A coaxial multi-band anamorphic beam expander system based on a fold hybrid lens

Abstract

The application relates to a coaxial multi-waveband different magnification beam expanding system based on a fold-diffraction hybrid lens, which comprises a first lens group and a second lens group which are coaxially arranged in sequence along the light ray incidence direction, and the axial mechanical distance between the first lens group and the second lens group is fixed; the first lens group is a fold-diffraction hybrid element with positive focal power, the divergence ability of the diffraction surface of the first lens group is enhanced with the increase of the wavelength, so that the total equivalent focal length of the first lens group is increased with the increase of the wavelength; the second lens group is a fold-diffraction hybrid element with positive focal power, the convergence ability of the diffraction surface of the second lens group is enhanced with the increase of the wavelength, so that the total equivalent focal length of the second lens group is decreased with the increase of the wavelength. The application designs a self-adapting optical system which can work coaxially at the fiber outlet directly, and can automatically reduce the long-wavelength light spot to avoid the aperture obstruction, while keeping the short-wavelength light spot large to fill the entrance pupil.

Description

Technical Field

[0001] This invention relates to the field of super-resolution microscopy imaging technology, and in particular to a coaxial multi-band heteromagnification beam expander system based on a refractive-diffractive hybrid lens. Background Technology

[0002] Stimulated emission depletion (STED) microscopy, as a mainstream super-resolution imaging technique, has broken the optical diffraction limit. Its typical working mode is to precisely overlap the excitation light (e.g., 561nm, 640nm) and the depletion light (e.g., 775nm) in space. The depletion light is usually modulated into a "vortex" or "donut" shape with zero intensity at the center to erase the fluorescence around the excitation spot.

[0003] To ensure extremely high overlap accuracy and system stability, modern STED microscopes often employ a single-mode fiber or coaxially transmit and export multi-wavelength lasers. However, this fiber coupling method presents significant physical contradictions in practical applications:

[0004] 1. Inconsistency in fiber optic emission characteristics: According to fiber optic transmission theory, the beam divergence angle at the fiber output end is proportional to the wavelength. This means that when using a traditional achromatic collimating lens to collimate the emitted light, the longer the wavelength of the beam (775nm), the larger the diameter of the collimated spot will naturally be.

[0005] 2. Conflicts in objective lens entry pupil requirements:

[0006] For excitation light (561nm / 640nm): In order to obtain the optimal confocal resolution, the incident spot diameter should be as large as possible to fully cover the back aperture of the microscope objective, thereby utilizing the full numerical aperture (NA) of the objective.

[0007] For the loss beam (775nm): due to its extremely high power and modulation into a hollow vortex beam, its energy is mainly concentrated at the periphery of the beam spot. If the diameter of the loss beam spot is too large (i.e., larger than the back aperture of the objective lens), the outer ring carrying the main energy will be directly clipped by the objective lens housing. This not only causes serious waste of STED loss beam energy and reduces the super-resolution effect, but may also cause thermal damage to the lens housing due to high-power laser irradiation.

[0008] Currently, the industry typically adopts a "spatial splitting-independent beam expansion-re-recombining" scheme, which involves using a dichroic mirror at the fiber optic outlet to separate the loss light from the excitation light, then using beam expanders of different magnifications to adjust the spot size before recombining the beams. This scheme results in a large system size and disrupts the coaxiality of the optical path.

[0009] In summary, existing technologies suffer from problems such as large size, difficult assembly and adjustment, and difficulty in maintaining coaxiality in multi-wavelength beam expander systems. Summary of the Invention

[0010] Therefore, the technical problem to be solved by the present invention is to overcome the problems of large size, difficult assembly and adjustment, and difficulty in maintaining coaxiality in the existing multi-wavelength beam expander system.

[0011] To solve the above-mentioned technical problems, the present invention provides a coaxial multi-band heterodyne beam expander system based on a refractive-diffractive hybrid lens, comprising a first lens group and a second lens group coaxially arranged along the incident direction of light, wherein the axial mechanical distance between the first lens group and the second lens group is fixed.

