Dispersion compensation-based two-stage dispersion objective lens design method, two-stage dispersion objective lens and spectrum confocal displacement measurement system

Abstract

The invention relates to a displacement measurement system, in particular to a two-stage dispersion objective lens design method based on dispersion compensation, a two-stage dispersion objective lens and a spectrum confocal displacement measurement system, and solves the problems that the resolution ratio and the dispersion range of an existing dispersion objective lens are mutually restricted and are difficult to improve at the same time; and the displacement measurement system is difficult to have high measurement precision and large measurement range at the same time. In the two-stage dispersion objective lens design method provided by the invention, the two-stage dispersion objective lens carries out primary pre-dispersion by adopting a GRIN optical fiber and carries out secondary dispersion in combination with a dispersion lens group, so that hierarchical dispersion regulation and control are realized, the dispersion range is further expanded, the non-linearity of GRIN optical fiber pre-dispersion is compensated, and the axial resolution is improved; meanwhile, the parameters of the dispersion lens group are optimized by adopting an XGBoost algorithm, so that dispersion control compensation and optimization are realized, and the dispersion range and the axial resolution are balanced. The invention further provides a spectrum confocal displacement measurement system, and the measurement range and the measurement precision can be improved at the same time.

Description

TECHNICAL FIELD

[0001] The present application relates to displacement measurement system, and particularly to a two-stage dispersion objective design method based on dispersion compensation, a two-stage dispersion objective and a spectral confocal displacement measurement system. BACKGROUND

[0002] The surface defects of semiconductor power devices can cause the breakdown voltage to decrease, which reduces the yield rate. Precise defect detection technology can effectively support the development of the semiconductor industry. The spectral confocal displacement sensing technology is based on the dispersion principle, and establishes an accurate coding relationship between the spatial position and the light beams of each wavelength. The precise displacement of the surface of the semiconductor power device sample can be obtained, and the measurement accuracy is extremely high.

[0003] With the continuous reduction of the feature size of semiconductor micro devices and the continuous improvement of the manufacturing precision, the requirement for micro displacement measurement accuracy is also increasing. The measurement accuracy of the spectral confocal displacement measurement system is closely related to the resolution of the dispersion objective, and the accuracy and the measurement range of the measurement value depend on the axial dispersion of the dispersion objective. The optical aberration of the dispersion objective also affects the axial response of the focused wavelength, and further affects the measurement accuracy of the system.

[0004] In order to improve the performance of the spectral confocal displacement measurement system, scholars have conducted a lot of research on the dispersion objective. Miks A et al. derived the axial chromatic aberration of the refractive lens group according to the primary phase difference theory, and calculated the dispersion linearity. The designed dispersion objective can realize the near-linear dispersion of 1200μm in the range of 200nm of complex light. Wang Yulong et al. proposed a new method of color confocal measurement of mixed diffraction-refraction lens. By etching a diffraction surface on a quartz aspherical lens, the dispersion range reaches 514.8μm and the dispersion linearity reaches 99.99% at the wavelength of 500-700nm. Li Chunyan et al. established the power model and dispersion model of GRIN dispersion objective by using optical aberration theory, and optimized the aberration distribution function. In the wavelength range of 420-620nm, the dispersion range is 1215μm, the dispersion linearity is 99.69%, and the resolution is 6.075nm. Huang Xiangdong et al. established a probe imaging model based on the self-focusing characteristics of GRIN lens, and realized a dispersion range of 3mm at the wavelength of 500-650nm.

[0005] However, the axial dispersion regulation capability of the dispersion objective lens in the above scheme is restricted by the performance of the lens material, and in order to reduce the cost, a spherical design is often selected, the capability of optimizing system aberration is limited, and in order to improve the resolution, the dispersion capability is strictly limited when correcting system aberration, so that the improvement of the resolution and the dispersion range is restricted, and it is also difficult for the displacement measurement system formed thereby to simultaneously have high measurement accuracy and large measurement range, which has become the main bottleneck of current technical development.

[0006] And the semiconductor power device is mostly made of metal / ceramic composite semiconductor material, which has a complex and diversified surface structure and pore distribution, and such multi-scale characteristics require the displacement measurement system to simultaneously have high measurement accuracy and large measurement range. SUMMARY

[0007] The purpose of the present application is to solve the technical problem that the resolution and the dispersion range of the existing dispersion objective lens are restricted and difficult to improve simultaneously, and further lead to the difficulty for the displacement measurement system to simultaneously have high measurement accuracy and large measurement range, and to provide a two-stage dispersion objective lens design method based on dispersion compensation, a two-stage dispersion objective lens and a spectral confocal displacement measurement system.

[0008] The design idea of the present application is:

[0009] The GRIN optical fiber has multiple degrees of freedom of refractive index parameters, and its effect is equivalent to that of a complex multi-faceted homogeneous optical element with high process requirements and high cost, and the multi-pitch periodic characteristics during light beam transmission make it have specific advantages in optimizing the performance of multi-wavelength optical systems during dispersion regulation, and it has great application potential and prospect in the development of miniature optical instruments.

[0010] In order to expand the measurement range of the spectral confocal displacement measurement system and improve the measurement accuracy of the system, the primary pre-dispersion of light of each color is realized by using the GRIN optical fiber, and the secondary dispersion is realized by using the dispersion lens group, so as to realize the regulation and control of the dispersion in stages and further expand the dispersion range of the system; the nonlinearity of the pre-dispersion of the GRIN optical fiber is compensated by the dispersion lens group, and the system aberration is optimized. In addition, the XGBoost algorithm is used to train and extract the features of the constraint relationship between the structure and performance characteristics of the GRIN optical fiber and the dispersion lens group, to realize the dispersion control compensation and optimization, balance the dispersion range and the axial resolution of the system, obtain high linear dispersion, and further improve the system performance.

[0011] In order to achieve the above-mentioned application purpose and complete the above-mentioned application design idea, the technical scheme adopted by the present application is:

[0012] The application discloses a two-stage dispersion objective lens design method based on dispersion compensation.

[0013] Step 1, determining that the two-stage dispersion objective lens comprises a GRIN optical fiber for performing primary pre-dispersion and a dispersion lens group for performing secondary dispersion, and determining an initial structure of the dispersion lens group, which comprises a first lens, a second lens, a third lens and a fourth lens arranged in sequence along a light beam incident direction, and materials and face types of the first lens, the second lens, the third lens and the fourth lens;

[0014] Step 2, selecting a material of the GRIN optical fiber, obtaining a refractive index parameter of the material of the GRIN optical fiber, then substituting the refractive index parameter into a Cauchy dispersion formula, and obtaining different wavelength light beam actual object point-pitch number curves of the different wavelength light beams at an axial focal point position of a GRIN optical fiber end changing with a pitch number of the GRIN optical fiber according to a refractive index distribution function of the GRIN optical fiber and a light beam trajectory equation;

[0015] Step 3, deriving the light beam trajectory equation of the GRIN optical fiber, and obtaining equivalent object point positions of the different wavelength light beams at the GRIN optical fiber end according to a geometric relationship, then respectively calculating equivalent object point offset amounts of the different wavelength light beams under different pitch numbers of the GRIN optical fiber according to the equivalent object point positions and the different wavelength light beam actual object point-pitch number curves obtained in step 2, and respectively obtaining equivalent object point chromatic focal shift curves under the different pitch numbers of the GRIN optical fiber;

[0016] Step 4, determining the pitch number of the GRIN optical fiber according to the different wavelength light beam actual-wavelength curves obtained in step 2 and dispersion performance of the two-stage dispersion objective lens required by design;

