Method for measuring small radius of curvature of convex surface based on droplet contact angle and macroscopic angle

Abstract

The application discloses a convex surface small curvature radius measurement method based on a liquid drop contact angle and a macroscopic angle, and belongs to optical measurement technology. The method calculates a quantitative correlation formula of the curvature radius of a curved surface according to the contact angle and the macroscopic angle; a standard piece with a known curvature radius is placed in a measurement light path to calibrate a value of a curvature influence coefficient; a to-be-measured piece with an unknown curvature radius is replaced with the standard piece and placed on an objective table in the measurement light path to calculate a second contact angle and a second macroscopic angle; and the curvature radius of the to-be-measured piece is obtained according to the second contact angle, the second macroscopic angle and the curvature influence coefficient. The application innovatively establishes a quantitative correlation formula of the liquid drop contact angle, the macroscopic angle and the curvature radius, and verifies the result by independently designing an experiment, thereby verifying the feasibility of the method, providing a brand-new scheme for the measurement of the small curvature radius, filling a research gap and providing a brand-new idea for the measurement of related precision fields.

Description

TECHNICAL FIELD

[0001] The present application relates to optical measurement technology, in particular to a convex surface small curvature radius measurement method based on droplet contact angle and macroscopic angle. BACKGROUND

[0002] In the field of micro-nano optics, micro-electro-mechanical systems and biomedical engineering, the precise measurement of the curvature radius of a curved surface, especially the small curvature radius, directly determines the performance of the device, such as the imaging resolution of a miniature lens and the visual correction effect of an intraocular lens.

[0003] At present, the main method used in teaching for measuring the curvature radius is the equal-thickness interference method, which uses the air film interference fringes between a plano-convex lens and a plane glass to calculate the curvature radius by formula. The core limitation of the equal-thickness interference method is that it is only applicable to convex surfaces with large curvature radius (greater than 50 mm). When facing small curvature radius (less than 20 mm), concave surfaces or irregular curved surfaces, there are the following unsolvable problems: (1) small curvature surface leads to interference fringe spacing less than 10 pm, adjacent fringes overlap, and the center of the fringe cannot be accurately positioned, resulting in large measurement error; (2) the concave surface reflection produces asymmetric optical path difference, and the interference pattern is distorted, so there is no standard formula that can be applied; (3) environmental vibration (amplitude greater than 0.01 mm) or air disturbance will further amplify the error.

[0004] In addition, existing small curvature radius measurement methods, such as three-coordinate measurement method, spherometer measurement method, self-collimation microscope measurement method and laser interference method, have the problems of complex operation, high price, low measurement accuracy and limited measurement range. Moreover, the current use of droplet contact angle is only used for material wettability characterization, and there is no related research to link the calculation of droplet contact angle, macroscopic angle and curvature radius, and no quantitative correlation formula between contact angle and curvature radius is established. SUMMARY

[0005] The present application aims to provide a convex surface small curvature radius measurement method based on droplet contact angle and macroscopic angle, and to establish a quantitative relationship between droplet contact angle, macroscopic angle and curvature radius, providing a new solution for the measurement of convex surface small curvature radius.

[0006] Technical solution: The convex surface small curvature radius measurement method based on droplet contact angle and macroscopic angle of the present application comprises:

[0007] A quantitative correlation formula for calculating the curvature radius of a curved surface is obtained according to the contact angle and the macroscopic angle;

[0008] The measurement optical path is constructed and calibrated. The measurement optical path includes, from left to right, a helium-neon laser, a beam expander lens, a collimating lens, a stage, a first Fourier lens, a dual-frequency grating filter, a second Fourier lens, and an image acquisition device.

[0009] A standard component with a known radius of curvature is placed on a stage in the measurement optical path, and a droplet is dropped on the standard component. Light emitted by a helium-neon laser is used to illuminate the standard component and the droplet. After the droplet shape stabilizes, an image acquisition device is used to acquire an image of the droplet on the standard component, and the first contact angle and the first macroscopic angle are calculated.

[0010] The calibration value of the curvature influence coefficient is obtained based on the first contact angle and the first macroscopic angle;

[0011] The test piece with an unknown radius of curvature is replaced with the standard piece and placed on the stage in the measurement optical path. A droplet is dropped on the test piece, and the light emitted by the helium-neon laser is irradiated onto the test piece and the droplet. After the droplet shape stabilizes, the image acquisition device is used to acquire the image of the droplet on the test piece, and the second contact angle and the second macroscopic angle are calculated.

