Real-time measurement method for 3D dynamic contact angle in slit flow field based on interferometry

Abstract

The present invention discloses a method for real-time measurement of 3D dynamic contact angle in a slit flow field based on interferometric measurement. The method includes: building an optical platform for real-time measurement of 3D dynamic contact angle, collecting reference interference images, and obtaining the phase distribution of the reference interference images according to the reference interference images; collecting interference images of the slit flow field to be measured in real time, obtaining the phase distribution of the interference images according to the interference images at the current moment, and obtaining the liquid surface height distribution at the current moment according to the phase distribution of the interference images at the current moment and the phase distribution of the reference interference images; obtaining the gas-liquid-solid contour line according to the liquid surface height distribution at the current moment; and obtaining the contact angle at the current moment according to the liquid surface height distribution at the current moment and the gas-liquid-solid contour line. The present invention can simultaneously achieve 3D measurement and real-time measurement of the contact angle, overcome the problem that the previous measurement methods cannot take into account both 3D measurement and real-time measurement, and is also applicable to the measurement of the contact angle of non-regularly shaped droplets or the gas-liquid interface of the flow field.

Description

Technical Field

[0001] The present invention relates to an interface analysis and testing method in the field of optical non-contact measurement, and particularly to a method for real-time measurement of 3D dynamic contact angle in a slit flow field based on interference measurement. Background Art

[0002] In an immersion lithography machine, there is a scanning and stepping movement of a silicon wafer during the exposure process, which pulls the slit flow field and forms a meniscus at the gas-liquid interface. Further, the stability of the meniscus in the slit flow field affects the yield and quality of exposure. Since the meniscus is generated during the scanning and pulling process of the silicon wafer, the dynamic contact angle formed between the meniscus and the silicon wafer is an important parameter for describing the stability of the meniscus.

[0003] For example, the critical contact angle empirical formula obtained through experiments or theories can be used to determine whether the meniscus undergoes instability and leakage, and relevant parameters such as the scanning speed of the silicon wafer that affect the dynamic contact angle can be constrained accordingly, so as to maintain the stability of the meniscus and ensure the lithography quality. Therefore, the dynamic measurement of the 3D contact angle at the gas-liquid interface of the slit flow field is crucial.

[0004] However, the real-time measurement of the 3D dynamic contact angle in the slit flow field is a technical problem. Existing testing methods often can only meet the 3D measurement or dynamic measurement of the contact angle, but cannot take both into account at the same time. For example, the Chinese invention patent with the publication number CN 110687018A discloses a 3D contact angle measurement device and method. Although it can obtain the 3D morphology images of the liquid droplet and the solid based on the interference pattern information and then obtain the 3D contact angle, since it needs to perform multi-angle scanning to obtain the 3D morphology images and the sample stage scanning angle needs to be adjusted for each scan, this will consume a certain amount of time, so it cannot achieve real-time dynamic contact angle measurement. For example, the Chinese invention patent with the publication number CN 106092832 B discloses a method for measuring the optical contact angle, but this method is only applicable to the measurement of the contact angle of small and relatively regular static liquid droplets. In addition, this method measures the contact angle by changing the laser wavelength, so this measurement method is not only relatively cumbersome, cannot perform real-time measurement, but also is not applicable to the measurement of the 3D contact angle of irregularly shaped liquid droplets or the gas-liquid interface of the flow field. For another example, the international invention patent with the publication number WO 2005 / 008220 A1 discloses a dynamic contact angle measurement device and method. This method is based on the image contour of the liquid droplet on the curved material surface captured, and image processing is performed to obtain the dynamic contact angle. Although this method can obtain the dynamic contact angle, it can only obtain the dynamic contact angle at a certain point in a certain direction and cannot obtain the 3D dynamic contact angle. Summary of the Invention

[0005] In view of the above problems, in order to overcome the deficiencies in the prior art, the object of the present invention is to provide a method for real-time measurement of 3D dynamic contact angle in a slit flow field based on interferometric measurement. The method of the present invention not only solves the problem that previous measurement methods cannot take into account both 3D measurement and real-time measurement, but also is applicable to the measurement of contact angles of irregularly shaped droplets or gas-liquid interfaces in a flow field.

[0006] The technical solution adopted by the present invention is as follows:

[0007] The real-time measurement method of 3D dynamic contact angle includes the following steps:

[0008] S1. Build an optical platform for real-time measurement of 3D dynamic contact angle.

[0009] Specifically, the optical platform for real-time measurement of 3D dynamic contact angle is built according to the interferometric optical measurement technology. The optical platform for real-time measurement of 3D dynamic contact angle uses an interferometric measurement optical path to measure the 3D dynamic contact angle in real time. The interferometric measurement optical path includes, but is not limited to, the M-Z interferometric optical path and the Michelson interferometric optical path.

[0010] Specifically, the optical platform for real-time measurement of 3D dynamic contact angle includes a helium-neon laser, a spatial filter, a collimating mirror, a first reflecting mirror, a first semi-transparent and semi-reflecting mirror, a second reflecting mirror, a third reflecting mirror, a slit flow field device to be measured, a second semi-transparent and semi-reflecting mirror, a bilateral telecentric lens, a high-speed camera, and an image processing device; the laser emitted by the helium-neon laser is expanded by the spatial filter and then forms a parallel light beam through the collimating mirror. The parallel light beam is reflected by the first reflecting mirror and then split into a reference light beam and an object light beam by the first semi-transparent and semi-reflecting mirror; the reference light beam is reflected by the second reflecting mirror and forms interference fringes with the object light beam that passes through the slit flow field device to be measured and then passes through the third reflecting mirror at the second semi-transparent and semi-reflecting mirror. The interference fringes are imaged on the CMOS sensor of the high-speed camera through the bilateral telecentric lens, and the high-speed camera inputs the collected image into the image processing device.

