Laser scanning system

By designing DOE free curved lenses and using them in combination with mirrors and F-lens groups, the problem of insufficient laser collimation and scanning uniformity in existing scanning systems is solved, and the effect of high-precision and uniform scanning is achieved.

CN119644580AActive Publication Date: 2025-03-18YIPU PHOTOELECTRIC (TIANJIN) CO LTD
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Patent Information

Application Number
CN202510185389.X
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-02-20
Publication Date
2025-03-18
Estimated Expiration
2045-02-20

AI Technical Summary

Technical Problem

During laser collimation and shaping, the existing scanning systems have high assembly accuracy and the distance between points and points changes greatly during the scanning process, resulting in poor picture uniformity.

Method used

The DOE free curved lens is designed for laser shaping and used in combination with the reflector and the F-lens group. By designing the various optical surfaces of the F-lens group, high-precision and uniform scanning of the scanned image are achieved.

Benefits of technology

Improves the accuracy and uniformity of the scanned image, reduces optical distortion and improves optical efficiency.

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Abstract

The invention relates to the technical field of laser scanning, and discloses a laser scanning system comprising a light source used for outputting laser; the DOE free-form surface lens is arranged on an emergent light path of the laser and is used for shaping the laser; the multi-surface reflecting mirror is used for reflecting the shaped laser at different angles; the F-# imgabs0 # lens group is used for converging the laser reflected at different angles; wherein the F-# imgabs 1 # lens group comprises a first lens and a second lens, the first lens is used for correcting the reflected laser, and the second lens is used for converging the corrected laser. According to the invention, the DOE free-form surface lens is designed to shape laser, and is combined with the reflector and the F-# imgabs2 lens group for use, so that high-precision and uniform scanning of a scanned image is realized, optical distortion is reduced, and optical efficiency is improved.
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Description

Technical Field

[0001] The invention relates to the technical field of laser scanning, and in particular to a laser scanning system. Background Art

[0002] The scanning system is a key component of the scanning equipment, responsible for capturing and processing the image or data of the scanned object. Scanning equipment can be applied to various fields, such as office automation, logistics management, medical imaging, etc., and the performance of the scanning system will directly affect the overall performance of the scanning equipment, including scanning speed, clarity, etc.

[0003] The principle of the scanning system is: use a light source to illuminate the surface of the target object, and the light is reflected or passed through the target object for scanning. For the scanned light, a photosensitive element or image sensor can be used to convert the optical signal into an electrical signal for subsequent processing and storage.

[0004] In existing scanning systems, when lasers are collimated and shaped, the commonly used collimation and shaping solutions require the use of a combination of cylindrical and aspherical surfaces, which requires high assembly and matching accuracy. In addition, the distance between points varies greatly during the scanning process, resulting in poor image uniformity.

[0005] Therefore, there is an urgent need to develop a laser scanning system to solve the above problems. Summary of the invention

[0006] In order to solve the above technical problems, the present invention provides a laser scanning system, which shapes the laser by designing a DOE free-form surface lens and combines it with a reflector, F- The combination of lens groups achieves high-precision and uniform scanning of the scanned image.

[0007] The present invention provides a laser scanning system, comprising: A light source, used for outputting laser light; A DOE free-form surface lens is arranged on the outgoing optical path of the laser and is used to shape the laser. A diffraction structure is arranged on the first optical surface of the DOE free-form surface lens close to the light source. Multi-faceted reflector, used to reflect the shaped laser at different angles; F- A lens group is used to converge lasers reflected at different angles; Among them, the F- The lens group includes a first lens and a second lens, wherein the first lens is used to correct the reflected laser light, and the second lens is used to converge the corrected laser light.

[0008] Furthermore, the F- The focal length of the lens group in the x direction is 210±10 mm, and the focal length in the y direction is 40±10 mm.

[0009] Furthermore, the side of the DOE free-form surface lens close to the multi-faceted reflector is a second optical surface; The first optical surface is a 16th-order first polynomial formula, and the first polynomial does not include odd-order terms; The second optical surface is a second polynomial formula of degree 16.

