A method and system for designing freeform surfaces of progressive multifocal lenses

Abstract

This invention relates to the field of progressive multifocal lens (PAL) design and manufacturing technology, specifically disclosing a method and system for designing freeform surfaces of progressive multifocal lenses. This method employs a curvature superposition (CS) algorithm instead of the traditional differential geometry (DG) algorithm, resulting in better consistency between the spherical power distribution and the design values. Based on this, a fast Fourier transform (FFT) is used to optimize the initial freeform surface, effectively reducing unwanted astigmatism and expanding the progressive corridor width, significantly enhancing visual function and wearing comfort. The manufactured product successfully replicates the simulated optical performance and maintains optimized characteristics even when combined with standard cylindrical astigmatism correction, proving the method's practicality and feasibility. This design method, combining the CS algorithm and FFT filtering, effectively improves the optical performance and wearing comfort of PAL, providing a new path for PAL design and optimization.

Description

Technical Field

[0001] This invention relates to the field of progressive multifocal lens design and manufacturing, and more specifically, to a method and system for designing freeform surfaces of progressive multifocal lenses. Background Technology

[0002] Progressive Addition Lenses (PAL) are lenses that utilize a freeform surface to achieve a continuous change in optical power. Through a transition zone (also called a fusion zone, transition corridor, or progressive channel) with progressively increasing refractive power, they achieve a natural connection between the surface shape and refractive power of the distance and near vision zones, resulting in continuous, uninterrupted, and clear imaging at various distances. However, the continuously changing curvature design inevitably introduces unintended astigmatism beyond the corrected prescription astigmatism, which is the main reason for their poor wearing comfort and difficulty in adaptation.

[0003] Unintended astigmatism cannot be completely eliminated; it can only be optimized and redistributed through design. Traditional design employs the classic Differential Geometry (DG) algorithm, which transforms the target photometric distribution (spherical, cylindrical, and irradiated) set by the optical designer into the three-dimensional geometry (sagitta) of the lens surface. The advantage of this algorithm is that it traditionally provides a wider channel and a lower initial peak astigmatism. However, the consistency between the generated spherical power distribution and the target design value is relatively insufficient, and there is still room for improvement in channel width and unintended astigmatism. Summary of the Invention

[0004] This invention aims to overcome the shortcomings of at least one of the above-mentioned prior art and provides a progressive multifocal lens (PAL) freeform surface design method based on curvature superposition and Fourier transform filtering. It adopts the curvature superposition (CS) algorithm and fast Fourier transform (FFT) processing to replace the traditional differential geometry (DG) algorithm, effectively reducing the unexpected astigmatism generated by the PAL freeform surface during simulation and manufacturing, while expanding the progressive channel, thereby improving the optical performance and wearing comfort of PAL.

[0005] The technical solution adopted by this invention is to provide a method for designing a freeform surface of a progressive multifocal lens, comprising the following steps: S1. Based on the refractive power and illumination parameters provided by the lens prescription, an initial freeform surface is constructed by iteratively splicing segmented circular arcs. S2. Establish a polar coordinate system based on the optical center of the initial freeform surface, define the radial direction as ρ and the circumferential direction as θ, calculate the orthogonal principal curvature at any point on the surface, and further calculate the spherical power of the initial freeform surface. S(ρ,θ), Cylindrical power C(ρ,θ) Total astigmatism (AST); S3. Iteratively optimize the initial freeform surface to reduce the AST. When the iteration terminates, output the final nth iteration optimization result Zn as the vector height to establish the optimized surface.

[0006] Furthermore, the initial freeform surface described in step S1 is constructed using the following equations:

[0007] Among them, R n r n and Z n Let the radius of curvature, vertex distance, and sag at the nth discrete point be represented respectively. This iterative relationship must satisfy the following boundary conditions: .

[0008] Furthermore, the iterative optimization described in step S3 applies a Fast Fourier Transform (FFT) filter, wherein the two-dimensional forward Fourier transform and the two-dimensional inverse Fourier transform are respectively performed using the following equations:

[0009]

[0010] in, and These represent the two-dimensional angular frequencies in the ρ and θ directions, respectively, where i represents the imaginary unit. The transfer function corresponding to the m-th angular frequency is smoothed in the frequency domain by attenuating high-frequency components. This process follows the basic filtering model. ,in It is the Fourier transform of the input signal. It is the filter transfer function, defined as:

[0011] Where, σ θ and σ ρ These represent the optimization parameters in the ρ and θ directions, respectively.

