Parameter calculation method of conic lens for generating bessel-like beam and conic lens
Patent Information
- Application Number
- CN202611216938.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-12
- Publication Date
- 2026-10-13
AI Technical Summary
这种方法还需配合空间光调制器进行验证，且算法本身较为复杂，因此其存在成本高、难度大
[0014]本申请实施例提供的生成类贝塞尔光束的锥透镜的参数计算方法及锥透镜，通过建立锥透镜的对数型相位函数，可拟合出锥透镜的轮廓曲线；采用高次项奇数非球面曲线拟合对数锥透镜轮廓，相比于遗传迭代算法，求解过程的复杂度更低，求解出的对数锥透镜更适合于加工；相比于普通锥透镜，本申请的锥透镜的出射光在焦深范围内的轴向能量分布更均匀，可生成类贝塞尔光束。
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Figure CN122902075A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of laser optics technology, specifically to a method for calculating the parameters of a cone lens for generating Bessel-like beams and the cone lens itself. Background Technology
[0002] Conventional conical lenses can produce diffraction-free Bessel beams, characterized by long focal depth and small spot size, making them applicable to laser processing, medical fields, and more. Especially with the development of the semiconductor industry, through-glass vias (TGVs), as a key technology for achieving three-dimensional integration of glass substrates, are leading semiconductor packaging from the silicon-based era to the glass-based era.
[0003] The fabrication of TGVs requires high speed, high precision, narrow pitch, smooth sidewalls, and good perpendicularity. However, glass hole-forming technology is one of the main challenges hindering the development of TGVs. The energy distribution of the emitted light from a conventional conical lens exhibits a Gaussian-like distribution within its focal depth range, meaning that the axial energy distribution is non-uniform, and the energy decreases rapidly on both sides of the point of maximum light intensity. This energy distribution characteristic will significantly affect the depth-to-diameter ratio in glass hole-forming.
[0004] Currently, most laser drilling products on the market use conventional conical lenses, which cannot meet actual processing requirements. Some research institutes have developed a method based on genetic algorithms to iteratively solve for the phase delay function of curved conical lenses, thereby achieving a Bessel-like beam with uniform energy distribution across the depth of focus. This method requires verification with a spatial light modulator, and the algorithm itself is quite complex, resulting in high cost and difficulty. Summary of the Invention
[0005] The purpose of this application is to provide a method for calculating the parameters of a conical lens for generating Bessel-like beams and a conical lens that can make the axial energy distribution of the emitted light more uniform within the focal depth range and is easy to obtain.
[0006] One aspect of this application provides a method for calculating the parameters of a conical lens that generates a Bessel-like beam, including: Establish a one-to-one energy equation relationship between each annulus of the cone lens and each focal depth distance of the cone lens; Set the starting point for the focal depth range of the output light from the conical lens; By integrating both sides of the energy equation, the logarithmic phase function of the conical lens can be calculated. The profile curve of the cone lens is fitted based on the logarithmic phase function.
[0007] Optionally, the energy equation relationship between the annular band and the depth of focus is as follows: Where r is the radius of the annular band, and dr is the width of the annular band. Let z(r) be the starting position of the depth of focus range, and z(r) be the mapped position point within the depth of focus range. This represents the power density of the incident light. The power density of the emitted light within the depth of focus.
[0008] Optionally, the step of integrating both sides of the energy equation to calculate the logarithmic phase function of the conical lens includes: The energy equation relationship Integrating, we get z(r) = + ;in, , R is the distance between the end point of the focal depth range of the conical lens and the zero point, and R is the light-transmitting half-aperture of the conical lens. The relationship between the logarithmic phase function and the light deflection angle θ is as follows: ; Integrating the relationship between the logarithmic phase function and the light deflection angle yields the logarithmic phase function. ; Wherein, d1 is the distance from the starting position of the focal depth range of the conical lens to the zero point, d2 is the distance from the ending position of the focal depth range of the conical lens to the zero point, R is the light-transmitting half-aperture of the conical lens, and r is the radial coordinate of the coordinate axis.
[0009] Optionally, fitting the contour curve of the cone lens based on the logarithmic phase function includes: The sag corresponding to multiple aperture positions is calculated using the logarithmic phase function; The contour curve of the cone lens is fitted using a high-order polynomial, and the fitting coefficients are output.
[0010] Optionally, the logarithmic phase function is related to the surface profile vector h of the conical lens. )satisfy: =k(n-1)h( ); k = 2π / λ.