[0010] Further, a Cartesian rectangular coordinate system O'-x'y'z' is established with the vertices of the first optical surface and the second optical surface as the origin O'; Based on the O'-x'y'z' coordinate system, the first polynomial formula is: , in, is the polar diameter, c is the surface curvature, k is the cone coefficient, , , , , , , , They are the aspheric coefficients corresponding to different order polar diameters; The second polynomial formula is: , in, is the surface curvature in the x' direction, is the radius of curvature in the x' direction, is the surface curvature in the y' direction, is the radius of curvature in the x' direction, k x is the cone coefficient in the x' direction, k y is the cone coefficient in the y' direction; is the aspheric coefficient in the x' direction, is the aspheric coefficient in the y' direction, m and n are the order in the x' and y' directions respectively.

[0011] Further, based on the O'-x'y'z' coordinate system of the first optical surface, the diffraction structure equation is: , in, is the optical path, M is the diffraction pole, N is the order, is the diffraction aspheric coefficient of the i-th order.

[0012] Further, the side of the first lens close to the multi-faceted reflector is a third optical surface, the side of the first lens close to the second lens is a fourth optical surface, the side of the second lens close to the first lens is a fifth optical surface, and the side of the second lens away from the first lens is a sixth optical surface; Constructing an O-xyz coordinate system using the vertices O of the optical surfaces of the first lens and the second lens as coordinate origins; The third optical surface and the first optical surface have the same surface expressions in different coordinate systems; The second optical surface and the fifth optical surface have the same surface expressions in different coordinate systems; The curved surface expressions of the fourth optical surface and the sixth optical surface in different coordinate systems are the same.

[0013] Further, based on the O-xyz coordinate system, the surface expression of the fourth optical surface or the sixth optical surface is: , in, They are the coefficients corresponding to different orders of y; is the surface curvature in the y direction, is the vertex curvature in the y direction, K y is the cone coefficient in the y direction, represents the vertex curvature in the x direction; ,in, are the aspheric coefficients corresponding to different orders in the x-direction and y-direction, and R is the radius of curvature.

[0014] The embodiments of the present invention have the following technical effects: This application designs a DOE free-form surface lens to shape the laser, and designs a diffraction structure on the first optical surface to improve the reflectivity of the lens and reduce light loss. The lens group is used in combination, wherein the F- Each optical surface of the lens group is designed to achieve high-precision and uniform scanning of the scanned image, reduce optical distortion and improve optical efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0016] Figure 1is a schematic structural diagram of a laser scanning system provided by an embodiment of the present invention; Figure 2 is a schematic diagram of the relationship between the magnification and the scanning frame width provided in Embodiment 2 of the present invention; Figure 3 is the spot diagram provided by Embodiment 2 of the present invention; Figure 4 This is the energy distribution diagram provided by Example 2 of the present invention.

[0017] In the figure, 1, light source; 2, DOE free-form surface lens; 3, multi-faceted reflector; 4, F- Lens group; 5. first lens; 6. second lens. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the scope of protection of the present invention. Example 1

[0019] Figure 1 Schematic diagram of the structure of a laser scanning system provided by an embodiment of the present invention. Figure 1 , specifically including: The light source 1 is used for outputting laser light; the single-wavelength Gaussian light emitted has a wavelength between 700 and 800 mm.

[0020] The DOE free-form surface lens 2 is arranged on the outgoing optical path of the laser and is used to shape the laser so that the light beam is accurately irradiated into a specific shape requirement and the energy distribution of the light beam is adjusted to make it more evenly distributed; The multi-faceted reflector 3 is used to reflect the shaped laser light at different angles, so that the light beam is scanned along a predetermined path; F- The lens group 4 is used to converge the lasers reflected at different angles, so as to control the diameter of the light beam to ensure the width and accuracy of the line, correct aberrations, etc.

[0021] Among them, the F- The lens group 4 includes a first lens 5 and a second lens 6. The first lens 5 is used to correct the reflected laser light, and the second lens 6 is used to converge the corrected laser light.

[0022] F- The focal length of lens group 4 in the x direction is 210 10mm, focal length in y direction is 40 10mm, further limiting the focal length range to ensure imaging quality in two different directions.