[0017] Step 5, determining a characteristic importance arrangement of each parameter of the dispersion lens group, then generating a plurality of sets of dispersion lens group parameters and corresponding actual dispersion performance values of the dispersion lens group parameters by using an optical design software according to the pitch number of the GRIN optical fiber obtained in step 4, the characteristic importance arrangement and the dispersion performance of the two-stage dispersion objective lens required by design, obtaining an initial data set, and dividing the initial data set into a training set and a test set; the dispersion performance of the two-stage dispersion objective lens comprises a dispersion range and dispersion linearity of the two-stage dispersion objective lens, and the dispersion lens group parameters comprise a curvature radius, a thickness, a pitch and a material of the first lens, the second lens, the third lens and the fourth lens;

[0018] Step 6, taking the dispersion lens group parameters as input characteristics, taking the dispersion performance of the two-stage dispersion objective lens as an optimization target, constructing a dispersion optimization decision tree based on an XGBoost algorithm model by using the training set, then optimizing the test set by using the dispersion optimization decision tree, obtaining optimal dispersion lens group parameters, and completing dispersion compensation design of the two-stage dispersion objective lens.

[0019] Further, step 6 is specifically:

[0020] Step 6.1, set the convergence condition and the regularization parameter of the XGBoost algorithm model, and determine the dispersion lens group parameters and the dispersion performance of the two-stage dispersion objective as the input features and the optimization target of the XGBoost algorithm model, respectively;

[0021] Step 6.2, based on the XGBoost algorithm model, determine the candidate split threshold of each parameter in the dispersion lens group parameters at the first split point according to all the dispersion lens group parameters in the training set, then traverse the candidate split threshold of each parameter in the dispersion lens group parameters at the first split point, and divide the dispersion lens group parameters in the training set into left and right subgroups, respectively, and calculate the gradient and Hessian sum of the left and right subgroups at each candidate split threshold of the first split point;

[0022] Step 6.3, according to the gradient and Hessian sum of the left and right subgroups at each candidate split threshold of the first split point, calculate the objective function gain of each candidate split threshold at the first split point, then find the optimal split threshold of the first split point by the greedy algorithm, and record the split contribution of each parameter in the dispersion lens group parameters;

[0023] Step 6.4, sort the parameters in the dispersion lens group parameters according to the split contribution, take the parameter with the largest split contribution as the optimal feature, then update the feature importance ranking, and construct the first split point of the dispersion optimization decision tree according to the feature importance ranking and the optimal split threshold of the first split point;

[0024] Step 6.5, divide the dispersion lens group parameters in the training set into left and right subgroups according to the optimal split threshold of the first split point in the dispersion optimization decision tree, and calculate the dispersion performance of the two-stage dispersion objective of the dispersion lens group parameters in the left and right subgroups at the first split point, respectively, to obtain the dispersion performance prediction value of the first split point, then calculate the residual value and fit according to the dispersion performance prediction value and the corresponding actual value of the first split point;

[0025] Step 6.6, judge whether the fitted residual value meets the convergence condition, if yes, execute step 6.7; if not, adjust the regularization parameter and return to step 6.2;

[0026] Step 6.7, add a next level split point under the first split point of the dispersion optimization decision tree, take each added next level split point as the current first split point, then return to step 6.2 until the depth of the dispersion optimization decision tree meets the design requirement, and obtain the dispersion optimization decision tree;

[0027] Step 6.8, take the test set as input, and make the dispersion optimization decision tree find the optimal dispersion lens group parameters according to the dispersion lens group parameters in the test set;

[0028] Step 6.9, judging whether the optimal dispersion lens group parameters are same as a set of dispersion lens group parameters in the test set, if yes, returning to step 5 and updating the feature importance arrangement by SHAP, otherwise, outputting the optimal dispersion lens group parameters, and completing the dispersion compensation design of the two-stage dispersion objective lens.

[0029] Further, in step 1, the first lens is a biconvex lens, and the material is P-BK7.

[0030] The second lens is a meniscus lens with a convex surface facing the incident direction of the light beam, and the material is P-BK7.

[0031] The third lens is a meniscus lens with a convex surface facing the incident direction of the light beam, and the material is SF5.

[0032] The fourth lens is a meniscus lens with a convex surface facing the incident direction of the light beam, and the material is SF5.

[0033] The application further provides a two-stage dispersion objective lens, which is obtained by using the two-stage dispersion objective lens design method based on dispersion compensation.

[0034] The incident end of the GRIN optical fiber is used for receiving polychromatic test light, and the outgoing end is arranged at the front end of the dispersion lens group.

[0035] The pitch number of the GRIN optical fiber is 3-7, and the GRIN optical fiber is used for primary pre-dispersion of the polychromatic test light.

[0036] The dispersion lens group is used for secondary dispersion of the polychromatic test light, and includes a first lens, a second lens, a third lens and a fourth lens arranged in sequence along the incident direction of the polychromatic test light.

[0037] The surface on which the polychromatic test light is incident is defined as a front surface, and the surface on which the polychromatic test light is outgoing is defined as a back surface.

[0038] The first lens is a biconvex lens, the curvature radius of the front surface is 20.437-20.851, and the curvature radius of the back surface is -33.763--33.095.

[0039] The second lens is a meniscus lens, the curvature radius of the front surface is 18.596-18.972, and the curvature radius of the back surface is 32.064-32.712.

[0040] The third lens is a meniscus lens, the curvature radius of the front surface is 9.941-11.141, and the curvature radius of the back surface is 49.023-52.033.

[0041] The fourth lens is a meniscus lens, the front surface has a radius of curvature of 28.031-28.597, and the back surface has a radius of curvature of 11.986-12.228.

[0042] Further, the first lens has a thickness of 1.98-2.02 mm, and a spacing of 0.99-1.01 mm between the first lens and the second lens;

[0043] The second lens has a thickness of 1.98-2.02 mm, and a spacing of 0.99-1.01 mm between the second lens and the third lens;

[0044] The third lens has a thickness of 2.861-2.919 mm, and a spacing of 0.99-1.01 mm between the third lens and the fourth lens;

[0045] The fourth lens has a thickness of 1.782-1.818 mm.

[0046] Further, the first lens is made of P-BK7, the second lens is made of P-BK7, the third lens is made of SF5, and the fourth lens is made of SF5.

[0047] Further, the GRIN fiber has a pitch number of 5, a length of 5.1787 cm, and a spacing of 99 mm between the exit end of the GRIN fiber and the dispersion lens group.

[0048] Further, the first lens has a radius of curvature of 20.644 on the front surface and a radius of curvature of -33.429 on the back surface;

[0049] The second lens has a radius of curvature of 18.784 on the front surface and a radius of curvature of 32.388 on the back surface;

[0050] The third lens has a radius of curvature of 10.041 on the front surface and a radius of curvature of 50.528 on the back surface;

[0051] The fourth lens has a radius of curvature of 28.314 on the front surface and a radius of curvature of 12.107 on the back surface.

[0052] Further, the first lens has a thickness of 2.000 mm, and a spacing of 1.000 mm between the first lens and the second lens;

[0053] The second lens has a thickness of 2.000 mm, and a spacing of 1.000 mm between the second lens and the third lens;

[0054] The third lens has a thickness of 2.890 mm, and a spacing of 1.000 mm between the third lens and the fourth lens;

[0055] The fourth lens has a thickness of 1.800 mm.

[0056] The application also provides a spectral confocal displacement measurement system, which is characterized in that comprising a light source, the two-stage dispersion objective lens, a beam splitter and a spectrometer.

