Interferometric liquid phase diffusion parameter measuring system and measuring method

Abstract

The invention relates to the technical field of diffusion, dissolution and absorption related parameter measurement, and discloses an interference type liquid phase diffusion parameter measurement system and measurement method.The interference type liquid core column lens is formed by combining two opposite meniscus column lenses, a partition plate is arranged between the two meniscus column lenses, and a reference cell and a diffusion cell are obtained; the interference type liquid core column lens is used for imaging an incident light beam onto the imaging system, the imaging system is used for acquiring an interference image, and the interference image comprises a plurality of interference fringes and a reference intersection point when a dispersion image and a reference image interfere with each other; the control device is used for analyzing each frame of interference image, determining the refractive index of the target interference fringes in combination with the number of the interference fringes, the reference points and the like, determining the concentration according to the fitted functional relationship between the refractive index and the concentration, and further measuring the liquid phase diffusion parameters; the measurement precision is improved, and the measurement application scene is expanded.

Description

Technical Field

[0001] This invention belongs to the field of diffusion, dissolution, and absorption related parameter measurement technology, specifically relating to an interferometric liquid phase diffusion parameter measurement system and method. Background Technology

[0002] The diffusion coefficient of binary solutions is a crucial fundamental parameter for studying mass transfer processes and calculating mass transfer rates. It provides essential data for fields such as biomedicine, environmental protection, physical chemistry, scientific research, and education. Therefore, its experimental determination methods have received considerable attention and importance. Currently, commonly used measurement methods include the membrane cell method (limited accuracy and long measurement time), the Taylor dispersion method (limited accuracy), holographic interferometry (requires sophisticated experimental conditions and specialized personnel), and the liquid-core lens method (difficult to measure solutions with small concentration gradients). Furthermore, except for the liquid-core lens method, these methods do not provide visualization of the diffusion process, making it difficult to quickly measure the liquid-phase diffusion coefficient, and they are challenging for non-professionals.

[0003] Currently, liquid core lenses are limited by their refractive index resolution measurement capability, making it difficult to measure liquids with small concentration gradients. Therefore, it is essential to design a new type of liquid core lens that can stably measure the liquid phase diffusion coefficient of liquids with small concentration gradients and to invent a rapid measurement method. Summary of the Invention

[0004] To address the shortcomings of existing technologies, the present invention aims to provide an interferometric liquid phase diffusion parameter measurement system and method.

[0005] According to one aspect of this application, an interferometric liquid-phase diffusion parameter measurement system is disclosed. The system includes a semiconductor laser, a beam adjustment module, an interferometric liquid-core lens, an imaging system, and a control device arranged sequentially. The semiconductor laser emits a monochromatic collimated beam. The beam adjustment module adjusts the monochromatic collimated beam to obtain an incident beam of a target width. The interferometric liquid-core lens is formed by combining two opposing meniscus lenses. Two solution cavities are formed between the two meniscus lenses by a partition. The partition extends from the middle of the arc segment of one meniscus lens to the middle of the arc segment of the other meniscus lens. The partition divides the solution cavities into a reference cell and a diffusion cell. The reference cell is used to hold a reference liquid with a refractive index of n2, and the diffusion cell is used to hold an upper diffusion liquid with a refractive index of n1 and a lower diffusion liquid with a refractive index of n3. A liquid-core lens is used to image an incident beam of the target width and transmit it to an imaging system, allowing the imaging system to acquire multiple consecutive interferometric images during the diffusion process. Each interferometric image is formed by the interference of the diffused images of the upper and lower diffusing liquids during the diffusion process with a reference image formed by the reference liquid. Each interferometric image includes multiple interference fringes from the current frame's diffused image and the current frame's reference image, as well as a reference intersection point. The reference intersection point is the point where the diffused image intersects with the reference image of the reference liquid when the diffusion transitions from the lower to the upper diffusing liquid. The control device analyzes each interferometric image to obtain the diffusion parameters of the upper and lower diffusing liquids at the time of the interferometric image frame. The refractive indices n1, n2, and n3 are related as follows: n1 <n2<n3。