[0023] The side of the DOE free-form surface lens 2 close to the polygonal reflector 3 is the second optical surface; The first optical surface is a first polynomial formula of degree 16, and the first polynomial does not include odd-order terms; the second optical surface is a second polynomial formula of degree 16.

[0024] The DOE free-form surface lens 2 establishes a Cartesian rectangular coordinate system O'-x'y'z' with the vertices of the first optical surface and the second optical surface as the origin O'; Based on the O'-x'y'z' coordinate system, the first polynomial formula is: , in, is the polar diameter, c is the surface curvature, k is the cone coefficient, , , , , , , , They are the aspheric coefficients corresponding to different orders of polar diameters.

[0025] Based on the O'-x'y'z' coordinate system of the first optical surface, the diffraction structure equation is: , in, is the optical path, M is the diffraction pole, N is the order, is the diffraction aspheric coefficient of the i-th order.

[0026] The design of the first optical surface adds a diffraction structure on the basis of the aspheric surface, and an optical coating is applied on the first optical surface formed by the first polynomial formula, which is equivalent to superimposing two aspheric surfaces to shorten the focal length, improve the reflectivity of the lens and reduce light loss.

[0027] Based on the O'-x'y'z' coordinate system, the second polynomial formula is: , in, is the surface curvature in the x' direction, is the radius of curvature in the x' direction, is the surface curvature in the y' direction, is the radius of curvature in the x' direction, k x is the cone coefficient in the x' direction, k y is the cone coefficient in the y' direction; is the aspheric coefficient in the x' direction, is the aspheric coefficient in the y' direction, m and n are the order in the x' and y' directions respectively.

[0028] The second optical surface is a non-rotationally symmetric free-form surface. This design makes the curvatures in the x and y directions different, so the fast and slow axes of the laser can be compressed separately to achieve a better compression effect.

[0029] The side of the first lens 5 close to the polygonal reflector 3 is the third optical surface, the side of the first lens 5 close to the second lens 6 is the fourth optical surface, the side of the second lens 6 close to the first lens 5 is the fifth optical surface, and the side of the second lens 6 far from the first lens 5 is the sixth optical surface; The O-xyz coordinate system is constructed with the vertices O of the optical surfaces of the first lens 5 and the second lens 6 as the coordinate origins; wherein: The surface expressions of the third optical surface and the first optical surface in different coordinate systems are the same; Based on O-xyz, the surface expression corresponding to the third optical surface is: , in, is the polar diameter, c' is the surface curvature, k' is the cone coefficient, , , , , , , , They are the aspheric coefficients corresponding to different order polar diameters; (2) The surface expressions of the second optical surface and the fifth optical surface in different coordinate systems are the same; Based on O-xyz, the surface expression corresponding to the fifth optical surface is: , in, is the surface curvature in the x direction, is the radius of curvature in the x direction, is the surface curvature in the y direction, is the radius of curvature in the x direction, k x ' is the cone coefficient in the x direction, k y ' is the cone coefficient in the y direction; is the aspheric coefficient in the x direction, is the aspheric coefficient in the y direction, m' and n' are the order in the x direction and the y direction respectively.

[0030] (3) The surface expressions of the fourth optical surface and the sixth optical surface in different coordinate systems are the same.

[0031] Based on the O-xyz coordinate system, the surface expression of the fourth optical surface or the sixth optical surface is: , in, They are the coefficients corresponding to different orders of y; is the surface curvature in the y direction, is the vertex curvature in the y direction, K y is the cone coefficient in the y direction, represents the vertex curvature in the x direction; ,in, are the aspheric coefficients corresponding to different orders in the x-direction and y-direction, and R is the radius of curvature.

[0032] The arrangement of the fourth optical surface and the sixth optical surface makes the corresponding surfaces smoother and easier to process, which is beneficial to the shaping of the surface.

[0033] Based on the above settings, the following instructions are given: The laser shaped by the DOE free-form surface lens 2 forms a linear spot on the polygonal reflector 3, and the width of the line is less than 0.5 mm.