[0011] S2. Use the optical platform for real-time measurement of 3D dynamic contact angle to collect a reference interference image, and obtain the phase distribution of the reference interference image according to the reference interference image.

[0012] S3. Real-time collect the interference image of the slit flow field to be measured, obtain the phase distribution of the interference image according to the interference image at the current moment, and obtain the liquid surface height distribution at the current moment according to the phase distribution of the interference image at the current moment and the phase distribution of the reference interference image.

[0013] Specifically, in step S3, the following formula is used to process the phase distribution difference between the current moment and the previous moment to obtain the liquid surface height change distribution at the current moment:

[0014]

[0015] where Δh m (x, y) represents the distribution of the liquid surface height change at the current moment, represents the difference in phase distribution between the current moment and the previous moment, n w represents the refractive index of the gap flow field to be measured, n a represents the refractive index of air, and m represents the serial number of the current moment.

[0016] Specifically, the step S3 includes the following steps:

[0017] S3.1. Collect the interference image of the gap flow field to be measured at the initial moment, obtain the initial interference image phase distribution from the interference image at the initial moment, and obtain the initial liquid surface height distribution of the gap flow field to be measured according to the phase distribution difference between the initial interference image phase distribution and the reference interference image phase distribution;

[0018] In the step S3.1, the initial interference image phase distribution is processed according to the following formula to obtain the initial liquid surface height distribution of the gap flow field:

[0019]

[0020] where h 0 (x, y) represents the initial liquid surface height distribution, represents the phase distribution difference between the initial interference image phase distribution and the reference interference image phase distribution, n w represents the refractive index of the gap flow field to be measured, n a represents the refractive index of air;

[0021] S3.2. Obtain the interference image phase distribution from the interference image of the gap flow field to be measured at the first moment, obtain the distribution of the liquid surface height change at the first moment according to the phase distribution difference between the interference image phase distribution at the first moment and the initial interference image phase distribution, and take the sum of the distribution of the liquid surface height change at the first moment and the initial liquid surface height distribution as the liquid surface height distribution at the first moment;

[0022] S3.3. Obtain the interference image phase distribution from the interference image of the gap flow field to be measured at the current moment, obtain the distribution of the liquid surface height change at the current moment according to the phase distribution difference between the current moment and the previous moment, and take the sum of the distribution of the liquid surface height change at the current moment and the liquid surface height distribution at the previous moment as the liquid surface height distribution at the current moment.

[0023] S4. Obtain the gas-liquid-solid contour line corresponding to the receding dynamic contact angle and the gas-liquid-solid contour line corresponding to the advancing dynamic contact angle according to the liquid surface height distribution at the current moment.

[0024] In the step S4, the process of obtaining the gas-liquid-solid contour line corresponding to the receding dynamic contact angle according to the liquid surface height distribution at the current moment is as follows: From the value range of h m (x, y), discrete points satisfying h m (x, y) = 0 are extracted as potential receding dynamic contact angle contour points. Through neighborhood analysis, the change in the neighborhood height value of each potential receding dynamic contact angle contour point is obtained. If the change in the neighborhood height value of the potential receding dynamic contact angle contour point is greater than the preset threshold, the potential receding dynamic contact angle contour point is a receding dynamic contact angle contour point; otherwise, it is not a receding dynamic contact angle contour point. All the receding dynamic contact angle contour points are connected in spatial order to form the contour line of the receding dynamic contact angle.

[0025] In the step S4, the process of obtaining the gas-liquid-solid contour line corresponding to the advancing dynamic contact angle according to the liquid surface height distribution at the current moment is as follows: From the value range of h m (x, y), discrete points satisfying h m (x, y) = H are extracted as potential advancing dynamic contact angle contour points. Through neighborhood analysis, the change in the neighborhood height value of each potential advancing dynamic contact angle contour point is obtained. If the change in the neighborhood height value of the potential advancing dynamic contact angle contour point is greater than the preset threshold, the potential advancing dynamic contact angle contour point is an advancing dynamic contact angle contour point; otherwise, it is not an advancing dynamic contact angle contour point. All the advancing dynamic contact angle contour points are connected in spatial order to form the contour line of the advancing dynamic contact angle.

[0026] S5. Obtain the receding contact angle at the current moment according to the liquid surface height distribution at the current moment and the gas-liquid-solid contour line corresponding to the receding dynamic contact angle, and obtain the advancing contact angle at the current moment according to the liquid surface height distribution at the current moment and the gas-liquid-solid contour line corresponding to the advancing dynamic contact angle.

[0027] In the step S5, the liquid surface height distribution and the gas-liquid-solid contour line at the current moment are processed according to the following formula to obtain the contact angle at the current moment:

[0028]

[0029] In the formula, θ m (x 0 , y 0 ) represents the contact angle corresponding to the point (x 0 , y 0 ) on the gas-liquid-solid contour line. respectively represent the values of the partial derivatives of the liquid surface height distribution h m (x, y) with respect to x and y at (x 0 , y 0 ). represents the point (x on the gas-liquid-solid contour line0 , y 0 , the normal vector of the tangent plane at represents the normal vector of the xy plane.

[0030] In the steps S2 and S3, the phase distribution of the interference image is obtained from the interference image through a phase demodulation algorithm.

[0031] Specifically, the phase demodulation algorithm adopts a spatial linear carrier technique combined with a Fourier transform demodulation algorithm.

[0032] The spatial linear carrier technique combined with the Fourier transform demodulation algorithm is specifically as follows: When collecting the interference image, the two interfering light beams (reference light and object light) are relatively inclined through the spatial linear carrier technique, thereby introducing a spatial linear carrier to obtain the interference image; the phase of the interference image is demodulated through the Fourier transform demodulation algorithm.