[0012] The first lens group is a refractive-diffractive hybrid element with positive optical power. The divergence capability of the diffraction surface of the first lens group increases with increasing wavelength, so that the total equivalent focal length of the first lens group increases with increasing wavelength.

[0013] The second lens group is a refractive-diffractive hybrid element with positive optical power. The converging ability of the diffraction surface of the second lens group increases with increasing wavelength, so that the total equivalent focal length of the second lens group decreases with increasing wavelength.

[0014] In one embodiment of the present invention, the working wavelength corresponding to the excitation light is set as the first wavelength, and the working wavelength corresponding to the loss light is set as the second wavelength, wherein the second wavelength is greater than the first wavelength; the change in the focal length of the first lens group is set to match the change in the focal length of the second lens group, so that at any working wavelength, the sum of the focal lengths of the first lens group and the second lens group is equal to the axial mechanical distance between the first lens group and the second lens group, so as to ensure that the beam emitted from the first lens group and the beam emitted from the second lens group are both in a collimated state.

[0015] Compared to the first wavelength, since the focal length of the first lens group increases and the focal length of the second lens group decreases at the second wavelength, the beam expansion ratio for the second wavelength is strictly less than that for the first wavelength.

[0016] In one embodiment of the present invention, the first lens group includes a first glass lens with positive optical power and a diffraction surface with negative optical power; the second lens group includes a second glass lens with positive optical power and a diffraction surface with positive optical power.

[0017] In one embodiment of the present invention, the front surfaces of the first glass lens and the second glass lens are both standard spherical surfaces, and the rear surfaces are both planar surfaces.

[0018] The diffraction surface with negative optical power corresponding to the first lens group is etched onto the rear surface of the first glass lens using binary optical processing technology.

[0019] The diffraction surface of the positive optical power corresponding to the second lens group is etched onto the rear surface of the second glass lens using binary optical processing technology.

[0020] In one embodiment of the present invention, the radius of curvature of the standard spherical surface of the first glass lens of the first lens group is in the range of 48mm to 58mm;

[0021] The radius of curvature of the standard spherical surface of the second glass lens in the second lens group ranges from -120mm to -130mm.

[0022] In one embodiment of the present invention, let the operating wavelength corresponding to the excitation light be the first wavelength, and the operating wavelength corresponding to the loss light be the second wavelength, wherein the second wavelength is greater than the first wavelength, then the following condition is satisfied:

[0023] The beam expansion ratio corresponding to the excitation light is: the ratio of the focal lengths of the first lens group and the second lens group at the first working wavelength is taken as the beam expansion ratio of the excitation light;

[0024] The beam expansion ratio corresponding to the loss light is: the ratio of the focal lengths of the first lens group and the second lens group at the second working wavelength is taken as the beam expansion ratio of the loss light.

[0025] To address the aforementioned technical problems, this invention provides a design method for a coaxial multi-band heterodyne beam expander system based on a refractive-diffractive hybrid lens, comprising:

[0026] Step S1: Determine the target optical power at each working wavelength, wherein the working wavelength includes a first wavelength corresponding to the excitation light and a second wavelength corresponding to the loss light, and the second wavelength is greater than the first wavelength;

[0027] Step S2: Establish a set of equations for the combined refractive and diffractive optical power based on the target optical power;

[0028] Step S3: Solve the set of equations for the combined diffraction and refraction optical power to obtain the diffraction optical power and the refraction optical power;

[0029] Step S4: Convert the diffraction power and refraction power into the geometric parameters required for designing the first lens group and the second lens group.

[0030] In one embodiment of the present invention, step S1, determining the target optical power at each working wavelength, specifically involves:

[0031] For excitation wavelength Let the target focal length of the first lens group or the second lens group be... The corresponding optical power ;

[0032] For lossy light wavelength Let the target focal length of the first lens group or the second lens group be... The corresponding optical power .