[0006] In some embodiments, the beam adjustment module includes an attenuator, a spatial filter, a converging lens, and a width-limiting slit arranged sequentially. The attenuator is used to attenuate the light intensity of the monochromatic collimated beam to obtain an attenuated beam. The spatial filter is used to filter the attenuated beam to obtain a filtered beam. The converging lens is used to converge the filtered beam to obtain a parallel beam. The width-limiting slit is used to limit the width of the parallel beam to obtain the incident beam of the target width.

[0007] According to another aspect of this application, an interferometric liquid phase diffusion parameter measurement method is also disclosed, the method being performed based on the liquid phase diffusion parameter measurement system described in any of the preceding claims, the method comprising:

[0008] Obtain the target refractive index of the target diffusion liquid, wherein the target diffusion liquid is an upper diffusion liquid or a lower diffusion liquid, and the target refractive index is the upper liquid refractive index corresponding to the upper diffusion liquid or the lower liquid refractive index corresponding to the lower diffusion liquid;

[0009] Acquire the target dispersion image at the target time;

[0010] Extract the number of upper interference fringes, the number of lower interference fringes, and the target reference point from the target diffusion image;

[0011] The target refractive index of the target interference fringes is determined based on the target refractive index, the number of upper interference fringes, the number of lower interference fringes, and the target reference point.

[0012] Obtain a fitting function, which characterizes the functional relationship between refractive index and concentration;

[0013] Based on the target refractive index of the target interference fringes and the fitting function, the target concentration of the target interference fringes is determined;

[0014] Obtain initial and boundary conditions;

[0015] Based on the target concentration of the target interference fringes, the initial conditions, and the boundary conditions, a concentration-time function is constructed.

[0016] Based on the concentration-time function, the liquid phase diffusion target coefficient of the target interference fringes is obtained.

[0017] In some embodiments, determining the target refractive index of the target interference fringes based on the target refractive index, the number of upper interference fringes, the number of lower interference fringes, and the target reference point includes:

[0018] A reference interference fringe is determined, wherein the reference interference fringe is the interference fringe corresponding to the target diffusion liquid, and the reference interference fringe has a reference refractive index;

[0019] Obtain the number of fringe intervals between the target interference fringes and the reference interference fringes;

[0020] The fringe refractive index difference is determined based on the number of upper interference fringes, the number of lower interference fringes, the thickness of the interferometric liquid-core lens, and the wavelength of the incident beam.

[0021] Based on the reference interference fringe, the number of fringe intervals, and the fringe refractive index difference, the target refractive index of the target interference fringe is determined, wherein the target interference fringe is one of the upper interference fringe or the lower interference fringe.

[0022] In some embodiments, determining the fringe refractive index difference includes:

[0023] Determine the number of fringes from the diffused liquid to the reference point, where the number satisfies:

[0024]

[0025] Determine the number of streaks from the reference point to the diffused liquid, such that the number satisfies:

[0026]

[0027] Adding the two equations together, we get:

[0028]

[0029] Let m = 1, then the refractive index difference between every two fringes can be obtained as:

[0030]

[0031] In the formula, n1 is the refractive index of the upper liquid corresponding to the diffusion upper liquid, n2 is the reference refractive index corresponding to the reference liquid, n3 is the refractive index of the lower liquid corresponding to the diffusion lower liquid, d is the maximum thickness at the center of the solution cavity, and m u m represents the number of upper interference fringes from the diffused liquid to the reference point. d λ represents the number of lower interference fringes from the reference point to the lower diffuser; m represents the number of fringes from the upper diffuser to the lower diffuser; and λ represents the wavelength of the incident beam.

