Beam shaping method and shaping system thereof

Abstract

A beam shaping method and shaping system, wherein at least one lens is used to perform beam shaping. The shaping method comprises: acquiring energy distribution of incident light and energy distribution of a target image (S101); on the basis of the light-spot shape of the target image, superposing a Zernike polynomial after a standard spherical formula, so as to obtain a superposed surface profile formula, and using the superposed surface profile formula to adjust the surface profile of at least one lens of a shaping system (S102); and on the basis of the energy distribution of the incident light, a shaping formula, and the energy distribution of the target image, calculating shaping parameters of the shaping system (S103).

Description

Light beam shaping method and light beam shaping system

[0001] This application claims priority to the Chinese patent application filed with the China Patent Office on December 26, 2023, with application number 202311821923.9, the entire contents of which are incorporated by reference into this application. Technical Field

[0002] The embodiments of the present application relate to the field of laser shaping technology, for example, to a light beam shaping method and a light beam shaping system. Background Art

[0003] Traditional laser output is typically Gaussian, meaning its energy follows a Gaussian distribution. However, in many applications, a Gaussian distribution isn't required, but rather a uniformly distributed light spot, such as a circular top-hat, annular top-hat, square top-hat, or strip-top-hat. Current beam shaping devices often use diffractive optical elements (DOEs) to shape the beam into various shapes. The most common beam shaping method, and also the most common in high-end lighting systems, is the diffractive optical element (DOE). However, DOE shaping elements are difficult to manufacture and expensive.

[0004] Shaping using traditional refraction methods has certain disadvantages. For example, microlens shaping is affected by the manufacturing of the edges of adjacent microlenses, and the edges of the microlenses generally have flare, which is more obvious when the light spot is small. In addition, the flat-top light shaped by traditional refraction for Gaussian light is not an absolute flat-top light, and still cannot achieve the best beam shaping effect.

[0005] Summary of the Invention

[0006] The present application provides a light beam shaping method and a light beam shaping system thereof, which uses a geometric optics method to shape Gaussian light into a flat-top light of a desired shape and size.

[0007] In a first aspect, the present application provides a light beam shaping method, which uses at least one lens to perform light beam shaping, and the shaping method includes:

[0008] Obtaining incident light energy distribution and target image energy distribution;

[0009] According to the spot shape of the target image, a Zernike polynomial is superimposed on the standard spherical formula to obtain a superimposed surface shape formula, and the surface shape of at least one lens of the shaping system is adjusted using the superimposed surface shape formula; wherein the superimposed surface shape formula is:

[0010] Where z is the distance from the aspheric lens to the aspheric vertex along the optical axis; k is the conic constant; r is the radial coordinate perpendicular to the optical axis; α i is the coefficient of the higher-order term, α i r 2i is the high-order term of the aspheric surface; N is the number of Zernike terms, Ai is the coefficient of the i-th term, Zi is the i-th term of the Zernike polynomial, ρ is the polar coordinate, is the angular coordinate, i is a positive integer, the units of z and r are both mm, and c is a constant;

[0011] Calculating shaping parameters of a shaping system according to the incident light energy distribution, the shaping formula and the target image energy distribution; wherein the shaping formula is: a+X=b;

[0012] Wherein, a is the incident light energy distribution, b is the target image energy distribution, and X is the shaping parameter of the shaping system.

[0013] In a second aspect, an embodiment of the present application provides a light beam shaping system, which uses the shaping method provided in the first aspect to shape the light beam, wherein the shaping system includes at least one lens, and the surface formula of the lens satisfies:

[0014] Where z is the distance from the aspheric lens to the aspheric vertex along the optical axis; k is the conic constant; r is the radial coordinate perpendicular to the optical axis; α i is the coefficient of the higher-order term, α i r 2i is the high-order term of the aspheric surface; N is the number of Zernike terms, Ai is the coefficient of the i-th term, Zi is the i-th term of the Zernike polynomial, ρ is the polar coordinate, are angular coordinates, i = 1, 2, ..., 8, the units of z and r are both mm, and c is a constant. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] FIG1 is a two-dimensional schematic diagram of light of a light beam shaping system provided by the present application;

[0016] FIG2 is a schematic diagram of a light beam shaping method provided by the present application;

[0017] FIG3A is a topographic diagram of an incident light spot in a light beam shaping method provided by the present application;

[0018] FIG3B is a morphology diagram of an image plane spot of a beam shaping method provided by the present application;

[0019] FIG4 is a schematic cross-sectional view of the image plane light spot in FIG3B ;

[0020] FIG5 is a schematic flow chart of a light beam shaping method provided by the present application;

[0021] FIG6 is a two-dimensional schematic diagram of light of another light beam shaping system provided by the present application;

[0022] FIG7A is a topographic diagram of an incident light spot of another light beam shaping method provided by the present application;

[0023] FIG7B is a morphology diagram of an image plane spot of another light beam shaping method provided in the present application. DETAILED DESCRIPTION

[0024] The present application is described below with reference to the accompanying drawings and embodiments.