[0033] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0034] 1. The method of the present invention obtains 3D contact angle data based on the interference non-contact measurement principle, and measures the dynamic contact angle in real time based on the spatial linear carrier and Fourier transform phase demodulation algorithm, thereby realizing the 3D measurement and real-time measurement of the contact angle simultaneously, and overcoming the drawback that the previous test methods cannot take both into account.

[0035] 2. The method of the present invention is not only applicable to the measurement of the contact angle of droplets with regular shapes, but also applicable to the measurement of the contact angle of the non-regular gas-liquid interface under non-regular droplet shapes or in a slit flow field. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 is a schematic diagram of the system solution for measuring the dynamic contact angle in a slit flow field based on the M-Z interference optical path in an embodiment of the present invention;

[0037] Figure 2 is a schematic diagram of the advancing contact angle, receding contact angle and upper and lower gas-liquid-solid interface contour lines in a slit flow field in the present invention; (a) is a graph of the liquid surface height in the A-A cross-section of the slit flow field varying with x; (b) is a schematic diagram of the A-A cross-section of the slit flow field; (c) is the projected contour of the slit flow field in the xy plane;

[0038] Figure 3 is a schematic diagram of the overall process for measuring the dynamic contact angle in a slit flow field in the present invention.

[0039] In the figure: 1. Helium-neon laser, 2. Spatial filter, 3. Collimating mirror, 4. First reflecting mirror, 5. First semi-transparent and semi-reflecting mirror, 6. Second reflecting mirror, 7. Third reflecting mirror, 8. Device for measuring the flow field of the slit to be measured, 9. Second semi-transparent and semi-reflecting mirror, 10. Double-sided telecentric lens, 11. High-speed camera, 12. Image processing device, 801. Upper plate, 802. Lower plate, 803. Flow field of the slit to be measured. Specific implementation mode

[0040] The present invention will be further described below in conjunction with the accompanying drawings and specific implementation modes.

[0041] The present invention provides a method for real-time measurement of 3D dynamic contact angle in a slit flow field based on interferometric measurement. The real-time measurement method provided by the present invention includes the following steps:

[0042] S1. Build an optical platform for real-time measurement of 3D dynamic contact angle based on interferometric measurement. The optical platform for real-time measurement of 3D dynamic contact angle uses an interferometric optical path to measure the 3D dynamic contact angle in real time. The interferometric optical path includes but is not limited to the M-Z interferometric optical path and the Michelson interferometric optical path.

[0043] As Figure 1 shown, taking the M-Z interferometric optical path of the interferometric optical path of the optical platform for real-time measurement of 3D dynamic contact angle as an example, the optical platform for real-time measurement of 3D dynamic contact angle includes a helium-neon laser 1, a spatial filter 2, a collimating mirror 3, a first reflecting mirror 4, a first semi-transparent and semi-reflecting mirror 5, a second reflecting mirror 6, a third reflecting mirror 7, a device 8 for measuring the flow field of the slit to be measured, a second semi-transparent and semi-reflecting mirror 9, a double-sided telecentric lens 10, a high-speed camera 11 and an image processing device 12. The laser emitted by the helium-neon laser 1 is expanded by the spatial filter 2 to generate an expanded laser, and the expanded laser forms a parallel light beam through the collimating mirror 3. After the parallel light beam passes through the first reflecting mirror 4, it is split by the first semi-transparent and semi-reflecting mirror 5 to generate a reference light beam split and an object light beam split. The reference light beam split passes through the air domain and is then reflected by the second reflecting mirror 6 and interferes with the object light passing through the device 8 for measuring the flow field of the slit to be measured after passing through the third reflecting mirror 7 to form interference fringes at the second semi-transparent and semi-reflecting mirror 9. The interference fringes are imaged on the COMS sensor of the high-speed camera 11 through the double-sided telecentric lens 10, and the high-speed camera 11 inputs the collected image into the image processing device 12, and the image processing device 12 performs image processing to obtain the dynamic contact angle of the flow field 803 of the slit to be measured.

[0044] The device 8 for measuring the flow field of the slit to be measured is mainly composed of an upper plate 801, a lower plate 802 and a flow field 803 of the slit to be measured; the upper plate 801 and the lower plate 802 are arranged in parallel at intervals, and the slit between the upper plate 801 and the lower plate 802 forms a test channel, and a flow field 803 of the slit to be measured with a gas-liquid interface is established by injecting liquid and gas into the test channel.

[0045] S2. Before establishing the flow field 803 of the gap to be measured, use a 3D dynamic contact angle real-time measurement optical platform to collect the reference interference image when only air is filled in the gap between the upper plate 801 and the lower plate 802, and obtain the phase distribution of the reference interference image according to the reference interference image.

[0046] Among them, the phase distribution of the reference interference image is obtained according to the reference interference image through a phase demodulation algorithm.

[0047] S3. Establish the flow field 803 of the gap to be measured by injecting liquid and gas into the gap between the upper plate 801 and the lower plate 802. Move the lower plate 802 parallel to the scanning direction, and collect the interference images of the flow field 803 of the gap to be measured at each moment in real time. Obtain the phase distribution of the interference image according to the interference image at the current moment, and obtain the liquid surface height distribution at the current moment according to the phase distribution of the interference image at the current moment and the phase distribution of the reference interference image. Among them, the phase distribution of the interference image is obtained according to the interference image at the current moment through a phase demodulation algorithm.

