A method for optimizing design of an end face parameter of a fiber connector based on Zemax

CN122886343APending Publication Date: 2026-10-09BEIJING AEROSPACE GUANGHUA ELECTRONIC TECH CO LTD
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Patent Information

Application Number
CN202610785022.6
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-06-02
Publication Date
2026-10-09

AI Technical Summary

Technical Problem

a)建模过程繁琐,当需要优化多个参数时,手动调整参数并重复仿真效率极低;

Benefits of technology

(1)实现全自动的光纤连接器端面参数优化,大幅缩短设计周期;

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Abstract

A kind of Zemax-based fiber connector end face parameter optimization design method, S1, establishes the initial model of fiber connector in Zemax, determines design variable;S2, construct multi-objective evaluation function;S3, call optimization algorithm, by iteration optimization to design variable in the minimum way of evaluation function, obtain multiple sets of design variables;S4, design end face pollution model simulates the situation when dust particles exist in fiber end face, calculates the coupling efficiency and insertion loss of each set of design variables under the condition of end face pollution, evaluates pollution sensitivity;S5, use Monte Carlo tolerance analysis to simulate the mechanical error that may occur in actual assembly, evaluate the stability of each set of design variables;S6, judge whether the pollution sensitivity and stability of each set of design variables meet the preset performance requirement threshold, output the design variable that meets the performance requirement threshold;If design variable does not meet the preset performance requirement threshold, adjust design variable range or evaluation function, return to step S2 and optimize again.
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Description

Technical Field

[0001] This invention relates to a Zemax-based method for optimizing the end-face parameters of fiber optic connectors, which can be used for rapid and high-precision simulation optimization and performance evaluation of the end-face structural parameters of fiber optic connectors, and belongs to the field of fiber optic communication technology. Background Technology

[0002] Fiber optic connectors are passive devices that enable detachable connections between optical fibers, widely used in fiber optic communication systems, fiber optic sensor networks, and other fields. Their performance is primarily measured by two indicators: insertion loss and return loss. These two indicators are closely related to the geometric parameters of the connector endface (such as radius of curvature, vertex offset, and tilt angle) and assembly tolerances. Traditional connector endface design mainly relies on geometric optics approximation formulas and empirical trial and error, making it difficult to accurately simulate the mode distribution of light waves in the fiber core, the diffraction effect of the endface gap, and the impact of non-ideal endfaces (such as contamination and damage) on the optical field. With the development of optical simulation software, professional tools such as Zemax can accurately analyze complex optical paths based on physical optics or geometric ray tracing. However, current methods for simulating fiber optic connectors using Zemax mostly remain at the stage of manual modeling and single-point verification, which has the following shortcomings: a) The modeling process is cumbersome. When multiple parameters need to be optimized, manually adjusting the parameters and repeating the simulation is extremely inefficient. b) There is a lack of systematic simulation of end-face contamination (such as dust and oil), which is a major factor in the increase of field connection losses; c) The impact of mechanical tolerances (such as lateral offset and angular tilt) on performance in actual assembly was not fully considered, resulting in a disconnect between the design results and actual production. d) The optimization objective is singular, often focusing only on insertion loss while ignoring return loss and the trade-off between the two.

[0003] Therefore, developing a method for automatically, efficiently, and comprehensively considering various practical factors to optimize the end-face parameters of fiber optic connectors is of great significance for improving the design quality and R&D efficiency of fiber optic connectors. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a Zemax-based method for optimizing the end-face parameters of fiber optic connectors. Through automated modeling, multi-objective optimization, contamination simulation, and tolerance analysis, high-precision design of the end-face parameters of fiber optic connectors can be achieved.

