Method for measuring 3D dynamic contact angle in gap flow field in real time based on interference measurement

Abstract

The invention discloses a real-time measurement method for a 3D dynamic contact angle in a gap flow field based on interference measurement. Comprising the steps that a 3D dynamic contact angle real-time measurement optical platform is built, a reference interference image is collected, and reference interference image phase distribution is obtained according to the reference interference image; an interference image of the gap flow field to be measured is collected in real time, interference image phase distribution is obtained according to the interference image at the current moment, and liquid level height distribution at the current moment is obtained according to the interference image phase distribution at the current moment and the reference interference image phase distribution; obtaining a gas-liquid-solid contour line according to the liquid level height distribution at the current moment; and obtaining the contact angle at the current moment according to the liquid level height distribution and the gas-liquid-solid contour line at the current moment. According to the invention, 3D measurement and real-time measurement of the contact angle can be realized at the same time, the problem that 3D measurement and real-time measurement cannot be realized at the same time in the conventional test method is solved, and the method is also suitable for contact angle measurement of irregular liquid drops or flow field gas-liquid interfaces.

Description

Technical Field

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

[0002] In an immersion lithography machine, the exposure process involves a stepping motion of the silicon wafer scanning, which pulls the gap flow field and forms a meniscus at the gas-liquid interface. Furthermore, the stability of the meniscus of the gap flow field affects the yield and yield of the 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 used to describe the stability of the meniscus.

[0003] For example, the critical contact angle empirical formula obtained from experiments or theories can be used to determine whether the meniscus has unstable leakage, and thus constrain the relevant parameters such as the wafer scanning speed that affect the dynamic contact angle, thereby maintaining the stability of the meniscus and ensuring the lithography yield. Therefore, the dynamic measurement of the 3D contact angle of the gas-liquid interface in the gap flow field is crucial.

[0004] However, the real-time measurement of 3D dynamic contact angle in the gap flow field is a technical problem. The existing test methods 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 publication number CN 110687018A discloses a 3D contact angle measurement device and measurement method. Although it can obtain the 3D topography image of the droplet and the solid based on the interference pattern information and then obtain the 3D contact angle, it needs to perform multi-angle scanning to obtain the 3D topography image, and the sample stage scanning angle needs to be adjusted for each scan, which will take a certain amount of time, so it cannot achieve real-time dynamic contact angle measurement. For example, the Chinese invention patent with publication number CN 106092832 B discloses a method for measuring optical contact angle, but this method is only applicable to the measurement of small and relatively regular static droplet contact angles. In addition, the method needs to change the laser wavelength to measure the contact angle, so this measurement method is not only relatively cumbersome and cannot be measured in real time, but also not applicable to the 3D contact angle measurement of irregular droplets or flow field gas-liquid interfaces. For another example, the international invention patent with publication number WO 2005 / 008220 A1 discloses a dynamic contact angle measurement device and method. The method performs image processing based on the image profile of a droplet on the surface of a curved material to obtain a dynamic contact angle. Although the method can obtain a dynamic contact angle, it can only obtain a dynamic contact angle corresponding to a certain point in a certain direction, and cannot obtain a 3D dynamic contact angle. Summary of the invention

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

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

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

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

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

[0010] Specifically, the 3D dynamic contact angle real-time measurement optical platform includes a helium-neon laser, a spatial filter, a collimator, a first reflector, a first semi-transparent and semi-reflective mirror, a second reflector, a third reflector, a gap flow field device to be measured, a second semi-transparent and semi-reflective mirror, a double-sided 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 formed into a parallel light beam by the collimator, and the parallel light beam is reflected by the first reflector and then split by the first semi-transparent and semi-reflective mirror to generate a reference light beam and an object light beam; the reference light beam is reflected by the second reflector and forms interference fringes at the second semi-transparent and semi-reflective mirror with the object light that passes through the gap flow field device to be measured after passing through the third reflector, and the interference fringes are imaged on the COMS sensor of the high-speed camera through the double-sided telecentric lens, and the high-speed camera inputs the collected image into the image processing device.

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

[0012] 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.

[0013] Specifically, 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:

[0014]

[0015] 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.

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

[0017] 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;

[0018] 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:

[0019]

[0020] 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;

[0021] 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;

[0022] 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.

[0023] S4. Obtaining 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 level distribution at the current moment.

[0024] 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 taken as the potential receding dynamic contact angle contour point. 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 the preset threshold, the potential receding dynamic contact angle contour point is the receding dynamic contact angle contour point, otherwise, it is not the receding dynamic contact angle contour point; all the receding dynamic contact angle contour points are connected in spatial order to form a contour line of the receding dynamic contact angle.

[0025] 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.

[0026] S5. Obtain the receding contact angle at the current moment 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 obtain the advancing contact angle at the current moment 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.

[0027] 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:

[0028]

[0029] 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.

[0030] In step S2 and step S3, the interference image phase distribution is obtained according to the interference image by using a phase demodulation algorithm.