[0012] Furthermore, the iteration termination condition in step S3 is that the distance refractive power Fd, the near refractive power Fn, and the downlight ADD all converge to the prescription value, and the decrease in total astigmatism AST tends to level off, with no significant reduction in further iterations.

[0013] Furthermore, the optimization parameter σ θ ∈[0.05,0.30], σ ρ∈[0.05,0.30]. The optimization parameters are adjustable empirical design parameters. In implementation, it is recommended to use normalized spatial frequencies, with typical values ​​taken from the above reference interval.

[0014] Further, in step S2, the orthogonal principal curvatures k1 and k2 at any point on the surface are obtained by solving the eigenvalues ​​of the shape operator. The spherical power S(ρ,θ), cylindrical power C(ρ,θ), and total astigmatism AST of the initial freeform surface are calculated using the following equations:

[0015]

[0016] .

[0017] Furthermore, the optimization parameter σ θ ∈[0.05,0.30], σ ρ ∈[0.05,0.30].

[0018] In one or more embodiments of the present invention, initial freeform surfaces were first constructed based on the Curvature Superposition (CS) algorithm and the traditional Differential Geometry (DG) algorithm, respectively. Comparison results showed that the CS algorithm had better consistency with the design values ​​in terms of spherical power distribution, but had limitations in terms of channel width and maximum unintended astigmatism. Subsequently, a Fast Fourier Transform (FFT) filter was applied to optimize the PAL surface, reducing total astigmatism by 26% and increasing the usable range of the asymptotic corridor width by 2.3 times. Finally, this embodiment compared the key optical performance parameters of the initial design, the manufactured product, and the optimization results. The manufactured product successfully reproduced the simulated optical performance, and even when used in conjunction with standard cylindrical lens astigmatism correction, it maintained its optimized characteristics, confirming the practical feasibility of the method.

[0019] Another objective of this invention is to provide a progressive multifocal lens freeform surface design system based on curvature superposition and Fourier transform filtering, comprising: Data input unit: used to input prescription parameters, including distal zone vertex refractive power, near zone vertex refractive power, and distal zone reference point position; Surface building unit: Based on prescription parameters, an initial free surface is constructed by iteratively splicing segmented circular arcs; Parameter calculation unit: Based on the initial freeform surface optical center, a polar coordinate system is established to calculate the orthogonal principal curvature at any point on the surface, and then the spherical power, cylindrical power and total astigmatism are calculated; Iterative optimization unit: The initial freeform surface is iteratively optimized by applying a fast Fourier transform filter, and frequency domain smoothing is achieved by attenuating high-frequency components to reduce AST, until the iteration terminates; Output unit: Outputs the final iterative optimization result vector height to establish the optimized surface.

[0020] Another object of the present invention is to provide a non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that the computer program, when executed by a processor, implements the progressive multifocal lens freeform surface design method as described in any one of claims 1 to 5.

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention provides a method and system for designing freeform surfaces of progressive multifocal lenses. It employs a curvature superposition (CS) algorithm instead of the traditional differential geometry algorithm, resulting in better consistency between the spherical power distribution and the design values. Furthermore, it combines this with Fast Fourier Transform (FFT) to optimize the initial freeform surface, reducing total astigmatism by 26% and expanding the usable range of the progressive corridor width by 2.3 times, significantly enhancing visual effectiveness and comfort. The manufactured product successfully replicates the simulated optical performance and maintains optimized characteristics even when combined with standard cylindrical astigmatism correction, proving the method's practicality and feasibility. This design method, combining the CS algorithm and FFT filtering, effectively improves the optical performance and wearing comfort of PAL lenses, providing a new path for PAL design and optimization. Attached Figure Description

[0022] Figure 1 A flowchart for optimizing the PAL surface using a Fast Fourier Transform filter.