[0032] In some embodiments, determining the target refractive index of the target interference fringe based on the reference interference fringe, the number of fringe spacings, and the fringe refractive index difference includes:

[0033] When the reference refractive index is the upper refractive index corresponding to the upper diffusing liquid, the target refractive index is:

[0034] n k =n1+k×Δn;

[0035] When the reference refractive index is the lower refractive index corresponding to the lower diffusing liquid, the target refractive index is:

[0036] n k =n³ - k × Δn;

[0037] In the formula, n k Let be the target refractive index of the target interference fringes. When the reference refractive index is the upper refractive index corresponding to the upper diffuser, the downward k is positive and the upward k is negative. When the reference refractive index is the lower refractive index corresponding to the lower diffuser, the upward k is positive and the downward k is negative.

[0038] In some embodiments, constructing the concentration-time function based on the target concentration of the target interference fringes, the initial conditions, and the boundary conditions includes:

[0039] Obtain the diffusion equation for the binary solution and construct the concentration distribution function;

[0040] By combining the concentration distribution function, initial conditions, and boundary conditions, a concentration-time function is constructed.

[0041] The concentration distribution function is:

[0042]

[0043] The initial conditions are:

[0044]

[0045] The boundary conditions are:

[0046]

[0047] The concentration-time function is:

[0048]

[0049] In the formula, C(Z,t) represents the target concentration corresponding to the target interference fringe Z at time t, Z is the target interference fringe, and C1 and C2 are the boundary concentrations.

[0050] In some embodiments, obtaining the liquid-phase diffusion coefficient of the target interference fringes based on the concentration-time function includes:

[0051] Based on the concentration-time function, the target liquid phase diffusion coefficient function of the target interference fringes is derived;

[0052] Solving the target liquid phase diffusion coefficient function yields the target liquid phase diffusion coefficient corresponding to the target interference fringes, wherein the expression for the target liquid phase diffusion coefficient is:

[0053]

[0054] In the formula, D is the liquid phase diffusion target coefficient of the target interference fringe Z at the target concentration C at time t.

[0055] The present invention includes, but is not limited to, the following beneficial effects: (1) This scheme obtains the refractive index of the target diffusing liquid, and determines the refractive index of the target interference fringes by combining the number of interference fringes, reference points, etc., and then determines the concentration based on the fitted refractive index and concentration function relationship, and further measures the liquid phase diffusion parameters. Since there is a fixed and small refractive index difference between adjacent interference fringes, the interference fringes can respond sensitively to small changes in refractive index. During the liquid phase diffusion process, the change in solution concentration will cause a slight change in refractive index, and the interference fringes can clearly present these subtle refractive index changes in the form of fringes, which is equivalent to providing a high-resolution measurement method. Compared with other measurement methods, the interference fringes can capture more refined refractive index changes, thereby more accurately reflecting the distribution of solution concentration during the liquid phase diffusion process. This scheme combined with the interference fringes can effectively improve the accuracy of liquid phase diffusion parameter measurement; (2) This scheme can be used to measure different target diffusing liquids and is applicable to a variety of (3) The target refractive index is calculated by using the number of fringe intervals and the difference in fringe refractive index determined by the number of upper and lower interference fringes, the thickness of the interferometric liquid core column lens and the incident light wavelength, combined with the reference refractive index of the reference interference fringes. This calculation method based on precise physical parameters and fringe relationships reduces the error caused by human estimation or inaccurate measurement, thereby improving the accuracy of the target interference fringe refractive index measurement; (4) The target refractive index can be determined by this method for both upper and lower interference fringes, indicating that this method is applicable to interference fringes at different positions, enhancing the versatility and universality of the measurement method, and can be applied to more diverse liquid diffusion measurement scenarios; (5) This scheme divides the interferometric liquid core column lens into a reference cell and a diffusion cell. The reference cell provides a stable refractive index reference, which cancels the beam distortion under low concentration gradients. It can measure binary solutions with different concentration gradients, no longer limited to high concentration gradient scenarios, and expands the applicable range of liquid diffusion coefficient measurement. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0057] Figure 1 This is a schematic diagram of the structure of the interferometric liquid phase diffusion parameter measurement system according to an embodiment of this application;