[0011] Optionally, the step of fitting the contour curve of the cone lens with a higher-order polynomial and outputting fitting coefficients includes: The profile curve of the cone lens is set as a high-order odd-order aspherical surface, and a fifth-order term is used to fit the profile curve: ; Where z is the sag of the optical axis, c is the reciprocal of the radius of curvature, k is the conic coefficient, r is the radial coordinate of the coordinate axis, and a1, a2, a3, a4, and a5 are coefficients of higher-order terms, which are dimensionless.
[0012] Optionally, a1 = 0.21~0.22, a2 = 0.46~0.47, a3 = -1.38~-1.39, a4 = 1.16~1.17, a5 = -0.42~-0.43.
[0013] In another aspect of this application, a conical lens is provided, which, according to the parameter calculation method for a conical lens that generates a Bessel-like beam described above, satisfies the following: ; Where z is the sag of the optical axis, c is the reciprocal of the radius of curvature, k is the conic coefficient, r is the radial coordinate of the coordinate axis, and a1, a2, a3, a4, and a5 are coefficients of higher-order terms, which are dimensionless.
[0014] The method for calculating parameters of the conical lens for generating Bessel-like beams provided in this application embodiment, and the conical lens itself, can fit the profile curve of the conical lens by establishing the logarithmic phase function of the conical lens; by using a high-order odd-number aspherical curve to fit the profile of the logarithmic conical lens, the complexity of the solution process is lower than that of the genetic iterative algorithm, and the logarithmic conical lens obtained is more suitable for processing; compared with ordinary conical lenses, the axial energy distribution of the emitted light of the conical lens of this application is more uniform within the focal depth range, and it can generate Bessel-like beams. Attached Figure Description
[0015] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments of this application will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.
[0016] Figure 1 This is the optical path diagram of the conical lens provided in this embodiment; Figure 2 This is a cross-sectional view of the light spot within the focal depth range of the conical lens provided in this embodiment; Figure 3 This is an axial energy distribution diagram of the focal depth range of the cone lens provided in this embodiment. Detailed Implementation
[0017] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings.
[0018] In the description of this application, it should be noted that the terms "inner" and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product is in use. They are used only for the convenience of describing this application and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this application. Furthermore, the terms "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.
[0019] It should also be noted that, unless otherwise explicitly specified and limited, the terms "setup" and "connection" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.
[0020] For the energy distribution of the outgoing light of a conventional conical lens within its focal depth range, to achieve a uniform axial energy distribution, the energy of the incident light in the equally spaced rings within the aperture of the conical lens must be equal to the energy of the outgoing light in the equally spaced axial regions.
[0021] It should be noted that the equidistant ring zone refers to the annular region within the aperture of the conical lens, divided radially at fixed equal intervals. The radial phase difference between adjacent ring zones remains constant, forming the basic structure for achieving conical phase modulation. The periodic parameter of the equidistant ring zone directly determines the deflection angle of the conical lens and the size of the annular beam, and is a key design parameter for controlling the diffraction-free distance and spot shape of the Bessel beam.
[0022] The profile of a conventional conical lens is a straight line, meaning its cone angle is constant, which causes the light deflection angle at different aperture positions to also be constant. The annular interval is proportional to the axial interval, making it impossible to achieve equal axial energy distribution, and its axial light intensity decreases with distance.
[0023] The method of establishing a cost function based on the target light intensity distribution and using a genetic algorithm to iterate the phase delay function of the curved conical lens also needs to be verified with a spatial light modulator. Moreover, the algorithm itself is quite complex, so it is costly and difficult.
[0024] In view of this, the present application provides a method for calculating the parameters of a conical lens 10 that generates a Bessel-like beam, which enables the emitted light from the conical lens 10 to achieve uniform axial energy distribution within the focal depth range, and can also design the profile curve of the corresponding logarithmic conical lens 10 according to different actual needs.
[0025] Based on the fundamental principle of energy conservation mapping, the energy of incident light in different aperture rings is uniformly mapped to a specified focal depth distance, thereby achieving uniform axial energy distribution.
[0026] Specifically, the method includes: Step 100: Establish a one-to-one energy equation relationship between each annulus of the cone lens 10 and each focal depth distance of the cone lens 10.
[0027] The total radial width of the annular band within the effective aperture of the conical lens 10 directly determines the maximum value of the incident light radius. According to the focal depth formula of the conical lens 10, the focal depth is proportional to the incident light radius. The larger the coverage area of the annular band, the longer the achievable focal depth distance.