[0057] The light source is used for emitting the polychromatic test light, and the emitting end of the polychromatic test light corresponds to the incident end of the GRIN optical fiber.

[0058] The rear end of the dispersion lens group is used for setting the target to be measured.

[0059] The beam splitter is arranged between the emitting end of the GRIN optical fiber and the dispersion lens group.

[0060] The GRIN optical fiber is used for performing primary pre-dispersion on the polychromatic test light to obtain first-stage dispersion light, and the first-stage dispersion light is transmitted to the first lens, the second lens, the third lens and the fourth lens of the dispersion lens group after being transmitted by the beam splitter to perform second-stage dispersion to form axial dispersion light, and the axial dispersion light is transmitted to the target to be measured, and the target to be measured generates reflected light after receiving the axial dispersion light, and the reflected light is reflected by the beam splitter after passing through the fourth lens, the third lens, the second lens and the first lens in turn.

[0061] The spectrometer is arranged on the light path of the reflected light of the target to be measured reflected by the beam splitter, and is used for collecting the spectral information of the reflected light of the target to be measured before and after displacement, so as to calculate the displacement value of the target to be measured according to the spectral change of the reflected light.

[0062] Compared with the prior art, the application has the beneficial effects as follows:

[0063] 1. The two-stage dispersion objective lens design method based on dispersion compensation provided by the application realizes hierarchical dispersion control by adopting the GRIN optical fiber to perform primary pre-dispersion and combining the dispersion lens group to perform second-stage dispersion, further expands the dispersion range, compensates the nonlinearity of the pre-dispersion of the GRIN optical fiber, and improves the axial resolution.

[0064] 2. The two-stage dispersion objective lens design method based on dispersion compensation provided by the application trains and extracts features of the constraint relationship between the parameters of the GRIN optical fiber and the dispersion performance of the dispersion lens group by adopting the XGBoost algorithm, realizes dispersion control compensation and optimization, balances the dispersion range and the axial resolution, can obtain high linear dispersion while expanding the dispersion range, and further improves the performance.

[0065] 3. The spectral confocal displacement measurement system provided by the application adopts two-stage dispersion, can expand the dispersion range, thereby expanding the measurement range, can compensate the nonlinearity of the pre-dispersion of the GRIN optical fiber, has excellent focusing performance, and significantly improves the spectral resolution, thereby improving the measurement accuracy and realizing the simultaneous improvement of the measurement range and the measurement accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0066] Figure 1 The structure diagram of the two-stage dispersion objective lens determined in step 1 of the embodiment of the two-stage dispersion objective lens design method based on dispersion compensation of the application;

[0067] Figure 2 The structure diagram of the dispersion lens group determined in step 1 of the embodiment of the two-stage dispersion objective lens design method based on dispersion compensation of the application;

[0068] Figure 3 The curve diagram of the change of the marginal rays of each wavelength in the GRIN fiber with the axial distance in step 2 of the embodiment of the two-stage dispersion objective lens design method based on dispersion compensation of the application;

[0069] Figure 4 The actual object point-pitch number curve diagram of the light beams of different wavelengths obtained in step 2 of the embodiment of the two-stage dispersion objective lens design method based on dispersion compensation of the application;

[0070] Figure 5 The equivalent object point chromatic focal shift curve diagram of the GRIN fiber under different pitch numbers obtained in step 3 of the embodiment of the two-stage dispersion objective lens design method based on dispersion compensation of the application;

[0071] Figure 6 The flowchart of steps 5 and 6 in the embodiment of the two-stage dispersion objective lens design method based on dispersion compensation of the application;

[0072] Figure 7 The principle diagram of the XGBoost algorithm used in step 6.1 of the embodiment of the two-stage dispersion objective lens design method based on dispersion compensation of the application;

[0073] Figure 8 The dispersion performance comparison diagram of the two-stage dispersion objective lens obtained by using the embodiment of the two-stage dispersion objective lens design method based on dispersion compensation of the application, wherein (a) is the curve diagram of the equivalent object point chromatic focal shift of the GRIN fiber varying with the wavelength of the light beam, and (b) is the curve diagram of the total chromatic focal shift of the two-stage dispersion objective lens varying with the wavelength of the light beam;

[0074] Figure 9 The structure schematic diagram of the embodiment of the spectral confocal displacement measurement system of the application;

[0075] Figure 10 The point column diagram of the light beams of different wavelengths obtained by using the embodiment of the spectral confocal displacement measurement system of the application, wherein the wavelengths of (a)-(l) are 485 nm, 503 nm, 517 nm, 533 nm, 549 nm, 564 nm, 580 nm, 595 nm, 611 nm, 628 nm, 642 nm, and 655 nm, respectively;

[0076] The reference signs are explained as follows:

[0077] 1 - light source, 2 - GRIN fiber, 3 - beam splitter, 4 - dispersion lens group, 5 - spectrometer, 6 - target to be measured; 41 - first lens, 42 - second lens, 43 - third lens, 44 - fourth lens. DETAILED DESCRIPTION

[0078] A two-stage dispersion objective design method based on dispersion compensation, a two-stage dispersion objective and a spectral confocal displacement measurement system according to the present application will be described in further detail below in conjunction with the accompanying drawings and specific embodiments. Those skilled in the art should understand that these embodiments are only used to explain the technical principles of the present application, and are not intended to limit the protection scope of the present application.

[0079] A dispersion compensation design method of the above two-stage dispersion objective, comprising the following steps:

[0080] Step 1, as shown in Figure 1 , determine that the two-stage dispersion objective includes a GRIN fiber 2 for performing primary pre-dispersion and a dispersion lens group 4 for performing secondary dispersion. Then as shown in Figure 2 , determine the initial structure of the dispersion lens group 4, which includes a first lens 41, a second lens 42, a third lens 43 and a fourth lens 44 arranged in sequence along the light beam incident direction, and the materials and face shapes of the first lens 41, the second lens 42, the third lens 43 and the fourth lens 44.

[0081] According to the basic definition of refractive optics, introduce dispersion differential analysis, through the multiple combination possibilities of multi-piece lenses, screen lens parameter combinations that meet the dispersion linearity compensation condition. In order to achieve the widening of the dispersion range while improving the overall dispersion linearity. For multi-piece lens group, the power of the dispersion lens is: In the formula, f is the focal length of the lens group, s' is the image distance, and s is the object distance. In addition:

[0082]

[0083] Where n i is the refractive index of the i-th lens, which has a specific functional relationship with the wavelength of the light beam; K i is the difference between the radii of curvature of the front and back surfaces of the i-th lens, which is independent of the wavelength of the light beam. r i , r i ' are the radii of curvature of the front and back surfaces of the i-th lens, respectively. Differentiate the power function to obtain the dispersion differential δs':

[0084]

[0085] Where N is the total number of lenses, n i is the refractive index of the i-th lens, and v i respectively the power and the Abbe number of the i-th lens, t is the lateral magnification, t = s'(λ) / s(λ), s'(λ) is the distance of the image point of the lens from the lens, s(λ) is the distance of the object point of the lens from the lens as a function of the wavelength, δs is the variation of the function (a small perturbation of the function space) or a finite small change, denotes an infinitesimal change, λ0is the wavelength of the light beam.

[0086] Based on the above relations, the second order dispersion can be obtained:

[0087]

[0088] where δs' λF is the dispersion differential of the wavelength λ to F, δs λF is the differential of the upper order dispersion in the same range, and v di respectively the power and the Abbe number of the i-th lens for d light, P λi denotes the relative dispersion coefficient of the i-th lens at the wavelength λ, P λi = n λi - n Fi / n Ci - n Fi , f' is the effective focal length of the lens group.