[0025] In view of one or more of the above-mentioned problems existing in the related art, this application proposes a beam shaping system. FIG1 is a two-dimensional schematic diagram of light rays of a beam shaping system provided by this application. Referring to FIG1 , the beam shaping system provided by an embodiment of this application uses the beam shaping method provided by the following embodiment to shape the beam. The shaping system includes at least one lens, and the surface formula of the lens satisfies:

[0026] Where z is the distance from the aspheric lens to the aspheric vertex along the optical axis; k is the conic constant; r is the radial coordinate perpendicular to the optical axis; α i is the coefficient of the higher-order term, α i r 2i is the high-order term of the aspheric surface; N is the number of Zernike terms, Ai is the coefficient of the i-th term, Zi is the i-th term of the Zernike polynomial, ρ is the polar coordinate, are angular coordinates, i = 1, 2, ..., 8, the units of z and r are both mm, and c is a constant.

[0027] Optionally, FIG1 illustrates a shaping system consisting of a first lens 1 and a second lens 2. This application employs the superposition of other polynomials, such as Zernike polynomials, on the standard spherical formula to change the spherical surface shape, thereby shaping the Gaussian beam into flat-top beams of different shapes, thereby achieving the purpose of beam shaping. Compared to diffractive optical elements, this solution is easier to process and implement, while possessing all the advantages of traditional optical elements over diffractive optical elements, such as high processing accuracy and low cost.

[0028] Optionally, the shaping system includes at least two shaping surfaces arranged in sequence, the surface shapes of the shaping surfaces satisfy the surface shape formula, and the shaping surfaces can be located on one lens, or on any two lenses.

[0029] Optionally, the shaping system can be a combination of multiple lenses, with the center of each lens located on the principal optical axis of the incident light. Based on the spot shape of the target image, multiple shaping surfaces are obtained by superimposing Zernike polynomials on the standard spherical formula. To reduce the difficulty of processing and other processes, for example, when there are two shaping surfaces, they can be respectively set on one side of each lens of any two selected lenses;

[0030] In other embodiments, a lens may be used, and the two shaping surfaces may be respectively provided on two side surfaces of the lens.

[0031] FIG2 is a schematic diagram of a beam shaping method provided by the present application. In combination with FIG1 and FIG2 , an embodiment of the present application provides a beam shaping method, which uses the beam shaping system provided by the above embodiment to perform beam shaping. The shaping method includes:

[0032] S101 : Obtain incident light energy distribution and target image energy distribution.

[0033] Optionally, when the incident light energy distribution is Gaussian, the energy integral calculation is performed on the input light. When the incident light conforms to the standard Gaussian distribution, the incident light energy distribution is:

[0034] Where k is the Gaussian apodization coefficient and t is the coordinate centered on the optical axis.

[0035] S102 , according to the spot shape of the target image, superimpose Zernike polynomials on the standard spherical formula to obtain a superimposed surface formula, and use the superimposed surface formula to adjust the surface shape of at least one lens of the shaping system.

[0036] Optionally, the incident light spot is a Gaussian light spot. It is necessary to determine the spot shape of the target image, perform energy distribution integral calculation on the target image, and superimpose Zernike polynomials on the standard spherical formula based on the shape of the output light spot to be shaped. This changes the spherical surface shape and obtains a superimposed surface shape formula. This superimposed surface shape formula is then used to adjust the surface shape of at least one lens of the shaping system to achieve the purpose of beam shaping. The superimposed surface shape formula is:

[0037] Where z is the distance from the aspheric lens to the aspheric vertex along the optical axis; k is the conic constant; r is the radial coordinate perpendicular to the optical axis; α i is the coefficient of the higher-order term, α i r 2iis the high-order term of the aspheric surface; N is the number of Zernike terms, Ai is the coefficient of the i-th term, Zi is the i-th term of the Zernike polynomial, ρ is the polar coordinate, is the angular coordinate, i is a positive integer, the units of z and r are both mm, and c is a constant.

