Secondary dispersion objective lens design method based on aberration correction, secondary dispersion objective lens and spectrum confocal displacement sensing system

Abstract

The invention relates to a secondary dispersion objective lens design method based on aberration correction, a secondary dispersion objective lens and a spectrum confocal displacement sensing system, and aims to solve the problems that the gradient refractive index of an existing dispersion objective lens based on a GRIN lens can generate aberration, so that the measurement precision of the spectrum confocal displacement sensing system adopting the dispersion objective lens is low, and the measurement precision is low. And the measurement range of a spectrum confocal displacement sensing system adopting the dispersion objective lens is relatively small. According to the aberration correction-based secondary dispersion objective lens design method provided by the invention, a secondary dispersion objective lens comprises a GRIN optical fiber and a dispersion objective lens group, the GRIN optical fiber is used for carrying out primary dispersion on incident light to form pre-dispersion light, and the dispersion objective lens group is used for carrying out secondary dispersion on the pre-dispersion light to form pre-dispersion light; a physical information neural network (PINN) algorithm is combined with ZEMAX software simulation, comprehensive compensation and correction of aberration of a dispersion objective lens group and a GRIN optical fiber are realized while the dispersion range of the system is expanded, and the design of the system is completed on the basis of the comprehensive compensation and correction of the aberration of the dispersion objective lens group and the GRIN optical fiber.

Description

Technical Field

[0001] The present invention relates to a secondary dispersion objective lens, and in particular to a secondary dispersion objective lens design method based on aberration correction, a secondary dispersion objective lens and a spectral confocal displacement sensing system. Background Art

[0002] In the manufacturing process of semiconductor power devices, precision micro-displacement measurement technology is often used to measure the real-time displacement of interface defects in semiconductor power devices to ensure that they meet accuracy standards and thus reduce the scrap losses of semiconductor power devices. The spectral confocal displacement sensing system uses dispersion encoding to establish a wavelength-axial position mapping relationship. Combined with confocal imaging to decode the reflectance spectrum, it achieves submicron real-time displacement measurement within the millimeter range, combining nanometer-level resolution with strong environmental adaptability.

[0003] The performance of the spectral confocal displacement sensing system is closely related to the dispersive objective lens. The dispersive objective lens can focus different wavelengths at different depths. It is a key optical device that encodes wavelength information into spatial position information and realizes spectral confocal technology. The refractive index of radial gradient index (GRIN) material changes gradiently along the radial direction of the optical fiber. It is small in size and has good focusing performance. It provides additional degrees of freedom for optical design and shows great potential in optical applications.

[0004] Existing dispersive objectives based on GRIN lenses achieve high linear dispersion and nanometer-level resolution through a refractive index gradient distribution. In the visible light band of 420-656 nm, an axial dispersion range of 1130-1215 μm can be achieved, and the wavelength-displacement linear correlation coefficient is as high as 99.69%, which is significantly better than traditional dispersive objectives. However, the measurement range of the spectral confocal displacement sensing system using this type of dispersive objective is small, and the gradient refractive index of the dispersive objective of the GRIN lens will produce aberrations, resulting in low measurement accuracy of the spectral confocal displacement sensing system using this type of dispersive objective. Summary of the Invention

[0005] The purpose of the present invention is to solve the technical problems that the gradient refractive index of the existing dispersive objective lens based on GRIN lens will produce aberration, which in turn leads to low measurement accuracy of the spectral confocal displacement sensing system using such dispersive objective lens, and small measurement range of the spectral confocal displacement sensing system using such dispersive objective lens, and to provide a secondary dispersive objective lens design method based on aberration correction, a secondary dispersive objective lens and a spectral confocal displacement sensing system.

[0006] To achieve the above objectives, the technical solutions provided by the present invention are as follows:

[0007] A method for designing a secondary dispersion objective lens based on aberration correction is special in that it includes the following steps:

[0008] S1. Determining that the secondary dispersion objective lens includes a GRIN fiber for primary dispersion and a dispersion objective lens group for secondary dispersion, and determining that the initial structure of the dispersion objective lens group includes a first lens, a second lens, a third lens, and a fourth lens sequentially arranged along the direction of incident light, and the materials and surface shapes of the first lens, the second lens, the third lens, and the fourth lens;

[0009] S2. Calculate the equivalent wavelength points of the GRIN fiber at M different pitch numbers based on the refractive index distribution constant of the GRIN fiber material and the Cauchy dispersion formula, and determine a preliminary optimal pitch number range of the GRIN fiber based on the equivalent points; M ≥ 5;

[0010] S3. Calculate the equivalent spherical aberration of the GRIN optical fiber at different pitch numbers within the preliminary optimal pitch number range, and determine the optimal pitch number of the GRIN optical fiber based on the equivalent spherical aberration;

[0011] S4. Determine the structure of the dispersion objective lens group based on the optimal pitch number of the GRIN optical fiber and the dispersion performance required by the design, perform ZEMAX simulation on the structures of the first lens, the second lens, the third lens, and the fourth lens in the dispersion objective lens group, and construct a lens parameter-aberration data set;

[0012] S5. Based on the PINN algorithm, a composite loss function including a data fitting term and a Zernike aberration constraint term is constructed; the Zernike aberration constraint term is determined by the axial spherical aberration constraint of the GRIN fiber and the Zernike aberration of the dispersion objective lens group;

[0013] S6, construct an initial aberration correction model for the secondary dispersion objective lens, using the lens parameter-aberration data set constructed in step S4 as input, and the composite loss function constructed in step S5 as a convergence function, to train the initial aberration correction model until the aberration correction model outputs the optimal lens parameters;

[0014] S7. Use the optimal pitch number obtained in step S3 as the pitch number of the GRIN fiber, and use the optimal lens parameters obtained in step S6 as the parameters of the dispersion objective lens group to complete the design of the secondary dispersion objective lens.

[0015] Furthermore, the specific process of step S6 is as follows:

[0016] S6.1. Constructing an initial aberration correction model for a secondary dispersion objective lens and initializing model parameters of the aberration correction model;

[0017] S6.2, using the lens parameter-aberration dataset constructed in step S4 as input, iteratively train the initial aberration correction model constructed in step S6.1, and calculate the value of the composite loss function constructed in step S5 based on the lens parameters output in this round of iteration, and judge whether the value of the composite loss function meets the convergence requirement. If the value of the composite loss function meets the convergence requirement, then judge whether the lens parameters output in this round of iteration meet the optical performance requirements. If they meet the optical performance requirements, the lens parameters output in this round of iteration are the optimal lens parameters. If they do not meet the optical performance requirements, optimize the lens parameter-aberration dataset, use the optimized lens parameter-aberration dataset as input, and perform a new round of iteration on the aberration correction model after this round of iterative training until the lens parameters output in the new round of iteration meet the optical performance requirements, i.e., obtain the optimal lens parameters.

[0018] If the composite loss function value does not meet the convergence requirements, the Adam optimizer is used to optimize the model parameters of the initial aberration correction model, and a new round of iteration is performed on the aberration correction model after the current round of iterative training. After the new round of iteration, it is judged whether the composite loss function value meets the convergence requirements. If it does not meet the requirements, the Adam optimizer is used to optimize the model parameters of the previous round of aberration correction model again until the composite loss function value meets the convergence requirements; if it meets the requirements, it is judged whether the lens parameters output by the new round of iteration meet the optical performance requirements. If the optical performance requirements are met, the lens parameters output by the new round of iteration are the optimal lens parameters. If the optical performance requirements are not met, the lens parameters-aberration data set are optimized, and the optimized lens parameters-aberration data set is used as input to perform a new round of iteration on the aberration correction model after the previous round of iterative training until the lens parameters output by the new round of iteration meet the optical performance requirements, that is, the optimal lens parameters are obtained.