[0089] In order to avoid the nonlinear dispersion effect of the dispersion lens group 4 itself to increase the total nonlinearity, it is necessary to correct by reasonably matching the lens material and the focal length, i.e. the combination of high Abbe number positive lens and low Abbe number negative lens, the positive lens is used to speed up the focusing, and the negative lens is used to expand the dispersion effect.

[0090] The dispersion generated by the GRIN fiber 2 conforms to the dispersion trend of the positive lens, i.e. the dispersion decreases with the increase of the wavelength, and only positive lenses are used in the dispersion lens group 4, and the dispersion superposition of the two will aggravate the nonlinear effect of the system. In order to meet the dispersion requirement, the initial structure is selected to include the first lens 41, the second lens 42, the third lens 43 and the fourth lens 44 arranged in turn along the incident direction of the complex test light, and the targeted optimization is carried out.

[0091] Step 2, select the material of the GRIN fiber 2, and obtain the refractive index parameters of the GRIN fiber 2 material, then substitute it into the Cauchy dispersion formula, and according to the refractive index distribution function and the ray trajectory equation of the GRIN fiber 2, the actual object point-pitch number curve of different wavelength beams at the end of the fiber is obtained.

[0092] The refractive index distribution function n(r, λ) of the GRIN fiber 2 is:

[0093]

[0094] wherein n0(λ) is the central refractive index of the GRIN fiber 2 when the wavelength of the light beam is λ, A, B, C are the refractive index parameters related to the wavelength λ.

[0095] Under the paraxial transmission condition, the light ray trajectory equation inside the GRIN fiber 2 is:

[0096]

[0097] r1' = -α λ r0 sin(α λ l)+r0'cos(α λ l)

[0098] wherein r0 and r1 are the positions of the light beam with wavelength λ at the entrance and exit end faces of the GRIN fiber 2, respectively, r0' and r1' are the slopes of the light beam with wavelength λ when it is incident and exit the GRIN fiber 2 at the maximum angle, respectively; α λ is the refractive index parameter determined by the Cauchy dispersion formula, which is l is the axial position of the light beam transmission.

[0099] Due to the refractive index gradient distribution of the GRIN fiber, the light beam is transmitted in a sinusoidal periodic manner therein. According to the GRIN material table of the Gofoton company, take n0(λ) = 1.5868 + 8.14 x 10 -3 λ 2 , A = 0.5945, B = 3.936 x 10 -3 , C = 5.539 x 10 -4 , substitute the Cauchy dispersion formula, and then perform a functional analysis on the refractive index distribution function according to the Fermat principle to obtain the following formula, according to which the focal point position z of the light beams of different wavelengths in the complex color test light on the optical axis can be obtained max :

[0100]

[0101] wherein m is the pitch number of the GRIN fiber 2.

[0102] When m = 1, the change of the edge light rays of the light beams of each wavelength in the GRIN fiber 2 with the axial distance z is shown in Figure 3 . After transmission through multiple pitches, the axial focal point positions of the light beams of each wavelength at the end of the fiber, i.e., the actual object points S o , change with the pitch number m as shown in Figure 4 . The actual object points are discrete points on the axial distance. As Figure 3As shown, the horizontal axis represents the axial distance z, and the vertical axis represents the radial distance r from the principal optical axis. It can be seen that the beams of each wavelength propagate in a sinusoidal trajectory within the GRIN fiber 2 with a radius of 50 μm. Due to the different propagation speeds, the shorter wavelength blue light always intersects the optical axis earlier. For example... Figure 4 As shown, the horizontal axis represents the number of pitches (m) of GRIN fiber 2, and the vertical axis represents the actual object point S. o Actual point S o The distance to the incident end increases with increasing wavelength, and the rate of increase tends to level off with increasing wavelength. Figure 4 It can be seen that the dispersion of white light is relatively small when the transmission is one pitch, with a dispersion range of 299.14 μm; when the length of GRIN fiber 2 is increased to 5 times the pitch, the axial dispersion range is 1495.7 μm.

[0103] Step 3: Differentiate the ray trajectory equation of GRIN fiber 2, and obtain the equivalent object point position of different wavelength beams at the end of GRIN fiber 2 according to the geometric relationship. Then, based on the equivalent object point position and the actual object point-pitch number curve of different wavelength beams obtained in Step 2, calculate the equivalent object point offset of different wavelength beams under different pitch numbers of GRIN fiber 2, and obtain the equivalent object point color focus shift curve of GRIN fiber 2 under different pitch numbers.

[0104] After the beam is pre-dispersed by GRIN fiber 2, each wavelength beam is emitted and then enters the dispersive lens group 4 for transmission. This is equivalent to the beam emitted by each monochromatic object point at different positions. The beam is transmitted in a curve in GRIN fiber 2. In order to facilitate the design of the dispersive lens group 4, the precise position of the equivalent object point of each wavelength beam needs to be determined.

[0105] like Figure 1 As shown, when the length of GRIN fiber 2 is L and the number of pitches is m, the actual object point S of a beam with wavelength λ after passing through GRIN fiber 2 is... o The distance to the dispersive lens group 4 is S oλ The corresponding equivalent object point S and the distance S between the dispersive lens group 4 λ for:

[0106]

[0107] Where s is the distance between the output end of GRIN fiber 2 and the dispersive lens group 4.

[0108] Differentiating the ray trajectory equation inside GRIN fiber 2 yields the angle function θ of each wavelength beam at the exit end face. From geometric relationships, the distance between the equivalent object point S and the exit end face of GRIN fiber 2, i.e., the equivalent object distance L, can be derived. λ for:

[0109]

[0110] Therefore, the equivalent object point positions of different wavelength beams at the end of GRIN fiber 2 can be obtained. Furthermore, the equivalent object point color focus shifts of each wavelength beam within GRIN fiber 2 can be obtained, such as... Figure 5 As shown, the horizontal axis λ is the beam wavelength, and the vertical axis h is the axial distance from the equivalent object point to the exit end face of GRIN fiber 2.

[0111] Step 4: Based on the actual object point-pitch number curves of different wavelength beams obtained in Step 2, the equivalent object point color focus shift curves of GRIN fiber 2 under different pitch numbers obtained in Step 3, and the dispersion performance of the two-stage dispersive objective lens required by the design, determine the pitch number of GRIN fiber 2.

[0112] like Figure 4 , Figure 5 As shown, the pitch number of GRIN fiber 2 is negatively correlated with dispersion linearity. When the pitch number decreases, the chromatic focus shift range decreases, but the dispersion linearity increases significantly; conversely, although the chromatic focus shift range expands, the dispersion linearity decreases significantly, which is not conducive to the overall linear dispersion design. Therefore, it is necessary to rationally select the pitch number. Figure 5 The polychromatic test light exhibits significant nonlinear dispersion after passing through GRIN fiber 2, especially when m increases to 6, the nonlinearity increases to 6.69%. To ensure a dispersion range greater than 4 mm, in this embodiment, a pitch number m = 5 is selected to generate a larger axial dispersion range.

[0113] Step 5: Determine the order of importance of the characteristic parameters of each lens in the dispersive lens group 4, and then proceed as follows: Figure 6 As shown, based on the GRIN fiber pitch number, feature importance ranking, and the dispersion performance of the two-stage dispersive objectives obtained in step 4, multiple sets of dispersive lens group parameters and their corresponding actual dispersion performance values ​​are generated using the optical design software ZEMAX, resulting in an initial dataset, which is then divided into a training set and a test set. The dispersion performance of the two-stage dispersive objectives includes the dispersion range and dispersion linearity of the two-stage objectives, and the dispersive lens group parameters include the radius of curvature, thickness, and spacing of the first lens 41, the second lens 42, the third lens 43, and the fourth lens 44.