[0023] Figure 2 PAL sag surface profiles calculated by the DG algorithm (a) and the CS algorithm (b). (c) Comparison of DG and CS algorithms based on Zernike fringe coefficient fitting.

[0024] Figure 3 The PAL spherical power distribution curves calculated by the DG algorithm (a1) and the CS algorithm (a2) are shown. (b1) and (b2) are the corresponding cylindrical power distribution curves. The red dashed line is the vertical meridian, and the white dashed line is the horizontal meridian.

[0025] Figure 4 From Figure 3 The spherical / cylindrical diopter distributions extracted from the vertical meridian (red dashed line) and horizontal meridian (white dashed line). (a) Compared to the design target curve (red line), the green and blue solid lines represent the spherical diopter functions along the vertical meridian using the DG algorithm and the CS algorithm, respectively, while the dashed lines represent the corresponding cylindrical diopter. (b) From Figure 3 Extraction of the horizontal meridian (white dashed line) in b1 and b2, and calculation results of the cylindrical power function along the horizontal meridian by the two algorithms.

[0026] Figure 5This describes the evolution of four key PAL parameters (near zone refractive power Fn, far zone refractive power Fd, downlighting ADD, and total astigmatism AST) during a continuous optimization cycle.

[0027] Figure 6 The diopter changes of the spherical (a) and cylindrical (b) components designed for the application of the CS algorithm before and after optimization.

[0028] Figure 7 The figures are the measurements of S (a1) and C (b1), where the inset is a designed PAL photograph, and (a2) and (b2) are the measurements of spherical / cylindrical diopter in the distance zone +1.00×180, where the cylindrical diopter is fabricated on the rear surface. Detailed Implementation

[0029] The present invention will now be further illustrated with specific examples. The following embodiments are merely illustrative and do not constitute a limitation thereof. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0030] 1. Traditional Differential Geometry (DG) Algorithm After determining the meridional refractive power and contour distribution, the vertex lens refractive power must be extended to the entire lens surface, and the sag must be calculated using the conventional differential geometry (DG) algorithm. Details of the DG algorithm can be found in equation (1): (1) Where (ξ, η, ζ) represents the center of curvature at (x, y) on the surface, and u is the integral function of the center of curvature.

[0031] 2. The curvature superposition (CS) algorithm of the present invention This invention proposes a novel curvature superposition (CS) algorithm for constructing freeform surfaces of PAL, as defined in equation (2): (2) Where Rn, rn, and Zn represent the radius of curvature, vertex distance, and sag at the nth discrete point, respectively. This iterative relationship must satisfy the following boundary conditions: This method can more accurately describe non-circular curves, accommodating both on-axis and off-axis curvature center positions. Therefore, the local radius of curvature at any given point can accurately reflect the radius of curvature.

[0032] 3. Total Astigmatism (AST) Calculation Relationship between Total Astigmatism (AST) and Unintended Astigmatism: This invention employs a "separate design of front and rear surfaces." The front surface is a progressive surface, its function being to achieve a progressive distribution of spherical power in the prescription (distribution of spherical power in the distance zone, near zone, and progressive zone). If the prescription requires cylindrical components, the rear surface provides cylindrical correction. Therefore, the cylindrical power at any point on the front surface originates entirely from the curvature change during the freeform surface design, and its physical meaning is unintended astigmatism. Thus, the definition of the total astigmatism value (AST) for the freeform surface in this invention can be used to quantitatively characterize the total amount of unintended astigmatism introduced by the continuous change in curvature of the freeform surface. This definition of the front surface remains valid regardless of whether the rear surface requires independent cylindrical power correction.

[0033] The optical performance of a PAL (parameter for optical optical systems) is typically evaluated using parameters such as optical diopter, astigmatism, and trapezoidal distortion. The orthogonal principal curvatures k1 and k2 at any point on the surface are calculated as follows: The principal curvature along the meridian tangent is denoted as k1, which is the curvature of the meridian itself, k1 = 1 / r(u). The principal curvature perpendicular to the meridian tangent (i.e., along the hyperbolic contour) is denoted as k2. This requires calculating the first and second partial derivatives of the function z with respect to x and y, substituting them into the principal curvature formula (or constructing the Weingarten matrix and finding eigenvalues) for numerical solution to obtain k1 and k2 at any point (x, y).