[0028] In other words, each ring of the conical lens 10 corresponds to a focal depth, and there is a one-to-one energy equation relationship between the rings and the focal depths.
[0029] Specifically, the energy equation relating the annular zone to the depth of focus is as follows: Where r is the radius of the annular band of the cone lens 10, and dr is the width of the annular band of the cone lens 10. Let z(r) be the starting position of the focal depth range of the conical lens 10, and z(r) be the mapping position point within the focal depth range. This represents the power density of the incident light from the conical lens 10. The power density of the emitted light from the conical lens 10 within the depth of focus range.
[0030] Step 101: Set the starting point of the focal depth range of the output light of the cone lens 10.
[0031] With the standard reference position as the zero point, the starting point of the focal depth range of the output light of the cone lens 10 is the position relative to the zero point. The focal depth range also has an ending point. The distance between the starting point and the ending point is the focal depth, which refers to the axial effective distance within the aperture range of the cone lens 10 that can stably output an approximately diffraction-free Bessel beam.
[0032] Step 102: Integrate both sides of the energy equation to calculate the logarithmic phase function of the conical lens 10.
[0033] Energy equations Integrating, we get z(r) = + ;in, , R is the distance between the end point of the focal depth range of the cone lens 10 and the zero point, and R is the light-transmitting half-aperture of the cone lens 10. The relationship between the logarithmic phase function and the ray deflection angle θ is as follows: ; Integrating the relationship between the logarithmic phase function and the ray deflection angle yields the logarithmic phase function of the conical lens 10. (1); in, d1 is the distance from the starting position of the depth of focus range to the zero point, d2 is the distance from the ending position of the depth of focus range to the zero point, R is the half-aperture of the cone lens 10, and r is the radial coordinate of the coordinate axis.
[0034] Step 103: Fit the profile curve of the conical lens 10 according to the logarithmic phase function.
[0035] The sag corresponding to multiple aperture positions is calculated using a logarithmic phase function, and then the profile curve of the cone lens 10 is fitted using a high-order polynomial to output the fitting coefficients.
[0036] For refractive lenses, the logarithmic phase function is related to the surface profile vector h of the cone lens. )satisfy: =k(n-1)h( k = 2π / λ; From this, the sag corresponding to multiple aperture positions can be obtained.
[0037] To facilitate machining with CNC aspherical equipment in practice, the contour curve of the cone lens 10 is set as a high-order odd-order aspherical surface, and a fifth-order term is used to fit the contour curve. The specific formula is as follows: (2); Where z is the sag of the optical axis, c is the reciprocal of the radius of curvature, k is the conic coefficient, r is the radial coordinate of the coordinate axis, and a1, a2, a3, a4, and a5 are coefficients of higher-order terms, which are dimensionless.
[0038] Since the sag z corresponding to multiple aperture positions has been calculated using the logarithmic phase function, a1, a2, a3, a4, and a5 can be obtained according to formula (2).
[0039] In formula (2), each parameter is a parameter of the conical lens 10. Once these parameters are determined, a specific conical lens 10 can be obtained, and the beam passing through the conical lens 10 forms a Bessel-like beam.
[0040] The values are determined as follows: a1 = 0.21~0.22, a2 = 0.46~0.47, a3 = -1.38~-1.39, a4 = 1.16~1.17, a5 = -0.42~-0.43.
[0041] In some embodiments, a1=0.2174, a2=0.4673, a3=-1.3882, a4=1.169, a5=-0.4213.
[0042] The parameter calculation method for the conical lens 10 for generating Bessel-like beams provided in this application embodiment can fit the contour curve of the conical lens 10 by establishing the logarithmic phase function of the conical lens 10. The contour of the logarithmic conical lens 10 is fitted by a high-order odd-number aspherical curve, which has lower complexity than the genetic iterative algorithm. The logarithmic conical lens 10 obtained by the solution is more suitable for processing. Compared with ordinary conical lenses 10, the axial energy distribution of the emitted light of the conical lens 10 of this application is more uniform in the focal depth range, which can generate Bessel-like beams.
[0043] On the other hand, this application embodiment also provides a cone lens, which is obtained by using the above-described parameter calculation method for the cone lens 10 that generates a Bessel-like beam. The cone lens 10 satisfies the following: ; Where z is the sag of the optical axis, c is the reciprocal of the radius of curvature, k is the conic coefficient, r is the radial coordinate of the coordinate axis, and a1, a2, a3, a4, and a5 are coefficients of higher-order terms, which are dimensionless.