[0114] The distance from the polychromatic test light to the front surface of the first lens 41 is selected as the object distance parameter, and multiple structural optimizations are performed on the dispersive lens group 4. The distance from the rear surface of the fourth lens 44 to the target 6 under test is used as a variable and as an optimization target to enable the two-stage dispersive objectives to produce excellent linearity dispersion characteristics within a specific wavelength range.

[0115] To select more suitable parameters for the dispersive lens group 2 to match the GRIN fiber, a mathematical model Δz for the nonlinear color correction quantity is performed, characterized by the fiber-lens group spacing, lens parameters, and dispersion shift:

[0116] Δz = f(s, R1, R2, D, δs') + ε

[0117] Wherein, s is the distance between the objective lens and the optical fiber, R1 and R2 are the radii of curvature of the front and rear surfaces of the lens respectively, D is the lens spacing matrix, and ε is the residual error.

[0118] In order to adapt to the dispersion performance of the two-stage dispersion objective lens designed, the pitch number of the GRIN optical fiber 2 obtained in step 3 is used to proportionally adjust the parameters of the dispersion lens group 4 and set the hyperparameters. The radii of curvature and spacing of the first lens 41, the second lens 42 and the third lens 43 are selected as the characteristic variables, the parameters of the fourth lens 44 are variable items, the ZPL script in the optical design software ZEMAX is used for automatic optimization, the variable parameters are adjusted when the dispersion performance of the two-stage dispersion objective lens meets the design requirements, the ZPL script is used to record the parameters meeting the design requirements, the parameter range is adjusted according to the results, the data set is updated, and the initial data set is obtained.

[0119] Step 6, taking the dispersion lens group parameters as input features and the dispersion performance of the two-stage dispersion objective lens as the optimization target, based on the XGBoost algorithm model, the training set is used to build a dispersion optimization decision tree, and then the dispersion optimization decision tree is used to optimize the test set, to obtain the optimal dispersion lens group parameters, and complete the dispersion compensation design of the two-stage dispersion objective lens. As shown in Figure 6 , specifically:

[0120] Step 6.1, set the convergence condition and the regularization parameter of the XGBoost algorithm model, and determine the dispersion lens group parameters and the dispersion performance of the two-stage dispersion objective lens as the input features and the optimization target of the XGBoost algorithm model.

[0121] The schematic diagram of the XGBoost algorithm is shown in Figure 7 , the XGBoost algorithm is a kind of efficient and scalable machine learning framework based on gradient boosting decision tree, which can effectively capture the nonlinear relationship existing in the data. It iteratively constructs decision trees through gradient boosting algorithm, optimizes the loss function using decision trees, and introduces a regularization term to avoid overfitting. The final prediction result is the weighted sum of the outputs of all decision trees, and the objective function Obj is:

[0122]

[0123] Wherein, is the loss function, y i is the actual value, is the predicted value; n is the number of data sets;

[0124] Ω(f k) is the regularization term of the kth tree, which is used to control the complexity of the tree, T is the number of leaf nodes of the tree, γ and η are the regularization parameters of the XGBoost algorithm, w j is the weight of the jth leaf node in the kth tree.

[0125] In the process of constructing weak learners, the target function gain is calculated at the candidate split threshold of the split point, and the optimal split threshold is found by a greedy algorithm. The target function gain Gain is:

[0126]

[0127] where G L and G R are the gradients of the left and right sub-trees, H L and H R are the Hessian sums of the left and right sub-trees, and the gradients and Hessian sums are the first and second derivatives of the loss function.

[0128] Step 6.2, based on the XGBoost algorithm model, determine the candidate split threshold of each parameter in the dispersion lens group parameters at the first split point in the training set, then traverse the candidate split threshold of each parameter in the dispersion lens group parameters at the first split point, and divide the dispersion lens group parameters in the training set into left and right sub-groups, and calculate the gradient and Hessian sum of the left and right sub-groups at the first split point for each candidate split threshold.

[0129] Step 6.3, according to the gradient and Hessian sum of the left and right sub-groups at the first split point for each candidate split threshold, calculate the target function gain of each candidate split threshold at the first split point, then find the optimal split threshold of the first split point by a greedy algorithm, and record the split contribution of each parameter in the dispersion lens group parameters.

[0130] Step 6.4, sort the parameters in the dispersion lens group parameters according to the split contribution, and take the parameter with the largest split contribution as the optimal feature, then update the feature importance ranking, and construct the first split point of the dispersion optimization decision tree according to the feature importance ranking and the optimal split threshold of the first split point.

[0131] Step 6.5, divide the dispersion lens group parameters in the training set into left and right sub-groups according to the optimal split threshold of the first split point in the dispersion optimization decision tree, and calculate the two-level dispersion performance of the dispersion lens group parameters in the left and right sub-groups at the first split point, respectively, to obtain the dispersion performance prediction value of the first split point, then calculate the residual value and fit according to the dispersion performance prediction value of the first split point and the corresponding actual value of the dispersion performance.

[0132] Step 6.6, judge whether the residual value after fitting meets the convergence condition, if yes, execute step 6.7; if not, adjust the regularization parameter and return to step 6.2.

[0133] Step 6.7, add a new next level split point under the first split point of the dispersion optimization decision tree, take each new next level split point as the current first split point respectively, and then return to step 6.2 until the depth of the dispersion optimization decision tree meets the design requirement, and the dispersion optimization decision tree is obtained.

[0134] Step 6.8, take the test set as input, and make the dispersion optimization decision tree find the optimal dispersion lens group parameters according to the dispersion lens group parameters in the test set.

[0135] Step 6.9, judge whether the optimal dispersion lens group parameters are the same as a set of dispersion lens group parameters in the test set, if yes, return to step 5 and update the feature importance ranking using SHAP; otherwise, output the optimal dispersion lens group parameters and complete the dispersion compensation design of the two-level dispersion objective lens.

[0136] In step 5, a two-way information transmission channel between ZEMAX and Python is constructed through the API interface in ZEMAX, the initial data set is obtained, and it is divided into training set and test set. In step 6, the dispersion optimization decision tree is obtained by using the training set combined with residual driving. Then the optimal dispersion lens group parameters are found by using the test set, and whether it is the parameter group in the test set is judged to assist the adjustment of the test set and expand the search space to obtain the optimal result.

[0137] During the optimization process, the SHAP explainable framework is embedded to dynamically rank the feature importance; among them, the front surface and the back surface of the third lens 43 have obvious influence on the dispersion linearity, and during the optimization process, the greater the curvature radius of the front surface, the more inclined to improve the accuracy of the model prediction result.

[0138] Based on the material and pitch number of the GRIN optical fiber 2 and the initial structure of the dispersion lens group 4, the XGBoost algorithm is used to iteratively optimize the parameters of the dispersion lens group 4, and finally the pitch number of the GRIN optical fiber 2 is determined as 5, the length is 5.1787 cm, and the distance between the GRIN optical fiber 2 and the dispersion lens group 4 is 99 mm. The parameters of the dispersion lens group 4 are shown in Table 1.