[0034] Based on these principal curvatures, the key optical properties of spherical (S) refractive power and cylindrical (C) refractive power can be derived using the refractive index n, and their expressions are shown in formulas (3) and (4) in polar coordinates.

[0035] (3) (4) Therefore, the total astigmatism (AST) of PAL is defined as follows: .

[0036] 4. Fast Fourier Transform (FFT) The Fast Fourier Transform (FFT) is an efficient algorithm for computing the Discrete Fourier Transform (DFT) or its inverse (IDFT) of a sequence. The two-dimensional (2D) forward and inverse Fourier transforms are given by equations (5) and (7), respectively: (5) (7) in and These represent the two-dimensional angular frequencies in the directions ρ and θ, respectively; i represents the imaginary unit; and This corresponds to the transfer function at the m-th angular frequency. Frequency domain smoothing is achieved by attenuating high-frequency components. This process follows the basic filtering model: ,in It is the Fourier transform of the input signal. It is the filter transfer function, defined as: (8) Where σθ and σρ represent the optimization parameters in the ρ and θ directions, respectively.

[0037] 5. Optimize the iterative process Guided by the basic principles of PAL optimization, the target distribution of spherical power (i.e., far-field refractive power Fd, near-field refractive power Fn, and down-light ADD) needs to remain unchanged. Conversely, irregular astigmatism in the fusion zone (quantified by the total astigmatism value AST) needs to be suppressed or eliminated. The overall optimization process is as follows: Figure 1 As shown, the specific steps include: S1. Initial Iteration Settings: Input the initial freeform surface elevation data of the lens generated by the initial design algorithm (the curvature superposition algorithm as described in claim 1), denoted as Z0, and set the iteration count m=0. Calculate the first derivative of z with respect to x and y, and substitute them into the principal curvature formula to obtain the curvature k in different α directions. Derive the spherical power (D), cylindrical power (C), and axial power (X) based on the curvature k and refractive index n.

[0038] S2, Frequency Domain Transformation and Filtering: For the surface data Z in the current iteration m A Fast Fourier Transform (FFT) is performed to convert the data to the frequency domain. Then, the optimization function defined in claim 2 is applied to selectively suppress spatial frequency components in specific directions (ρ and θ directions) within the frequency domain, thereby achieving a smooth adjustment of the surface curvature. After filtering, an Inverse Fast Fourier Transform (IFFT) is performed to convert the data back to the spatial domain, yielding the preliminarily optimized new surface elevation data Z. m+1 .

[0039] S3. Optical Performance Evaluation and Constraint Judgment: Based on Z m+1 Calculate the key optical performance parameters of the new surface, including: far-field spherical power Fd. m+1 Near-field spherical power Fn m+1 ; In practice, add light to ADD m+1 (calculated as Fn) m+1 - Fd m+1 ); and total astigmatism value AST m+1 The above parameters are compared with the preset target value (Fd). m , Fn m ADD m ) and the previous iteration state (AST) m A comparison and judgment are performed. The judgment criteria must simultaneously meet the following: Prescription restrictions: Fd m+1With Fn m+1 It needs to steadily approach the target prescription value to ensure that the core corrective function remains unchanged.

[0040] Performance optimization goal: AST m+1 It should be significantly lower than AST. m This means that unintended astigmatism is effectively suppressed.

[0041] S4. Iterative Decision: If all the judgment results in step S3 satisfy the preset convergence conditions, then the current Z... m+1 The optimized surface Z is determined to meet the requirements. m+1 Then proceed to step S5; if any condition is not met, then use Z m+1 As the new Z m The iteration count m is incremented by 1, and the process returns to step S2 for the next optimization loop. The loop stops when all constraints are met or the preset maximum number of iterations is reached.

[0042] S5. Output the final optimization result: When the iteration loop terminates, output the final optimization result Z of the nth iteration. n .