[0048] Step S3 includes the following steps:

[0049] S3.1. Collect the interference image of the flow field 803 of the gap to be measured at the initial moment (the 0th moment), obtain the initial interference image phase distribution according to the interference image at the initial moment, and obtain the initial liquid surface height distribution of the flow field 803 of the gap to be measured according to the phase distribution difference between the initial interference image phase distribution and the reference interference image phase distribution;

[0050] In step S3.1, process the initial interference image phase distribution according to the following formula to obtain the initial liquid surface height distribution of the flow field 803 of the gap to be measured:

[0051]

[0052] In the formula, h 0 (x, y) represents the initial liquid surface height distribution, represents the phase distribution difference between the initial interference image phase distribution and the reference interference image phase distribution, n w represents the refractive index of the flow field of the gap to be measured, n a represents the refractive index of air, and 0 represents the initial moment, that is, the 0th moment.

[0053] S3.2. Collect the interference image of the flow field 803 of the gap to be measured at the first moment, obtain the phase distribution of the interference image according to the interference image at the first moment through a phase demodulation algorithm, obtain the liquid surface height change distribution at the first moment according to the phase distribution difference between the phase distribution of the interference image at the first moment and the initial interference image phase distribution, and use the sum of the liquid surface height change distribution at the first moment and the initial liquid surface height distribution as the liquid surface height distribution at the first moment;

[0054] In step S3.2, the phase distribution difference between the interference image phase distribution at the first moment and the initial interference image phase distribution is processed according to the following formula to obtain the liquid surface height change distribution at the first moment:

[0055]

[0056] In the formula, Δh 1 (x, y) represents the liquid surface height change distribution at the first moment, represents the phase distribution difference between the interference image phase distribution at the first moment and the initial interference image phase distribution, n w represents the refractive index of the slit flow field to be measured, n a represents the refractive index of air, x represents the coordinate of the x-axis, y represents the coordinate of the y-axis, and the x-y plane is parallel to the upper plate 801 and the lower plate 802.

[0057] S3.3. Obtain the interference image phase distribution from the interference image at the current moment through the phase demodulation algorithm, obtain the liquid surface height change distribution at the current moment according to the phase distribution difference between the current moment and the previous moment, and use the sum of the liquid surface height change distribution at the current moment and the liquid surface height distribution at the previous moment as the liquid surface height distribution at the current moment.

[0058] In step S3.3, the phase distribution difference between the current moment and the previous moment is processed according to the following formula to obtain the liquid surface height change distribution at the current moment:

[0059]

[0060] In the formula, Δh m (x, y) represents the liquid surface height change distribution at the current moment, represents the phase distribution difference between the current moment and the previous moment, n w represents the refractive index of the slit flow field to be measured, n a represents the refractive index of air, x represents the coordinate of the x-axis, y represents the coordinate of the y-axis, and m represents the serial number of the current moment. When m = 1, Δh 1 (x, y) represents the liquid surface height change distribution at the first moment, represents the phase distribution difference between the interference image phase distribution at the first moment and the initial interference image phase distribution.

[0061] S4. Obtain the gas-liquid-solid contour line according to the liquid surface height distribution at the current moment: identify the gas-liquid-solid contour lines corresponding to the advancing dynamic contact angle and the receding dynamic contact angle.

[0062] Taking the parallel movement of the lower plate 802 along the scanning direction as an example, during the movement, the lower plate 802 generates shear force, so that the fluid close to the lower plate 802 obtains a component velocity along the scanning direction, thereby causing the upper and lower surfaces of the initially columnar gap flow field 803 to be measured to be misaligned and the bottom contour to be deformed. The interface dynamic contact angle corresponding to the gas-liquid-solid contour line when the upper surface of the moving lower plate 802 enters the gap flow field 803 to be measured is called the forward dynamic contact angle; the interface dynamic contact angle corresponding to the gas-liquid-solid contour line when the upper surface of the lower plate 802 leaves the gap flow field 803 to be measured is called the receding dynamic contact angle. Figure 2 As shown in (b) and (c), the scanning direction is the U direction, the gas-liquid-solid contour line corresponding to the upper plate receding dynamic contact angle is ebf; the gas-liquid-solid contour line corresponding to the upper plate advancing dynamic contact angle is eaf; the gas-liquid-solid contour line corresponding to the lower plate receding dynamic contact angle is ecf; the gas-liquid-solid contour line corresponding to the lower plate advancing dynamic contact angle is edf. Therefore, the gas-liquid-solid contour line corresponding to the receding dynamic contact angle is ebfc; and the gas-liquid-solid contour line corresponding to the advancing dynamic contact angle is edfa.

[0063] In step S4, the process of obtaining the gas-liquid-solid contour line corresponding to the receding dynamic contact angle according to the liquid level height distribution at the current moment is as follows: m Extract the value range (x,y) that satisfies h m A discrete point where (x, y)=0 is taken as a potential receding dynamic contact angle contour point, and a neighborhood analysis is performed on each potential receding dynamic contact angle contour point to obtain a change in the neighborhood height value of each potential receding dynamic contact angle contour point. If the change in the neighborhood height value of the potential receding dynamic contact angle contour point is greater than a preset threshold, the potential receding dynamic contact angle contour point is a receding dynamic contact angle contour point; if the change in the neighborhood height value of the potential receding dynamic contact angle contour point is less than the preset threshold, the potential receding dynamic contact angle contour point is not a receding dynamic contact angle contour point; all receding dynamic contact angle contour points are connected in spatial order to form a contour line of the receding dynamic contact angle.