[0033] In one embodiment of the present invention, the method for establishing a set of refractive-diffractive hybrid optical power equations based on the target optical power in step S2 includes:

[0034] Total optical power of the first or second lens group Divided into refractive power and diffraction power ;

[0035] Utilizing the physical property that the optical power of the diffraction surface of the first or second lens group is proportional to the wavelength, a set of equations for the combined refraction and diffraction optical power is established:

[0036] ;

[0037] in, As the reference wavelength, To the first wavelength corresponding to the excitation light, This is the second wavelength corresponding to the loss light;

[0038] Step S3 involves solving the set of equations for the combined diffraction and refraction optical power to obtain the diffraction optical power and the refraction optical power, specifically as follows:

[0039] Solving the aforementioned set of equations for the combined refraction and diffraction power yields the emitted power. and refractive power .

[0040] In one embodiment of the present invention, step S4, which converts the diffraction power and refraction power into the geometric parameters required for designing the first lens group and the second lens group, includes:

[0041] According to the thin lens formula Calculate the radius of curvature;

[0042] Assuming the rear surface of the glass lens in the first or second lens group is planar, then the radius of curvature of the rear surface satisfies Then the radius of curvature of the front surface for:

[0043] ;

[0044] in, The refractive index of the glass lens of the first or second lens group at 561 nm;

[0045] Under the paraxial approximation, according to the diffraction power Calculate the second-order phase coefficient of the first or second lens group :

[0046] ;

[0047] ;

[0048] in, Phase function with the diffraction surface of the first or second lens group Related, among which, The radial distance from the lens surface to the optical axis Additional phase introduced at that point, Let be the radial distance from any point on the lens surface to the optical axis. The highest number of terms, For level index, For the first Phase control coefficient of the term, The reference wavelength is used.

[0049] Compared with the prior art, the above-described technical solution of the present invention has the following advantages:

[0050] This invention designs an adaptive optics system that can work coaxially directly at the fiber optic exit and can automatically "shrink" the long wavelength (775nm) light spot (loss light spot) to avoid aperture obstruction, while maintaining the short wavelength (561nm) light spot (excitation light spot) to fill the entrance pupil.

[0051] This invention replaces multiple dichroic mirrors and multiple beam expanders in the traditional solution with two lenses (located in a coaxial lens barrel), reducing the volume by more than 80%. The system of this invention does not require beam splitting and beam combining. Without any mechanical moving parts and while maintaining a fixed distance between the two lenses, it can achieve different magnifications of beam expansion in specific wavelength bands using only a single-axis optical path, and the outgoing light in each wavelength band is strictly collimated.

[0052] Since there is no beam splitting and beam combining process, the beam of the present invention is transmitted on the same optical axis from beginning to end, fundamentally eliminating the pointing drift caused by mechanical vibration;

[0053] This invention requires no mechanical zoom motor. The system relies on the natural physical dispersion characteristics of photons of different wavelengths on the diffraction surface to automatically match the corresponding magnification. The response time is zero, and the reliability is extremely high. Attached Figure Description

[0054] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0055] Figure 1 This is a schematic diagram of the coaxial multi-band heterodyne beam expander system based on a refractive-diffractive hybrid lens of the present invention;

[0056] Figure 2 This is a simplified structural diagram of the first lens group and the second lens group of the present invention. Detailed Implementation

[0057] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0058] Example 1

[0059] Reference Figure 1 and Figure 2 As shown, the present invention relates to a coaxial multi-band heterodyne beam expander system based on a refractive-diffraction hybrid lens, which adopts a Keplerian telescope structure, with a first lens group (front group) and a second lens group (rear group) arranged coaxially along the incident light direction, and the two lens groups are located in a coaxial telescope tube.

[0060] The axial mechanical distance between the first lens group and the second lens group is fixed.

[0061] The first lens group is a refractive-diffractive hybrid element with positive optical power, comprising a refractive substrate (a first glass lens, a plano-convex lens) with positive optical power and a diffractive surface with negative optical power (divergence). Since the divergence capability of the diffractive surface increases with increasing wavelength, the total equivalent focal length of the first lens group increases with increasing wavelength.

