of the angle between the tangent line at a point on the aspherical section curve and the Z-axis as a function of the x-coordinate. Expressed as follows: ； Where z'' is the second derivative of the vertical coordinate z with respect to the horizontal coordinate x, representing the curvature of the tangent line at the point (x, y0, z) on the aspherical cross-section curve. sgn(·) represents the symbolic function.
5. The method for fabricating a blazed grating on a curved substrate based on oscillating etching according to claim 4, characterized in that: In S3, rotation is used to align the tangent direction of the initial etching point with the etching direction. Simultaneously, the angle between the ion beam incident direction and the tangent direction of the current etching point determines the blaze angle, including: By controlling the rotating disk, the tangent direction of the starting etching point is made parallel to the etching direction. At the same time, the angle θ between the ion beam incident direction and the tangent direction of the current etching point determines the blaze angle. The required blaze angle is adjusted by controlling the angle θ.
6. The method for fabricating a blazed grating on a curved substrate based on oscillating etching according to claim 5, characterized in that: In S4, the etching start point is moved to the ion beam etching region by translation, including: By controlling the first and second strip tracks in tandem, the etching start point is moved to the ion beam etching area.
7. The method for fabricating a blazed grating on a curved substrate based on oscillating etching according to claim 6, characterized in that: In S5, the curved substrate is moved along the fitted curve in S2 by translation, and the rotating disk is correlated with the type of the curved substrate and the preset blaze angle to perform oscillating etching on the curved substrate, including: For a spherical base: 1) When the required scintillation angle is a uniform scintillation angle, through the coordinated control of the first and second strip tracks, each segment of the spherical substrate to be etched moves at a uniform speed v1 along the arc curve fitted in S2. Simultaneously, the attitude of the spherical substrate is adjusted by controlling the first angular velocity ω1 of the rotating disk, ensuring that the first angle θ1 between the ion beam incident direction and the tangent direction of the current etching point remains constant, satisfying the following: ； ； Where t1 is the time for each segment of the etched area on the spherical substrate to undergo uniform curvilinear motion, c is the length of the fitted arc curve corresponding to each segment of the etched area on the spherical substrate, and α is the central angle of the fitted arc curve corresponding to each segment of the etched area on the spherical substrate. 2) When the required scorch angle is the partitioned scorch angle, through the linkage control of the first strip track and the second strip track, each segment of the area to be etched on the spherical substrate moves at a constant speed v1 along the arc curve fitted in S2, while simultaneously performing segmented uniform etching on each segment of the area to be etched on the spherical substrate. 3) When the required scorch angle is a gradual scorch angle, through the coordinated control of the first and second strip tracks, each segment of the spherical substrate to be etched moves at a uniform speed v1 along the arc curve fitted in S2. Simultaneously, by controlling the second angular velocity ω2 of the rotating disk, the attitude of the spherical substrate is adjusted so that the angle between the ion beam incident direction and the tangent direction of the current etching point gradually changes from the second angle θ2 to the third angle θ3, which must satisfy: ； 。 8. The method for fabricating a blazed grating on a curved substrate based on oscillating etching according to claim 7, characterized in that: In S5, the curved substrate is moved along the fitted curve in S2 by translation, and the rotating disk is correlated with the type of the curved substrate and the preset blaze angle to perform oscillating etching on the curved substrate, including: For aspherical substrates: 1) When the required scintillation angle is a uniform scintillation angle, through the linkage control of the first and second strip tracks, each segment of the area to be etched on the aspherical substrate moves at a uniform speed v2 along the conic curve fitted in S2, while simultaneously rotating the disk by the first rotation amount. The angle between the tangent line at a point on the aspherical section curve in S2 and the Z-axis changes with the x-coordinate in the same way: ； Where △x represents the change in the x-coordinate; 2) When the required scorch angle is the partitioned scorch angle, through the linkage control of the first strip track and the second strip track, each segment of the area to be etched on the aspherical substrate moves at a constant speed along the conic curve fitted in S2 at the second speed v2, while simultaneously performing segmented uniform etching on each segment of the area to be etched on the aspherical substrate. 3) When the required scintillation angle is a gradient scintillation angle, through the coordinated control of the first and second strip tracks, each segment of the aspherical substrate to be etched moves at a constant speed v2 along the fitted conic curve in S2. Simultaneously, the fitted conic curve corresponding to each segment of the aspherical substrate to be etched is divided into n conic sub-curves of length Δc. The angle between the ion beam incident direction and the tangent direction of the current etching point starts from the fourth angle θ4. The angle corresponding to each segment of the conic curve increases by Δθ, thus increasing the second momentum of the rotating disk. for: 。 9. An apparatus for fabricating blazed gratings on curved substrates based on oscillating etching, applicable to the method for fabricating blazed gratings on curved substrates based on oscillating etching as described in claim 1, characterized in that: Includes the following components: A liftable platform is fixedly installed on a rotating disk and used to drive the curved base to move up and down. A rotating disk, mounted on the first and second strip tracks, is used to drive the curved base to rotate. The first and second strip tracks are used to drive the curved base to move horizontally; An ion source is used to etch a curved substrate through a square slit. The controller, through the coordinated control of the liftable stage, rotating disk, first strip track and second strip track, dynamically adjusts the angle between the ion beam incident direction and the tangent direction of the current etching point according to a preset rule, thereby realizing the fabrication of uniform, partitioned and gradient blazed angle gratings on spherical and aspherical substrates with known shape equations.