[0038] Among them, i, α in the superimposed Zernike polynomial i , α i r 2i 、Ai、ρ、 Parameters such as the beam spot shape and the energy distribution integral of the target image need to be reasonably selected.

[0039] S103 , calculating shaping parameters of the shaping system according to the incident light energy distribution, the shaping formula, and the target image energy distribution.

[0040] Among them, the shaping formula of the shaping system is: a+X=b, (1.3);

[0041] a is the incident light energy distribution, b is the target image energy distribution, and X is the shaping parameter of the shaping system.

[0042] Optionally, X includes multiple variables, and the least squares method or orthogonal integration method can be used to obtain the optimal solution to determine the shaping parameter X of the shaping system. The solution process of the least squares method and orthogonal integration method is beyond the scope of the embodiment of this application.

[0043] In some embodiments, selective superposition can be performed based on the spot shape of the target image to be formed. The spot shape of the target image includes a rotationally symmetric spot. For example, if a circular or annular flat top light is to be formed, in step 102, it is necessary to superimpose the rotationally symmetric Zernike polynomials after the standard spherical formula to obtain the superimposed rotationally symmetric surface formula; j=i 2 , i≥2.

[0044] For example, in combination with formula (1.4), j = 4, 9, 16, 25, etc., the rotationally symmetric surface formula after lens superposition is obtained as follows:

[0045] In some embodiments, the spot shape of the target image includes a non-rotationally symmetric spot. When a non-rotationally symmetric spot is to be formed, in step 102, non-rotationally symmetric Zernike polynomials may be superimposed. When a non-rotationally symmetric spot is to be obtained, the non-rotationally symmetric Zernike polynomials need to be superimposed after the standard spherical formula to obtain the superimposed non-rotationally symmetric surface formula.

[0046] The non-rotationally symmetric Zernike polynomials are the polynomials remaining after removing the rotationally symmetric polynomials from the Zernike polynomials.

[0047] In some embodiments, the non-rotationally symmetric light spot includes a square flat top light or a rectangular flat top light. In step S102, the same power order term in the non-rotationally symmetric Zernike polynomial in the superimposed non-rotationally symmetric surface formula is set to be composed of orthogonal functions in two directions, thereby obtaining a square flat top light or a rectangular flat top light. Similarly, the specific Zernike polynomial that needs to be superimposed is obtained according to the relevant formula.

[0048] Some specific embodiments are listed below to illustrate the light beam shaping method and shaping system provided in the embodiments of the present application.

[0049] Continuing with Figure 1, the present embodiment uses a shaping system comprising two lenses as an example. Two surfaces are added to the standard spherical surface and additional Zernike polynomials, and the superimposed surface formula satisfies formula (1.1). To produce a non-rotationally symmetric flat-top beam, at least two surfaces must be added. These two surfaces can belong to the front and back surfaces of the same lens, or to two separate lenses. The more Zernike polynomial terms added, the better the final beam shaping effect. The more surfaces selected for superposition calculation, the better the final beam shaping effect.

[0050] FIG3A and FIG3B are morphological comparison diagrams of the incident light spot and the image plane light spot of the beam shaping provided by the present application; FIG4 is a cross-sectional schematic diagram of the image plane light spot in FIG3B , FIG3A is the morphology of the incident light spot, and FIG3B is the morphology of the image plane light spot after shaping. In combination with FIG1-FIG4 , the embodiment of the present application selected Zernike's eight-term polynomial for calculation, and selected a surface as a variable in each of the first lens and the second lens, namely the shaping surface. The multinomial coefficients of the optical system obtained by calculation are shown in Table 1:

[0051] Table 1

[0052] As shown in Table 1, since a non-rotationally symmetric flat-top light is to be formed, eight asymmetric Zernike polynomials are rationally selected from the Zernike polynomials. Their coefficients are calculated as A2, A3, A5, A6, A7, A8, A10, and A11 shown in the above table. After superimposing these Zernike polynomials, the curvature radii of the first lens 1 and the second lens 2 are shown in the above table.

[0053] Optionally, the incident spot has a Gaussian distribution. The shaped spot is shown in Figures 3B and 4. The shaped spot size is 0.756mm*0.126mm, and can be designed according to actual needs. The spot size is not less than the diffraction-limited spot, but there is no limit to the maximum spot size, which depends on the focal length of the shaping system. In principle, the shaped spot can be from the diffraction-limited spot to infinity.

[0054] In other embodiments, other traditional polynomials may be superimposed on the standard spherical formula, such as: Where ρ' represents the normalized polar coordinates, α i represents the coefficient.