[0043] Experiment 1 Initial Freeform Surface Design This embodiment uses a 60mm lens diameter, with the PAL surface located on the front surface of the lens. The vertex diopter of the distance and near vision zones is set to Fd = +4.00D and Fn = +6.00D, respectively, equivalent to an additional +2.00D. The progressive corridor length is defined as 22mm, and the distance reference point (DRP) is located 11mm above the lens geometric center (point O). The lens material is polycarbonate (PC) with a refractive index of 1.586. This set of data represents one of the more common prescription ranges in clinical practice, demonstrating that the above method can effectively reduce unintended astigmatism, and that this method itself can be extended to other parameter ranges.

[0044] Using these target parameters, the sagitta of the PAL surface was calculated using both the traditional DG method (Equation 1) and the newly proposed CS method (Equation 2); the resulting profiles are shown below. Figure 2 As shown in (a) and (b).

[0045] To facilitate a quantitative comparison of the two algorithms, we used Zernike polynomials to fit the freeform surface. Figure 2(c) shows a comparison of the absolute values ​​of the first seven Zenick coefficients derived from these fitting results. The red and blue bars in the figure represent the coefficients of the DG and CS algorithms, respectively. The chart presents the magnitudes of the Zenick coefficients in logarithmic form, facilitating the evaluation of the performance differences between the two algorithms. Of particular note are the second-order coefficients (n=2) corresponding to the spherical and cylindrical corrections commonly used in ophthalmic optics, while the first-order coefficients (n=1) represent prism correction. The results show that the surfaces generated by the two algorithms are essentially equivalent, with the main differences lying in the higher-order terms.

[0046] Based on the aforementioned method, the main curvatures (k1 and k2) of the surface generated by the two algorithms are derived, and S and cylindrical power are calculated using formulas (3) and (4). The resulting refractive power curves are shown in the figure. Figure 3 The calculation results of the DG (a1, b1) and CS (a2, b2) algorithms were compared. The left column (a1, a2) shows the spherical power distribution curves, demonstrated using the progressive scaling function of ADD=+2.00 D; the right column (b1, b2) presents the corresponding cylindrical power (astigmatism) distribution curves. It is worth noting that although the cylindrical power value generated by the CS algorithm is larger than that of the DG algorithm, it provides a larger usable area in both the telephoto and near-field regions.

[0047] To more clearly illustrate the differences between the DG and CS algorithms, we start from... Figure 3 The spherical / cylindrical refractive power distributions along the vertical meridian (red dashed line) and the horizontal meridian (white dashed line) were extracted and displayed. Figure 4 . Figure 4 (a) The S-curve and cylindrical diopter distribution curves along the vertical meridian were compared. The solid red line represents the design curve, while the green and blue curves represent the DG and CS algorithms, respectively. Compared to the DG algorithm, the CS algorithm better matches the design value in terms of spherical power. The dashed lines correspond to the cylindrical diopter distribution curves of the same algorithm. The DG algorithm has a higher corridor cylindrical power than the CS algorithm, but DG performs better in non-target astigmatism in the far and near use areas. Corridor width (CW) is defined as the width of the area where astigmatism is less than 0.5D. This parameter is displayed by a double-headed arrow (astigmatism ≤ 0.5D) at the center point (y = 0mm), where the cylindrical power is... Figure 4 (b) reaches the minimum value. The CS algorithm has two limitations: the corridor width is smaller than that of the traditional DG method, and the maximum non-target astigmatism value is larger.

[0048] Experiment 2 Optimization of Freeform Surfaces To further reduce maximum astigmatism and increase the asymptotic channel width, an initial freeform surface of the PAL was first constructed using the CS algorithm based on the target parameters set in Experiment 1. Then, the S and C distributions of this surface were calculated using formulas (3) and (4). Unintended astigmatism mainly occurs in the fusion region of the irregular freeform surface of the PAL, due to the difference between the two orthogonal principal curvatures k1 and k2 in this region. Therefore, to mitigate this effect, we applied a Fast Fourier Transform filter to smooth the PAL surface according to formulas (5)-(8) given in the Methods section to reduce unintended astigmatism.