[0058] Figure 2 This is a schematic diagram of the structure of the interference-type liquid-core column lens according to an embodiment of this application;

[0059] Figure 3This is a schematic diagram of the width image formed on a CMOS surface by a monochromatic collimated beam passing through a reference cell containing a single homogeneous solution with refractive indices of "n1, n2, n3, n4, n5" in an interference-type liquid-core lens according to an embodiment of this application.

[0060] Figure 4 This is a schematic diagram showing the overlap and intersection of a diffusion image of the diffusion cell during diffusion in an embodiment of this application and a single liquid convergence image of the reference cell.

[0061] Figure 5 This is an enlarged view of the interference fringes of an embodiment of this application;

[0062] Figure 6 This is a flowchart of an interferometric liquid phase diffusion parameter measurement method according to an embodiment of this application;

[0063] Figure 7 This is another flowchart of the interference-type liquid phase diffusion parameter measurement method according to the embodiments of this application;

[0064] In the diagram, 1-semiconductor laser, 2-attenuator, 3-spatial filter, 4-converging lens, 5-width-limiting slit, 6-interferometric liquid core lens, 7-imaging system. Detailed Implementation

[0065] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” or “having,” and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0066] For details, please refer to Figure 1 and Figure 2This application provides a liquid phase diffusion parameter measurement system. The system includes a semiconductor laser 1, a beam adjustment module, an interferometric liquid-core lens 6, an imaging system 7, and a control device arranged sequentially. The semiconductor laser 1 emits a monochromatic collimated beam. The beam adjustment module adjusts the monochromatic collimated beam to obtain an incident beam of the target width. The interferometric liquid-core lens 6 is formed by combining two opposing meniscus lenses, forming a solution cavity between the two meniscus lenses. A partition is provided in the solution cavity, extending from the middle of the arc segment of one meniscus lens to the middle of the arc segment of the other meniscus lens. The partition divides the solution cavity into a reference cell and a diffusion cell. The reference cell is used to hold a reference liquid with a refractive index of n2, and the diffusion cell is used to hold an upper diffusion liquid with a refractive index of n1 and a lower diffusion liquid with a refractive index of n3. The interferometric liquid-core lens... Lens 6 is used to transmit the incident beam of the target width onto imaging system 7, so that imaging system 7 can acquire multiple consecutive interference images during the diffusion process. Each interference image is formed by the interference of the diffuse images of the upper and lower diffusing liquids during the diffusion process with the reference image formed by the reference liquid. Each interference image includes multiple interference fringes when the diffuse image and the reference image of the current frame interfere with each other, as well as a reference intersection point. The reference intersection point is the point where the diffuse image and the reference image of the reference liquid intersect when the diffusion transitions from the lower to the upper diffusing liquid. Control device 7 is used to analyze each interference image to obtain the diffusion parameters of the upper and lower diffusing liquids at the time of the frame interference image. The relationship between the refractive indices n1, n2, and n3 is as follows: n1 <n2<n3。

[0067] In some embodiments, the beam adjustment module includes an attenuator 2, a spatial filter 3, a converging lens 4, and a width-limiting slit 5 arranged sequentially. The attenuator 2 is used to attenuate the light intensity of the monochromatic collimated beam to obtain an attenuated beam. The spatial filter 3 is used to filter stray light from the attenuated beam to obtain a filtered beam. The converging lens 4 is used to converge the filtered beam to obtain a parallel beam. The width-limiting slit 5 is used to limit the width of the parallel beam to obtain an incident beam of the target width.