10. The apparatus for fabricating a blazed grating on a curved substrate based on oscillating etching according to claim 9, characterized in that: The controller, through coordinated control of the liftable stage, rotating disk, first strip track, and second strip track, dynamically adjusts the angle between the ion beam incident direction and the tangent direction of the current etching point according to a preset rule. This enables the fabrication of uniform, partitioned, and gradient blazed angle gratings on spherical and aspherical substrates with known shape equations, including: For a spherical base: 1) When the required scintillation angle is a uniform scintillation angle, through the coordinated control of the first and second strip tracks, each segment of the spherical substrate to be etched moves at a uniform speed v1 along the arc curve fitted in S2. Simultaneously, the attitude of the spherical substrate is adjusted by controlling the first angular velocity ω1 of the rotating disk, ensuring that the first angle θ1 between the ion beam incident direction and the tangent direction of the current etching point remains constant, satisfying the following: ； ； Where t1 is the time for each segment of the etched area on the spherical substrate to undergo uniform curvilinear motion, c is the length of the fitted arc curve corresponding to each segment of the etched area on the spherical substrate, and α is the central angle of the fitted arc curve corresponding to each segment of the etched area on the spherical substrate. 2) When the required scorch angle is the partitioned scorch angle, through the linkage control of the first strip track and the second strip track, each segment of the area to be etched on the spherical substrate moves at a constant speed v1 along the arc curve fitted in S2, while simultaneously performing segmented uniform etching on each segment of the area to be etched on the spherical substrate. 3) When the required scorch angle is a gradual scorch angle, through the coordinated control of the first and second strip tracks, each segment of the spherical substrate to be etched moves at a uniform speed v1 along the arc curve fitted in S2. Simultaneously, by controlling the second angular velocity ω2 of the rotating disk, the attitude of the spherical substrate is adjusted so that the angle between the ion beam incident direction and the tangent direction of the current etching point gradually changes from the second angle θ2 to the third angle θ3, which must satisfy: ； ； For aspherical substrates: 1) When the required scintillation angle is a uniform scintillation angle, through the linkage control of the first and second strip tracks, each segment of the area to be etched on the aspherical substrate moves at a uniform speed v2 along the conic curve fitted in S2, while simultaneously rotating the disk by the first rotation amount. The angle between the tangent line at a point on the aspherical section curve in S2 and the Z-axis changes with the x-coordinate in the same way: ； Where △x represents the change in the x-coordinate; 2) When the required scorch angle is the partitioned scorch angle, through the linkage control of the first strip track and the second strip track, each segment of the area to be etched on the aspherical substrate moves at a constant speed along the conic curve fitted in S2 at the second speed v2, while simultaneously performing segmented uniform etching on each segment of the area to be etched on the aspherical substrate. 3) When the required scintillation angle is a gradient scintillation angle, through the coordinated control of the first and second strip tracks, each segment of the aspherical substrate to be etched moves at a constant speed v2 along the fitted conic curve in S2. Simultaneously, the fitted conic curve corresponding to each segment of the aspherical substrate to be etched is divided into n conic sub-curves of length Δc. The angle between the ion beam incident direction and the tangent direction of the current etching point starts from the fourth angle θ4. The angle corresponding to each segment of the conic curve increases by Δθ, thus increasing the second momentum of the rotating disk. for: 。