[0062] The second lens group is a refractive-diffractive hybrid element with positive optical power, comprising a refractive substrate (a second glass lens, a plano-convex lens) with positive optical power and a diffractive surface with positive optical power (converging). Since the converging ability of the diffractive surface increases with increasing wavelength, the total equivalent focal length of the second lens group decreases with increasing wavelength.

[0063] The front surfaces of both the first and second glass lenses are standard spherical surfaces, and the rear surfaces are both planar surfaces. The diffraction surface of the negative optical power corresponding to the first lens group is etched onto the rear surface of the first glass lens using binary optical processing technology. The diffraction surface of the positive optical power corresponding to the second lens group is etched onto the rear surface of the second glass lens using binary optical processing technology.

[0064] Collimation and magnification conditions: For at least the first wavelength (e.g., 561nm or 640nm) and the second wavelength (e.g., 775nm), where the second wavelength is greater than the first wavelength, the amount of increase in the focal length of the first lens group matches the amount of decrease in the focal length of the second lens group. This ensures that, at any operating wavelength, the sum of the focal lengths of the first and second lens groups is equal to the fixed axial mechanical spacing, thus guaranteeing that the emitted beams in each band are in a collimated state. At the same time, since the focal length of the first lens group increases and the focal length of the second lens group decreases at longer wavelengths, the beam expansion ratio of the system for the second wavelength (775nm) is strictly less than that for the first wavelength (561nm or 640nm).

[0065] Let the working wavelength corresponding to the excitation light be the first wavelength, and the working wavelength corresponding to the loss light be the second wavelength, where the second wavelength is greater than the first wavelength. Then, the following conditions are met: the beam expansion ratio corresponding to the excitation light is: the ratio of the focal lengths of the first lens group and the second lens group at the first working wavelength is used as the beam expansion ratio of the excitation light; the beam expansion ratio corresponding to the loss light is: the ratio of the focal lengths of the first lens group and the second lens group at the second working wavelength is used as the beam expansion ratio of the loss light.

[0066] Preferably, both the first lens group and the second lens group are composed of a single glass lens, and the diffraction surface is etched onto one surface of the lens using binary optical processing technology.

[0067] Parameter Customization: In a specific embodiment, the input beam includes three wavelength bands: 561nm, 640nm, and 775nm. The focal length of the first lens group at 561nm is equal to that of the second lens group at 561nm, making the beam expansion ratio (the ratio of the focal lengths of the two bands) of 1 in the 561nm band. The ratio of the focal lengths of the second lens group to the first lens group at 775nm is 0.7, making the beam expansion ratio (the ratio of the focal lengths of the two bands) of 0.7 in the 775nm band. It should be noted that in this embodiment, the wavelengths 561nm and 775nm are equivalent to taking two boundary values, that is, the beam expansion ratio corresponding to the wavelength 640nm is between the beam expansion ratios corresponding to the wavelengths 561nm and 775nm.

[0068] Aberration correction: In addition to the second-order phase term that controls the focal length, the phase function of the diffraction surface also includes fourth-order and higher-order even-order phase terms for correcting higher-order aberrations (such as spherical aberration and second-order spectroscopy) at each wavelength, so as to ensure that the outgoing beam at the center wavelength (such as 640nm) also meets the collimation condition.

[0069] Summary: For the first lens group (front group, focal length) ) and the second lens group (rear group, focal length) A Keplerian beam expander system consisting of ) is given, with a fixed mechanical spacing of . To ensure arbitrary operating wavelengths The collimated beam output and specific magnification The system must simultaneously satisfy the following basic system of equations:

[0070]

[0071] The above system of equations can be solved to show that the system operates at any wavelength. The required target focal length is:

[0072]

[0073] Regarding the first wavelength in this embodiment (e.g., 561nm, requiring beam expansion ratio) ) and the second wavelength (e.g., 775nm, requiring beam expansion ratio) Substituting into the formula, we can conclude that: due to This necessitates increasing the focal length of the front element at longer wavelengths. The focal length of the rear element must be reduced. ).