[0055] In terms of actual surface shape, compared with superimposing other traditional polynomials, the surface shape of the standard spherical formula superimposed by Zernike polynomials in this application can be directly and accurately measured by interferometer and compared with theoretical data. Accurate measurement can guide processing and refinement; while superimposing other polynomials generally requires comparative measurement with the best fit sphere, which is an indirect measurement. Therefore, the use of superimposed Zernike polynomials is more direct and more accurate for actual measurement.

[0056] The surface shape provided by the embodiment of the present application, which superimposes Zernike polynomials on the standard spherical formula, has the following advantages over DOE:

[0057] 1. Low manufacturing cost. The cost of traditional optical elements is much lower than that of diffractive optical elements.

[0058] 2. High manufacturing precision. Traditional optical elements are more mature than diffractive optical elements, and the manufacturing process is more stable, so the results are closer to the theoretical design values;

[0059] 3. Higher efficiency. The shaping system provided in the embodiment of the present application is a refractive system. The light energy efficiency of the shaping system is equivalent to that of the refractive system. The transmittance of the coating and the material is the main factor affecting the light efficiency. For commonly used wavelengths, the light energy efficiency of the shaping system can generally exceed 99%;

[0060] 4. Components are easier to detect and accept. Since they are superimposed Zernike polynomials, they can be directly detected by a common interferometer with extremely small detection errors.

[0061] Optionally, taking shaping a Gaussian beam into a flat-top beam as an example, FIG5 is a flow chart of a beam shaping method provided by the present application. Referring to FIG5 , the beam shaping method provided by the present application includes:

[0062] S201. Calculate input light energy distribution a.

[0063] Optionally, refer to formula (1.2) provided in the above embodiment.

[0064] S202: Perform energy integration calculation on the input light.

[0065] S203: Calculate target flat-top light energy distribution b.

[0066] Optionally, reference may be made to FIG. 3A , FIG. 3B and FIG. 4 provided in the above embodiment.

[0067] S204: Perform energy integration calculation on the target flat-top light.

[0068] S205. Select a surface and a suitable superimposed Zernike polynomial as variables.

[0069] S206: Calculate the shaping coefficient X.

[0070] Optionally, the shaping parameter X of the shaping system can be obtained by combining formulas (1.1)-(1.4) and using the least square method or Gaussian integral method for calculation.

[0071] S207. Evaluate the target flat-top light index.

[0072] Optionally, since there may be many variables, the calculation can be performed using the least square method or the Gaussian integral method. When the flat-top light evaluation does not meet the requirements, the calculation can be performed again by increasing the number of Zernike polynomials.

[0073] The beam shaping is completed until the evaluation flat-top light meets the index and the evaluation target flat-top light is obtained.

[0074] Optionally, in combination with formulas (1.1)-(1.4), and continuing to refer to Figures 1-3B, in some embodiments, as shown in Figure 1, standard spherical formulas are added to the back surfaces of the first lens 1 and the second lens 2 and Zernike non-rotationally symmetric polynomials are superimposed. Gaussian light passes through the first lens 1 and the second lens 2 in sequence, and after passing through the first lens 1 and the second lens 2, forms a rectangular flat-top light on the final image plane, as shown in Figure 3B.

[0075] Figure 6 is a two-dimensional schematic diagram of light rays from another beam shaping system provided by the present application. Figures 7A and 7B are comparative diagrams of the incident light spot and image light spot of the beam shaping system provided by the present application, with Figure 7A showing the morphology of the incident light spot and Figure 7B showing the morphology of the image light spot. In conjunction with formulas (1.1)-(1.4), as shown in Figure 6, in some embodiments, by superimposing rotationally symmetric Zernike polynomials on the third lens 3 and the fourth lens 4, a rotationally symmetric top hat light, such as an annular top hat light, can be formed. Gaussian light sequentially passes through the third lens 3 and the fourth lens 4, passing through two sets of third lenses 3 and fourth lenses 4 superimposed with rotationally symmetric Zernike polynomials, ultimately forming an annular top hat light on the image plane, as shown in Figure 7B. In Figures 3A, 3B, and 7A, 7B, darker colors represent higher light energy, i.e., denser shading lines and closer to black represent higher energy.

[0076] The shaping method provided by the above embodiment is more flexible than traditional optical shaping, and can be shaped into a variety of light spot forms. It can be shaped not only into a circular / annular flat top, but also into a square / rectangular flat top light spot, and there is no limit on the size of the flat top light; at the same time, the present application is not limited to forming only these two types of light spots, but can also form flat top lights of other different shapes based on flexibly superimposed Zernike polynomials. It is also not limited to using two sets of lenses, and one to multiple surfaces can be selected as variables according to needs and the required degrees of freedom until the desired effect is achieved.