[0005] The technical solution of this invention is: a method for optimizing the end-face parameters of an optical fiber connector based on Zemax, comprising: S1. Establish an initial model of the fiber optic connector in Zemax and determine the design variables; S2. Construct a multi-objective evaluation function based on the objectives of maximizing coupling efficiency, minimizing insertion loss, and maximizing return loss; S3. Utilize the Zemax API to call the optimization algorithm and obtain multiple sets of design variables by iteratively optimizing the design variables to minimize the evaluation function; S4. Design an end-face contamination model to simulate the situation when there are dust particles on the fiber end face. Calculate the coupling efficiency and insertion loss of each set of design variables under end-face contamination conditions, and evaluate the contamination sensitivity by comparing with the values ​​before contamination. S5. Use Monte Carlo tolerance analysis to simulate the mechanical errors that may occur in actual assembly. Randomly generate a large number of mechanical error samples. Use Zemax's API to perform batch simulations to calculate the insertion loss and return loss of each set of design variables under each error sample, and evaluate the stability of each set of design variables. S6. Determine whether the pollution sensitivity and stability of each group of design variables meet the preset performance requirement threshold, and output the design variables that meet the performance requirement threshold; if none of the design variables meet the preset performance requirement threshold, adjust the range of design variables or the evaluation function, and return to step S2 to re-optimize.

[0006] Preferably, the design variables include: The fiber optic connector connects the two optical fibers, with the end face curvature radius R and end face tilt angle. d, the air gap between the fiber end faces.

[0007] Preferred multi-objective evaluation function The weighted summation of coupling efficiency, insertion loss, and return loss is as follows:

[0008] in, Coupling efficiency is the ratio of the output optical power of the receiving fiber to the incident optical power of the transmitting fiber in the two connected optical fibers. For insertion loss, ; For return loss, , where P i P is the incident light power. r This refers to the optical power reflected back from the end face of the transmitting fiber. , , These are the weights for coupling efficiency, insertion loss, and return loss, respectively.

[0009] Preferably, the optimization algorithm used in step S3 includes: particle swarm optimization, genetic algorithm, or the damped least squares method built into Zemax; In each iteration, the design variable values ​​in the Zemax model are automatically modified via API, ray tracing is performed, and coupling efficiency, insertion loss, and return loss are extracted to calculate the evaluation function value.

[0010] Preferably, in step S4, the contamination model is achieved by setting randomly distributed scattering particles on the end face of the connected optical fiber; The scattering particles are modeled as spherical or ellipsoidal particles, with a refractive index referenced to SiO2 or typical dust materials, and a particle size range of 1-50. The distribution density is set according to the cleanliness level.

[0011] Preferably, when calculating the coupling efficiency and insertion loss under contamination conditions, the scattered light rays are traced using the non-sequential mode of Zemax.

[0012] Preferably, in step S5, the mechanical errors in the actual assembly include: positional offset and angular tilt between the two connected optical fibers, as well as changes in the air gap between the two optical fibers.

[0013] Preferably, the fiber optic connector types include: Physical contact type, oblique physical contact type, super-physical contact type; For angled physical contact connectors, the end face tilt angle is 8°. 0.02°, or set as needed.

[0014] Preferably, the fiber optic connector also includes a bundle-expanding fiber optic connector; When the fiber optic connector is a beam-expanding fiber optic connector, two beam-expanding lenses need to be added to the model, and the parameters of the beam-expanding lenses need to be included in the design variables. The design variables of the beam-expanding lenses include: The length of the lens, the radius of curvature of each surface of the lens, the tilt angle, and the width of the air gap between the optical fiber and the lens.

[0015] Preferably, the Zemax API interacts with external programming languages ​​through the ZOS-API interface to achieve automatic modeling, parameter modification, ray tracing, and data extraction.

[0016] Compared with the prior art, the present invention has the following advantages: (1) Achieve fully automated optimization of fiber optic connector end face parameters, significantly shortening the design cycle; (2) Multi-objective optimization takes into account both insertion loss and return loss, and the weights can be flexibly adjusted; (3) Introduce a pollution model to make the design more closely resemble the actual usage environment; (4) Tolerance analysis is used to assess design stability and increase the performance stability of the finished product; Attached Figure Description Figure 1 This is the overall flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the optical fiber connector model structure of the present invention. The reference numerals are: 101-first optical fiber core, 102-first optical fiber cladding, 103-second optical fiber core, 104-second optical fiber cladding, 105-air gap, 106-end face contamination particles. Figure 3 This is a 2D schematic diagram of the Zemax optical path tracing of the beam-expanding fiber optic connector provided in an embodiment of the present invention; Figure 4 This is a comparison diagram of optical performance before and after contamination provided in an embodiment of the present invention; Figure 5 This is a histogram of Monte Carlo tolerance analysis results provided in an embodiment of the present invention. Detailed Implementation

[0017] The purpose of this invention is to overcome the shortcomings of the prior art and provide a Zemax-based method for optimizing the end-face parameters of fiber optic connectors. Through automated modeling, multi-objective optimization, contamination simulation, and tolerance analysis, this method achieves high-precision design of the end-face parameters of fiber optic connectors.