[0049] In this embodiment, the optimized parameter (σ) was selected. θ and σ ρ The appropriate value of σ was determined, and the corresponding optimization function was calculated. It is suggested that when using normalized spatial frequency, σ... θ ∈[0.05,0.30], σ ρ ∈[0.05,0.30]. This range is only a reference interval and is not a necessary limitation of the present invention. Subsequently, the optimized PAL surface was obtained through an iterative process. Guided by the basic principles of PAL optimization, the target distribution of spherical power (i.e., far-field refractive power Fd, near-field refractive power Fn, and under-illuminated power ADD) needs to remain unchanged. Conversely, irregular astigmatism in the fusion zone (quantified by the total astigmatism value AST) needs to be suppressed or eliminated. The overall optimization process is as follows: Figure 1 As shown, when the iteration loop terminates, the final optimization result Zn of the nth iteration is output.

[0050] After applying the CS algorithm and the FFT-based optimization method, this embodiment tracks the evolution of four key PAL parameters (Fn, Fd, ADD, and total AST) over consecutive optimization cycles, such as... Figure 5 As shown, cycle 0 corresponds to the initial unoptimized design. In the early cycles, the refractive power values ​​of Fn, Fd, and ADD underwent rapid initial adjustments, subsequently converging to the target design values. In contrast, the total AST showed a continuous and gradual decreasing trend throughout the optimization process. Based on the dual criteria of stable zone refractive power and minimizing AST, the surface in the 11th optimization cycle was determined to be optimal, and its detailed parameters are listed in Table 1 (see next page). This resulted in a total AST of 14.13 D in the 11th optimization cycle. cm², compared to the initial value of 19.13 D The cm² was reduced by 26%. This indicates that the optimization method can be widely applied to PAL design and can effectively suppress irregular astigmatism in the fusion region.

[0051] The changes in refractive power of the spherical (a) and cylindrical (b) components designed using the CS algorithm before and after optimization are as follows: Figure 6 As shown. Figure 6(a) shows that the changes in spherical power are mainly concentrated in the channel and aberration zones, while the spherical power values ​​in the distance and near zones remain basically unchanged. Figure 6 The same trend was observed in the cylinder power distribution plot in (b), showing a significant reduction in astigmatism of approximately 1.70 D within the fusion zone. Furthermore, the cylinder power values ​​in both the distance and near vision zones remained largely stable. This result aligns with the optimization principles of progressive multifocal lenses, namely, achieving a more uniform distribution of irregular astigmatism, characterized by a reduction in spatial range and a decrease in peak level.

[0052] After optimization using the CS algorithm, it still needs to be processed into a lens, and... Figure 3 The CS design refractive power distribution is compared to demonstrate that the optimized design does not change the refractive power distribution required by the lens prescription. The measured refractive power of the manufactured lens is shown below. Figure 7 As shown, it is similar to Figure 3 The simulated curves shown in (a2) and (b2) are highly consistent. Figure 7 (a1) presents a spherical photometric map, confirming the successful realization of the refractive power gradient from the far-field to the near-field region. Figure 7 (b1) shows the corresponding cylindrical photometric diagram, which visually presents the distribution of unexpected astigmatism. An embedded photograph of the lens manufacturing process is included in the diagram for reference. Figure 7 (a2) and (b2) illustrate the performance of the optimized lens in a standard user prescription. (a2) and (b2) respectively present the spherical and cylindrical power graphs after adding cylindrical correction (+1.00D, 180°) to the posterior surface of the lens. It should be noted that this cylindrical correction is applied only to the distance vision zone to correct astigmatism related to distance vision. Overall, the graphs bridge the gap between simulation and physical manufacturing, confirming that the optimized freeform surface can be precisely manufactured and verifying that the final product retains its intended optical gradation characteristics even when combined with standard astigmatism correction.

[0053] Table 1 compares and summarizes the key optical performance parameters of PAL across three stages (initial design, finished product manufacturing, and optimization results). The data fully demonstrate the effectiveness of the FFT-based optimization process. Most notably, the maximum cylindrical diopter (C) was significantly reduced. maxThe peak unintended astigmatism value (i.e., the maximum value) decreased significantly from 3.27D in the initial design to 1.49D in the optimized version, indicating that the peak unintended astigmatism was significantly suppressed. Simultaneously, the corridor width (defined as the area with astigmatism ≤ 0.50D) expanded from 3.01mm to 6.93mm, an increase of approximately 2.3 times, which greatly improved the usable range of mid-range vision. The optimization process successfully maintained the core functional requirements, with the far-field power Fd, near-field power Fn, and downlight ADD remaining near the target values. The manufactured lens successfully transitioned from simulation to practical application, showing a high degree of consistency with the designed PAL in terms of ADD value. The corridor width and area width of the manufactured lens are highly consistent with the design intent, confirming the practicality of the method.