[0012] The radius of curvature of the test piece is obtained based on the second contact angle, the second macro angle, and the curvature influence coefficient.

[0013] Furthermore, the steps for calculating the quantitative correlation formula for the radius of curvature of the surface based on the contact angle and the macroscopic angle include:

[0014] A droplet is placed onto the surface to be tested. After the droplet stabilizes on the surface, the interfacial tension equilibrium is described using the Young's equation, which is:

[0015] ,

[0016] Where θ is the contact angle of the droplet, which is an inherent property of the material and does not change with the shape of the surface; For solid-gas interfacial tension, For solid-liquid interfacial tension, The interfacial tension between liquid and gas;

[0017] Calculate the contact angle θ and macro angle. With wetting angle The geometric relationship satisfied by the three exists. ;

[0018] Calculate the radius of curvature at the droplet vertex The radius r of the solid-liquid contact line and the radius of curvature of the surface to be measured The geometric matching condition is expressed as:

[0019] ;

[0020] A curvature influence coefficient C is defined, and the expression is:

[0021] C= ,

[0022] A quantitative correlation formula between the contact angle, the macroscopic angle and the radius of curvature is calculated as:

[0023] .

[0024] Further, in the measurement light path, the dual-frequency grating filter is located at the rear focal point of the first Fourier lens, and the image acquisition device is located at the rear focal point of the second Fourier lens.

[0025] Further, the liquid drop image on the measured piece is acquired by using the image acquisition device, and the steps of calculating the second contact angle and the second macroscopic angle include:

[0026] The image of the liquid drop is collected at 60-90 seconds after dropping, and the liquid drop image is pre-processed, including gray scale, denoising, image enhancement and sharpening;

[0027] The liquid drop contour is taken, at least 16 points on the liquid drop contour are selected, and then elliptical fitting is performed to fit the complete shape of the liquid drop;

[0028] Then the baseline is confirmed, and the included angle between the tangent of the contact point and the baseline is calculated, i.e. the contact angle and the macroscopic angle are obtained.

[0029] Further, the step of dropping the liquid drop on the standard piece includes:

[0030] The surface of the standard piece is uniformly sprayed with a hydrophobic material.

[0031] Advantages: compared with the prior art, the present application has the following advantages:

[0032] 1. Precision improvement:

[0033] The present application uses the combination of 4f light path and dual-frequency grating, combined with multiple average strategies, compares the measured value (about 15.07mm) of the unknown lens with the standard value (15.5mm), and the relative error is only 2.81%, which is lower than the current existing small curvature radius measurement method; the key parameter uncertainty: contact angle ±0.28°, macroscopic angle ±0.64°, C value ±0.014mm, combined uncertainty ±0.33mm, which meets the precision requirements of micro-nano optical devices;

[0034] 2. Range expansion:

[0035] The present application firstly combines the droplet contact angle with the measurement of small curvature radius, provides a brand-new idea for the measurement of small curvature radius, fills the blank of the traditional method such as the equal-thickness interference method which is only applicable to the radius greater than 50 mm, and can be further expanded to concave surfaces and irregular curved surfaces and the like in the future;

[0036] 3. The operation process is relatively simple:

[0037] In the present application, the image preprocessing, angle calculation and curvature radius inversion are automatically completed by using Python and OpenCV, and the single measurement time is less than 10 minutes;

[0038] 4. The cost is controllable:

[0039] The total cost of the equipment in the present application is only 1 / 10 of that of a commercial small curvature radius measuring instrument, and is suitable for university scientific research and batch detection scenes of small and medium-sized enterprises. BRIEF DESCRIPTION OF DRAWINGS

[0040] Figure 1 It is a flow chart of the small curvature radius measurement method based on the coupling of droplet contact angle and macroscopic angle;

[0041] Figure 2 It is a single contour droplet contact angle schematic diagram;

[0042] Figure 3 It is a schematic diagram of solid-liquid contact line, wetting angle, contact angle and macroscopic angle;

[0043] Figure 4 It is a schematic diagram of the geometric relationship between radii;

[0044] Figure 5 It is a schematic diagram of the experimental device;

[0045] Figure 6 It is a data processing image.

[0046] Wherein: 1 is a helium-neon laser; 2 is a beam expander lens; 3 is a collimating lens; 4 is a droplet tube; 5 is a sample stage; 6 is a first Fourier lens; 7 is a dual-frequency grating filter; 8 is a second Fourier lens; 9 is an image acquisition device. DETAILED DESCRIPTION

[0047] The embodiments of the present application will be further described in detail below in combination with the drawings and examples. It can be understood that the specific embodiments described herein are only used to explain the embodiments of the present application, and not to limit the embodiments of the present application. In addition, it should be noted that, in order to facilitate description, only parts related to the embodiments of the present application are shown in the drawings, not all structures.