[0018] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for optimizing fiber optic connector end-face parameters based on Zemax includes the following steps: Step 1: Establish an initial model of the fiber optic connector and determine the design variables and their value ranges; such as Figure 2 As shown, the fiber optic connector model includes a first fiber (transmitter-side fiber), a second fiber (receiver-side fiber), and an air gap between them. Each fiber includes a core and a cladding, and the end face shape is spherical or beveled. The fiber optic connector structure is symmetrical from left to right. Design variables include the end face curvature radius R of the first and second fibers and the end face tilt angle. The air gap d between the fiber end faces; if the fiber optic connector is a beam expander connector, then two beam expander lenses need to be added to the model, and the parameters of the beam expander lenses should be taken into account in the design variables.

[0019] Step 2: Set a multi-objective evaluation function, which includes the objectives of maximizing coupling efficiency, minimizing insertion loss, and maximizing return loss; specifically, the coupling efficiency... Insertion loss is defined as the ratio of the output optical power of the second fiber (receiving fiber) to the incident optical power of the first fiber (transmitting fiber). Return loss , where P i P is the incident light power. r The evaluation function represents the optical power reflected back from the end face of the first optical fiber (the transmitting fiber); it can be constructed as a weighted sum. ,in, , , The evaluation function is constructed by assigning weights to each of them, or by using constrained optimization methods.

[0020] Step 3: Using the Zemax application programming interface (API), call the optimization algorithm to iteratively optimize the design variables to minimize the evaluation function and obtain multiple sets of design variables; the optimization algorithm includes, but is not limited to, particle swarm optimization, genetic algorithm, or Zemax's built-in damped least squares method; in each iteration, automatically modify the parameter values ​​in the Zemax model through the API, perform ray tracing, and extract coupling efficiency and reflected light power (reflected light power includes: insertion loss and return loss), and calculate the evaluation function value.

[0021] Step 4: Introduce an end-face contamination model to simulate the optical performance when dust particles are present on the end face. The contamination model is achieved by setting randomly distributed tiny scattering particles on the fiber end face. The size, refractive index, and distribution density of the particles are set according to the actual environment. The scattered light is traced using the non-sequential mode of Zemax to calculate the coupling efficiency and insertion loss under contamination conditions. The contamination sensitivity is evaluated by comparing the values ​​with those before contamination.

[0022] Step 5: Perform Monte Carlo tolerance analysis to simulate potential mechanical errors during actual assembly; tolerance parameters include the lateral offset between the first and second optical fibers. , , angle tilt , The change in the air gap d between optical fibers; Set the probability distribution of each tolerance parameter (such as normal distribution), randomly generate a large number of mechanical error samples, and use API to call the mechanical error samples in batches to simulate and calculate the performance index of each set of design variables under each sample. Statistically analyze the distribution law of insertion loss and return loss, and evaluate the stability of the design scheme.

[0023] Step 6: Based on the optimization results and tolerance analysis results, output the end face parameter combination that meets the performance requirements (contamination sensitivity) and has the best stability; if the optimization results do not meet the preset threshold, adjust the design variable range or evaluation function weight, and return to step 2 to re-optimize.

[0024] The fiber optic connector types mentioned in step 1 include, but are not limited to, PC (physical contact), APC (oblique physical contact), and UPC (ultra-physical contact); for APC type connectors, the end face tilt angle is 8° or can be set according to requirements.

[0025] In addition to contact fiber optic connectors, the fiber optic connector type mentioned in step 1 can also be a bundle-expanding fiber optic connector. If it is a bundle-expanding fiber optic connector, then two or more lenses (such as C-Lens or G-Lens) need to be added to the above model. The variables need to include the length of the lens, the radius of curvature of each surface of the lens, the tilt angle, and the width of the air gap between the fiber and the lens. Furthermore, the dust particles in the subsequent contamination model need to exist in the air gap between the two lenses.