[0064] In step S4, the process of obtaining the gas-liquid-solid contour line corresponding to the advancing dynamic contact angle according to the liquid level height distribution at the current moment is as follows: m Extract the value range (x,y) that satisfies h mThe discrete points of (x, y) = H are used as potential advancing dynamic contact angle profile points. Neighborhood analysis is performed on each potential advancing dynamic contact angle profile point to obtain the change in neighborhood height value of each potential advancing dynamic contact angle profile point. If the change in neighborhood height value of the potential advancing dynamic contact angle profile point is greater than the preset threshold, the potential advancing dynamic contact angle profile point is an advancing dynamic contact angle profile point. If the change in neighborhood height value of the potential advancing dynamic contact angle profile point is less than the preset threshold, the potential advancing dynamic contact angle profile point is not an advancing dynamic contact angle profile point. All advancing dynamic contact angle profile points are connected in spatial order to form the contour line of the advancing dynamic contact angle.

[0065] S5. Obtain the receding contact angle at the current moment according to the liquid surface height distribution at the current moment and the gas-liquid-solid contour line corresponding to the receding dynamic contact angle, and obtain the advancing contact angle at the current moment according to the liquid surface height distribution at the current moment and the gas-liquid-solid contour line corresponding to the advancing dynamic contact angle.

[0066] In step S5, the liquid surface height distribution and the gas-liquid-solid contour line at the current moment are processed according to the following formula to obtain the contact angle at the current moment:

[0067]

[0068] In the formula, θ m (x 0 , y 0 ) represents the contact angle corresponding to the point (x 0 , y 0 ) on the gas-liquid-solid contour line. respectively represent the values of the partial derivatives of the liquid surface height distribution h m (x, y) with respect to x and y at the point (x 0 , y 0 ). represents the normal vector of the tangent plane at the point (x 0 , y 0 ) on the gas-liquid-solid contour line. represents the normal vector of the xy plane, that is, (0, 0, 1).

[0069] Furthermore, in the method of the present invention, the phase demodulation algorithm adopts the spatial linear carrier technology combined with the Fourier transform demodulation algorithm. Since the spatial carrier interferometry is based on the analysis of a single interference pattern and is suitable for the measurement of dynamic phenomena, the combination of the spatial linear carrier technology and the Fourier transform demodulation algorithm can realize the measurement of the dynamic contact angle.

[0070] The spatial linear carrier technology is combined with the Fourier transform demodulation algorithm as follows: first, by making the two interfering light beams tilt relative to each other, that is, when interference occurs, the reference light has a certain angle with the object light, thereby introducing a linear carrier signal in the spatial domain, so that the phase information of the original signal is modulated to a specific position of the spectrum, and the interference image is obtained; for the interference image, the signal is converted to the frequency domain through Fourier transform, and the corresponding spectral components are isolated and extracted in the frequency domain; finally, the phase information is restored through inverse Fourier transform, thereby completing the demodulation process.

[0071] In the 3D dynamic contact angle real-time measurement optical platform provided by the present invention, a small rotation angle is introduced by fine-tuning the rotation adjustment bolt of the second reflector 6 or the third reflector 7, so that a certain relative tilt is generated between the reference light and the object light when interference occurs.

[0072] The specific embodiments of the present invention are as follows:

[0073] This embodiment is based on the MZ interference optical path to establish Figure 1 The optical platform for real-time measurement of dynamic contact angle is shown. The 632.8nm laser emitted by the helium-neon laser 1 is expanded to a certain diameter through the spatial filter 2 (the diameter must be greater than the maximum distance between any two points on the projection contour of the slit flow field 803 to be measured on the lower plate 802). The expanded laser passes through the collimator 3 to form a parallel light beam. The parallel light beam passes through the first reflector 4 and reaches the first semi-transparent mirror 5. The first semi-transparent mirror 5 divides the parallel light beam into a transmitted light beam and a reflected light beam. The transmitted light beam is used as the reference light, and the reflected light beam is used as the object light. The reference light passes through the air domain and is reflected by the second reflector 6. After passing through the third reflector 7 and passing through the slit flow field 803 to be measured, interference fringes are formed at the second semi-transparent mirror 9. The interference fringes are imaged on the COMS sensor of the high-speed camera 11 through the double-sided telecentric lens 10. Finally, image processing is performed on the image processing device 12 to obtain the dynamic contact angle data of the slit flow field.

[0074] In this embodiment, both the upper plate 801 and the lower plate 802 are made of quartz glass. Figure 2 As shown in (b), the gap flow field 803 to be measured is located between the upper plate 801 and the lower plate 802. When the lower plate 802 moves to the left at a speed U, a shear force will be generated, and the fluid close to the lower plate 802 will obtain a component velocity along the scanning direction, so that the upper and lower surfaces of the originally columnar gap flow field to be measured will be misaligned and the bottom contour will be deformed. At this time, the gas-liquid-solid contour line corresponding to the receding dynamic contact angle of the upper plate is ebf; the gas-liquid-solid contour line corresponding to the advancing dynamic contact angle of the upper plate is eaf; the gas-liquid-solid contour line corresponding to the receding dynamic contact angle of the lower plate is ecf; and the gas-liquid-solid contour line corresponding to the advancing dynamic contact angle of the lower plate is edf. In summary, the gas-liquid-solid contour line corresponding to the receding dynamic contact angle is ebfc; and the gas-liquid-solid contour line corresponding to the advancing dynamic contact angle is edfa.

[0075] Next, this embodiment will further introduce the measurement principle of the dynamic contact angle in the slit flow field in combination with the measurement process as shown below: Figure 3

[0076] S1. Build an optical platform for real-time measurement of 3D dynamic contact angle based on interference measurement as shown below: Figure 1

[0077] S2. Use the optical platform for real-time measurement of 3D dynamic contact angle to collect the reference interference image I(x,y) (i.e., the interference image under the condition of filling air), and obtain the phase distribution of the reference interference image according to the reference interference image, which is expressed as: a That is

[0078] S3. Inject liquid and gas to establish the slit flow field 803 to be measured, and start to collect the interference images of the slit flow field 803 to be measured at each moment in real time. According to the interference image of the slit flow field 803 to be measured at the current moment mΔt, obtain the phase distribution of the interference image at the current moment mΔt, which is expressed as: The phase distribution of the interference image at the current moment mΔt is expressed as:

[0079]

[0080] In the formula, n w represents the refractive index of the slit flow field to be measured, and n a represents the refractive index of air; represents the phase distribution of the interference image at the current moment mΔt, and s represents the integration domain along the optical path.