[0019] Furthermore, the specific process of step S2 is as follows:

[0020] S2.1. Determine the refractive index distribution and ray trace propagation function of the GRIN fiber based on the refractive index distribution constant of the GRIN fiber material and the Cauchy dispersion formula;

[0021] S2.2. Calculate the equivalent wavelength points of the GRIN fiber at M different pitches based on the refractive index distribution and ray trace propagation function of the GRIN fiber, where 5≤M≤10;

[0022] S2.3. Determine the wavelength variation curve of the chromatic focal shift of the GRIN fiber at different pitch numbers based on the equivalent point of the wavelength at different pitch numbers.

[0023] S2.4. Quantitatively analyze the linearity of the curve of chromatic focus shift versus wavelength, and determine the preliminary optimal pitch number range of the GRIN fiber based on the linearity.

[0024] Furthermore, the specific process of step S3 is as follows:

[0025] S3.1. Calculate the equivalent object points and equivalent image points of the GRIN fiber at different pitch numbers within the preliminary optimal pitch range. Calculate the equivalent spherical aberration of the GRIN fiber at different pitch numbers within the preliminary optimal pitch range based on the equivalent object points and equivalent image points.

[0026] S3.2. Based on the equivalent spherical aberration, determine the curves of the equivalent spherical aberration of the GRIN fiber as a function of wavelength at different pitch numbers within the preliminary optimal pitch number range;

[0027] S3.3. Determine the curve with optimal imaging performance from the curves of equivalent spherical aberration versus wavelength of the GRIN optical fiber at different pitch numbers within the preliminary optimal pitch number range. The pitch number corresponding to the curve is the optimal pitch number of the GRIN optical fiber.

[0028] Furthermore, in step S5, the composite loss function L total The formula is as follows:

[0029]

[0030] Where, are the lens parameter values ​​output by the aberration correction model and the actual values ​​of the lens parameters obtained by ZEMAX simulation, N is the number of samples, K is the number of sampling points, and W j is the aberration of the secondary dispersion objective, β n is the aberration coefficient, W(ρ,θ) is the Zernike aberration function, and n is the order parameter of the Zernike coefficient.

[0031] Furthermore, in step 1, the first lens is a biconvex lens, and its material is P-BK7; the second lens is a meniscus lens, which is bent toward the side of the incident light and its material is P-BK7; the third lens is a meniscus lens, which is bent toward the side of the incident light and its material is SF5; the fourth lens is a meniscus lens, which is bent toward the side of the incident light and its material is SF5.

[0032] At the same time, the present invention also provides a secondary dispersion objective lens, which is special in that it is obtained by adopting the above-mentioned secondary dispersion objective lens design method based on aberration correction, including GRIN optical fiber and a dispersion objective lens group;

[0033] The incident end of the GRIN optical fiber is used to receive incident light, and the output end is arranged at the front end of the dispersive objective lens group. The GRIN optical fiber is used to perform primary dispersion on the incident light to form pre-dispersed light, and transmit it to the dispersive objective lens group; the dispersive objective lens group is used to perform secondary dispersion on the pre-dispersed light to form axially dispersed light, and transmit it to the sample to be measured;

[0034] The dispersion objective lens group includes a first lens, a second lens, a third lens and a fourth lens arranged in sequence along the propagation direction of the pre-dispersed light;

[0035] The pre-dispersed light passes through the first lens, the second lens, the third lens and the fourth lens in sequence to form axially dispersed light, and is transmitted to the sample to be measured;

[0036] The pitch number of the GRIN optical fiber ranges from 4 to 6;

[0037] Define the surface where the pre-dispersed light enters as the front surface, and the surface where the pre-dispersed light exits as the back surface;

[0038] The first lens is a biconvex lens, with a front surface curvature radius ranging from 20.480 mm to 20.808 mm and a rear surface curvature radius ranging from -33.696 mm to -33.162 mm;

[0039] The second lens is a meniscus lens, with a front surface curvature radius ranging from 18.634 mm to 18.934 mm and a rear surface curvature radius ranging from 32.137 mm to 32.639 mm;

[0040] The third lens is a meniscus lens, with a front surface curvature radius ranging from 9.961 mm to 10.121 mm and a rear surface curvature radius ranging from 50.124 mm to 50.932 mm;

[0041] The fourth lens is a meniscus lens, with a front surface curvature radius ranging from 28.088 mm to 28.540 mm and a rear surface curvature radius ranging from 12.011 mm to 12.203 mm;

[0042] The thickness of the first lens is in the range of 1.984 mm to 2.016 mm, and the distance between the first lens and the second lens is in the range of 0.992 mm to 1.008 mm;

[0043] The thickness of the second lens is in the range of 1.984 mm to 2.016 mm, and the distance between the second lens and the third lens is in the range of 0.992 mm to 1.008 mm;

[0044] The thickness of the third lens is in the range of 2.867 mm to 2.913 mm, and the distance between the third lens and the fourth lens is in the range of 0.992 mm to 1.008 mm;

[0045] The thickness of the fourth lens is in the range of 1.786 mm to 1.814 mm.

[0046] Furthermore, the material of the first lens is P-BK7, with a thickness of 2.005 mm, a front surface curvature radius of 20.642 mm, a rear surface curvature radius of -33.429 mm, and a spacing of 1.001 mm from the second lens; the material of the second lens is P-BK7, with a thickness of 1.997 mm, a front surface curvature radius of 18.784 mm, a rear surface curvature radius of 32.388 mm, and a spacing of 0.999 mm from the third lens; the material of the third lens is SF5, with a thickness of 2.891 mm, a front surface curvature radius of 10.041 mm, a rear surface curvature radius of 50.527 mm, and a spacing of 1.005 mm from the fourth lens; the material of the fourth lens is SF5, with a thickness of 1.802 mm, a front surface curvature radius of 28.316 mm, and a rear surface curvature radius of 12.107 mm.

[0047] Furthermore, the pitch number of the GRIN optical fiber is 5, the length is 5.1787 cm, and the distance between the output end and the first lens is 99 mm.

[0048] At the same time, the present invention also provides a spectral confocal displacement sensing system, which is special in that it includes a white light source, a secondary dispersion objective lens, a spectroscope, a confocal pinhole plate and a spectrometer;

[0049] The secondary dispersion objective lens adopts the above-mentioned secondary dispersion objective lens;

[0050] The white light source is used to emit incident light to the incident end of the GRIN optical fiber;

[0051] The GRIN optical fiber is used to perform first-order dispersion on the incident light to form pre-dispersed light, and transmit it to the spectroscope;

[0052] The beam splitter is used to split the pre-dispersed light to form transmitted light, and transmit the transmitted light to the dispersion objective lens group;

[0053] The transmitted light is sequentially dispersed by the first lens, the second lens, the third lens, and the fourth lens of the dispersion objective lens group to form axially dispersed light, which is then transmitted to the sample to be measured;

[0054] The sample to be tested generates reflected light after receiving the axially dispersed light. The reflected light passes through the fourth lens, the third lens, the second lens, and the first lens in sequence, is reflected by the beam splitter, and finally enters the spectrometer through the confocal pinhole plate.

[0055] The spectrometer calculates the displacement value of the sample to be measured according to the spectral change of the reflected light.