[0139] Table 1

[0140]

[0141]

[0142] The dispersion compensation design method of the two-stage dispersion objective provided in this embodiment first determines the pitch number of the GRIN fiber 2 as 5 according to the dispersion range and dispersion linearity required by the design. On this basis, the dispersion lens group 4 corrects the pre-dispersion of the GRIN fiber 2. After correction, the total dispersion not only greatly weakens the nonlinearity of the pre-dispersion of the GRIN fiber 2, but also expands the axial dispersion range of the GRIN fiber 2 alone from 1.5 mm to 4.045 mm. The performance is better, and the linearity can be optimized to 99.89%, as shown in Figure 8 .

[0143] Since the equivalent object points of the obtained GRIN fiber 2 are discrete data, it is necessary to perform a quadratic term fitting on the chromatic shift generated by the two-stage dispersion objective, and then use the least squares method to characterize the linearity of the fitting curve. The chromatic shift of the equivalent object points of the GRIN fiber 2 is shown in (a) of Figure 8 , and the linearity is only 95.05%. The maximum error is that the measurement range error can reach 14.496 μm per unit nanometer of wavelength change. After adding the dispersion lens group 4, the chromatic shift of the equivalent object points of the two-stage dispersion objective designed by the dispersion compensation design method of the two-stage dispersion objective provided in this embodiment is shown in (b) of Figure 8 . The measurement error is reduced to 2.563 μm, and the dispersion linearity is improved to 99.89%.

[0144] In this embodiment, first, the pitch number is determined according to the optical properties of the GRIN fiber 2, and the pitch number is coupled into the two-stage dispersion objective. Then, a suitable dispersion lens group 4 is designed by using the ZEMAX software to match it. While expanding the measurement range, the dispersion linearity is corrected. Finally, by establishing the relationship and constraint between the parameters of the GRIN fiber 2 and the dispersion lens group 4, the XGBoost algorithm is used to extract the features of the parameters of the dispersion lens group 4 to obtain the optimization direction, so as to compensate and optimize the dispersion linearity. The results show that the two-stage dispersion objective provided in this embodiment can realize an axial linear dispersion of 4.045 mm, and the dispersion linearity reaches 99.89%. It can be applied to displacement measurement of complex and diverse surfaces such as metal / ceramic composite semiconductor materials, and can meet the measurement requirements of multi-scale characteristics.

[0145] This embodiment also provides a two-stage dispersion objective, as shown in Figure 1 , which includes a GRIN fiber 2 and a dispersion lens group 4. The incident end of the GRIN fiber 2 is used to receive polychromatic test light, and the exit end is arranged at the front end of the dispersion lens group 4. The GRIN fiber 2 is used to perform primary pre-dispersion on the polychromatic test light, and the dispersion lens group 4 is used to perform secondary dispersion on the polychromatic test light. In this embodiment, the pitch number of the GRIN fiber 2 is 5, and the length is 5.1787 cm. The distance between the exit end of the GRIN fiber 2 and the dispersion lens group 4 is 99 mm.

[0146] As shown in Figure 2 the first lens 41, the second lens 42, the third lens 43 and the fourth lens 44 are sequentially arranged along the incident direction of the polychromatic test light. Defining the surface on which the polychromatic test light is incident as the front surface and the surface from which the polychromatic test light is emitted as the back surface, the radius of curvature of the front surface of the first lens 41 is 20.437-20.851, and the radius of curvature of the back surface is -33.763--33.095; the radius of curvature of the front surface of the second lens 42 is 18.596-18.972, and the radius of curvature of the back surface is 32.064-32.712; the radius of curvature of the front surface of the third lens 43 is 9.941-11.141, and the radius of curvature of the back surface is 49.023-52.033; the radius of curvature of the front surface of the fourth lens 44 is 28.031-28.597, and the radius of curvature of the back surface is 11.986-12.228. The thickness of the first lens 41 is 1.98-2.02 mm, and the distance between the first lens 41 and the second lens 42 is 0.99-1.01 mm; the thickness of the second lens 42 is 1.98-2.02 mm, and the distance between the second lens 42 and the third lens 43 is 0.99-1.01 mm; the thickness of the third lens 43 is 2.861-2.919 mm, and the distance between the third lens 43 and the fourth lens 44 is 0.99-1.01 mm; the thickness of the fourth lens 44 is 1.782-1.818 mm.

[0147] In the embodiment, the optical parameters of the lenses of the dispersion lens group 4 are shown in Table 1. The material of the first lens 41 is P-BK7, the thickness is 2.000 mm, and the distance between the first lens 41 and the second lens 42 is 1.000 mm. The material of the second lens 42 is P-BK7, the thickness is 2.000 mm, and the distance between the second lens 42 and the third lens 43 is 1.000 mm. The material of the third lens 43 is SF5, the thickness is 2.890 mm, and the distance between the third lens 43 and the fourth lens 44 is 1.000 mm. The material of the fourth lens 44 is SF5, and the thickness is 1.800 mm. In the embodiment, P-BK7 is used as the front lens to speed up focusing, and SF5 is used as the rear lens to expand the dispersion range and optimize the aberration.

[0148] The first lens 41 is a biconvex lens, the radius of curvature of the front surface is 20.644, and the radius of curvature of the back surface is -33.429. The second lens 42 is a meniscus lens, the radius of curvature of the front surface is 18.784, and the radius of curvature of the back surface is 32.388. The third lens 43 is a meniscus lens, the radius of curvature of the front surface is 10.041, and the radius of curvature of the back surface is 50.528. The fourth lens 44 is a meniscus lens, the radius of curvature of the front surface is 28.314, and the radius of curvature of the back surface is 12.107.

[0149] The refractive index of the GRIN fiber 2 is distributed in a gradient manner, and the complex test light follows a sinusoidal curve to transmit forward in the GRIN fiber 2 periodically at a pitch. Under the dispersion effect of the fiber material, the focal points of the light beams of different wavelengths are separated after the complex test light emitted from the same point transmits for one period, and the separation effect is significant after multiple periods. In order to expand the measurement range, the embodiment uses the GRIN fiber 2 instead of the traditional fiber, uses the multi-pitch periodicity of the GRIN fiber 2 to preliminarily realize the axial dispersion distribution of the light beams of different wavelengths, and completes the pre-dispersion. On this basis, the dispersion lens group 4 is designed to compensate for the nonlinearity of the pre-dispersion of the GRIN fiber 2, and the dispersion range is further expanded by using the second-order dispersion of the dispersion lens group 4, so as to realize the hierarchical dispersion regulation while optimizing the aberration.

[0150] The complex test light is coupled into the GRIN fiber 2 at the same point, and due to the dispersion of the GRIN fiber 2 material, the axial focusing positions of the light beams of different wavelengths change after the light beams transmit in the GRIN fiber 2 for one period of sinusoidal curve transmission, and the light beams are no longer focused at the same point. After multiple periods of transmission, the axial focusing positions of the light beams of different wavelengths are more significantly separated, and when entering the dispersion lens group 4 for transmission, the dispersion lens group 4 is equivalent to each monochromatic object point at different positions in the axial direction. The dispersion lens group 4 focuses the image points at different positions on the optical axis by using its imaging ability, and further expands the dispersion range by using its dispersion ability. Through hierarchical dispersion regulation and aberration optimization, the nonlinearity of the pre-dispersion of the GRIN fiber 2 is compensated for, so that a larger dispersion range can be realized while meeting the demand for higher measurement accuracy.