[0074] Furthermore, a specific optical design example is given below.

[0075] Entrance pupil size: 2mm.

[0076] Magnification: 1x magnification for wavelength 561nm, 1x magnification for wavelength 775nm.

[0077] Please see Figure 2 ( Figure 2 (The lens groups are separated for easier viewing; they are actually attached.) The first lens group (L1): The first glass lens is made of N-BK7 glass, with a standard spherical front surface (radius of curvature ranging from 48mm to 58mm) and a flat rear surface with a binary diffraction surface having negative optical power. The equivalent focal length at 561nm is approximately 50mm; at 775nm, the equivalent focal length extends to approximately 58.8mm.

[0078] Please see Figure 2 The second lens group (L2) uses N-BK7 glass. The front surface is a standard spherical surface (radius of curvature ranging from -120mm to -130mm), and the rear surface is a flat surface with a binary diffraction surface of positive optical power. The equivalent focal length at 561nm is approximately 50mm; at 775nm, the equivalent focal length is shortened to approximately 41.2mm.

[0079] Working process: When a 561nm laser is incident, the focal length ratio of the first lens group and the second lens group is 50:50, the magnification is 1x, and L=50+50=100mm (satisfying collimation); when a 775nm laser is incident, the focal lengths of L1 and L2 automatically change to 58.8 and 41.2, respectively, the magnification is 41.2 / 58.8≈0.7x, and 58.8+41.2=100mm (maintaining collimation).

[0080] This invention relates to a design method for a coaxial multi-band heteromagnification beam expander system based on a refractive-diffractive hybrid lens, comprising:

[0081] Step S1: Determine the target optical power at each working wavelength, wherein the working wavelength includes a first wavelength corresponding to the excitation light and a second wavelength corresponding to the loss light, and the second wavelength is greater than the first wavelength;

[0082] Step S2: Establish a set of equations for the combined refractive and diffractive optical power based on the target optical power;

[0083] Step S3: Solve the set of equations for the combined diffraction and refraction optical power to obtain the diffraction optical power and the refraction optical power;

[0084] Step S4: Convert the diffraction power and refraction power into the geometric parameters required for designing the first lens group and the second lens group.

[0085] It should be noted that since the geometric structure parameters of the first lens group and the second lens group are designed using the same method, this embodiment will use the first lens group for detailed description.

[0086] Step S1 determines the target optical power at each wavelength, specifically as follows:

[0087] Based on the aforementioned geometric optics constraint equations, let the total length of the system be... .

[0088] For excitation light ( ), target multiplier The target focal length of the first lens group (L1) is... Corresponding optical power .

[0089] For lossy light ( ), target multiplier The target focal length of the first lens group (L1) is... Corresponding optical power .

[0090] Step S2 establishes a set of equations for the combined refractive and diffractive optical power based on the target optical power, specifically as follows:

[0091] The total optical power of the first lens group By refracted optical power and diffraction power It is formed by stacking.

[0092] Assume the glass material of the first lens group is N-BK7 (refractive index at 561 nm). ), diffraction surface design wavelength .

[0093] The optical power of the diffraction surface of the first lens group is proportional to the wavelength. Based on the physical properties of ), the following set of equations for mixed refraction and diffraction optical power is established:

[0094]

[0095] in, As the reference wavelength, in this embodiment Values ​​and Consistent; To the first wavelength corresponding to the excitation light, This is the second wavelength corresponding to the loss light.

[0096] Step S3 involves solving the set of equations for the combined diffraction and refraction optical power to obtain the diffraction optical power and the refraction optical power, specifically as follows:

[0097] Let wavelength ratio Solve the following set of equations for the combined refractive and diffractive power:

[0098] Solving for diffraction power :

[0099]

[0100]

[0101] Solve for the refracted focal length. :

[0102]

[0103] Step S4, the method for converting the diffraction power and refraction power into the geometric parameters required for designing the first lens group, includes:

[0104] (1) The radius of curvature is based on the thin lens formula. calculate.