[0056] Beneficial effects of the present invention:

[0057] 1. The present invention provides a method for designing a secondary dispersion objective lens based on aberration correction. By constructing an aberration correction model based on the PINN algorithm, the optimal lens parameters of the secondary dispersion objective lens are obtained, thereby solving the problem of certain errors in measurement range and measurement accuracy caused by aberrations generated by the gradient refractive index of GRIN optical fiber.

[0058] 2. The present invention provides a design method for a secondary dispersion objective lens based on aberration correction. Based on the PINN algorithm, a composite loss function including a data fitting term and a Zernike aberration constraint term is constructed. The method improves generalization capability by minimizing data loss and physical loss, thereby overcoming the limitations of the traditional damped least squares method in ZEMAX, which is easily affected by the initial structure and has difficulty in handling strong nonlinear problems, resulting in local optimal solutions.

[0059] 3. The present invention provides a secondary dispersion objective lens, which performs primary dispersion on incident light through a GRIN optical fiber, and a dispersion objective lens group performs secondary dispersion on the incident light after primary dispersion, thereby increasing the measurement range of the secondary dispersion objective lens;

[0060] 4. The present invention provides a spectral confocal displacement sensing system. Based on the pre-dispersion of GRIN optical fiber, the dispersion and aberration compensation correction of the secondary dispersion objective lens is performed to compensate for the pre-dispersion nonlinear characteristics of the GRIN optical fiber, expand the measurement range of the spectral confocal displacement sensing system, achieve a highly linear axial dispersion distribution, and improve measurement accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 This is a schematic structural diagram of an embodiment of a spectral confocal displacement sensing system of the present invention;

[0062] Figure 2 This is a schematic structural diagram of a dispersion objective lens assembly according to an embodiment of a secondary dispersion objective lens of the present invention;

[0063] Figure 3 This is a flow chart of a method for designing a secondary dispersion objective lens based on aberration correction according to the present invention;

[0064] Figure 4 This is a graph showing the variation of the chromatic focal shift of the GRIN fiber with wavelength at different pitch numbers in step S2.3 of an embodiment of a method for designing a secondary dispersion objective lens based on aberration correction of the present invention;

[0065] Figure 5 Schematic diagram of spherical aberration of monochromatic light of GRIN fiber at different pitch numbers according to an embodiment of a method for designing a secondary dispersion objective lens based on aberration correction of the present invention;

[0066] Figure 6 Schematic diagram of the GRIN fiber blue light path in step S3.1 of an embodiment of a method for designing a secondary dispersion objective lens based on aberration correction according to the present invention;

[0067] Figure 7 Schematic diagram of the axial positions of the equivalent image point and the equivalent object point in steps S3.1 to S3.3 of an embodiment of a method for designing a secondary dispersion objective lens based on aberration correction according to the present invention;

[0068] Figure 8 This is a graph showing the variation of the equivalent spherical aberration of the GRIN fiber with wavelength in step S3.2 of an embodiment of a method for designing a secondary dispersion objective lens based on aberration correction according to the present invention;

[0069] Figure 9 This is a diagram illustrating the training principle of the aberration correction model in steps S4-S6 of an embodiment of a method for designing a secondary dispersion objective lens based on aberration correction according to the present invention;

[0070] Figure 10 Schematic diagram of the variation of training loss value and test error with the number of iterations in step S6.2 of an embodiment of a method for designing a secondary dispersion objective lens based on aberration correction according to the present invention;

[0071] Figure 11 Schematic diagram comparing spherical aberration before and after correction in an embodiment of a method for designing a secondary dispersion objective lens based on aberration correction according to the present invention;

[0072] Figure 12 This is a light wave spot diagram at different wavelengths obtained by an embodiment of a method for designing a secondary dispersion objective lens based on aberration correction of the present invention;

[0073] Figure 13 A schematic diagram of the variation of chromatic focal shift with wavelength for original data, quadratic fitting data, and least squares fitting data of an embodiment of a parameter design method for a secondary dispersion objective lens of the present invention;

[0074] Description of reference numerals:

[0075] 1-white light source, 2-GRIN optical fiber, 3-beam splitter, 4-dispersion objective lens group, 41-first lens, 42-second lens, 43-third lens, 44-fourth lens, 5-confocal pinhole plate, 6-spectrometer, 7-sample to be measured, 8-measuring platform. DETAILED DESCRIPTION

[0076] The present invention will be further described below with reference to the accompanying drawings and examples.

[0077] This embodiment provides a method for designing a secondary dispersion objective lens based on aberration correction, such as Figure 3 As shown, the specific process is as follows:

[0078] S1. Determine that the secondary dispersion objective lens includes a GRIN fiber 2 for primary dispersion and a dispersion objective lens group 4 for secondary dispersion, and determine that the initial structure of the dispersion objective lens group 4 includes a first lens 41, a second lens 42, a third lens 43, and a fourth lens 44 sequentially arranged along the direction of incident light, as well as the materials and surface shapes of the first lens 41, the second lens 42, the third lens 43, and the fourth lens 44;

[0079] Perform primary dispersion analysis on GRIN fiber 2 to determine the number of pitches of GRIN fiber 2. The specific process is as follows:

[0080] S2. Obtain the refractive index distribution constant of the GRIN fiber 2 material. Based on the Cauchy dispersion formula, calculate the equivalent points of the wavelengths of the GRIN fiber 2 at 10 different pitch numbers. Based on the equivalent points, determine the preliminary optimal pitch number range of the GRIN fiber 2, specifically:

[0081] S2.1. Based on the selected GRIN fiber 2 material, obtain the refractive index distribution constant of the GRIN fiber 2 material, and determine the refractive index distribution and ray trace propagation function of the GRIN fiber 2 based on the Cauchy dispersion formula;

[0082] Under the paraxial approximation (αr<<1), the refractive index of the ideal GRIN fiber 2 is parabolic. Assuming the wavelength of the incident light is λ, the fiber refractive index distribution constant is α(λ), and the radial distance from the optical axis is r, the ideal refractive index distribution n(r,λ) of the first-order GRIN fiber 2 is:

[0083]

[0084] Where n0(λ) is the refractive index on the optical axis of GRIN fiber 2;

[0085] According to the Cauchy dispersion formula, α(λ) can be expressed as: α(λ)=A+B / λ 2 +C / λ 4 , where A, B, C are dielectric coefficients;

[0086] Using the refractive index distribution constant of Go-Foton's GRIN material, we take n0(λ)=1.568+8.14×10 3 / λ 2 , then the ideal refractive index distribution n(r,λ) and ray trace propagation function r(z,λ) of GRIN fiber 2 are:

[0087]

[0088] Where r0′ is the initial slope of the light in the lens, z is the focus position of the red light;

[0089] S2.2. Based on the refractive index profile n(r,λ) and the ray trace propagation function r(z,λ) of GRIN fiber 2, calculate the equivalent wavelength points of GRIN fiber 2 at 10 different pitch numbers.

[0090] Derivative the light trajectory propagation function r(z,λ), assuming the angle between the light and the optical axis is θ, then θ=arctan(r′(z)), let l λ Represents the equivalent point before the light of wavelength λ is emitted from a certain height of the optical fiber, then:

[0091]

[0092] Where z m Indicates the focus position of the red light when the pitch number is m;

[0093] S2.3. Based on the equivalent point of wavelength at different pitch numbers, determine the curve of the chromatic focal shift of GRIN fiber 2 with different pitch numbers as a function of wavelength, such as Figure 4 As shown in the figure, the chromatic focal shift of GRIN fiber 2 varies with wavelength at different pitch numbers. As the pitch number increases, the dispersion range increases monotonically, but the linearity of the curve decreases.

