Method for measuring surface type of equidistant Fresnel structure product

Abstract

The invention provides a method for measuring the surface type of an equidistant Fresnel structure product, and relates to the technical field of product surface type measurement. The method sequentially comprises the steps that a UA3P atomic force probe is used for measuring the equidistant Fresnel part in a contact mode, and original coordinate point data are exported; an equidistant Fresnel regression model is constructed through an MATLAB (matrix laboratory) stair function; original measurement coordinates and model point location data are combined in Excel, and aspheric surface structure contour point locations are restored; a Data Tool tool is used for converting the splicing point positions into binary codes compatible with UA3P; calling a UA3P general aspheric structure equation and a coefficient; and filtering a high-angle interference data area with a draft angle greater than 60 degrees, intercepting real surface type data and outputting a result. The problems that in the prior art, a Fresnel structure is difficult to restore, the risk of probe breakage is high, and data splicing is complex are solved, the model building loss is converged to the nanoscale, the real object repeatability measurement error is smaller than or equal to 0.2 micrometer, quantitative and standardized management and control are achieved, and the measurement efficiency is improved by 40% or above.

Description

Technical Field

[0001] This invention relates to the field of product surface shape measurement technology, specifically a method for measuring the surface shape of equidistant Fresnel structure products. Background Technology

[0002] Fresnel lenses (also known as threaded lenses) are thin sheet components injection molded from polyolefin material. One side is smooth, while the other side is engraved with concentric circular threads of increasing size. They utilize the principles of light interference and diffraction to achieve light focusing or imaging functions. These components have advantages such as low cost, light weight, and large area; however, the surface accuracy directly affects optical performance, thus requiring precise measurement for quality control.

[0003] Existing surface measurement technology for equidistant Fresnel structures faces three major bottlenecks:

[0004] 1. The thread structure of solid equidistant Fresnel is a segmented stepped profile, which is difficult to directly restore to the continuous aspherical structure in the design stage, resulting in the surface accuracy being unable to match the design value;

[0005] 2. Fresnel threads can have a slope of over 60°. When using a traditional contact probe for direct measurement, the probe is prone to breakage during the probe's ascent, and interference data in high-angle regions is easily distorted.

[0006] 3. Complete surface measurement requires step data covering different radius areas. The data analysis and splicing process of traditional step-by-step needle-stitching procedures is complex, inefficient, and results in significant error accumulation.

[0007] Existing measurement methods cannot solve the above problems simultaneously, resulting in low measurement accuracy (error is usually >1μm), cumbersome operation, and high cost, making it difficult to meet the quantitative and standardized control requirements of industrialized mass production.

[0008] Therefore, developing an efficient, accurate, and low-risk method for measuring the surface profile of equidistant Fresnel structures has significant practical application value. Summary of the Invention

[0009] To address the shortcomings of existing technologies, this invention provides a method for measuring the surface profile of equidistant Fresnel structure products. It aims to solve the problems of difficulty in Fresnel structure restoration, high risk of probe breakage, and complex data splicing, achieving rapid and accurate surface profile measurement, reducing measurement errors, improving measurement efficiency, and meeting the quality control requirements of industrialized mass production. It is applicable to the surface profile inspection of Fresnel lenses, threaded lenses, and other components made of polyolefin and other materials, and can be widely used in product quality control in fields such as slide projectors, thin-film magnifying glasses, infrared detectors, and solar concentrators.

[0010] To achieve the above objectives, the present invention provides the following technical solution:

[0011] A method for measuring the surface profile of an equidistant Fresnel structure product includes the following steps:

[0012] Step 1: Use the UA3P atomic force probe to scan the equidistant Fresnel component in a contact measurement manner and export the original measurement space coordinate point data;

[0013] Step 2: Use the stair function in MATLAB to construct an equidistant Fresnel regression model;

[0014] Step 3: In Excel, combine the original measured spatial coordinates from Step 1 with the equidistant model point data obtained from Step 2 to reconstruct the aspherical structure contour points. The overall fitting equation is:

[0015]

[0016] Where R is the reference radius of curvature, and K is the quadratic surface coefficient. For higher-order terms, For the step function term;

[0017] Step 4: Use the Data Tool to convert the stitched aspherical structure contour point data into binary code that can be read by the UA3P atomic force measuring instrument;

[0018] Step 5: Call the universal aspherical structure equation and corresponding coefficients built into the UA3P atomic force measuring instrument.