[0048] In the following description, for purposes of explanation and not limitation, specific details are set forth such as target system configurations, techniques, etc. in order to provide a thorough understanding of the embodiments of the present application. However, it will be apparent to those skilled in the art that the present application can be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present application with unnecessary detail.

[0049] It is to be understood that the terminology "includes", "has", "holds", "contains" and / or "comprising", when used in this specification and in the following claims, indicates the presence of the described features, integers, steps, operations, elements, and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0050] It is also to be understood that the terminology "and / or" when used in this specification and in the following claims, refers to at least one of the items, or any combination of one or more of the items, associated with the "and / or" term.

[0051] In addition, in the description of the application and in the following claims, the terms "first", "second", etc. are used only for distinguishing between similar elements, and do not imply a relative importance.

[0052] The description of the application in this specification uses reference "one embodiment" or "some embodiments" etc. to mean that a specific feature, structure, or characteristic described is included in at least one embodiment of the application. Thus, appearances of the phrases "in one embodiment" or "in some embodiments" or "in other embodiments" or "in yet other embodiments" etc. in various places in the specification are not necessarily all referring to the same embodiment, although the phrases can be so referring in some cases. Furthermore, the phrase "in other embodiments" is not necessarily referring to different but similar embodiments of the application, although it can in some cases.

[0053] As shown in the following figure, the method for measuring the small curvature radius of the convex surface based on the contact angle and the macroscopic angle of the liquid droplet of the present application comprises the following steps: Figure 1 Step 1, according to the contact angle and the macroscopic angle, a quantitative correlation formula of the curvature radius of the surface is calculated.

[0054] Further, the step of calculating the quantitative correlation formula of the curvature radius of the surface according to the contact angle and the macroscopic angle comprises:

[0055] The liquid droplet is dropped onto the surface to be measured, and when the liquid droplet is stable on the surface, as shown in the following figure, the contact angle and the macroscopic angle of the liquid droplet are measured.

[0056] Figure 2 ​As shown, the liquid-gas interface and the solid-liquid interface form an included angle at the three-phase contact line, i.e. the droplet contact angle θ, when the droplet reaches equilibrium on the curved surface, the interfacial tension balance is described by Young equation, the formula is:

[0057] ,

[0058] Wherein, θ is the contact angle of the droplet, which is a material intrinsic property and does not change with the curved surface morphology; is the solid-gas interfacial tension, is the solid-liquid interfacial tension, is the liquid-gas interfacial tension;

[0059] As shown in Figure 3 , the macroscopic angle and the wetting angle are formed between the droplet and the curved surface, the macroscopic angle is the included angle between the liquid-gas interface and the horizontal plane of the contact line, and the wetting angle is the included angle between the solid-liquid interface and the horizontal plane of the contact line, the geometric relationship satisfied by the contact angle θ, the macroscopic angle and the wetting angle is ;

[0060] As shown in Figure 4 , the geometric matching conditions of the droplet vertex curvature radius , the solid-liquid contact line radius r and the curvature radius of the curved surface to be measured are calculated, and the expression is:

[0061] ;

[0062] The curvature influence coefficient C is defined, which does not need to measure the interfacial tension separately, but can be obtained by standard calibration, and the expression is:

[0063] C= ,

[0064] The quantitative correlation formula between the contact angle, the macroscopic angle and the curvature radius is calculated as:

[0065] ,

[0066] From the formula, by measuring the contact angle θ and the macroscopic angle , and substituting the calibrated C value, the curved surface radius can be calculated.

[0067] The small curvature radius in the example refers to the case where the curvature radius is less than 50mm, and the curved surface is a convex surface, but the material of the curved surface is not limited, which can be a lens or other material curved surface, such as resin, etc.

[0068] Step 2: Construct and calibrate the measurement optical path. The measurement optical path includes, from left to right, a helium-neon laser, a beam expander lens, a collimating lens, a stage, a first Fourier lens, a dual-frequency grating filter, a second Fourier lens, and an image acquisition device.

[0069] Furthermore, in the measurement optical path, the dual-frequency grating filter is located at the rear focal point of the first Fourier lens, and the image acquisition device is located at the rear focal point of the second Fourier lens.