[0044] The phase function of the cone lens 10 obtained in this application is logarithmic, the formula is relatively simple, the solution process has low complexity, and it does not involve complex iterative algorithms. The fitted contour curve is as follows: Figure 1 As shown. Depend on Figure 2 It can be seen that the light spot within the focal depth range of the logarithmic cone lens 10 exhibits a Bezier-like distribution, consisting of a central main lobe and peripheral side lobes, which is similar to that of a conventional cone lens 10.
[0045] Figure 3 In the figure, the horizontal axis represents the axial distance (in mm), and the vertical axis represents the light intensity. As can be seen from the figure, the light intensity within the focal depth range exhibits a flat-top distribution, and the axial energy distribution is relatively uniform.
[0046] The above description is merely an embodiment of this application and is not intended to limit the scope of protection of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.
Claims
1. A method for calculating the parameters of a conical lens that generates a Bessel-like beam, characterized in that, include: Establish a one-to-one energy equation relationship between each annulus of the cone lens and each focal depth distance of the cone lens; Set the starting point for the focal depth range of the output light from the conical lens; By integrating both sides of the energy equation, the logarithmic phase function of the conical lens can be calculated. The profile curve of the cone lens is fitted based on the logarithmic phase function.
2. The method for calculating the parameters of the conical lens for generating a Bessel-like beam according to claim 1, characterized in that, The energy equation relating the annular band to the depth of focus is: Where r is the radius of the annular band, and dr is the width of the annular band. Let z(r) be the starting position of the focal depth range, and z(r) be the mapped position point within the focal depth range. This represents the power density of the incident light. The power density of the emitted light within the focal depth range.
3. The method for calculating the parameters of the conical lens for generating a Bessel-like beam according to claim 2, characterized in that, The step of integrating both sides of the energy equation to calculate the logarithmic phase function of the conical lens includes: The energy equation relationship Integrating, we get z(r) = + ;in, , R is the distance between the end point of the focal depth range of the conical lens and the zero point, and R is the light-transmitting half-aperture of the conical lens. The relationship between the logarithmic phase function and the light deflection angle θ is as follows: ; Integrating the relationship between the logarithmic phase function and the light deflection angle yields the logarithmic phase function. ; Wherein, d1 is the distance from the starting position of the focal depth range of the conical lens to the zero point, d2 is the distance from the ending position of the focal depth range of the conical lens to the zero point, R is the light-transmitting half-aperture of the conical lens, and r is the radial coordinate of the coordinate axis.
4. The method for calculating the parameters of the conical lens for generating a Bessel-like beam according to claim 3, characterized in that, The step of fitting the contour curve of the cone lens according to the logarithmic phase function includes: The sag corresponding to multiple aperture positions is calculated using the logarithmic phase function; The contour curve of the cone lens is fitted using a high-order polynomial, and the fitting coefficients are output.
5. The method for calculating the parameters of the conical lens for generating a Bessel-like beam according to claim 4, characterized in that, The logarithmic phase function is related to the surface profile height h of the conical lens. )satisfy: =k(n-1)h( );k=2π / λ。 6. The method for calculating the parameters of the conical lens for generating a Bessel-like beam according to claim 4 or 5, characterized in that, The step of fitting the contour curve of the cone lens using a high-order polynomial and outputting fitting coefficients includes: The profile curve of the cone lens is set as a high-order odd-order aspherical surface, and a fifth-order term is used to fit the profile curve: ； Where z is the sag of the optical axis, c is the reciprocal of the radius of curvature, k is the conic coefficient, r is the radial coordinate of the coordinate axis, and a1, a2, a3, a4, and a5 are coefficients of higher-order terms, which are dimensionless.
7. The method for calculating the parameters of the conical lens for generating a Bessel-like beam according to claim 6, characterized in that, a1=0.21~0.22, a2=0.46~0.47, a3=-1.38~-1.39, a4=1.16~1.17, a5=-0.42~-0.
43.
8. A conical lens, obtained by the parameter calculation method for a conical lens generating a Bessel-like beam according to any one of claims 1 to 7, characterized in that, The conical lens satisfies: ； Where z is the sag of the optical axis, c is the reciprocal of the radius of curvature, k is the conic coefficient, r is the radial coordinate of the coordinate axis, and a1, a2, a3, a4, and a5 are coefficients of higher-order terms, which are dimensionless.