[0081] According to the above formula, it can be obtained that:

[0082]

[0083] In the formula, nw represents the refractive index of the slit flow field to be measured, na represents the refractive index of air, h(x,y) represents the liquid surface height distribution at the current moment mΔt, m represents the phase distribution of the reference interference image, represents the phase distribution of the interference image at the current moment mΔt.

[0084] Thus, the phase difference between the initial interference image phase distribution and the reference interference image phase distribution can be obtained, that is, the phase distribution difference:

[0085] ​​​​​​

[0086] In the formula, represents the phase distribution difference between the initial interference image phase distribution and the reference interference image phase distribution, represents the initial interference image phase distribution, represents the reference interference image phase distribution, h 0 (x, y) represents the initial liquid surface height distribution, nw represents the refractive index of the slit flow field to be measured, and na represents the refractive index of air.

[0087] Thus, the initial liquid surface height distribution h 0 (x, y) can be expressed as:

[0088]

[0089] In the formula, represents the phase distribution difference between the initial interference image phase distribution and the reference interference image phase distribution, h 0 (x, y) represents the initial liquid surface height distribution, nw represents the refractive index of the slit flow field to be measured, n a represents the refractive index of air.

[0090] Within the sampling interval Δt (the reciprocal of the camera frame rate), the phase difference distribution between two adjacent frames of interference images, that is, the phase distribution difference between the current moment and the previous moment is expressed as:

[0091]

[0092] In the formula, represents the phase distribution difference between the current moment and the previous moment, represents the interference image phase distribution at the current moment mΔt, represents the interference image phase distribution at the previous moment, h m (x, y) represents the liquid surface height distribution at the current moment, h m-1 (x, y) represents the liquid surface height distribution at the previous moment.

[0093] Furthermore, the liquid surface height change distribution corresponding to two adjacent frames of interference images, that is, the liquid surface height change distribution at the current moment can be expressed as:

[0094]

[0095] In the formula, Δh m (x, y) represents the liquid surface height change distribution at the current moment, represents the phase distribution difference between the current moment and the previous moment, n w represents the refractive index of the slit flow field to be measured, n arepresents the refractive index of air, x represents the coordinate of the x-axis, y represents the coordinate of the y-axis, m represents the serial number of the current moment, h m (x,y) represents the liquid surface height distribution at the current moment, h m-1 (x,y) represents the liquid surface height distribution at the previous moment.

[0096] Thus, the liquid surface height distribution corresponding to the current moment mΔt can be obtained:

[0097]

[0098] In the formula, h m (x,y) represents the liquid surface height distribution at the current moment, h 0 (x,y) represents the initial liquid surface height distribution, Δh m (x,y) represents the liquid surface height change distribution at the current moment, represents the cumulative sum of the liquid surface height change distribution from the first moment to the current moment.

[0099] Convert the above formula into a discrete dynamic explicit equation of the liquid surface curve:

[0100] Σ m : z = h m (x,y)

[0101] In the formula, z represents the coordinate of the z-axis, h m (x,y) represents the liquid surface height change distribution at the current moment.

[0102] S4. Obtain the gas-liquid-solid contour line according to the liquid surface height distribution at the current moment.

[0103] For any point (x 0 , y 0 ) on the gas-liquid-solid interface line contour, its tangent plane equation can be expressed as:

[0104]

[0105] Among them, respectively represent the values of the derivative of the liquid surface height distribution h m (x,y) with respect to x and y at (x 0 , y 0 ), and z represents the coordinate of the z-axis.

[0106] The specific process of obtaining the gas-liquid-solid contour line according to the liquid surface height distribution at the current moment is as follows:

[0107] S4.1. Obtain the gas-liquid-solid contour line (ebfc) corresponding to the receding dynamic contact angle.

[0108] S4.1.1. Traverse the liquid surface height distribution hm (x, y) data, find the set of discrete points that satisfy the following conditions:

[0109] Υ ret ={(x, y)h m (x, y)=0}

[0110] In the formula, Υ ret represents the set of potential receding dynamic contact angle profile points.

[0111] S4.1.2. Obtain the change in neighborhood height value for each potential receding dynamic contact angle profile point. Specifically, the change in neighborhood height value is: the maximum value of the height differences between the potential receding dynamic contact angle profile point and each of its neighborhood points.

[0112] For each potential receding dynamic contact angle profile point (x ret , y ret ) ∈ Υ ret , calculate the height value h m (x δ , y δ ) of each neighborhood point of the potential receding dynamic contact angle profile point. Among them, (x δ , y δ ) represents the neighborhood point (taking the four-neighborhood as an example (x δ , y δ ) ∈ {(x ret + 1, y ret ), (x ret - 1, y ret ), (x ret , y ret + 1), (x ret , y ret - 1)}.

[0113] Calculate the neighborhood height change according to the following formula:

[0114]

[0115] In the formula, Δh m represents the neighborhood height change. (x δ , y δ ) represents the neighborhood point, (x ret , y ret ) represents the potential receding dynamic contact angle profile point, h m (x δ , y δ ) represents the height value of the neighborhood point, h m (x ret , y ret ) represents the height value of the potential receding dynamic contact angle profile point.