[0151] The embodiment also provides a spectral confocal displacement measurement system, as shown in Figure 9 The light source 1 is used to emit complex test light, and the light emitting end of the light source 1 is connected with the incident end of the GRIN fiber 2. The rear end of the dispersion lens group 4 is used to set the target to be measured 6, and the distance between the dispersion lens group 4 and the target to be measured 6 is less than the distance between the focusing position of the light beam with the maximum wavelength in the complex test light and the dispersion lens group 4. The beam splitter 3 is arranged between the exit end of the GRIN fiber 2 and the dispersion lens group 4. As shown in Figure 9As shown, the polychromatic test light enters the GRIN fiber 2 from the same point, and under the primary pre-dispersion of the GRIN fiber 2, the focal points of light beams of different wavelengths are discretely distributed at the end of the fiber to obtain first-order dispersion light. After being transmitted by the beam splitter 3, the first-order dispersion light is transmitted to the first lens 41, the second lens 42, the third lens 43 and the fourth lens 44 of the dispersion lens group 4 to form axial dispersion light through secondary dispersion, and is transmitted to the target to be measured 6. After the target to be measured 6 receives the axial dispersion light, reflected light is generated, and the reflected light is reflected by the beam splitter 3 after passing through the fourth lens 44, the third lens 43, the second lens 42 and the first lens 41 in turn. The spectrometer 5 is arranged on the light path of the beam splitter 3 reflecting the reflected light of the target to be measured, and is used to collect the spectral information of the reflected light before and after the displacement of the target to be measured 6, so as to calculate the displacement value of the target to be measured 6 according to the spectral change of the reflected light.

[0152] After the polychromatic test light emitted by the light source 1 is pre-dispersed by the GRIN fiber 2, it is transmitted to the dispersion lens group 4 through the beam splitter 3, and the focal positions of different whole nanometer wavelength light beams are discretely distributed under the action of axial dispersion to form axial dispersion light. The size of the dispersion value determines the measurement range of the system. The surface of the target to be measured 6 receives the axial dispersion light, and according to the position of the target to be measured 6, only light beams of specific wavelengths are focused at this position. After the axial dispersion light is reflected by the target to be measured 6, it returns to the system along the original light path, is reflected by the beam splitter 3, and is received by the spectrometer. The energy of the light beams of the remaining light beams, which are not focused and return to the original system, is extremely weak and can be ignored. When the position of the measured sample changes, the peak wavelength of the spectral response also changes accordingly. By using the corresponding relationship between each wavelength and the axial position of each focus, the surface displacement of the sample is calculated to realize displacement measurement.

[0153] The existing spectral confocal displacement measurement system and the spectral confocal displacement measurement system provided in the embodiment are measured to obtain the comparative measurement results shown in Table 2.

[0154] Table 2

[0155] Prior art The present embodiment Growth rate Average RMS radius (pm) 2.296 2.283 -0.57％ Sensitivity (pm / nm) 20.588 23.529 14.29％ Maximum residual (mm) 0.235 0.086 -269.81％ Measurement range (mm) 4.335 4.045 -1.54％ Linearity R 2 ]]> 0.9976 0.9989 0.13％

[0156] As shown in Table 2, compared with the existing spectral confocal displacement measurement system, in the spectral confocal displacement measurement system provided in the embodiment, the average root mean square (RMS) radius of the diffraction spot decreases by 0.57%, but the measurement sensitivity and linearity increase by 14.29% and 0.14%, respectively, and the maximum residual error is greatly reduced.

[0157] When the RMS of the diffraction spot is less than the Airy spot radius, the focusing effect of the light beam at the focal point is the best, especially when the wavelength of the light beam is near 611 nm, the focusing effect is the best, and the spot diagram of the focal points of light beams of different wavelengths is as shown in Figure 10 Table 3. As shown in Table 3, when the wavelength of the light beam is near 611 nm, the RMS of the diffraction spot is the smallest, and the focusing effect of the light beam at the focal point is the best.Figure 10 As shown, the wavelengths of (a)-(l) are 485 nm, 503 nm, 517 nm, 533 nm, 549 nm, 564 nm, 580 nm, 595 nm, 611 nm, 628 nm, 642 nm, 655 nm, respectively, and the RMS radii are 2.866, 2.658, 2.420, 2.258, 1.811, 1.456, 1.055, 0.625, 0.119, 0.576, 1.093, 1.668, respectively. It can be seen that the focused spots of each wavelength are all within the Airy disk, indicating that the spectral confocal displacement measurement system provided in the embodiment has excellent focusing performance, the spectral resolution is significantly improved, and thus the measurement accuracy is significantly improved.

Claims

1. A two-stage dispersion objective design method based on dispersion compensation, characterized in that, The method comprises the following steps: Step 1, determining a two-stage dispersion objective lens comprising a GRIN optical fiber (2) for performing primary pre-dispersion and a dispersion lens group (4) for performing secondary dispersion, and determining an initial structure of the dispersion lens group (4) comprising a first lens (41), a second lens (42), a third lens (43) and a fourth lens (44) arranged in sequence along the light beam incident direction, and the materials and face shapes of the first lens (41), the second lens (42), the third lens (43) and the fourth lens (44); Step 2, selecting the material of the GRIN optical fiber (2), obtaining the refractive index parameters of the material of the GRIN optical fiber (2), then substituting the parameters into the Cauchy dispersion formula, and obtaining the actual object point-pitch number curves of different wavelength light beams at the end of the GRIN optical fiber (2) with the change of the pitch number of the GRIN optical fiber according to the refractive index distribution function of the GRIN optical fiber (2) and the light beam trajectory equation; Step 3, deriving the light beam trajectory equation of the GRIN optical fiber (2), and obtaining the equivalent object point positions of different wavelength light beams at the end of the GRIN optical fiber (2) according to the geometric relationship, then calculating the equivalent object point offset of different wavelength light beams under different pitch numbers of the GRIN optical fiber (2) according to the equivalent object point positions and the actual object point-pitch number curves of different wavelength light beams obtained in step 2, and obtaining the equivalent object point chromatic focal shift curves of the GRIN optical fiber (2) under different pitch numbers; Step 4, determining the pitch number of the GRIN optical fiber (2) according to the actual object point-pitch number curves of different wavelength light beams obtained in step 2, the equivalent object point chromatic focal shift curves of the GRIN optical fiber (2) under different pitch numbers obtained in step 3, and the dispersion performance of the two-stage dispersion objective lens required by the design; Step 5, determining the feature importance arrangement of each parameter of the dispersion lens group (4), then generating multiple sets of dispersion lens group parameters and their corresponding actual dispersion performance values by using an optical design software according to the pitch number of the GRIN optical fiber (2) obtained in step 4, the feature importance arrangement and the dispersion performance of the two-stage dispersion objective lens required by the design, obtaining an initial data set, and dividing the initial data set into a training set and a test set; The dispersion performance of the two-stage dispersion objective lens comprises a dispersion range and a dispersion linearity of the two-stage dispersion objective lens, and the dispersion lens group parameters comprise the curvature radii, thicknesses and spacings of the first lens (41), the second lens (42), the third lens (43) and the fourth lens (44); Step 6, taking the dispersion lens group parameters as input features and the dispersion performance of the two-stage dispersion objective lens as an optimization target, constructing a dispersion optimization decision tree based on an XGBoost algorithm model by using the training set, then optimizing the test set by using the dispersion optimization decision tree to obtain optimal dispersion lens group parameters, and completing the dispersion compensation design of the two-stage dispersion objective lens.