[0068] Specifically, by dividing the interferometric liquid core column lens into a reference cell and a diffusion cell, the reference cell provides a stable refractive index reference to compensate for beam distortion under low concentration gradients. It can measure binary solutions with different concentration gradients, no longer limited to high concentration gradient scenarios, thus expanding the applicable range of liquid phase diffusion coefficient measurement.

[0069] According to another aspect of this application, an interferometric liquid phase diffusion parameter measurement method is also disclosed, the method being performed based on an interferometric liquid phase diffusion parameter measurement system, such as... Figure 6 The diagram shown is a flowchart of an interferometric liquid phase diffusion parameter measurement method according to an embodiment of this application. (See attached diagram.) Figure 6The method includes the following steps:

[0070] S100, Obtain the target refractive index of the target diffusing liquid.

[0071] Specifically, the target diffusion level is the upper or lower diffusion level, and the target refractive index is the upper refractive index corresponding to the upper diffusion level or the lower diffusion level corresponding to the lower diffusion level.

[0072] S102. Obtain the target diffusion image at the target time.

[0073] Specifically, the target diffusion image can be acquired based on an image acquisition system (CMOS).

[0074] S104. Extract the number of upper interference fringes, lower interference fringes, and target reference point from the target diffusion image.

[0075] Specifically, the target reference point is a point extracted from the target diffusion image, such as... Figure 5 Point A in the middle.

[0076] S106. Based on the target refractive index, the number of upper interference fringes, the number of lower interference fringes, and the target reference point, determine the target refractive index of the target interference fringes.

[0077] In one example, Figure 7 This is another flowchart of the interferometric liquid phase diffusion parameter measurement method according to an embodiment of this application. This flowchart is an exemplary illustration of step S106, as follows: Figure 7 As shown, it includes the following steps:

[0078] S200, Determine the reference interference fringes.

[0079] Specifically, the reference interference fringes are the interference fringes corresponding to the target diffusion liquid, and the reference interference fringes have a reference refractive index.

[0080] S202. Obtain the number of fringe intervals between the target interference fringes and the reference interference fringes.

[0081] Specifically, the target interference fringes are fringes representing the desired refractive index, and the number of fringe intervals between them and the reference interference fringes can be determined by counting.

[0082] S204. Determine the difference in refractive index of the fringes.

[0083] The fringe refractive index difference is determined based on the number of upper and lower interference fringes, the thickness of the interferometric liquid-core lens, and the wavelength of the incident beam. The thickness of the interferometric liquid-core lens is... Figure 2 The width of the partition is shown as d in the figure.

[0084] Specifically, we can first determine the number of fringes from the diffused liquid to the reference point, and the number should satisfy:

[0085]

[0086] Next, determine the number of streaks from the reference point to the diffused liquid, and the number should satisfy:

[0087]

[0088] Adding the two equations together, we get:

[0089]

[0090] Let m = 1, then the refractive index difference between every two fringes can be obtained as:

[0091]

[0092] In the formula, n1 is the refractive index of the upper liquid corresponding to the diffusion upper liquid, n2 is the reference refractive index corresponding to the reference liquid, n3 is the refractive index of the lower liquid corresponding to the diffusion lower liquid, d is the maximum thickness at the center of the solution cavity, and m u m represents the number of upper interference fringes from the diffused liquid to the reference point. d λ represents the number of lower interference fringes from the reference point to the lower diffuser; m represents the number of fringes from the upper diffuser to the lower diffuser; and λ represents the wavelength of the incident beam.

[0093] S206. Based on the reference interference fringes, the number of fringe intervals, and the difference in fringe refractive index, determine the target refractive index of the target interference fringes.

[0094] The target interference fringe is either the upper interference fringe or the lower interference fringe.