[0070] like Figure 5 As shown, the helium-neon laser 1 emits a laser beam, which passes through the beam expander lens 2 and the collimating lens 3 in sequence, forming a parallel beam that passes through the object surface (where the standard / test piece is placed). It then passes through a 4f optical path containing a dual-frequency grating filter 7 to enhance the edges of the liquid image and form a double-contour curve. Finally, the image is captured by an image acquisition device to visualize the image, further preparing for subsequent image processing and data analysis. This image acquisition device can be a camera 9, etc. The object surface consists of a stage 5 and the test surface placed on the stage 5. Liquid droplets are dropped onto the surface of the test surface through a dropper 4. The 4f optical path refers to placing a dual-frequency grating with 100 and 102 lines etched on the Fourier surface between two lenses, namely the first Fourier lens 6 and the second Fourier lens 8. This further enhances the image edges and forms a double-contour curve, allowing for analysis of the acquired image to obtain the droplet contact angle and macroscopic angle. This 4f optical path has functions such as light field manipulation, image enhancement, and spatial filtering.

[0071] In this example, a combination of a 4f optical path and a dual-frequency grating, along with a multi-class averaging strategy, is used to compare the measured value of the unknown lens (approximately 15.07 mm) with the standard value (15.5 mm). The relative error is only 2.81%, which is lower than the current measurement methods for small radii of curvature. The uncertainties of key parameters are: contact angle ±0.28°, macroscopic angle ±0.64°, C value ±0.014 mm, and combined uncertainty ±0.33 mm, which meets the accuracy requirements of micro-nano optical devices.

[0072] In one example, the helium-neon laser is fixed to the left of the optical axis, with the beam expander lens 9.8 mm away from it; the collimating lens is 150 mm away; the distance between the first and second Fourier lenses is the sum of their focal lengths; the dual-frequency grating filter is located at the focal point behind the first Fourier lens; and the camera is located at the focal point behind the second Fourier lens. A liquid droplet area (containing a pipette, a standard, and the sample to be tested) is placed on the stage. Coaxial and level conditions are maintained throughout the process, and the optical path is calibrated and verified using a grid screen and an F-shaped test board.

[0073] Step 3, place a standard piece with a known radius of curvature on the stage in the measurement light path, and drop a liquid droplet on the standard piece, so that the light emitted by the helium-neon laser irradiates the standard piece and the liquid droplet, and after the liquid droplet stabilizes, the image acquisition device is used to obtain the liquid droplet image on the standard piece, and the first contact angle and the first macroscopic angle are calculated.

[0074] Further, the step of obtaining the liquid droplet image on the measured piece by the image acquisition device to calculate the second contact angle and the second macroscopic angle comprises:

[0075] The image of the liquid droplet is collected 60-90 seconds after the droplet, and the liquid droplet image is pre-processed, including grayscale, denoising, image enhancement and sharpening;

[0076] The liquid droplet profile is taken, at least 16 points on the liquid droplet profile are selected, and then elliptical fitting is performed to fit the complete shape of the liquid droplet;

[0077] Then the baseline is confirmed, and the included angle between the tangent at the contact point and the baseline is calculated, i.e. the contact angle and the macroscopic angle are obtained.

[0078] As shown in Figure 6 , OpenCV image processing and Python programming technology are used to pre-process and extract the liquid droplet profile, and the double contour curve is fitted by elliptical fitting. The baseline is the straight line where the plane is located when the plane is measured, and the baseline is the three-phase contact line between the liquid droplet and the convex surface of the lens when the convex surface is measured. The included angle between the tangent at the contact point and the baseline is calculated, i.e. the contact angle and the macroscopic angle are obtained, and the reliability of the data is ensured by averaging the double contour and averaging multiple images.

[0079] Step 4, according to the first contact angle and the first macroscopic angle, the calibration value of the curvature influence coefficient is obtained.

[0080] The first contact angle and the first macroscopic angle formed between the standard piece with a known radius of curvature and the liquid droplet are brought into the quantitative correlation formula, and the radius value of the standard piece, so that the calibration value of the curvature influence coefficient C of the experimental environment can be calculated.

[0081] Step 5, replace the standard piece with the measured piece with an unknown radius of curvature, place it on the stage in the measurement light path, and drop a liquid droplet on the measured piece, so that the light emitted by the helium-neon laser irradiates the measured piece and the liquid droplet, and after the liquid droplet stabilizes, the image acquisition device is used to obtain the liquid droplet image on the measured piece, and the second contact angle and the second macroscopic angle are calculated.