[0019] Step 6: Filter out the draft angle and high-angle interference data areas, extract the actual surface data for analysis, and output the measurement results.

[0020] Furthermore, in step one, the UA3P atomic force probe has a measurement resolution of 0.1 nm, a scanning speed of 1-5 mm / s, and a measurement range covering the entire effective optical diameter of the equidistant Fresnel components.

[0021] Furthermore, the calculation expression for the MATLAB stair function in step two is as follows:

[0022]

[0023] Where x=0:M:D, M is the equidistant spacing, ranging from 0.01 to 0.1 mm, and D is half the effective optical diameter of the equidistant Fresnel component.

[0024] Furthermore, in step three, the absolute value of the coefficient Ai of the higher-order term in the fitted equation is ≤ 1 × 10⁻⁶. -6 The order of the higher-order terms n is 3-8, and the positional error of the restored aspherical structure contour is ≤0.1nm.

[0025] Furthermore, in step six, the filtering threshold for the high-angle interference data region is a draft angle > 60°, and the abnormal data points in this region are shielded by the built-in algorithm of the UA3P atomic force measuring instrument.

[0026] Furthermore, the measurement results output in step six include aspherical surface profile deviation value, surface roughness, radius of curvature deviation, and fitting accuracy of higher-order term coefficients. All results are output simultaneously in the form of numerical tables and surface profile diagrams.

[0027] This invention provides a method for measuring the surface profile of equidistant Fresnel structure products. It offers the following advantages:

[0028] 1. This invention provides a method for measuring the surface profile of equidistant Fresnel structure products. By using step function modeling and aspherical restoration equations, the equidistant Fresnel structure can be accurately restored to the designed aspherical surface. This eliminates the need to directly measure high-slope areas, fundamentally avoiding the risk of probe breakage. Data stitching is automatically completed by software, simplifying the process and reducing error accumulation.

[0029] 2. This invention provides a method for measuring the surface profile of equidistant Fresnel structure products. The model building loss converges to the nanometer level, and the physical repeatability measurement error is ≤0.2μm. The accuracy is improved by more than 5 times compared with traditional methods. Moreover, the integrated process eliminates the need for step-by-step needle insertion and manual splicing, improving the measurement efficiency by more than 40%, which can meet the needs of industrial batch testing.

[0030] 3. This invention provides a method for measuring the surface profile of equidistant Fresnel structure products. The output results include quantitative indicators and visualization graphics, realizing the standardization and quantifiable evaluation of surface profile quality, and facilitating quality traceability in the production process. Attached Figure Description

[0031] Figure 1 This is a distribution diagram of the equidistant Fresnel original profile measurement points of the present invention;

[0032] Figure 2 The distribution map of the points of the equidistant Fresnel regression model constructed by the MATLAB stair function of this invention;

[0033] Figure 3 This is a contour diagram of the restored aspherical structure of the present invention;

[0034] Figure 4 This is a surface deviation analysis diagram output by the UA3P measuring instrument of the present invention. Detailed Implementation

[0035] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0036] In the description of this invention, unless otherwise explicitly specified and limited, the terms "connected," "linked," and "fixed" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0037] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0038] In the description of this embodiment, the terms "upper," "lower," "right," etc., refer to the orientation or positional relationship shown in the accompanying drawings. They are used only for ease of description and simplification of operation, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the present invention. In addition, the terms "first" and "second" are used only for distinction in description and have no special meaning.

[0039] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0040] like Figure 1-4 As shown, this embodiment of the invention provides a method for measuring the surface profile of equidistant Fresnel structure products. This method constructs an integrated measurement system of "physical measurement - mathematical modeling - data restoration" through a six-step process of "measurement-modeling-reconstruction-transcoding-calling-filtering." The specific steps are as follows:

[0041] Step 1: Measurement Phase

[0042] The UA3P atomic force probe was selected for contact measurement. This probe features nanometer-level resolution (0.1 nm) and an adjustable scanning speed of 1-5 mm / s, enabling precise acquisition of full-domain spatial coordinate point data for equidistant Fresnel components, avoiding the measurement blind spots of traditional probes in fine thread areas. During measurement, the probe scans uniformly along the thread profile. The exported raw data contains two-dimensional spatial information in x (radial coordinate) and z (axial coordinate), with a data point density ≥ 1000 points / mm. The exported raw measurement coordinate point data is used to construct a point profile diagram, as shown below. Figure 1 As shown.