[0116] S4.1.3. Extract the set of receding dynamic contact angle profile points from the set of potential receding dynamic contact angle profile points by analyzing the change in neighborhood height values. Specifically:

[0117] If the neighborhood height change is greater than the preset threshold, then the potential receding dynamic contact angle profile point is a receding dynamic contact angle profile point; otherwise, it is not a receding dynamic contact angle profile point.

[0118] S4.1.4. Connect all the receding dynamic contact angle profile points in spatial order to form the contour line of the receding dynamic contact angle.

[0119] S4.2. Obtain the gas-liquid-solid contour line (edfa) corresponding to the advancing dynamic contact angle.

[0120] S4.2.1. Traverse the liquid surface height distribution h m (x, y) to find the set of discrete points that satisfy the following conditions:

[0121] Υ for ={(x, y)h m (x, y)=H}

[0122] In the formula, Υ for represents the set of potential advancing dynamic contact angle profile points.

[0123] S4.1.2. Obtain the change in neighborhood height value for each potential advancing dynamic contact angle profile point. Among them, the change in neighborhood height value is specifically: the maximum value of the height differences between the potential advancing dynamic contact angle profile point and its respective neighborhood points.

[0124] For each potential advancing dynamic contact angle profile point (x for , y for ) ∈ Υ for , calculate the height value h m (x δ , y δ ) of each neighborhood point of the potential advancing dynamic contact angle profile point. Among them, (x δ , y δ ) represents the neighborhood point (taking the four-neighborhood as an example (x δ , y δ ) ∈{(x for + 1, y for ), (x for - 1, y for ), (x for , y for + 1), (x for , y for - 1)}.

[0125] Calculate the neighborhood height change according to the following formula:

[0126]

[0127] In the formula, Δh m represents the change in neighborhood height. (x δ , y δ ) represents a neighborhood point, (x for , y for ) represents a potential advancing dynamic contact angle profile point, h m (x δ , y δ ) represents the height value of the neighborhood point, h m (x for , y for ) represents the height value of the potential advancing dynamic contact angle profile point.

[0128] S4.1.3. Extract the advancing dynamic contact angle profile point set from the set of potential advancing dynamic contact angle profile points by analyzing the change in neighborhood height values. Specifically:

[0129] If the neighborhood height change is greater than the preset threshold, then the potential advancing dynamic contact angle profile point is an advancing dynamic contact angle profile point; otherwise, it is not.

[0130] S4.1.4. Connect all the advancing dynamic contact angle profile points in spatial order to form the contour line of the advancing dynamic contact angle.

[0131] S5. Obtain the contact angle at the current moment based on the liquid surface height distribution and the gas-liquid-solid contour line at the current moment.

[0132] The contact angle corresponding to the point (x 0 , y 0 ) on the gas-liquid-solid contour line at the current moment mΔt is expressed as the angle between the tangent plane normal vector and the x-y plane normal vector (0, 0, 1):

[0133]

[0134] In the formula, θ m (x 0 , y 0 ) represents the contact angle corresponding to the point (x 0 , y 0 ) on the gas-liquid-solid contour line, respectively represent the values obtained by taking the derivatives of the liquid surface height distribution h m (x, y) with respect to x and y and evaluating them at (x 0 , y 0 ), n 1 represents the gas-liquid-solid contour line at the point (x 0 , y 0The normal vector of the tangent plane at (), n 2 represents the normal vector of the xy plane, i.e., (0, 0, 1).

[0135] As can be seen from the implementation, the present invention can simultaneously achieve 3D measurement and real-time measurement of the contact angle, overcoming the drawback that the previous testing methods cannot take both into account. In addition, this method is applicable not only to the measurement of the contact angle of droplets with regular shapes, but also to the measurement of the contact angle of irregularly shaped droplets or the irregular gas-liquid interface under a slit flow field

[0136] In the description of the positional relationship of the present invention, terms such as "inner", "outer", "upper", "lower", "left", "right", etc., indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the embodiments and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention.

[0137] The above content and structure describe the basic principle, main features and advantages of the product of the present invention, which should be understood by those skilled in the art. What is described in the above examples and the specification only illustrates the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A real-time measurement method of 3D dynamic contact angle in a gap flow field based on interferometry, characterized in that: The following steps are involved: S1. Build an optical platform for real-time measurement of 3D dynamic contact angle; S2, using the 3D dynamic contact angle real-time measurement optical platform to collect a reference interference image, and obtaining a reference interference image phase distribution according to the reference interference image; S3, collecting the interference image of the gap flow field to be measured in real time, obtaining the interference image phase distribution according to the interference image at the current moment, and obtaining the liquid level height distribution at the current moment according to the interference image phase distribution at the current moment and the reference interference image phase distribution; S4, obtaining a gas-liquid-solid contour line corresponding to a receding dynamic contact angle and a gas-liquid-solid contour line corresponding to an advancing dynamic contact angle according to the liquid level height distribution at the current moment; S5. The receding contact angle at the current moment is obtained according to the liquid level height distribution at the current moment and the gas-liquid-solid contour line corresponding to the receding dynamic contact angle, and the advancing contact angle at the current moment is obtained according to the liquid level height distribution at the current moment and the gas-liquid-solid contour line corresponding to the advancing dynamic contact angle.

2. The real-time measurement method of 3D dynamic contact angle in a gap flow field according to claim 1, characterized in that: The step S3 comprises the following steps: S3.1, collecting the interference image of the gap flow field to be measured at the initial moment, obtaining the initial interference image phase distribution according to the interference image at the initial moment, and obtaining the initial liquid level height distribution of the gap flow field to be measured according to the phase distribution difference between the initial interference image phase distribution and the reference interference image phase distribution; S3.2, obtaining an interference image phase distribution according to the interference image of the gap flow field to be measured at the first moment, obtaining a liquid level height change distribution at the first moment according to a phase distribution difference between the interference image phase distribution at the first moment and the initial interference image phase distribution, and taking the sum of the liquid level height change distribution at the first moment and the initial liquid level height distribution as the liquid level height distribution at the first moment; S3.