2. The method of designing a two-stage dispersion-compensated objective lens based on dispersion according to claim 1, wherein, Step 6 specifically comprises: Step 6.1, setting a convergence condition and a regularization parameter of the XGBoost algorithm model, and determining the dispersion lens group parameters and the dispersion performance of the two-stage dispersion objective lens as input features and an optimization target of the XGBoost algorithm model respectively. Step 6.2, based on the XGBoost algorithm model, according to all the parameters of the dispersion lens group in the training set, determine the candidate split threshold of each parameter of the dispersion lens group at the first split point, then traverse the candidate split threshold of each parameter of the dispersion lens group at the first split point, and divide the dispersion lens group parameters in the training set into left and right subgroups, respectively calculate the gradient and Hessian sum of each candidate split threshold left and right subgroup at the first split point; Step 6.3, according to the gradient and Hessian sum of each candidate split threshold left and right subgroup at the first split point, calculate the objective function gain of each candidate split threshold at the first split point, then find the optimal split threshold of the first split point by greedy algorithm, and record the split contribution of each parameter of the dispersion lens group; Step 6.4, sort the parameters in the dispersion lens group according to the split contribution, take the parameter with the largest split contribution as the optimal feature, then update the feature importance ranking, and construct the first split point of the dispersion optimization decision tree according to the feature importance ranking and the optimal split threshold of the first split point; Step 6.5, divide the dispersion lens group parameters in the training set into left and right subgroups according to the optimal split threshold of the first split point in the dispersion optimization decision tree, and calculate the two-level dispersion objective lens dispersion performance of the dispersion lens group parameters in the left and right subgroups at the first split point respectively, to get the dispersion performance prediction value of the first split point, then calculate the residual value and fit according to the dispersion performance prediction value and the corresponding actual value of the first split point; Step 6.6, judge whether the fitted residual value meets the convergence condition, if yes, execute step 6.7; if not, adjust the regularization parameter and return to step 6.2; Step 6.7, add a new level split point under the first split point of the dispersion optimization decision tree, take each new level split point as the current first split point respectively, then return to step 6.2 until the depth of the dispersion optimization decision tree meets the design requirement, to get the dispersion optimization decision tree; Step 6.8, take the test set as input, make the dispersion optimization decision tree find the optimal dispersion lens group parameters according to the dispersion lens group parameters in the test set; Step 6.9, judge whether the optimal dispersion lens group parameters are the same as a certain group of dispersion lens group parameters in the test set, if yes, return to step 5 and update the feature importance ranking by SHAP; Otherwise, output the optimal dispersion lens group parameters, complete the dispersion compensation design of the two-level dispersion objective lens.

3. The method of designing a two-stage dispersion-compensated objective according to claim 1 or 2, characterized in that, In step 1, the first lens (41) is a double convex lens, and the material is P-BK7; The second lens (42) is a meniscus lens with the convex surface facing the incident direction of the light beam, and the material is P-BK7; The third lens (43) is a meniscus lens with the convex surface facing the incident direction of the light beam, and the material is SF5; The fourth lens (44) is a meniscus lens with the convex surface facing the incident direction of the light beam, and the material is SF5.

4. A two-stage dispersive objective characterized in that: The two-stage dispersion objective lens is designed by the method of claim 1-3, comprising a GRIN fiber (2) and a dispersion lens group (4). The incident end of the GRIN fiber (2) is used for receiving polychromatic test light, and the outgoing end is arranged at the front end of the dispersion lens group (4). The pitch number of the GRIN fiber (2) is 3-7, which is used for primary pre-dispersion of the polychromatic test light. The dispersion lens group (4) is used for secondary dispersion of the polychromatic test light, comprising a first lens (41), a second lens (42), a third lens (43) and a fourth lens (44) arranged in sequence along the incident direction of the polychromatic test light. The surface where the polychromatic test light is incident is defined as a front surface, and the surface where the polychromatic test light is incident is defined as a rear surface. The first lens (41) is a double-convex lens, the front surface has a curvature radius of 20.437-20.851, and the rear surface has a curvature radius of -33.763--33.

095. The second lens (42) is a meniscus lens, the front surface has a curvature radius of 18.596-18.972, and the rear surface has a curvature radius of 32.064-32.

712. The third lens (43) is a meniscus lens, the front surface has a curvature radius of 9.941-11.141, and the rear surface has a curvature radius of 49.023-52.

033. The fourth lens (44) is a meniscus lens, the front surface has a curvature radius of 28.031-28.597, and the rear surface has a curvature radius of 11.986-12.

228.

5. The two-stage dispersive objective of claim 4, characterized in that: The thickness of the first lens (41) is 1.98-2.02mm, and the interval between the first lens (41) and the second lens (42) is 0.99-1.01mm. The thickness of the second lens (42) is 1.98-2.02mm, and the interval between the second lens (42) and the third lens (43) is 0.99-1.01mm. The thickness of the third lens (43) is 2.861-2.919mm, and the interval between the third lens (43) and the fourth lens (44) is 0.99-1.01mm. The thickness of the fourth lens (44) is 1.782-1.818mm.

6. The two-stage dispersive objective of claim 5, wherein: The material of the first lens (41) is P-BK7, the material of the second lens (42) is P-BK7, the material of the third lens (43) is SF5, and the material of the fourth lens (44) is SF5.

7. The two-stage dispersive objective of claim 6, characterized in that: The pitch number of the GRIN fiber (2) is 5, the length is 5.1787cm, and the interval between the outgoing end of the GRIN fiber (2) and the first lens (41) of the dispersion lens group (4) is 99mm.

8. The two-stage dispersive objective of claim 7, wherein: The curvature radius of the front surface of the first lens (41) is 20.644, and the curvature radius of the rear surface is -33.

429. The curvature radius of the front surface of the second lens (42) is 18.784, and the curvature radius of the rear surface is 32.

388. The curvature radius of the front surface of the third lens (43) is 10.041, and the curvature radius of the rear surface is 50.

528. The curvature radius of the front surface of the fourth lens (44) is 28.314, and the curvature radius of the rear surface is 12.

107.

9. The two-stage dispersive objective of claim 8, characterized in that: The thickness of the first lens (41) is 2.000 mm, and the interval between the first lens (41) and the second lens (42) is 1.000 mm; The thickness of the second lens (42) is 2.000 mm, and the interval between the second lens (42) and the third lens (43) is 1.000 mm; The thickness of the third lens (43) is 2.890 mm, and the interval between the third lens (43) and the fourth lens (44) is 1.000 mm; The thickness of the fourth lens (44) is 1.800 mm.

10. A spectroscopic confocal displacement measurement system characterized by: The light source (1), the two-stage dispersion objective lens according to any one of claims 4-9, the beam splitter (3) and the spectrometer (5) are included; The light source (1) is used for emitting a polychromatic test light, and the emitting end of the polychromatic test light corresponds to the incident end of the GRIN fiber (2); The rear end of the dispersion lens group (4) is used for setting a to-be-measured target (6); The beam splitter (3) is arranged between the emitting end of the GRIN fiber (2) and the dispersion lens group (4); The GRIN fiber (2) is used for performing primary pre-dispersion on the polychromatic test light to obtain first-stage dispersion light, and the first-stage dispersion light is transmitted to the first lens (41), the second lens (42), the third lens (43) and the fourth lens (44) of the dispersion lens group (4) after being transmitted by the beam splitter (3) to perform second-stage dispersion to form axial dispersion light, and the axial dispersion light is transmitted to the to-be-measured target (6), and the to-be-measured target (6) generates reflected light after receiving the axial dispersion light, and the reflected light is reflected by the beam splitter (3) after sequentially passing through the fourth lens (44), the third lens (43), the second lens (42) and the first lens (41); The spectrometer (5) is arranged on the light path of the reflected light of the to-be-measured target (6) reflected by the beam splitter (3), and is used for collecting spectral information of the reflected light before and after displacement of the to-be-measured target (6), so as to calculate a displacement value of the to-be-measured target (6) according to spectral changes of the reflected light.

Images