[0094] S2.4. Quantitatively analyze the linearity of the chromatic focus shift versus wavelength curve and determine the preliminary optimal pitch range of GRIN fiber 2 based on the linearity.

[0095] Quantitative analysis of the linearity R of each curve 2 , when the pitch number m is 4, 5, or 6, R 2 are 96.33%, 95.16%, and 93.31% respectively; when m is 7, 8, and 9, the linearity of the curve drops sharply, and R 2 They are 90.31%, 85.22%, and 75.68% respectively. Subsequent correction is difficult and it is difficult to meet the high linearity requirements of the system. Therefore, considering the dispersion range and the system linearity requirements, 4, 5, and 6 can be preliminarily selected as the pitch number of GRIN fiber 2.

[0096] The aberration of GRIN fiber 2 is analyzed to determine the optimal pitch number of GRIN fiber 2. The specific process is as follows:

[0097] S3. Calculate the equivalent spherical aberration of the GRIN optical fiber 2 within the preliminary optimal pitch number range, and determine the optimal pitch number of the GRIN optical fiber 2 based on the equivalent spherical aberration;

[0098] The aberrations of GRIN fiber 2 are analyzed. The gradient refractive index distribution characteristics of GRIN fiber 2 provide additional degrees of freedom for designing optical systems with compact structure and excellent image quality. Based on Hamiltonian optical theory, the aberrations of GRIN fiber 2 can be systematically derived. However, there is a difference between the primary aberrations of GRIN fiber 2 and the actual aberrations, so higher-order aberrations must be introduced. The power series expansion of the ideal refractive index distribution n(r,λ) of GRIN fiber 2 under the paraxial approximation condition is:

[0099]

[0100] Where, L4 and L6 are the coefficients of the fourth-order term and the sixth-order term respectively;

[0101] If U=r 2 ,Q(λ)=α(λ) 2 , then under the paraxial approximation condition, the power series expansion of n(r,λ) can be written as:

[0102]

[0103] Since the series is developed around r = 0, the high-order terms are zero, so the high-order terms of r do not affect the aberration of the low-order terms, so r 2 The first-order term determines the basic characteristics of the paraxial image, r 4 The term determines the third-order aberration. The third-order aberration coefficient expression of GRIN fiber 2 is:

[0104]

[0105] Where Γ is the paraxial optical invariant of the optical system, A, B, C, D, and E correspond to the five Seidel aberrations, namely spherical aberration, coma, astigmatism, field curvature, and distortion, G(z), g(z), θ(z) is a function related to z, is a special solution of the paraxial image plane Z1, H 11 、H 12 、H 22 is the expansion coefficient of the Taylor series of the optical Hamiltonian equation:

[0106]

[0107] Select the object plane z0=0, then the object point is located at (x0,0). Under this condition, g(z), G(z) and θ(z) are two linearly independent special solutions of the paraxial ray. The paraxial ray equation satisfies any boundary conditions. The solution of the paraxial ray equation that satisfies any boundary conditions can be expressed as a linear combination of these two special solutions:

[0108]

[0109] Then the expression of the third-order aberration coefficient of GRIN fiber is simplified to:

[0110]

[0111] Where z1 = 2mπ / Q(λ) 1 / 2 .

[0112] In the entire optical system, system aberrations mainly come from the primary dispersion of the GRIN fiber 2 and the secondary dispersion of the dispersive objective lens group 4. The spectral confocal displacement measurement system scans point by point through a mechanical translation stage. The system only collects the focus signal on the optical axis. Off-axis points cannot form an effective spectral peak, so the aberrations of off-axis points do not need to be considered. The on-axis imaging characteristics are mainly affected by monochromatic spherical aberration. The monochromatic spherical aberration of on-axis points will cause the spot size on the image plane to increase, causing the spectral response curve to widen and the resolution to decrease. Therefore, it is necessary to correct the axial spherical aberration.

[0113] In this paper, according to the actual process parameters, a parabolic refractive index distribution is selected, and L4 and L6 are set to 0. Then, under different pitches, the monochromatic spherical aberration of GRIN fiber 2 is as follows: Figure 5 As shown in the figure, within the wavelength range of 450-670nm, the spherical aberration of GRIN fiber 2 decreases as the wavelength λ increases. Furthermore, at the same wavelength, the larger the pitch number m, the greater the spherical aberration, demonstrating the rationality of selecting pitch numbers of 4, 5, and 6. The ray trajectory equation r(z,λ) shows that short-wavelength light has a shorter focusing period. When the focusing period is short, the focus separation between the marginal and paraxial rays becomes more pronounced, increasing the spherical aberration.

[0114] In a specific design, theoretical spherical aberration cannot be directly used as the monochromatic spherical aberration generated by the GRIN fiber 2 in the spectral confocal displacement measurement system. This is because during light wave propagation, the radial gradient of the refractive index inside the GRIN fiber 2 changes, the light is deflected, and its convergence point is offset. At this time, the convergence point of the light cannot be directly used as the monochromatic point light source designed in the subsequent dispersion objective lens group 4. Therefore, it is necessary to calculate the equivalent object point and equivalent spherical aberration of the light inside the GRIN fiber 2.

[0115] S3.1. Calculate the equivalent object points and equivalent image points of the GRIN fiber 2 at different pitch numbers within the preliminary optimal pitch range, and calculate the equivalent spherical aberration of the GRIN fiber 2 at different pitch numbers within the preliminary optimal pitch range based on the equivalent object points and equivalent image points.

[0116] like Figure 6As shown, O is the optical fiber output end. The blue light propagates through the optical fiber and converges at point A on the principal optical axis. Affected by the axial spherical aberration, the marginal light and the paraxial light focus A are separated and converge at A'. The distance S between A and A' is the axial spherical aberration. After the blue light is emitted through the GRIN optical fiber 2, its reverse extension line intersects the principal optical axis at P, which is the equivalent object point. Due to the existence of spherical aberration, after the marginal light focus A' is emitted, its reverse extension line intersects the principal optical axis at P', which is the equivalent image point. The distance S' between P and P' is the equivalent spherical aberration generated by the GRIN optical fiber 2. As a key parameter for evaluating the imaging quality of an optical system, the equivalent spherical aberration is defined as the axial position difference between P and P'. The axial distance between P and P' relative to the optical fiber output end O is denoted as Z. P , Z P′ , then the equivalent spherical aberration S′ can be characterized as:

[0117]

[0118] Where, α λ is the refractive index parameter related to λ;

[0119] S3.2. Based on the equivalent spherical aberration, the curves of the equivalent spherical aberration of the GRIN fiber 2 varying with wavelength at different pitch numbers within the preliminary optimal pitch number range are determined, such as Figure 8 As shown;

[0120] S3.3. Determine the curve with optimal imaging performance from the curves of equivalent spherical aberration versus wavelength for the GRIN fiber 2 at different pitch numbers within the preliminary optimal pitch number range. The pitch number corresponding to the curve is the optimal pitch number for the GRIN fiber 2.