[0026] The multi-objective evaluation function described in step 2 is optimized using the Pareto front method to obtain a set of non-dominated solutions, which designers can choose according to actual needs.

[0027] The ZemaxAPI mentioned in step 3 can interact with external programming languages ​​(such as Python, MATLAB, etc.) through the ZOS-API interface to achieve automatic modeling, parameter modification, ray tracing and data extraction.

[0028] The pollution model described in step 4 can be further refined, modeling dust particles as spherical or ellipsoidal particles with a refractive index of SiO2 or typical dust materials (such as silicates), and a particle size range of 1-50. The distribution density is set according to the cleanliness level.

[0029] The tolerance analysis described in step 5 uses a combination of sensitivity analysis and statistical tolerance. First, key tolerance parameters are identified through sensitivity analysis, and then detailed Monte Carlo simulations are performed on the key parameters.

[0030] The present invention will now be described in conjunction with the accompanying drawings and specific embodiments. The following embodiments are only for illustrating the present invention in more detail, but are not intended to limit the scope of application of the Zemax-based fiber optic connector end-face parameter optimization design method of the present invention.

[0031] Example This embodiment focuses on optimizing the end-face parameters of an APC type fiber optic connector that uses C-Lens as the beam expander. Based on a single-mode fiber (SMF-28) with a center wavelength of 1550nm, a symmetrical structure with dual C-Lens collimators is designed to achieve beam expansion, collimation, and efficient coupling.

[0032] Traditional fiber optic expander connector designs suffer from complex parameter matching, difficulties in APC upper integration, and a lack of systematic tolerance analysis. This embodiment addresses these issues by providing an optimized design method for C-Lens expander APC connectors based on Zemax simulation. The flowchart is attached. Figure 1 As shown. The specific implementation steps are as follows: Step 1: Select the following typical parameters as the design benchmark based on the specifications of mainstream C-Lens products on the market: lens material is BK7, lens diameter is 1.8mm, and length is 3.85mm; Step 2: Construct a symmetric model of the dual C-Lens collimator in Zemax non-sequential mode. A schematic diagram is attached. Figure 3 As shown, the structure includes a first optical fiber, a first C-Lens, an air gap (working distance), a second C-Lens, and a second optical fiber; Step 3: Based on the characteristics of the C-Lens expander connector, determine the following design variables: radii of curvature R1 and R2 of the first and second C-Lens, air gap distance d1 between the first fiber end face and the first C-Lens, air gap distance d2 between the second fiber end face and the second C-Lens, air gap distance D between the two lenses, and the bevel angles of the first and second C-Lens. , ; Step 4: Define performance metrics and multi-objective evaluation functions: Coupling efficiency Represented as:

[0033] in, The incident light power of the first fiber. This represents the output optical power of the second optical fiber.

[0034] Insertion loss Expressed as: (unit dB)

[0035] Return loss Expressed as: (unit dB)

[0036] in, This refers to the optical power reflected back to the light source from the end face of the first optical fiber.

[0037] This embodiment uses a weighted sum form of the evaluation function, which simultaneously maximizes coupling efficiency, minimizes insertion loss, and maximizes return loss.

[0038] Among them, the weighting coefficient , , (when The third item is automatically set to zero (when the time is right), and the optimization goal is: , ; Step 5: Employ Particle Swarm Optimization (PSO) algorithm, using Python to call the Zemax ZOS-API for automated iterative optimization. Initial settings include 30 particles, 50 iterations, an inertia weight of 0.7, and a learning factor of... Each iteration optimizes the model by modifying the variable values ​​in step 3 using the API. The number of rays in Zemax ray tracing is set to... To ensure statistical accuracy, the detector power and reflected light power were read and repeatedly calculated. , , and When the maximum number of iterations is reached or the change in the evaluation function is less than The iteration terminates at a certain time. During the optimization process, the best individual in each generation is recorded, and finally converges to the optimal parameter combination. Step 6: After obtaining the optimization results, randomly distributed dust particles are added to the C-Lens end face to simulate environmental pollution during actual use, optical path tracing is performed, and the performance parameters of the fiber optic connector are calculated.