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

[0032] The spatial linear carrier technology is combined with the Fourier transform demodulation algorithm as follows: when collecting the interference image, the spatial linear carrier technology is used to make the two interference light beams (reference light and object light) tilt relative to each other, thereby introducing the spatial linear carrier and obtaining the interference image; the interference image is phase demodulated by the Fourier transform demodulation algorithm.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

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

[0035] 2. The method of the present invention is not only applicable to the measurement of contact angles of regular-shaped droplets, but also to the measurement of contact angles of irregular-shaped droplets or irregular gas-liquid interfaces under slit flow fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Schematic diagram of a system solution for measuring the dynamic contact angle in a gap flow field based on the MZ interference optical path in an embodiment of the present invention;

[0037] Figure 2 Schematic diagram of the advancing contact angle and the receding contact angle of the gap flow field and the contour lines of the upper and lower gas-liquid-solid interfaces in the present invention; (a) is a curve diagram of the liquid level height of the AA section of the gap flow field changing with x; (b) is a schematic diagram of the AA section of the gap flow field; (c) is the projection contour of the gap flow field in the xy plane;

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

[0039] In the figure: 1. Helium-neon laser, 2. spatial filter, 3. collimator, 4. first reflector, 5. first semi-transparent and semi-reflective mirror, 6. second reflector, 7. third reflector, 8. gap flow field device to be measured, 9. second semi-transparent and semi-reflective mirror, 10. double-sided telecentric lens, 11. high-speed camera, 12. image processing equipment, 801. upper plate, 802. lower plate, 803. gap flow field to be measured. DETAILED DESCRIPTION

[0040] The present invention is further described below in conjunction with the accompanying drawings and specific implementation methods.

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

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

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

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

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

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

[0047] S3, by injecting liquid and gas into the gap between the upper plate 801 and the lower plate 802 to establish the gap flow field 803 to be measured, moving the lower plate 802 parallel to the scanning direction, collecting the interference image of the gap flow field 803 to be measured at each moment 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. Among them, the interference image phase distribution is obtained according to the interference image at the current moment by a phase demodulation algorithm.

[0048] Step S3 includes the following steps:

[0049] S3.1, collecting the interference image of the gap flow field 803 to be measured at the initial moment (the 0th 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 803 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, 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 803 to be measured:

[0051]

[0052] 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, and 0 represents the initial moment, that is, the 0th moment.

[0053] S3.2, collecting the interference image of the gap flow field 803 to be measured at the first moment, obtaining the interference image phase distribution according to the interference image at the first moment by using the phase demodulation algorithm, obtaining the liquid level height change distribution 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 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;

[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 level height change distribution at the first moment:

[0055]

[0056] In the formula, Δh 1(x,y) represents the liquid level change distribution at the first moment, 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 gap 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 xy plane is parallel to the upper plate 801 and the lower plate 802.

[0057] S3.3. Obtain the phase distribution of the interference image according to the interference image at the current moment through the phase demodulation algorithm, obtain the liquid level height change distribution at the current moment according to the difference in phase distribution 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.

[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 level height change distribution at the current moment:

[0059]

[0060] 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, x represents the coordinate of the x-axis, y represents the coordinate of the y-axis, and m represents the sequence number of the current moment. When m = 1, Δh 1 (x,y) represents the liquid level 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. Obtaining the gas-liquid-solid contour line according to the liquid level height distribution at the current moment: identifying the gas-liquid-solid contour line 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 2As 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 m The discrete points where (x, y) = H are taken as potential forward dynamic contact angle contour points, and neighborhood analysis is performed on each potential forward dynamic contact angle contour point to obtain the change in neighborhood height value of each potential forward dynamic contact angle contour point. If the change in neighborhood height value of the potential forward dynamic contact angle contour point is greater than a preset threshold, then the potential forward dynamic contact angle contour point is a forward dynamic contact angle contour point; if the change in neighborhood height value of the potential forward dynamic contact angle contour point is less than the preset threshold, then the potential forward dynamic contact angle contour point 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.

[0065] S5. Obtain the receding contact angle at the current moment 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 obtain the advancing contact angle at the current moment 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.

[0066] 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:

[0067]

[0068] 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, that is, (0,0,1).

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

[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 1The 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] Below, this embodiment will be combined with Figure 3 The measurement process shown in the figure further introduces the measurement principle of the dynamic contact angle in the gap flow field:

[0076] S1. Build Figure 1 As shown, the optical platform for real-time measurement of 3D dynamic contact angle based on interferometry.

[0077] S2. Collect reference interference images using the 3D dynamic contact angle real-time measurement optical platform I a (x, y) (i.e., the interference image when filled with air), and the reference interference image phase distribution is obtained based on the reference interference image And expressed as Right now

[0078] S3, inject liquid and gas to establish the gap flow field 803 to be measured, start collecting the interference image of the gap flow field 803 to be measured at each time in real time, and calculate the interference image of the gap flow field 803 to be measured at the current time mΔt. Get the interference image phase distribution at the current time mΔt The phase distribution of the interference image at the current moment mΔt is expressed as:

[0079]

[0080] Where n w Represents the refractive index of the gap flow field to be measured, 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 integral domain along the light path.