[0121] The axial positions of the equivalent object point P and the equivalent image point P′ at different wavelengths for each pitch number are as follows: Figure 7 As shown, the vertical axis is the axial position from the output end of the lower GRIN fiber 2. Figure 7 The downward position difference and equivalent spherical aberration S′ of the same pitch can be obtained. The equivalent spherical aberration of GRIN fiber 2 is as follows: Figure 8 As shown by Figure 7 It can be seen that the axial position and spacing between the equivalent object point P and the equivalent image point P′ vary significantly with the incident wavelength λ and the pitch number m. The difference in their changing rates reveals the influence of m on the axial dispersion. Figure 8 The results show that the equivalent spherical aberration S′ decreases with increasing wavelength λ, but the m value has a significant impact on it: when m = 6, the spherical aberration is maximum, and the imaging quality is severely affected by spherical aberration; when m = 5, the spherical aberration is relatively low and decreases smoothly with wavelength, showing excellent imaging performance; when m = 4, the spherical aberration is minimum, but the variation range is narrow. Among them, m = 5 maintains moderate chromatic focus shift while combining low spherical aberration and good linearity. Therefore, in this embodiment, the GRIN fiber 2 pitch number m = 5 is selected.

[0122] The process of selecting the dispersion objective lens set 4 based on the GRIN fiber 2 is as follows:

[0123] The incident light beam generates first-order dispersion through the GRIN fiber 2, and then the axial dispersion is further expanded by the dispersive objective lens group 4 to achieve second-order dispersion. As one of the core optical components of the spectral confocal sensing system, the dispersive objective lens group 4 must meet two key characteristics: the axial dispersion of different wavelengths forms a focal distribution; and the convergence point corresponding to each wavelength should be as close to the ideal point as possible. Therefore, the structure of the dispersive objective lens group 4 needs to be optimized in a targeted manner to ensure coordinated matching with the parameters of the GRIN fiber 2. Among them, the Zernike aberration function W(ρ,θ′) of the dispersive objective lens group 4 is:

[0124] W(ρ,θ′)=2π(W 040 ρ 4 +W 131 ρ 3 cosθ′+W 222 ρ 2 cosθ ′2 )

[0125] Where W 040 , W 131 , W 222 are the coefficients of spherical aberration, coma, and astigmatism, ρ is the vertical distance from the incident light to the optical axis, and θ′ is the angle between the incident light and the spherical surface. The design of the dispersion objective lens group 4 should meet the requirement of a linear relationship between axial dispersion and wavelength. This is usually achieved by using a positive and negative lens separation structure and a reasonable distribution of optical power. The dispersion objective lens group 4 composed of S lenses must meet the following conditions:

[0126]

[0127] Where, is the focal power of the dispersion objective lens group 4, is the focal length of the i-th lens, S is the number of lenses, and υ di are the focal length and Abbe number of the i-th lens at wavelength d; δ S′CF is the chromatic aberration of the dispersion objective lens group 4 between wavelengths C and F (i.e., axial dispersion); f′ 2 and m are the focal length and lateral magnification of the dispersion objective lens group 4 respectively; R λi is the dispersion coefficient of the glass material. λi =P λi -(λ D -λ C ) / (λ F -λ C ), P λi =(n pi -n ci ) / (nFi -n Ci ), P λi is the relative dispersion of a single lens material, λ D is the wavelength of D light; C is the wavelength of C light; λ F is the wavelength of light F. The above shows that to obtain high linear axial dispersion, a single lens combination of at least two glass materials is required.

[0128] In conventional dispersive objective lens design, expanding the dispersion range and optimizing dispersion linearity are typically core design goals. The dispersive objective lens assembly 4 in this embodiment is designed based on the axial dispersion and aberrations generated by the GRIN fiber 2. This introduces a controllable nonlinear dispersion component through the GRIN fiber 2, and paired with a matching dispersive objective lens assembly 4, constructing an optical system with dispersion compensation. Based on the above analysis, to improve focal shift linearity and correct for higher-order aberrations, a ZEMAX lens assembly was designed using a combination of positive and negative lenses with opposite optical powers. By rationally allocating the optical power of each lens, two glasses from the Schott glass library, P-BK7 and SF5, were selected as the initial structure for the dispersive objective lens assembly 4.

[0129] To optimize the focusing performance of a secondary dispersive objective lens and achieve on-axis convergence of multi-wavelength monochromatic light, axial spherical aberration correction is required. Therefore, during the parameter design process for the secondary dispersive objective lens, a system aberration correction model is constructed. Based on this system aberration correction principle, the parameters of the secondary dispersive objective lens are designed. A spherical aberration evaluation model is established based on the initial structure of the dispersive objective lens assembly 4 simulated using ZEMAX software. Using the distance from the equivalent object point P of GRIN fiber 2 to the dispersive objective lens assembly 4 corresponding to different wavelengths as a multiple structural configuration, a "lens parameter-aberration" dataset is constructed. Combined with the PINN algorithm, axial spherical aberration constraints and Zernike aberrations are embedded as physical constraints in the loss function. This approach improves generalization capabilities by minimizing both data and physical losses, overcoming the limitations of the traditional damped least squares method in ZEMAX, which is susceptible to initial structure influences and has difficulty handling strongly nonlinear problems, leading to local optimal solutions.

[0130] The training principle diagram of the constructed system aberration correction model is as follows: Figure 9As shown, a ZEMAX simulation is first performed on glass selected based on the design theory of dispersive objective lens set 4. A lens parameter-aberration dataset is constructed, and a fully connected network is designed with Zernike coefficients and lens parameters as input and adjusted lens parameters as output. Data fitting terms and Zernike aberration constraints are then embedded in the loss function. The network is trained using the Adam optimizer, ensuring that the predictions match both the simulation data and the laws of optical physics. The adjusted lens parameters are fed back to ZEMAX for re-simulation, and the RMS wavefront error and Zernike aberrations are evaluated until the optical performance meets the requirements. If data is insufficient, additional sampling points are added during the ZEMAX simulation, such as increasing the number of sampling points within the original parameter space, with more object points and smaller wavelength intervals. If local optimality is encountered, the parameter bounds are relaxed. During the ZEMAX simulation, the range of the original design variables is expanded, such as increasing the lens curvature radius from ±2 mm to ±4 mm and the thickness range from 0.5 mm–1 mm to 0.3 mm–1.2 mm. This process is then repeated. This method achieves high-precision and low-cost aberration correction by combining physical equation constraints with data iteration. The specific process is as follows:

[0131] S4. Determine the structure of the dispersion objective lens group 4 based on the optimal pitch number of the GRIN optical fiber 2 and the dispersion performance required by the design, perform ZEMAX simulation on the structure of the dispersion objective lens group 4, and construct a lens parameter-aberration data set; the lens parameter-aberration training data set includes Zernike coefficients and lens parameters.

[0132] S5. Based on the PINN algorithm, a composite loss function including a data fitting term and a Zernike aberration constraint term is constructed; the Zernike aberration constraint term is determined by the axial spherical aberration constraint of the GRIN fiber 2 and the Zernike aberration of the dispersion objective lens group 4; the composite loss function L total The formula is as follows:

[0133]

[0134] Where, are the predicted value of axial spherical aberration model and the ZEMAX simulation value, N is the number of samples, β n is the aberration coefficient, W j is the aberration of the secondary dispersion objective, K is the number of sampling points, and n is the order parameter of the Zernike coefficient.