[0043] Step Two: Modeling Stage

[0044] An equidistant Fresnel regression model is constructed using the `stair` function in MATLAB. This function fits discrete original measurement points into a continuous step-like model based on the equidistant characteristics of the Fresnel thread. Its core expression is:

[0045]

[0046] Where x takes values ​​ranging from 0:M:D (M is the equidistant spacing, 0.01-0.1mm; D is half the optical effective diameter), ensuring that the thread spacing of the model and the solid part are perfectly matched, a radius step function model is constructed using Matlab to symmetrically construct the full-diameter step function graph as shown below. Figure 2 As shown.

[0047] Step 3: Restoration Phase

[0048] This method integrates raw measurement data with model data in Excel to reconstruct the contour of a continuous aspherical structure. The fitting equation combines the fundamental equations of aspherical surfaces with step function terms.

[0049]

[0050] The first half consists of the general aspherical equation (R is the reference radius of curvature, K is the quadratic surface coefficient), and the second half consists of the step function correction term (…). (where n is the coefficient of the higher-order term, n=3-8). This equation can be used to restore the piecewise stepped profile to a continuous aspherical design profile with a restoration error ≤0.1nm. The restored aspherical structure profile is shown in the figure below. Figure 3 As shown.

[0051] Step 4: Transcoding Stage

[0052] The Data Tool was used to convert the stitched aspherical contour point data into binary encoding compatible with the UA3P atomic force measuring instrument. This encoding format can be directly recognized by the instrument, avoiding information loss caused by data format incompatibility and ensuring data transmission accuracy.

[0053] Step 5: Invocation Phase

[0054] The UA3P instrument utilizes its built-in general aspherical structure equations and coefficient library, which contains standard aspherical parameters for different types of Fresnel lenses. These parameters can be compared and analyzed with the restored aspherical profile, providing a benchmark for surface accuracy evaluation.

[0055] Step Six: Filtering Stage

[0056] The instrument's built-in algorithm filters out high-angle interference data regions with draft angles greater than 60°. This region is a high-risk area for needle breakage in traditional measurements, and the data is easily distorted by probe interference. After filtering, the true surface shape data is extracted, and key indicators such as surface shape deviation, roughness, and radius of curvature deviation are analyzed. The results are finally output in the form of numerical tables and contour diagrams, such as... Figure 4 As shown.

[0057] Example 1: Measurement of the surface profile of an infrared detector using an equidistant Fresnel lens

[0058] ①Measuring object

[0059] The equidistant Fresnel lens has an effective optical diameter of 100 mm, an equidistant thread spacing of M = 0.05 mm, is made of polyolefin, has a design reference radius of curvature R = 500 mm, and a quadratic surface coefficient K = -1.

[0060] ② Measurement steps

[0061] Step 1: Fix the lens on the stage of the UA3P atomic force measuring instrument, set the probe measurement resolution to 0.1nm, the scanning speed to 3mm / s, scan the entire area radially, and export the original xz coordinate point data with a data point density of 1500 points / mm.

[0062] Step 2: Open MATLAB software, input the original coordinate data, call the stair function to build a regression model, set x=0:0.05:50 (D=50mm), and generate stepped model point data.

[0063] Step 3: Import the original coordinate data and model data into Excel, and substitute them into the fitting equation.

[0064]

[0065] The fitting yielded the coefficients of the higher-order terms, A1 = 2 × 10. -7 A2 = 5 × 10 -8A3 = 3 × 10 -9 To restore the contour points of the aspherical structure.

[0066] Step 4: Use the Data Tool to convert the stitched point data into UA3P-compatible binary code and transmit it to the measuring instrument.

[0067] Step 5: Call the built-in general aspherical equation of UA3P, input the design parameters R=500mm and K=-1, and match the corresponding coefficient library.

[0068] Step 6: Set the filter threshold to draft angle > 60° to filter out abnormal data areas, analyze indicators such as surface deviation and roughness, and output the measurement results.

[0069] ③ Measurement results

[0070] Surface profile deviation: ±0.15μm, meeting design requirements (≤±0.2μm);

[0071] Surface roughness: Ra = 0.03 μm;

[0072] Curvature radius deviation: +0.8mm (relative deviation 0.16%);

[0073] Repeatability measurement error: 0.12μm, which meets the accuracy specifications of this invention.

[0074] Example 2: Surface profile measurement of equidistant Fresnel lenses for slide projectors

[0075] ①Measuring object

[0076] Equidistant Fresnel lens with an effective optical diameter of 80mm, thread spacing M=0.08mm, made of polyolefin, with a design reference radius of curvature R=400mm and a quadratic surface coefficient K=0.