[0039] The dust particle simulation settings are as follows: dust particle diameter 1-50 mm. Uniformly distributed, particle density taken The particulate material is silicate (n=1.5+0.01i), and non-sequential scattering tracing is used for optical path tracing (considering scattering and absorption).

[0040] The pollution simulation results are attached. Figure 4 As shown, the results indicate that the optimized C-Lens expanded fiber optic connector structure has a high tolerance for minute dust particles. Step 7: To evaluate the impact of manufacturing and assembly errors on performance, Monte Carlo tolerance analysis is performed. Optical component processing tolerances are generally labeled according to ISO 10110, in conjunction with industry standards such as MIL-PRF-13830B appearance and DIN 3140 impurities, with tolerances taken at a precision level. The main tolerance types in the design of the expanded fiber optic connector are axial offset error, perpendicular offset error, eccentricity, radius of curvature error, and angular tolerance. 500 Monte Carlo cycles are performed using Zemax's tolerance analysis function. Insertion loss and return loss for each sample are statistically analyzed using API. If over 95% of the samples meet the insertion loss and return loss standards, the design is considered to have good stability.

[0041] In step one, the refractive index of the lens material BK7 is... The lens length is 3.85mm, corresponding to a pitch of 0.23mm. The aperture diameter is the same as the lens diameter. Anti-reflective coatings should be applied to both the front and back surfaces of the lens. Typical specifications for the anti-reflective coating are as follows: The initial end face tilt angle is 8°, and the initial alignment distance between the collimators is 100mm.

[0042] In step two, the constructed fiber model is an SMF-28 single-mode fiber with a core diameter of [missing information]. Cladding diameter Core refractive index 1.4682, cladding refractive index 1.4628, mode field diameter The C-Lens front end is spherical, and the rear end is coupled to the fiber end face, which is set to an 8° bevel.

[0043] In step four, the weights of each item in the multi-objective evaluation function are adjustable. If the evaluation function converges slowly or the optimization results are not ideal during subsequent optimization processes, it can be modified.

[0044] In step five, the learning parameters of the particle swarm optimization algorithm can also be adjusted appropriately to ensure faster convergence and obtain better optimization results. In this embodiment, the optimized single-mode fiber bundle expander connector coupling efficiency... Insertion loss Return loss It meets and exceeds typical commercial values.

[0045] In step six, the simplified particle model is spherical in shape, and the particle density corresponds to ISO Class 8 cleanliness. After incorporating the contamination model, optical path tracing is performed, and the coupling efficiency and other indicators of the new model are calculated to obtain the insertion loss of the contaminated single-mode fiber optic bundle expander connector. Return loss Performance degradation Increased by 0.04dB. The performance decreased by 4.5 dB. Pollution simulation results show that the optimized C-Lens structure has a certain tolerance to fine dust particles, and the performance degradation is within an acceptable range.

[0046] In step seven, manufacturing and assembly errors are not limited to the types of errors mentioned. Error limits can be added to the tolerance analysis wizard in the simulation based on the actual assembly and processing process to obtain better processing results and improve product stability.

[0047] Compared to traditional designs, this embodiment uses an automated algorithm to precisely match the radius of curvature and working distance of the dual C-Lens, incorporating the 8° slope parameter into the optimization variables. This effectively reduces insertion loss and improves return loss. Furthermore, the system assesses the impact of dust contamination in the C-Lens connector design, providing a basis for performance prediction in real-world application environments. Figure 5 As shown, after optimization, Monte Carlo analysis ensures that more than 95% of the samples meet the standards, significantly improving the engineering practicality and stability of the design; the fully automated optimization is achieved by Python scripts based on ZOS-API, improving design efficiency by more than 90%, which is significantly better than the manual debugging process.