[0034] The function of the multi-faceted reflector 3 is to reflect the shaped light to F- In the lens group 4 , the polygonal reflector 3 is driven by a high-speed motor to rotate, and different rotation angles result in different reflection angles, so when the light beam is reflected by the rotating polygonal reflector 3 , multi-angle scanning is achieved.

[0035] Specifically, the motor speed is limited to the range of 20000RPM to 50000RPM. The dynamic scanning balance is less than 0.05%PP. The flatness of each surface of the multi-faceted reflector 3 is less than 0.6μm, and the pyramidal error is less than 300.

[0036] The laser reflected by the multi-faceted mirror 3 is incident on F- In the lens group 4, the contribution of the first lens 5 is mainly to correct the distortion. After the light passes through the third optical surface of the first lens 5, the light angle is expanded, the scanning angle is increased, and the concave aspheric surface of the third optical surface plays a role in correcting the distortion. The light passes through the fourth optical surface of the lens 5 for the first convergence. The fourth optical surface is a free-form surface, and the ratio of the optical power in the X direction to the Y direction is greater than 1 / 20, which corrects the spherical aberration in the X and Y directions.

[0037] The main function of the second lens 6 is to converge the light spot. The light passes through the fifth optical surface of the second lens 6 to correct the field curvature in the Y direction and expand the depth of field. The fourth optical surface is a free-form surface, which converges the light in the X direction and corrects the field curvature in the Y direction.

[0038] The light passes through the sixth optical surface and further corrects the Y direction F- Distortion, final F- The distortion is less than 0.1%, and the light spot is converged in the X direction so that the final convergence point in the X direction is at the same position as the convergence point in the Y direction, and finally a uniform light spot distribution is presented on the imaging surface.

[0039] In summary, the combination of the first lens 5 and the second lens 6 converges the reflected laser into a circular spot. The difference in the spot size at different positions is less than 5 μm, and each spot position is evenly distributed, that is, F- The distortion is less than 0.1%.

[0040] Based on the above technical solution, after the light source 1 emits the laser, it is collimated and shaped by the DOE free-form surface lens 2, and a line spot is presented on the multi-faceted reflector 3, and the line width is less than 0.5mm. On the lens group, F- The lens group converges the light and finally converges it onto the scanning surface to form a circular light spot. Example 2