[0081] According to the above formula, we can get:

[0082]

[0083] In the formula, nw represents the refractive index of the gap flow field to be measured, na represents the refractive index of air, and h m (x,y) represents the liquid level distribution at the current time mΔt, represents the reference interference image phase distribution, Represents the interference image phase distribution at the current time mΔt.

[0084] The initial interference image phase distribution can be obtained Phase distribution of the reference interference image The phase difference between them, that is, the difference in phase distribution:

[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 level height distribution, nw represents the refractive index of the gap flow field to be measured, and na represents the refractive index of air.

[0087] Therefore, the initial liquid level 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 level distribution, nw represents the refractive index of the gap flow field to be measured, n a Represents the refractive index of air.

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

[0091]

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

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

[0094]

[0095] 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, x represents the coordinate of the x-axis, y represents the coordinate of the y-axis, m represents the sequence number of the current moment, and h m (x, y) represents the liquid level distribution at the current moment, h m-1 (x,y) represents the liquid level distribution at the previous moment.

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

[0097]

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

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

[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 level change distribution at the current moment.

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

[0103] For any point (x0, y0) on the gas-liquid-solid interface line contour, the tangent plane equation can be expressed as:

[0104]

[0105] in, Respectively represent the liquid level height distribution h at the current moment m (x,y) is the value of (x0,y0) after taking the derivative of x and y, 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 level distribution at the current moment is:

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

[0108] S4.1.1、Traversing the liquid level height distribution h m (x,y) data, find a 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 a set of potential receding dynamic contact angle contour points.

[0111] S4.1.2, obtaining the neighborhood height value change of each potential receding dynamic contact angle contour point, wherein the neighborhood height value change is specifically: the maximum value of the height difference between the potential receding dynamic contact angle contour point and each of its own neighborhood points.

[0112] For each potential receding dynamic contact angle contour point (x ret ,y ret )∈Υ ret , calculate the height value h of each neighboring point of the potential receding dynamic contact angle contour pointm (x δ ,y δ ). Among them, (x δ ,y δ ) represents the neighborhood point (taking four neighborhoods 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] The neighborhood height change is calculated using the following formula:

[0114]

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

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

[0117] If the neighborhood height change 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.

[0118] S4.1.4. Connect all the receding dynamic contact angle contour points in spatial order to form a 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. Traversing the liquid level height distribution h m (x,y), find a 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 a set of potential advancing dynamic contact angle contour points.

[0123] S4.1.2, obtaining the neighborhood height value change of each potential advancing dynamic contact angle contour point, wherein the neighborhood height value change is specifically: the maximum value of the height difference between the potential advancing dynamic contact angle contour point and each of its own neighborhood points.

[0124] For each potential advancing dynamic contact angle contour point (x for ,y for )∈Υ for , calculate the height value h of each neighboring point of the potential advancing dynamic contact angle contour point m (x δ ,y δ ). Among them, (x δ ,y δ ) represents the neighborhood point (taking four neighborhoods 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] The neighborhood height change is calculated using the following formula:

[0126]

[0127] In the formula, Δh m Indicates the neighborhood height change. (x δ ,y δ ) represents the neighborhood point, (x for ,y for ) represents the potential advancing dynamic contact angle contour 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 contour point.

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

[0129] If the neighborhood height change is greater than a 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.

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

[0131] S5. Obtain the contact angle at the current moment according to the liquid level height distribution and the gas-liquid-solid contour line at the current moment.

[0132] The contact angle corresponding to the point (x0, y0) on the gas-liquid-solid contour line at the current time mΔt is expressed as the tangent plane normal vector The angle with the normal vector (0,0,1) of the xy plane:

[0133]

[0134] 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,y), n1 represents the normal vector of the tangent plane at the point (x0,y0) on the gas-liquid-solid contour line, and n2 represents the normal vector of the xy plane, that is, (0,0,1).

[0135] It can be seen from the implementation that the present invention can simultaneously realize 3D measurement and real-time measurement of contact angle, overcoming the drawback of the previous test method that cannot take both into account. In addition, the method is not only applicable to the measurement of contact angle of regular shaped droplets, but also to the measurement of contact angle of irregular shaped droplets or irregular gas-liquid interface under gap flow field.

[0136] In the description of the positional relationship of the present invention, terms such as "inside", "outside", "up", "down", "left", "right", etc. that indicate orientation or positional relationship are based on the orientation or positional relationship shown in the drawings and are only for the convenience of describing the embodiments and simplifying the description. They do not indicate or imply 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 understood as a limitation on 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. The above examples and descriptions are only for explaining the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which are within the scope of the present invention. The scope of the present invention is defined by the attached 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).

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