[0048] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0049] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A method for optimizing the end-face parameters of an optical fiber connector based on Zemax, characterized in that... include: S1. Establish an initial model of the fiber optic connector in Zemax and determine the design variables; S2. Construct a multi-objective evaluation function based on the objectives of maximizing coupling efficiency, minimizing insertion loss, and maximizing return loss; S3. Utilize the Zemax API to call the optimization algorithm and obtain multiple sets of design variables by iteratively optimizing the design variables to minimize the evaluation function; S4. Design an end-face contamination model to simulate the situation when there are dust particles on the fiber end face. Calculate the coupling efficiency and insertion loss of each set of design variables under end-face contamination conditions, and evaluate the contamination sensitivity by comparing with the values ​​before contamination. S5. Use Monte Carlo tolerance analysis to simulate the mechanical errors that may occur in actual assembly. Randomly generate a large number of mechanical error samples. Use Zemax's API to perform batch simulations to calculate the insertion loss and return loss of each set of design variables under each error sample, and evaluate the stability of each set of design variables. S6. Determine whether the pollution sensitivity and stability of each group of design variables meet the preset performance requirement threshold, and output the design variables that meet the performance requirement threshold. If none of the design variables meet the preset performance requirement threshold, adjust the range of design variables or the evaluation function, and return to step S2 to re-optimize.

2. The method for optimizing the end-face parameters of a fiber optic connector based on Zemax according to claim 1, characterized in that: Design variables include: The fiber optic connector connects the two optical fibers, with the end face curvature radius R and end face tilt angle. d, the air gap between the fiber end faces.

3. The method for optimizing the end-face parameters of a fiber optic connector based on Zemax according to claim 1, characterized in that: Multi-objective evaluation function The weighted summation of coupling efficiency, insertion loss, and return loss is as follows: in, Coupling efficiency is the ratio of the output optical power of the receiving fiber to the incident optical power of the transmitting fiber in the two connected optical fibers. For insertion loss, ; For return loss, , where P i P is the incident light power. r This refers to the optical power reflected back from the end face of the transmitting fiber. , , These are the weights for coupling efficiency, insertion loss, and return loss, respectively.

4. The method for optimizing the end-face parameters of a fiber optic connector based on Zemax according to claim 1, characterized in that: The optimization algorithms used in step S3 include: particle swarm optimization, genetic algorithm, or the damped least squares method built into Zemax; In each iteration, the design variable values ​​in the Zemax model are automatically modified via API, ray tracing is performed, and coupling efficiency, insertion loss, and return loss are extracted to calculate the evaluation function value.

5. The method for optimizing the end-face parameters of a fiber optic connector based on Zemax according to claim 1, characterized in that: In step S4, the contamination model is achieved by setting randomly distributed scattering particles on the end face of the connected optical fiber; The scattering particles are modeled as spherical or ellipsoidal particles, with a refractive index referenced to SiO2 or typical dust materials, and a particle size range of 1-50. The distribution density is set according to the cleanliness level.

6. The method for optimizing the end-face parameters of a fiber optic connector based on Zemax according to claim 5, characterized in that: When calculating the coupling efficiency and insertion loss under contamination conditions, the scattered light rays are traced using the non-sequential mode of Zemax.

7. The method for optimizing the end-face parameters of an optical fiber connector based on Zemax according to claim 1, characterized in that: In step S5, the mechanical errors in the actual assembly include: positional offset and angular tilt between the two connected optical fibers, as well as changes in the air gap between the two optical fibers.

8. The method for optimizing the end-face parameters of a fiber optic connector based on Zemax according to claim 2, characterized in that: Fiber optic connector types include: Physical contact type, oblique physical contact type, super-physical contact type; For angled physical contact connectors, the end face tilt angle is 8°. 0.02°, or set as needed.

9. The method for optimizing the end-face parameters of a fiber optic connector based on Zemax according to claim 2, characterized in that: Fiber optic connectors also include bundle-expanding fiber optic connectors; When the fiber optic connector is a beam-expanding fiber optic connector, two beam-expanding lenses need to be added to the model, and the parameters of the beam-expanding lenses need to be included in the design variables. The design variables of the beam-expanding lenses include: The length of the lens, the radius of curvature of each surface of the lens, the tilt angle, and the width of the air gap between the optical fiber and the lens.

10. The method for optimizing the end-face parameters of a fiber optic connector based on Zemax according to claim 1, characterized in that: The Zemax API interacts with external programming languages ​​through the ZOS-API interface to achieve automatic modeling, parameter modification, ray tracing, and data extraction.