[0041] Based on the content of Example 1, the present application provides a specific implementation scheme: Specific values ​​for setting the diffraction structure and each surface are shown in Tables 1 to 6; Table 1 Parameter settings of the first optical surface and diffraction structure Numeric 1 / c 22.00027014 k -10.96701214 <![CDATA[α2]]> 0 <![CDATA[α4]]> 0 <![CDATA[α6]]> 0 <![CDATA[α8]]> 0 <![CDATA[α 10 ]]> 0 <![CDATA[P2]]> 82.27890350 <![CDATA[P4]]> 0.53546872 <![CDATA[P6]]> 0.00269054 Table 2 Second optical surface parameter settings Numeric <![CDATA[r y ]]> -1.281950809E+01 <![CDATA[k y ]]> 0.000000000E+00 <![CDATA[r x ]]> -1.043357764E+01 <![CDATA[k x ]]> 3.197154740E+02 <![CDATA[β1]]> 0.0000000E+00 <![CDATA[β2]]> 0.0000000E+00 <![CDATA[β3]]> 0.0000000E+00 <![CDATA[β4]]> 0.0000000E+00 <![CDATA[β5]]> 0.0000000E+00 <![CDATA[β6]]> 0.0000000E+00 <![CDATA[β7]]> 0.0000000E+00 <![CDATA[β8]]> 0.0000000E+00 <![CDATA[γ1]]> 2.7033694E-14 <![CDATA[γ2]]> -1.1811041E-10 <![CDATA[γ3]]> 7.9951704E-11 <![CDATA[γ4]]> -1.1811041E-10 <![CDATA[γ5]]> 7.9951704E-11 <![CDATA[γ6]]> 0.0000000E+00 <![CDATA[γ7]]> 0.0000000E+00 <![CDATA[γ8]]> 0.0000000E+00 <![CDATA[γ9]]> 0.0000000E+00 Table 3 Parameter settings of the third optical surface Numeric 1 / c 5.327778E+01 k -1.096701E+01 <![CDATA[α1]]> 0.000000E+00 <![CDATA[α2]]> 5.895536E-07 <![CDATA[α3]]> -7.450482E-10 <![CDATA[α4]]> -4.621565E-13 <![CDATA[α5]]> 1.177703E-17 <![CDATA[α6]]> 0 <![CDATA[α7]]> 0 <![CDATA[α8]]> 0 Table 4 Parameter settings for the fourth optical surface Numeric R inf <![CDATA[C x ]]> -3.1742084075E-02 <![CDATA[C y ]]> 2.8388115263E-02 <![CDATA[K x ]]> 0.0000000000E+00 <![CDATA[K y ]]> -1.2987564069E+00 <![CDATA[A n ]]> -2.809541013E-06 <![CDATA[B n ]]> 1.034861757E-09 <![CDATA[C n ]]> 1.134526037E-13 <![CDATA[D n ]]> -6.895849935E-16 <![CDATA[E n ]]> 0.000000000E+00 <![CDATA[F n ]]> 0.000000000E+00 <![CDATA[a n ]]> -1.0900061478E-04 <![CDATA[b n ]]> 4.7744010498E-06 <![CDATA[c n ]]> -2.7176110394E-07 <![CDATA[d n ]]> 1.2507867022E-07 <![CDATA[e n ]]> 1.1120921632E-09 <![CDATA[f n ]]> -1.0492783809E-10 <![CDATA[j n ]]> -8.9978494997E-13 Table 5 Fifth optical surface parameter settings Numeric <![CDATA[r y ]]> 1.7746108E+02 <![CDATA[k y ]]> 0.0000000E+00 <![CDATA[r x ]]> 3.4354594E+03 <![CDATA[k x ]]> 3.1971547E+02 <![CDATA[β1]]> 0.0000000E+00 <![CDATA[β2]]> -7.3888732E-03 <![CDATA[β3]]> 0.0000000E+00 <![CDATA[β4]]> 1.6571395E-05 <![CDATA[β5]]> 0.0000000E+00 <![CDATA[β6]]> -3.7344608E-07 <![CDATA[β7]]> 0.0000000E+00 <![CDATA[β8]]> -4.9185599E-08 <![CDATA[γ1]]> -1.3744418E-03 <![CDATA[γ2]]> 2.7216854E-07 <![CDATA[γ3]]> -5.2507877E-07 <![CDATA[γ4]]> -1.1811041E-10 <![CDATA[γ5]]> 7.9951704E-11 <![CDATA[γ6]]> 2.7033694E-14 <![CDATA[γ7]]> -2.4016548E-15 <![CDATA[γ8]]> -2.3763260E-18 <![CDATA[γ9]]> -4.8276534E-19 Table 6 Parameter settings of the sixth optical surface Numeric R inf <![CDATA[C x ]]> 4.006130900E-06 <![CDATA[C y ]]> -4.120813900E-06 <![CDATA[K x ]]> -9.181756600E-10 <![CDATA[K y ]]> 3.956387700E-10 <![CDATA[A n ]]> 3.830322700E-07 <![CDATA[B n ]]> -1.114284800E-10 <![CDATA[C n ]]> 2.355219200E-14 <![CDATA[D n ]]> -2.238117700E-18 <![CDATA[E n ]]> 5.383609000E-23 <![CDATA[F n ]]> 0.000000000E+00 <![CDATA[a n ]]> -1.0900061478E-04 <![CDATA[b n ]]> 4.7744010498E-06 <![CDATA[c n ]]> -2.7176110394E-07 <![CDATA[d n ]]> 1.2507867022E-07 <![CDATA[e n ]]> 1.1120921632E-09 <![CDATA[f n ]]> -1.0492783809E-10 <![CDATA[j n ]]> -8.9978494997E-13 In the table, inf means infinity. Based on the above parameter settings, relevant experimental verification was carried out: Figure 2The horizontal axis represents the width of the scanning frame, and the vertical axis represents the magnification. The absolute value is the change in magnification corresponding to every 10mm of the scanning frame width, and the relative value is the change in magnification of the entire frame relative to every 10mm of the scanning frame width. It can be clearly seen from the figure that the magnification is less than 0.2%.