[0054] Table 1. Key optical parameters of PAL design, manufacturing, and optimization

[0055] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the technical solutions of the present invention, and are not intended to limit the specific implementation of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the claims of the present invention should be included within the protection scope of the claims of the present invention.

Claims

1. A method for designing freeform surfaces of progressive multifocal lenses, characterized in that, Includes the following steps: S1. Based on the refractive power and illumination parameters provided by the lens prescription, an initial freeform surface is constructed by iteratively splicing segmented circular arcs. S2. Establish a polar coordinate system based on the optical center of the initial freeform surface, define the radial direction as ρ and the circumferential direction as θ, calculate the orthogonal principal curvature at any point on the surface, and further calculate the spherical power of the initial freeform surface. S(ρ,θ), Cylindrical power C(ρ,θ) Total astigmatism (AST); S3. Iteratively optimize the initial freeform surface to reduce the AST. When the iteration terminates, output the final nth iteration optimization result Zn as the vector height to establish the optimized surface.

2. The design method according to claim 1, characterized in that, The initial freeform surface described in step S1 is constructed using the following equations: Among them, R n r n and Z n Let the radius of curvature, vertex distance, and sag at the nth discrete point be represented respectively. This iterative relationship must satisfy the following boundary conditions: .

3. The design method according to claim 1, characterized in that, Step S3 describes the iterative optimization using a Fast Fourier Transform (FFT) filter, where the two-dimensional forward Fourier transform and the two-dimensional inverse Fourier transform are respectively implemented using the following equations: in, and These represent the two-dimensional angular frequencies in the ρ and θ directions, respectively, where i represents the imaginary unit. The transfer function corresponding to the m-th angular frequency is smoothed in the frequency domain by attenuating high-frequency components. This process follows the basic filtering model. ,in It is the Fourier transform of the input signal. It is the filter transfer function, defined as: Where, σ θ and σ ρ These represent the optimization parameters in the ρ and θ directions, respectively.

4. The design method according to claim 3, characterized in that, The iteration termination condition in step S3 is that the distance refractive power Fd, the near refractive power Fn, and the downlight ADD all converge to the prescription value, and the decrease in total astigmatism AST tends to level off, and there is no significant reduction after further iteration.

5. The design method according to claim 3, characterized in that, The optimization parameter σ θ ∈[0.05,0.30], σ ρ ∈[0.05,0.30].

6. The design method according to claim 1, characterized in that, In step S2, the orthogonal principal curvatures k1 and k2 at any point on the surface are obtained by solving the eigenvalues ​​of the shape operator. The spherical power S(ρ,θ), cylindrical power C(ρ,θ), and total astigmatism AST of the initial freeform surface are calculated using the following equations: 。 7. A system for designing freeform surfaces of progressive multifocal lenses based on curvature superposition and Fourier transform filtering, characterized in that, include: Data input unit: used to input prescription parameters, including distal zone vertex refractive power, near zone vertex refractive power, and distal zone reference point position; Surface building unit: Based on prescription parameters, an initial free surface is constructed by iteratively splicing segmented circular arcs; Parameter calculation unit: Based on the initial freeform surface optical center, a polar coordinate system is established to calculate the orthogonal principal curvature at any point on the surface, and then the spherical power, cylindrical power and total astigmatism are calculated; Iterative optimization unit: The initial freeform surface is iteratively optimized by applying a fast Fourier transform filter, and frequency domain smoothing is achieved by attenuating high-frequency components to reduce AST, until the iteration terminates; Output unit: Outputs the final iterative optimization result vector height to establish the optimized surface.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the progressive multifocal lens freeform surface design method as described in any one of claims 1 to 6.

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