Claims

1. A method for shaping a light beam, which uses at least one lens for light beam shaping. The shaping method includes: Obtaining the incident light energy distribution and the target image energy distribution; According to the spot shape of the target image, a Zernike polynomial is superimposed after the standard spherical formula to obtain the surface shape formula after superposition, and the surface shape of at least one lens of the shaping system is adjusted by using the surface shape formula after superposition; wherein, the surface shape formula after superposition is: where z is the sagitta of the aspheric lens along the optical axis from the vertex of the aspheric surface; k is the conic constant; r is the radial coordinate in the direction perpendicular to the optical axis; α i is the coefficient of the high-order term, α i r 2i is the high-order term of the aspheric surface; N is the number of Zernike terms, Ai is the coefficient of the i-th term, Zi is the i-th term of the Zernike polynomial, ρ is the polar coordinate, is the angular coordinate, i is a positive integer, the units of z and r are both mm, and c is a constant; Calculating the shaping parameters of the shaping system according to the incident light energy distribution, the shaping formula, and the target image energy distribution; wherein, the shaping formula is: a + X = b; Wherein, a is the incident light energy distribution, b is the target image energy distribution, and X is the shaping parameter of the shaping system.

2. The shaping method according to claim 1, wherein, The spot shape of the target image includes a rotationally symmetric spot; according to the spot shape of the target image, a Zernike polynomial is superimposed after the standard spherical formula to obtain the superimposed surface formula, including: The spot shape of the target image is the rotationally symmetric spot. After superimposing the rotationally symmetric Zernike polynomial on the standard spherical surface formula, the obtained rotationally symmetric surface formula after superposition is as follows:

3. The shaping method according to claim 1, wherein, The spot shape of the target image includes a non-rotationally symmetric spot; according to the spot shape of the target image, a Zernike polynomial is superimposed after the standard spherical formula to obtain the superimposed surface formula, including: The spot shape of the target image is the non-rotationally symmetric spot. A non-rotationally symmetric Zernike polynomial is superimposed after the standard spherical formula to obtain the superimposed non-rotationally symmetric surface formula; Wherein, the non-rotationally symmetric Zernike polynomial is the polynomial remaining after removing the rotationally symmetric polynomial from the Zernike polynomial.

4. The shaping method according to claim 3, wherein, The non-rotationally symmetric spot includes a square flat top light or a rectangular flat top light; according to the spot shape of the target image, a Zernike polynomial is superimposed after the standard spherical formula to obtain the superimposed surface formula, further including: The spot shape of the target image is a square flat top light or a rectangular flat top light. It is set that the same power level terms in the non-rotationally symmetric Zernike polynomial in the superimposed non-rotationally symmetric surface formula are composed of orthogonal functions in two directions.

5. The shaping method according to claim 1, wherein, The calculating the shaping parameters of the shaping system according to the incident light energy distribution, the shaping formula, and the target image energy distribution includes: Using the least squares method or the orthogonal integration method for the shaping formula to obtain the optimal solution of the shaping parameter X, and determining the shaping parameters of the shaping system.

6. The shaping method according to claim 1, wherein, The obtaining the incident light energy distribution includes: The incident light energy distribution is a Gaussian distribution, and energy integration calculation is performed on the input light.

7. The shaping method according to claim 1, wherein, The obtaining the target image energy distribution includes: Determining the type of the target image energy distribution, and performing energy distribution integration calculation on the target image.

8. A shaping system for a light beam, which shapes the light beam by using the shaping method according to any one of claims 1-7. The shaping system includes at least one lens, and the surface formula of the lens satisfies: Among them, z is the sagitta, which is the distance along the optical axis from the vertex of the aspherical lens; k is the conic constant; r is the radial coordinate in the direction perpendicular to the optical axis; α i is the coefficient of the high-order term, α i r 2i is the high-order term of the aspherical surface; N is the number of Zernike terms, Ai is the coefficient of the i-th term, Zi is the i-th term of the Zernike polynomial, and ρ is the polar coordinate, is the angular coordinate, i = 1, 2, ……, 8, the units of z and r are both mm, and c is a constant.

9. The shaping system according to claim 8, wherein, The shaping system includes two shaping surfaces arranged in sequence. The surface shape of the shaping surface satisfies the surface formula, and the shaping surface can be located on two sides of one lens, or on any two lenses.

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