[0105] Assuming the rear surface of the glass lens (plano-convex lens) in the first lens group is planar, then the radius of curvature of the rear surface satisfies... Then the radius of curvature of the front surface for:

[0106]

[0107] in, The refractive index of the glass lens of the first or second lens group at 561 nm;

[0108] (2) Phase coefficient of the two-dimensional surface Calculation

[0109] Under the paraxial approximation, according to the diffraction power Calculation of the second-order phase coefficient of the first lens group :

[0110]

[0111]

[0112] Substitute the numerical values ​​into the calculation:

[0113]

[0114] in, Phase function with the diffraction surface of the first or second lens group Related, among which, The radial distance from the lens surface to the optical axis Additional phase introduced at that point, Let be the radial distance from any point on the lens surface to the optical axis. The highest number of terms, For level index, For the first Phase control coefficient of the term, The reference wavelength is used. It should be noted that this embodiment solves... Only used In other embodiments, depending on the specific circumstances, the following may be used: , wait.

[0115] (3) Lens thickness The determination

[0116] The center thickness of a lens is primarily limited by the edge thickness requirements of the manufacturing process. For positive lenses (thicker at the center and thinner at the edges), the edge thickness must meet certain requirements. According to the formula for sagitta. Set the light transmission aperture The calculation of the minimum height of the sag is as follows: For the arrow height, Where is the radius of curvature. To ensure mechanical strength and ease of processing, the lens center thickness in this embodiment is selected as: the thickness of the glass sheet in the first lens group. The thickness of the glass plate in the second lens group .

[0117] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A coaxial multi-band anamorphic beam expander system based on a hybrid refractive-diffractive lens, characterized in that, It includes a first lens group and a second lens group arranged coaxially along the incident direction of light, and the axial mechanical distance between the first lens group and the second lens group is fixed. The first lens group is a refractive-diffractive hybrid element with positive optical power. The divergence capability of the diffraction surface of the first lens group increases with increasing wavelength, so that the total equivalent focal length of the first lens group increases with increasing wavelength. The second lens group is a refractive-diffractive hybrid element with positive optical power. The converging ability of the diffraction surface of the second lens group increases with increasing wavelength, so that the total equivalent focal length of the second lens group decreases with increasing wavelength.

2. The coaxial multi-band heterodyne beam expander system based on a refractive-diffractive hybrid lens according to claim 1, characterized in that: Let the working wavelength corresponding to the excitation light be the first wavelength, and the working wavelength corresponding to the loss light be the second wavelength, wherein the second wavelength is greater than the first wavelength; set the change in the focal length of the first lens group to match the change in the focal length of the second lens group, then at any working wavelength, the sum of the focal lengths of the first lens group and the second lens group is equal to the axial mechanical distance between the first lens group and the second lens group, so as to ensure that the beam emitted from the first lens group and the beam emitted from the second lens group are both in a collimated state. Compared to the first wavelength, since the focal length of the first lens group increases and the focal length of the second lens group decreases at the second wavelength, the beam expansion ratio for the second wavelength is strictly less than that for the first wavelength.

3. The coaxial multi-band ratio expansion beam system based on the folding and diffractive hybrid lens according to claim 1, characterized in that: The first lens group includes a first glass lens with positive optical power and a diffraction surface with negative optical power; the second lens group includes a second glass lens with positive optical power and a diffraction surface with positive optical power.

4. The coaxial multi-band heterodyne beam expander system based on a refractive-diffraction hybrid lens according to claim 3, characterized in that: The front surfaces of both the first and second glass lenses are standard spherical surfaces, and the rear surfaces are both planar surfaces. The diffraction surface with negative optical power corresponding to the first lens group is etched onto the rear surface of the first glass lens using binary optical processing technology. The diffraction surface of the positive optical power corresponding to the second lens group is etched onto the rear surface of the second glass lens using binary optical processing technology.