[0077] ② Measurement steps

[0078] Step 1: UA3P probe scanning speed 2mm / s, data point density 1200 points / mm, export raw coordinate data;

[0079] Step 2: In MATLAB, set x = 0:0.08:40 to construct a ladder model;

[0080] Step 3: In the Excel fitting equation, the order of the higher-order terms is n=4, and the fitting result is A1=3×10. -7 A2 = 4 × 10 -8 ;

[0081] The subsequent steps are the same as in Example 1.

[0082] ③ Measurement results

[0083] Surface profile deviation: ±0.18μm;

[0084] Surface roughness: Ra = 0.04 μm;

[0085] Curvature radius deviation: -0.6mm (relative deviation 0.15%);

[0086] Repeatability measurement error: 0.15μm, meeting the quality control requirements for industrial production.

[0087] This invention constructs an equidistant Fresnel regression model using the MATLAB stair function. In Excel, the original Fresnel measurement space coordinates are combined with the equidistant model point data fitted by the stair function to restore the aspherical structure contour points. This solves the problem of analytical models and enables convenient and rapid measurement of product surface shape with high accuracy and small error, reaching the nanometer level, with the error controllable within 0.2µm.

[0088] Therefore, this invention has the advantages of being able to conveniently and quickly measure the surface shape of a product, with high measurement accuracy, small error, and controllable measurement error of 0.2um for physical repeatability, enabling quantitative standardized control, and has great promotional value.

[0089] The following points should be noted in this article:

[0090] 1. The accompanying drawings of the embodiments disclosed herein only relate to the structures involved in the embodiments disclosed herein; other structures can be referred to in a general design.

[0091] 2. Where there is no conflict, the embodiments of this disclosure and the features in the embodiments can be combined with each other to obtain new embodiments.

[0092] Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

Claims

1. A method for measuring the surface profile of an equidistant Fresnel structure product, characterized in that, Includes the following steps: Step 1: Use the UA3P atomic force probe to scan the equidistant Fresnel component in a contact measurement manner and export the original measurement space coordinate point data; Step 2: Use the stair function in MATLAB to construct an equidistant Fresnel regression model; Step 3: In Excel, combine the original measured spatial coordinates from Step 1 with the equidistant model point data obtained from Step 2 to reconstruct the aspherical structure contour points. The overall fitting equation is: ； Where R is the reference radius of curvature, and K is the quadratic surface coefficient. For higher-order terms, For the step function term; Step 4: Use the Data Tool to convert the stitched aspherical structure contour point data into binary code that can be read by the UA3P atomic force measuring instrument; Step 5: Call the universal aspherical structure equation and corresponding coefficients built into the UA3P atomic force measuring instrument. Step 6: Filter out the draft angle and high-angle interference data areas, extract the actual surface data for analysis, and output the measurement results.

2. The method for measuring the surface profile of an equidistant Fresnel structure product according to claim 1, characterized in that, In step one, the UA3P atomic force probe has a measurement resolution of 0.1 nm, a scanning speed of 1-5 mm / s, and a measurement range covering the entire effective optical diameter of equidistant Fresnel components.

3. The method for measuring the surface profile of an equidistant Fresnel structure product according to claim 1, characterized in that, The calculation expression for the MATLAB stair function in step two is as follows: ； Where x=0:M:D, M is the equidistant spacing, ranging from 0.01 to 0.1 mm, and D is half the effective optical diameter of the equidistant Fresnel component.

4. The method for measuring the surface profile of an equidistant Fresnel structure product according to claim 1, characterized in that, In step three, the absolute value of the coefficient Ai of the higher-order term in the fitted equation is ≤ 1 × 10⁻⁶. -6 The order of the higher-order terms n is 3-8, and the positional error of the restored aspherical structure contour is ≤0.1nm.

5. The method for measuring the surface profile of an equidistant Fresnel structure product according to claim 1, characterized in that, In step six, the filtering threshold for the high-angle interference data region is a draft angle > 60°, and the abnormal data points in this region are shielded by the built-in algorithm of the UA3P atomic force measuring instrument.

6. The method for measuring the surface profile of an equidistant Fresnel structure product according to claim 1, characterized in that, The measurement results output in step six include aspherical surface deviation value, surface roughness, radius of curvature deviation, and fitting accuracy of higher-order coefficients. All results are output simultaneously in the form of numerical tables and surface profile diagrams.

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