[0135] S6. Constructing an initial aberration correction model for the secondary dispersion objective lens, using a lens parameter-aberration dataset as input, a composite loss function as a convergence function, and outputting optimal lens parameters as a training goal, and training the initial aberration correction model until the aberration correction model outputs the optimal lens parameters;

[0136] S6.1. Constructing an initial aberration correction model for a secondary dispersion objective lens and initializing model parameters of the aberration correction model;

[0137] S6.2, using the lens parameter-aberration dataset constructed in step S4 as input, iteratively train the initial aberration correction model constructed in step S6.1, and calculate the value of the composite loss function constructed in step S5 based on the lens parameters output in this round of iteration, and judge whether the value of the composite loss function meets the convergence requirement. If the value of the composite loss function meets the convergence requirement, then judge whether the lens parameters output in this round of iteration meet the optical performance requirements. If they meet the optical performance requirements, the lens parameters output in this round of iteration are the optimal lens parameters. If they do not meet the optical performance requirements, optimize the lens parameter-aberration dataset, use the optimized lens parameter-aberration dataset as input, and perform a new round of iteration on the aberration correction model after this round of iterative training until the lens parameters output in the new round of iteration meet the optical performance requirements, i.e., obtain the optimal lens parameters.

[0138] If the composite loss function value does not meet the convergence requirements, the Adam optimizer is used to optimize the model parameters of the initial aberration correction model, and a new round of iteration is performed on the aberration correction model after the current round of iterative training. After the new round of iteration, it is judged whether the composite loss function value meets the convergence requirements. If it does not meet the requirements, the Adam optimizer is used to optimize the model parameters of the previous round of aberration correction model again until the composite loss function value meets the convergence requirements; if it meets the requirements, it is judged whether the lens parameters output by the new round of iteration meet the optical performance requirements. If the optical performance requirements are met, the lens parameters output by the new round of iteration are the optimal lens parameters. If it does not meet the optical performance requirements, the lens parameters-aberration data set are optimized again, and the optimized lens parameters-aberration data set is used as input to perform a new round of iteration on the aberration correction model after the previous round of iterative training until the lens parameters output by the new round of iteration meet the optical performance requirements, that is, the optimal lens parameters are obtained.

[0139] The process of judging whether the lens parameters meet the optical performance requirements is as follows:

[0140] Use ZEMAX to simulate the lens parameters output in step 6.2 to obtain the RMS wavefront error and Zernike aberration, and judge whether the RMS wavefront error and Zernike aberration meet the optical performance requirements. If so, the lens parameters meet the optical performance requirements; if not, the lens parameters do not meet the optical performance requirements.

[0141] S7. Use the optimal pitch number obtained in step S3 as the pitch number of the GRIN fiber 2, and use the optimal lens parameters obtained in step S6 as the parameters of the dispersion objective lens group 4 to complete the design of the secondary dispersion objective lens parameters.

[0142] The neural network training loss value is as follows Figure 10 As shown by Figure 10 The network converges normally. As the number of iterations increases, the model loss on the training set approaches zero and stabilizes, indicating that the model fits the training data well. The test error, used to assess the model's generalization ability, fluctuates within ±0.01 of the training loss, indicating strong generalization and effective overall training.

[0143] According to the initial structural parameters of the dispersion objective lens group 4, the Seidel aberration coefficient of the dispersion objective lens is simulated by ZEMAX software. The numerical analysis results are as follows: Figure 11 As shown, Figure 11 The spherical aberration values ​​of the system were generally high before correction. At a wavelength of around 460 nm, the spherical aberration exceeded 20 μm. After correction, the spherical aberration at the same wavelength was reduced to 10 μm. Within the operating wavelength range, the spherical aberration values ​​after correction were significantly lower than before correction, with the correction amplitude being more significant in the short-wavelength region. The spherical aberration values ​​corresponding to each wavelength were significantly optimized after correction, demonstrating the effectiveness of the closed-loop verification aberration correction model established using ZEMAX software combined with the PINN algorithm.

[0144] After optimization, the optimized dispersion objective lens group 42D layout diagram is obtained as follows: Figure 2 As shown in the figure, the RMS diffuse spot radius at the focal plane corresponding to each wavelength is used as the image quality evaluation index, and the quantitative evaluation and optimization of the spherical aberration correction effect is achieved by minimizing the diffuse spot size. In order to evaluate the system performance and analyze the system imaging quality, 12 wavelengths are equally divided and the paraxial focal plane point diagram at each wavelength is drawn as shown in the figure. Figure 12 As shown, Figure 12 The figure shows a spot diagram of light at different wavelengths. Each graph represents the distribution of light of a specific wavelength at the focal position. The spot diagram demonstrates the system's focusing performance for different wavelengths and how different wavelengths affect the scattering of the focal point. The diffuse spot at the focal point of all wavelengths in the figure is smaller than the Airy disk, indicating that the sensing system's focusing capability at different wavelengths reaches the diffraction limit, exhibiting good imaging quality that is suitable for high-precision applications and can provide reliable data support for displacement measurement. The chromatic focal shift is highly linear with wavelength, which can significantly reduce measurement errors caused by nonlinearity and improve measurement accuracy.

[0145] Analysis of the relationship between color focus shift and wavelength is as follows Figure 13 As shown, Figure 13 In the comparative analysis, the least square fitting and quadratic fitting are used. The least square fitting has higher linearity and the working wavelength Δ λ In the interval, the system axial dispersion Δ d The linearity is 0.9985. The linear regression relationship between the focal shift and the wavelength λ is: f(λ) = 25430λ-8563, and the theoretical resolution of the displacement measurement system can be obtained as:

[0146]

[0147] In the formula, k represents the slope of the linear equation, σ λ represents the resolution of the spectrometer, and the theoretical resolution of the system is about 25nm.

[0148] This embodiment provides a secondary dispersion objective lens, including a GRIN optical fiber 2 and a dispersion objective lens group 4; the incident end of the GRIN optical fiber 2 is used to receive incident light, and the output end is arranged at the front end of the dispersion objective lens group 4. The GRIN optical fiber 2 is used to perform primary dispersion on the incident light to form pre-dispersed light and transmit it to the dispersion objective lens group 4; Figure 2 As shown, the dispersive objective lens group 4 includes a first lens 41, a second lens 42, a third lens 43, and a fourth lens 44 arranged in sequence along the propagation direction of the pre-dispersed light; the dispersive objective lens group 4 is used to perform secondary dispersion on the pre-dispersed light. The pre-dispersed light passes through the first lens 41, the second lens 42, the third lens 43, and the fourth lens 44 in sequence to form axially dispersed light, which is then transmitted to the sample 7 to be measured;

[0149] In this embodiment, the pitch number of the GRIN fiber 2 is designed to be 5, the length is 5.1787 cm, and the distance between its output end and the first lens 41 is 99 mm; the material of the first lens 41 is P-BK7, the thickness is 2.005 mm, the distance between it and the second lens 42 is 1.001 mm, the front surface curvature radius is 20.642 mm, and the rear surface curvature radius is -33.429 mm; the material of the second lens 42 is P-BK7, the thickness is 1.997 mm, and the distance between it and the third lens 43 is 0 .999mm, the front surface curvature radius is 18.784mm, and the rear surface curvature radius is 32.388mm; the material of the third lens 43 is SF5, the thickness is 2.891mm, the distance between it and the fourth lens 44 is 1.005mm, the front surface curvature radius is 10.041mm, and the rear surface curvature radius is 50.527mm; the material of the fourth lens 44 is SF5, the thickness is 1.802mm, the front surface curvature radius is 28.316mm, and the rear surface curvature radius is 12.107mm.