[0042] Figure 3 The middle circle is the diffraction limit, and the center of the circle shows the size of the imaging focal spot. The smaller the focal spot, the higher the resolution of the imaging screen. The defocus position is the defocus range. 2mm is a relatively large defocus range. The larger the defocus position, the more likely the light spot is still within the diffraction limit, indicating that the tolerance of the system of the present application is better.

[0043] Figure 4 The horizontal axis represents the scanning frame width, and the vertical axis represents the energy distribution. It can be seen that the energy uniformity is greater than 95%.

[0044] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the technical solutions of the embodiments of the present invention.

Claims

1. A laser scanning system, characterized in that: include: A light source (1) for outputting laser light; A DOE free-form surface lens (2) is arranged on an exit optical path of the laser and is used to shape the laser; a diffraction structure is provided on a first optical surface of the DOE free-form surface lens (2) on a side close to the light source (1); A multi-faceted reflector (3) is used to reflect the shaped laser light at different angles; F- A lens group (4) is used to converge laser beams reflected at different angles; Among them, the F- The lens group (4) comprises a first lens (5) and a second lens (6), wherein the first lens (5) is used to correct the reflected laser light, and the second lens (6) is used to converge the corrected laser light.

2. A laser scanning system according to claim 1, characterized in that: The F- The focal length of lens group (4) in the x direction is 210 10mm, focal length in y direction is 40 10mm.

3. A laser scanning system according to claim 1, characterized in that: The side of the DOE free-form surface lens (2) close to the multi-faceted reflector (3) is a second optical surface; The first optical surface is a 16th-order first polynomial formula, and the first polynomial does not include odd-order terms; The second optical surface is a second polynomial formula of degree 16.

4. A laser scanning system according to claim 3, characterized in that: Establish a Cartesian rectangular coordinate system O'-x'y'z' with the vertices of the first optical surface and the second optical surface as the origin O'; Based on the O'-x'y'z' coordinate system, the first polynomial formula is: , in, is the polar diameter, c is the surface curvature, k is the cone coefficient, , , , , , , They are the aspheric coefficients corresponding to different order polar diameters; The second polynomial formula is: , in, is the surface curvature in the x' direction, is the radius of curvature in the x' direction, is the surface curvature in the y' direction, is the radius of curvature in the x' direction, k x is the cone coefficient in the x' direction, k y is the cone coefficient in the y' direction; is the aspheric coefficient in the x' direction, is the aspheric coefficient in the y' direction, m and n are the order in the x' and y' directions respectively.

5. A laser scanning system according to claim 4, characterized in that: Based on the O'-x'y'z' coordinate system of the first optical surface, the diffraction structure equation is: , in, is the optical path, M is the diffraction pole, N is the order, is the diffraction aspheric coefficient of the i-th order.

6. A laser scanning system according to claim 4, characterized in that: The side of the first lens (5) close to the multi-faceted reflector (3) is a third optical surface, the side of the first lens (5) close to the second lens (6) is a fourth optical surface, the side of the second lens (6) close to the first lens (5) is a fifth optical surface, and the side of the second lens (6) far from the first lens (5) is a sixth optical surface; Constructing an O-xyz coordinate system using the vertices O of the optical surfaces of the first lens (5) and the second lens (6) as coordinate origins; The third optical surface and the first optical surface have the same surface expressions in different coordinate systems; The second optical surface and the fifth optical surface have the same surface expressions in different coordinate systems; The curved surface expressions of the fourth optical surface and the sixth optical surface in different coordinate systems are the same.

7. A laser scanning system according to claim 6, characterized in that: Based on the O-xyz coordinate system, the surface expression of the fourth optical surface or the sixth optical surface is: , in, They are the coefficients corresponding to different orders of y; is the surface curvature in the y direction, is the vertex curvature in the y direction, K y is the cone coefficient in the y direction, represents the vertex curvature in the x direction; ,in, are the aspheric coefficients corresponding to different orders in the x-direction and y-direction, and R is the radius of curvature.

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