3. Obtain the interference image phase distribution based on the interference image of the gap flow field to be measured at the current moment, obtain the liquid level height change distribution at the current moment based on the phase distribution difference between the current moment and the previous moment, and take the sum of the liquid level height change distribution at the current moment and the liquid level height distribution at the previous moment as the liquid level height distribution at the current moment.

3. The real-time measurement method of 3D dynamic contact angle in a gap flow field according to claim 2, characterized in that: In step S3, the phase distribution difference between the current moment and the previous moment is processed according to the following formula to obtain the liquid level height change distribution at the current moment: In the formula, Δh m (x,y) represents the liquid level change distribution at the current moment, Indicates the difference in phase distribution between the current moment and the previous moment, n w Represents the refractive index of the gap flow field to be measured, n a represents the refractive index of air, and m represents the sequence number of the current moment.

4. The real-time measurement method of 3D dynamic contact angle in a gap flow field according to claim 2, characterized in that: In step S3.1, the initial interference image phase distribution is processed according to the following formula to obtain the initial liquid level height distribution of the gap flow field: In the formula, h 0 (x,y) represents the initial liquid level distribution, represents the phase distribution difference between the initial interference image phase distribution and the reference interference image phase distribution, n w Represents the refractive index of the gap flow field to be measured, n a Represents the refractive index of air.

5. The real-time measurement method of 3D dynamic contact angle in a gap flow field according to claim 1, characterized in that: In step S4, the process of obtaining the gas-liquid-solid contour line corresponding to the receding dynamic contact angle according to the liquid level height distribution at the current moment is as follows: m Extract the value range (x,y) that satisfies h m The discrete point where (x, y)=0 is used as a potential receding dynamic contact angle contour point, and the neighborhood height value change of each potential receding dynamic contact angle contour point is obtained through neighborhood analysis. If the neighborhood height value change of the potential receding dynamic contact angle contour point is greater than a preset threshold, the potential receding dynamic contact angle contour point is a receding dynamic contact angle contour point, otherwise, it is not a receding dynamic contact angle contour point; all receding dynamic contact angle contour points are connected in spatial order to form a contour line of the receding dynamic contact angle; In step S4, the process of obtaining the gas-liquid-solid contour corresponding to the advancing dynamic contact angle according to the liquid level height distribution at the current moment is as follows: m Extract the value range (x,y) that satisfies h m The discrete points where (x, y) = H are taken as potential forward dynamic contact angle contour points. The changes in the neighborhood height values ​​of each potential forward dynamic contact angle contour point are obtained through neighborhood analysis. If the changes in the neighborhood height values ​​of the potential forward dynamic contact angle contour point are greater than a preset threshold, the potential forward dynamic contact angle contour point is a forward dynamic contact angle contour point, otherwise, it is not a forward dynamic contact angle contour point. All forward dynamic contact angle contour points are connected in spatial order to form a contour line of the forward dynamic contact angle.

6. The real-time measurement method of 3D dynamic contact angle in a gap flow field according to claim 1, characterized in that: In step S5, the liquid level height distribution and the gas-liquid-solid contour line at the current moment are processed according to the following formula to obtain the contact angle at the current moment: In the formula, θ m (x0, y0) represents the contact angle corresponding to the point (x0, y0) on the gas-liquid-solid contour line. Respectively represent the liquid level height distribution h at the current moment m The value of (x,y) at (x0,y0) after taking the derivative of x and y, represents the normal vector of the tangent plane at the point (x0, y0) on the gas-liquid-solid contour line, Represents the normal vector of the xy plane.

7. The real-time measurement method of 3D dynamic contact angle in a gap flow field according to claim 1, characterized in that: The phase distribution of the interference image is obtained according to the interference image through a phase demodulation algorithm.

8. The real-time measurement method of 3D dynamic contact angle in a gap flow field according to claim 7, characterized in that: The phase demodulation algorithm adopts spatial linear carrier technology combined with Fourier transform demodulation algorithm; the spatial linear carrier technology combined with Fourier transform demodulation algorithm is specifically: the two interference light beams are tilted relative to each other through spatial linear carrier technology to obtain an interference image; the interference image is phase demodulated through the Fourier transform demodulation algorithm.

9. The real-time measurement method of 3D dynamic contact angle in a gap flow field according to claim 1, characterized in that: The 3D dynamic contact angle real-time measurement optical platform is built based on interference optical measurement technology.

10. The real-time measurement method of 3D dynamic contact angle in a gap flow field according to claim 1, characterized in that: The 3D dynamic contact angle real-time measurement optical platform comprises a helium-neon laser (1), a spatial filter (2), a collimator (3), a first reflector (4), a first semi-transparent and semi-reflective mirror (5), a second reflector (6), a third reflector (7), a gap flow field device to be measured (8), a second semi-transparent and semi-reflective mirror (9), a double-sided telecentric lens (10), a high-speed camera (11) and an image processing device (12); the laser light emitted by the helium-neon laser (1) is expanded by the spatial filter (2) and then forms a flat beam through the collimator (3). The parallel light beam is reflected by a first reflector (4) and then split by a first semi-transparent and semi-reflective mirror (5) to generate a reference light beam and an object light beam; the reference light beam is reflected by a second reflector (6) and then forms interference fringes at the second semi-transparent and semi-reflective mirror (9) with the object light that passes through a slit flow field device (8) to be measured after passing through a third reflector (7); the interference fringes are imaged on a COMS sensor of a high-speed camera (11) via a double-sided telecentric lens (10); and the high-speed camera (11) inputs the collected image into an image processing device (12).

Images