[0150] Based on the secondary dispersion objective lens of this embodiment, a spectral confocal displacement sensing system is established, such as Figure 1 As shown, it includes a white light source 1, a secondary dispersion objective lens, a beam splitter 3, a confocal pinhole plate 5 and a spectrometer 6;

[0151] The secondary dispersion objective lens is composed of a GRIN fiber 2 and a dispersion objective lens group 4;

[0152] A white light source 1 is used to transmit incident light to the incident end of a GRIN optical fiber 2. The GRIN optical fiber 2 is used to perform primary dispersion on the incident light to form pre-dispersed light, and transmit the pre-dispersed light to a spectroscope 3. The spectroscope 3 is used to split the pre-dispersed light to form transmitted light, and transmit the transmitted light to a dispersion objective lens group 4. The transmitted light sequentially passes through a first lens 41, a second lens 42, a third lens 43, and a fourth lens 44 of the dispersion objective lens group 4 to perform secondary dispersion to form axially dispersed light, and is transmitted to a sample to be measured 7, which is placed on a measuring table 8.

[0153] The sample 7 to be tested generates reflected light after receiving the axially dispersed light. The reflected light passes through the fourth lens 44, the third lens 43, the second lens 42 and the first lens 41 in sequence, is reflected by the beam splitter 3, and finally enters the spectrometer 6 through the confocal pinhole plate 5.

[0154] The spectrometer 6 calculates the displacement value of the sample to be measured according to the spectral change of the reflected light.

[0155] In this embodiment, in order to increase the measurement range and improve the accuracy of the spectral confocal displacement sensing system, a secondary dispersion objective lens based on GRIN fiber 2 was designed, and the aberration was theoretically analyzed and corrected. A spectral confocal displacement sensing system based on GRIN fiber 2 was designed. Theoretical analysis found that the pitch number m of GRIN fiber 2 has a significant impact on the system's pre-dispersion chromatic focal shift linearity and equivalent spherical aberration; comparative analysis shows that when the pitch number m = 5, GRIN fiber 2 can achieve good chromatic focal shift linearity and dispersion range within the band, and the linearity R 2 It is about 95%, and the dispersion range can reach 1.496mm. Then, based on the GRIN fiber 2 pre-dispersion unit, the dispersion and aberration compensation correction is carried out through the secondary dispersion objective lens, and the positive and negative lens combination of P-BK7 and SF5 glass is optimized by using ZEMAX software to compensate for the pre-dispersion nonlinear characteristics of GRIN fiber 2, significantly expand the measurement range of the system, and achieve high linearity axial dispersion distribution. In order to correct the system aberration, an aberration correction method using PINN combined with ZEMAX to form a closed-loop verification is proposed, which reduces the system axial spherical aberration to within 10μm, reflecting the effectiveness of the correction technology. Simulation and experimental results show that the linearity of the system R 2 The optimized system has an RMS diffuse spot radius at each wavelength focus within the visible light band that is smaller than the Airy disk, reaching the diffraction limit and meeting the needs of high-precision displacement measurement.

Claims

1. A method for designing a secondary dispersion objective lens based on aberration correction, characterized in that: The following steps are involved: S1. Determining that the secondary dispersion objective lens includes a GRIN optical fiber (2) for performing primary dispersion and a dispersion objective lens group (4) for performing secondary dispersion, and determining that the initial structure of the dispersion objective lens group (4) includes a first lens (41), a second lens (42), a third lens (43), and a fourth lens (44) sequentially arranged along the direction of incident light, as well as the materials and surface shapes of the first lens (41), the second lens (42), the third lens (43), and the fourth lens (44); S2. According to the refractive index distribution constant of the GRIN optical fiber (2) material and based on the Cauchy dispersion formula, the equivalent points of the wavelength of the GRIN optical fiber (2) at M different pitch numbers are calculated, and based on the equivalent points, the preliminary optimal pitch number range of the GRIN optical fiber (2) is determined; M ≥ 5; S3, respectively calculating the equivalent spherical aberration of the GRIN optical fiber (2) at different pitch numbers within the preliminary optimal pitch number range, and determining the optimal pitch number of the GRIN optical fiber (2) based on the equivalent spherical aberration; S4, determining the structure of the dispersion objective lens group (4) according to the optimal pitch number of the GRIN optical fiber (2) and the dispersion performance required by the design, performing ZEMAX simulation on the structures of the first lens (41), the second lens (42), the third lens (43) and the fourth lens (44) in the dispersion objective lens group (4), and constructing a lens parameter-aberration data set; S5. Based on the PINN algorithm, a composite loss function including a data fitting term and a Zernike aberration constraint term is constructed; the Zernike aberration constraint term is determined by the axial spherical aberration constraint of the GRIN optical fiber (2) and the Zernike aberration of the dispersion objective lens group (4); S6, construct an initial aberration correction model for the secondary dispersion objective lens, using the lens parameter-aberration data set constructed in step S4 as input, and the composite loss function constructed in step S5 as a convergence function, to train the initial aberration correction model until the aberration correction model outputs the optimal lens parameters; S7. Using the optimal pitch number obtained in step S3 as the pitch number of the GRIN optical fiber (2), and using the optimal lens parameters obtained in step S6 as the parameters of the dispersion objective lens group (4), the design of the secondary dispersion objective lens is completed.

2. The method for designing a secondary dispersion objective lens based on aberration correction according to claim 1, wherein: The specific process of step S6 is as follows: S6.

1. Constructing an initial aberration correction model for a secondary dispersion objective lens and initializing model parameters of the aberration correction model; S6.2, using the lens parameter-aberration dataset constructed in step S4 as input, iteratively train the initial aberration correction model constructed in step S6.1, and calculate the value of the composite loss function constructed in step S5 based on the lens parameters output in this round of iteration, and judge whether the value of the composite loss function meets the convergence requirement. If the value of the composite loss function meets the convergence requirement, then judge whether the lens parameters output in this round of iteration meet the optical performance requirements. If they meet the optical performance requirements, the lens parameters output in this round of iteration are the optimal lens parameters. If they do not meet the optical performance requirements, optimize the lens parameter-aberration dataset, use the optimized lens parameter-aberration dataset as input, and perform a new round of iterative training on the aberration correction model after this round of iterative training until the lens parameters output in the new round of iteration meet the optical performance requirements, i.e., the optimal lens parameters are obtained; If the composite loss function value does not meet the convergence requirements, the Adam optimizer is used to optimize the model parameters of the initial aberration correction model, and a new round of iteration is performed on the aberration correction model after the current round of iterative training. After the new round of iteration, it is judged whether the composite loss function value meets the convergence requirements. If it does not meet the requirements, the Adam optimizer is used to optimize the model parameters of the previous round of aberration correction model again until the composite loss function value meets the convergence requirements; if it meets the requirements, it is judged whether the lens parameters output by the new round of iteration meet the optical performance requirements. If the optical performance requirements are met, the lens parameters output by the new round of iteration are the optimal lens parameters. If the optical performance requirements are not met, the lens parameters-aberration data set are optimized, and the optimized lens parameters-aberration data set is used as input to perform a new round of iteration on the aberration correction model after the previous round of iterative training until the lens parameters output by the new round of iteration meet the optical performance requirements, that is, the optimal lens parameters are obtained.

3. The method for designing a secondary dispersion objective lens based on aberration correction according to claim 2, wherein: The specific process of step S2 is as follows: S2.