5. The coaxial multi-band heterodyne beam expander system based on a refractive-diffractive hybrid lens according to claim 4, characterized in that: The radius of curvature of the standard spherical surface of the first glass lens of the first lens group ranges from 48mm to 58mm; The radius of curvature of the standard spherical surface of the second glass lens in the second lens group ranges from -120mm to -130mm.

6. The coaxial multi-band ratio extender system based on the folded catadioptric lens according to claim 1, wherein: Let the operating wavelength corresponding to the excitation light be the first wavelength, and the operating wavelength corresponding to the loss light be the second wavelength, where the second wavelength is greater than the first wavelength. Then the following condition is satisfied: The beam expansion ratio corresponding to the excitation light is: the ratio of the focal lengths of the first lens group and the second lens group at the first working wavelength is taken as the beam expansion ratio of the excitation light; The beam expansion ratio corresponding to the loss light is: the ratio of the focal lengths of the first lens group and the second lens group at the second working wavelength is taken as the beam expansion ratio of the loss light.

7. A design method for a coaxial multi-band beam expander system based on a refractive-diffractive hybrid lens, characterized in that, include: Step S1: Determine the target optical power at each working wavelength, wherein the working wavelength includes a first wavelength corresponding to the excitation light and a second wavelength corresponding to the loss light, and the second wavelength is greater than the first wavelength; Step S2: Establish a set of equations for the combined refractive and diffractive optical power based on the target optical power; Step S3: Solve the set of equations for the combined diffraction and refraction optical power to obtain the diffraction optical power and the refraction optical power; Step S4: Convert the diffraction power and refraction power into the geometric parameters required for designing the first lens group and the second lens group.

8. The coaxial multi-band heterodyne beam expander system based on a refractive-diffractive hybrid lens according to claim 7, characterized in that: Step S1, which determines the target optical power at each working wavelength, specifically involves: For excitation wavelength Let the target focal length of the first lens group or the second lens group be... The corresponding optical power ; For lossy light wavelength Let the target focal length of the first lens group or the second lens group be... The corresponding optical power .

9. The coaxial multi-band heterodyne beam expander system based on a refractive-diffractive hybrid lens according to claim 7, characterized in that: The method for establishing the refractive-diffractive hybrid optical power equation set based on the target optical power in step S2 includes: Total optical power of the first or second lens group Divided into refractive power and diffraction power ; Utilizing the physical property that the optical power of the diffraction surface of the first or second lens group is proportional to the wavelength, a set of equations for the combined refraction and diffraction optical power is established: ； in, As the reference wavelength, To the first wavelength corresponding to the excitation light, This is the second wavelength corresponding to the loss light; Step S3 involves solving the set of equations for the combined diffraction and refraction optical power to obtain the diffraction optical power and the refraction optical power, specifically as follows: Solving the set of equations for the combined refraction and diffraction power yields the emitted power. and refractive power .

10. The coaxial multi-band heterodyne beam expander system based on a refractive-diffractive hybrid lens according to claim 1, characterized in that: The method for converting the diffraction power and refractive power into the geometric parameters required for designing the first and second lens groups includes: According to the thin lens formula Calculate the radius of curvature; Assuming the rear surface of the glass lens in the first or second lens group is planar, then the radius of curvature of the rear surface satisfies Then the radius of curvature of the front surface for: ； in, The refractive index of the glass lens of the first or second lens group at 561 nm; Under the paraxial approximation, according to the diffraction power Calculate the second-order phase coefficient of the first or second lens group : ； ； in, Phase function with the diffraction surface of the first or second lens group Related, among which, The radial distance from the lens surface to the optical axis Additional phase introduced at that point, Let be the radial distance from any point on the lens surface to the optical axis. The highest number of terms, For level index, For the first Phase control coefficient of the term, The reference wavelength is used.

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