[0082] Step 6, according to the second contact angle, the second macroscopic angle and the curvature influence coefficient, the radius of curvature of the measured piece is obtained.

[0083] Subsequently, the surface with small radius of curvature to be measured is replaced, and in this example, a lens is taken as an example to illustrate the previous operation. The contact angle and macroscopic angle are measured, and the C value obtained before is brought into the quantitative correlation formula derived, so that the value of the small radius of curvature of the lens to be measured can be calculated.

[0084] Further, the step of dropping the liquid droplet on the standard part before includes:

[0085] Spraying the surface of the standard part with a hydrophobic material to reduce its hydrophilicity.

[0086] In one example, for the problem of excessive hydrophilicity of the lens surface, a uniform waterproof paint is sprayed on the surface to reduce the surface hydrophilicity, so as to obtain a good liquid droplet shape image.

Claims

1. A method for measuring a convex surface of small radius of curvature based on the contact angle of a droplet and a macroscopic angle, characterized in that, The application relates to a method for measuring the curvature radius of a curved surface. A quantitative correlation formula of the curvature radius of a curved surface is calculated according to the contact angle and the macroscopic angle; A measurement light path is built and calibrated, and the measurement light path comprises, from left to right, a helium-neon laser, a beam expander lens, a collimating lens, a stage, a first Fourier lens, a dual-frequency grating filter, a second Fourier lens and an image acquisition device; A standard piece with a known curvature radius is placed on the stage in the measurement light path, and a liquid drop is dripped on the standard piece, so that the light emitted by the helium-neon laser irradiates the standard piece and the liquid drop; after the liquid drop is stable, an image of the liquid drop on the standard piece is acquired by the image acquisition device, and a first contact angle and a first macroscopic angle are calculated; A calibration value of a curvature influence coefficient is obtained according to the first contact angle and the first macroscopic angle; A to-be-measured piece with an unknown curvature radius is replaced with the standard piece and is placed on the stage in the measurement light path, and a liquid drop is dripped on the to-be-measured piece, so that the light emitted by the helium-neon laser irradiates the to-be-measured piece and the liquid drop; after the liquid drop is stable, an image of the liquid drop on the to-be-measured piece is acquired by the image acquisition device, and a second contact angle and a second macroscopic angle are calculated; The curvature radius of the to-be-measured piece is obtained according to the second contact angle, the second macroscopic angle and the curvature influence coefficient. The step of obtaining a quantitative correlation formula of the curvature radius of a curved surface according to a contact angle and a macroscopic angle comprises the following steps: A liquid drop is dripped on the to-be-measured curved surface, and when the liquid drop is stable on the curved surface, the Young equation is used to describe the interfacial tension balance, and the formula is as follows: ， Wherein, θ is the contact angle of the droplet, which is a material inherent property and does not change with the surface shape; is the solid-gas interfacial tension, is the solid-liquid interfacial tension, is the liquid-gas interfacial tension; calculating the contact angle θ, the macroscopic angle with the wetting angle geometrical relationships that are satisfied by all three, exist ; Calculate the radius of curvature at the droplet vertex The radius r of the solid-liquid contact line and the radius of curvature of the surface to be measured The geometric matching condition is expressed as: ； A curvature influence coefficient C is defined, and the expression is as follows: C= ， A quantitative correlation formula of the contact angle, the macroscopic angle and the curvature radius is calculated as follows: 。 2. The method of claim 1, wherein the macroscopic angle is a contact angle. In the measurement light path, the dual-frequency grating filter is located at the rear focal point of the first Fourier lens, and the image acquisition device is located at the rear focal point of the second Fourier lens.

3. The method of claim 1, wherein the macroscopic angle is a contact angle. The step of acquiring the image of the liquid drop on the to-be-measured piece by the image acquisition device and calculating the second contact angle and the second macroscopic angle comprises the following steps: An image of the liquid drop in a stable state is acquired 60-90 seconds after dripping, and the liquid drop image is preprocessed, including grayscale, denoising, image enhancement and sharpening; At least 16 points on the liquid drop contour are selected, and then ellipse fitting is performed to fit the complete shape of the liquid drop; Subsequently, the baseline is confirmed, and the included angle between the tangent of the contact point and the baseline is calculated, that is, the contact angle and the macroscopic angle are obtained.

4. The method of claim 1, wherein the macroscopic angle is a contact angle. The step of dripping a liquid drop on the standard piece comprises the following steps: The surface of the standard piece is uniformly sprayed with a hydrophobic material.

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