1. Determine the refractive index distribution and light trajectory propagation function of the GRIN optical fiber (2) based on the refractive index distribution constant of the GRIN optical fiber (2) material and the Cauchy dispersion formula; S2.2, calculating the equivalent points of the wavelength of the GRIN optical fiber (2) at M different pitch numbers based on the refractive index distribution and the light trajectory propagation function of the GRIN optical fiber (2); wherein 5≤M≤10; S2.3, according to the equivalent point of the wavelength at different pitch numbers, determine the chromatic focus shift versus wavelength curve of the GRIN optical fiber (2) at different pitch numbers; S2.

4. Quantitatively analyze the linearity of the curve of chromatic focus shift versus wavelength, and determine the preliminary optimal pitch number range of the GRIN optical fiber (2) based on the linearity.

4. The method for designing a secondary dispersion objective lens based on aberration correction according to claim 3, wherein: The specific process of step S3 is as follows: S3.

1. Calculate the equivalent object points and equivalent image points of the GRIN optical fiber (2) at different pitch numbers within the preliminary optimal pitch number range, and calculate the equivalent spherical aberration of the GRIN optical fiber (2) at different pitch numbers within the preliminary optimal pitch number range based on the equivalent object points and equivalent image points; S3.2, based on the equivalent spherical aberration, respectively determine the curves of the equivalent spherical aberration of the GRIN optical fiber (2) varying with wavelength at different pitch numbers within the preliminary optimal pitch number range; S3.

3. Determine the curve with the best imaging performance from the curves of the equivalent spherical aberration of the GRIN optical fiber (2) varying with wavelength at different pitch numbers within the preliminary optimal pitch number range. The pitch number corresponding to the optimal curve is the optimal pitch number of the GRIN optical fiber (2).

5. The method for designing a secondary dispersion objective lens based on aberration correction according to claim 4, wherein: In step S5, the composite loss function L total The formula is as follows: Where, are the lens parameter values ​​output by the aberration correction model and the actual values ​​of the lens parameters obtained by ZEMAX simulation, N is the number of samples, K is the number of sampling points, and W j is the aberration of the secondary dispersion objective, β n is the aberration coefficient, W(ρ,θ) is the Zernike aberration function, and n is the order parameter of the Zernike coefficient.

6. The method for designing a secondary dispersion objective lens based on aberration correction according to any one of claims 1 to 5, characterized in that: In step 1, the first lens (41) is a biconvex lens, the material of which is P-BK7; the second lens (42) is a meniscus lens, which is bent toward the side of the incident light and the material of which is P-BK7; the third lens (43) is a meniscus lens, which is bent toward the side of the incident light and the material of which is SF5; the fourth lens (44) is a meniscus lens, which is bent toward the side of the incident light and the material of which is SF5.

7. A secondary dispersion objective lens, characterized in that: Obtained by the design method of a secondary dispersion objective lens based on aberration correction according to any one of claims 1 to 6, comprising a GRIN optical fiber (2) and a dispersion objective lens group (4); The incident end of the GRIN optical fiber (2) is used to receive incident light, and the output end is arranged at the front end of the dispersion objective lens group (4). The GRIN optical fiber (2) is used to perform primary dispersion on the incident light to form pre-dispersed light, and transmit the pre-dispersed light to the dispersion objective lens group (4); the dispersion objective lens group (4) is used to perform secondary dispersion on the pre-dispersed light to form axially dispersed light, and transmit the pre-dispersed light to the sample to be measured (7). The dispersion objective lens group (4) comprises a first lens (41), a second lens (42), a third lens (43) and a fourth lens (44) which are sequentially arranged along the propagation direction of the pre-dispersed light; The pre-dispersed light passes through the first lens (41), the second lens (42), the third lens (43) and the fourth lens (44) in sequence to form axially dispersed light, which is then transmitted to the sample to be measured (7); The pitch number of the GRIN optical fiber (2) ranges from 4 to 6; Define the surface where the pre-dispersed light enters as the front surface, and the surface where the pre-dispersed light exits as the back surface; The first lens (41) is a biconvex lens, the front surface curvature radius ranges from 20.480 mm to 20.808 mm, and the rear surface curvature radius ranges from -33.696 mm to -33.162 mm; The second lens (42) is a meniscus lens, the front surface curvature radius ranges from 18.634 mm to 18.934 mm, and the rear surface curvature radius ranges from 32.137 mm to 32.639 mm; The third lens (43) is a meniscus lens, the front surface curvature radius ranges from 9.961 mm to 10.121 mm, and the rear surface curvature radius ranges from 50.124 mm to 50.932 mm; The fourth lens (44) is a meniscus lens, the front surface curvature radius ranges from 28.088 mm to 28.540 mm, and the rear surface curvature radius ranges from 12.011 mm to 12.203 mm; The thickness of the first lens (41) ranges from 1.984 mm to 2.016 mm, and the distance between the first lens (41) and the second lens (42) ranges from 0.992 mm to 1.008 mm; The thickness of the second lens (42) ranges from 1.984 mm to 2.016 mm, and the distance between the second lens (42) and the third lens (43) ranges from 0.992 mm to 1.008 mm; The thickness of the third lens (43) ranges from 2.867 mm to 2.913 mm, and the distance between the third lens (43) and the fourth lens (44) ranges from 0.992 mm to 1.008 mm; The thickness of the fourth lens (44) ranges from 1.786 mm to 1.814 mm.

8. The secondary dispersion objective lens according to claim 7, wherein: The first lens (41) is made of P-BK7, has a thickness of 2.005 mm, a front surface curvature radius of 20.642 mm, a rear surface curvature radius of -33.429 mm, and a spacing of 1.001 mm from the second lens (42); the second lens (42) is made of P-BK7, has a thickness of 1.997 mm, a front surface curvature radius of 18.784 mm, a rear surface curvature radius of 32.388 mm, and a spacing of 1.001 mm from the third lens (42). ) is 0.999mm; the material of the third lens (43) is SF5, the thickness is 2.891mm, the front surface curvature radius is 10.041mm, the rear surface curvature radius is 50.527mm, and the distance between the third lens (43) and the fourth lens (42) is 1.005mm; the material of the fourth lens (44) is SF5, the thickness is 1.802mm, the front surface curvature radius is 28.316mm, and the rear surface curvature radius is 12.107mm.

9. The secondary dispersion objective lens according to claim 8, wherein: The pitch number of the GRIN optical fiber (2) is 5, the length is 5.1787 cm, and the distance between the output end and the first lens (41) is 99 mm.

10. A spectral confocal displacement sensing system, characterized by: It includes a white light source (1), a secondary dispersion objective lens, a spectroscope (3), a confocal pinhole plate (5) and a spectrometer (6); The secondary dispersion objective lens is the secondary dispersion objective lens according to any one of claims 7 to 9; The white light source (1) is used to emit incident light to the incident end of the GRIN optical fiber (2); The GRIN optical fiber (2) is used to perform first-order dispersion on the incident light to form pre-dispersed light, and transmit the pre-dispersed light to the spectroscope (3); The beam splitter (3) is used to split the pre-dispersed light to form transmitted light, and transmit the transmitted light to the dispersion objective lens group (4); The transmitted light is sequentially dispersed by the first lens (41), the second lens (42), the third lens (43) and the fourth lens (44) of the dispersion objective lens group (4) to form axially dispersed light, which is then transmitted to the sample to be measured (7); The sample to be tested (7) generates reflected light after receiving the axially dispersed light, and the reflected light passes through the fourth lens (44), the third lens (43), the second lens (42), and the first lens (41) in sequence, and then is reflected by the beam splitter (3), and finally enters the spectrometer (6) through the confocal pinhole plate (5); The spectrometer (6) calculates the displacement value of the sample to be measured according to the spectral change of the reflected light.

Images