[0095] Specifically, when the reference refractive index is the upper refractive index corresponding to the upper diffuser, the target refractive index is:

[0096] n k =n1+k×Δn;

[0097] When the reference refractive index is the lower refractive index corresponding to the lower diffusing liquid, the target refractive index is:

[0098] n k =n³ - k × Δn;

[0099] In the formula, n k Let be the target refractive index of the target interference fringes. When the reference refractive index is the upper refractive index corresponding to the upper diffuser, the downward k is positive and the upward k is negative. When the reference refractive index is the lower refractive index corresponding to the lower diffuser, the upward k is positive and the downward k is negative.

[0100] Specifically, in this example, the target refractive index is calculated by using the number of fringe intervals and the difference in fringe refractive index determined based on the number of upper and lower interference fringes, the thickness of the interferometric liquid core lens, and the incident light wavelength, combined with the reference refractive index of the reference interference fringes. This calculation method, based on precise physical parameters and fringe relationships, reduces errors caused by human estimation or inaccurate measurement, thereby improving the accuracy of the target interference fringe refractive index measurement. The target refractive index can be determined according to this method for both upper and lower interference fringes, indicating that the method is applicable to interference fringes at different positions, enhancing the versatility and universality of the measurement method, and can be applied to more diverse liquid phase diffusion measurement scenarios.

[0101] S108. Obtain the fitting function.

[0102] Specifically, the fitting function characterizes the functional relationship between refractive index and concentration;

[0103] S110. Based on the target refractive index and fitting function of the target interference fringes, determine the target concentration of the target interference fringes.

[0104] Specifically, based on the known target refractive index of the target interference fringes, the fitting function is solved to obtain the target concentration of the target interference fringes.

[0105] S112. Obtain initial and boundary conditions.

[0106] S114. Based on the target concentration, initial conditions, and boundary conditions of the target interference fringes, construct the concentration-time function.

[0107] Specifically, the diffusion equation of the binary solution is obtained, and the concentration distribution function is constructed;

[0108] By combining the concentration distribution function, initial conditions, and boundary conditions, a concentration-time function is constructed.

[0109] The concentration distribution function is:

[0110]

[0111] The initial conditions are:

[0112]

[0113] The boundary conditions are:

[0114]

[0115] The concentration-time function is:

[0116]

[0117] In the formula, C(Z,t) represents the target concentration corresponding to the target interference fringe Z at time t, Z is the target interference fringe, and C1 and C2 are the boundary concentrations.

[0118] S116. Based on the concentration-time function, the liquid phase diffusion target coefficient of the target interference fringes is obtained.

[0119] Specifically, based on the concentration-time function, the target liquid phase diffusion coefficient function of the target interference fringes is derived;

[0120] Solving for the target liquid phase diffusion coefficient function yields the target liquid phase diffusion coefficient corresponding to the target interference fringes. The expression for the target liquid phase diffusion coefficient is as follows:

[0121]

[0122] In the formula, D is the liquid phase diffusion target coefficient of the target interference fringe Z at the target concentration C at time t.

[0123] Specifically, in this example, the refractive index of the target diffusing liquid is obtained, and the refractive index of the target interference fringes is determined by combining the number of interference fringes and reference points. Then, the concentration is determined based on the fitted relationship between refractive index and concentration function, and further liquid-phase diffusion parameters are measured. Since there is a fixed and tiny difference in refractive index between adjacent interference fringes, the interference fringes can respond sensitively to tiny changes in refractive index. During liquid-phase diffusion, changes in solution concentration will cause subtle changes in refractive index, and the interference fringes can clearly present these subtle refractive index changes in the form of fringes, which is equivalent to providing a high-resolution measurement method. Compared with other measurement methods, interference fringes can capture more refined changes in refractive index, thus more accurately reflecting the distribution of solution concentration during liquid-phase diffusion. This solution, combined with interference fringes, can effectively improve the accuracy of liquid-phase diffusion parameter measurement; and it can be used to measure different target diffusing liquids, applicable to various liquid-phase system diffusion parameter measurement scenarios.

[0124] To facilitate understanding, the following will provide a detailed explanation in conjunction with the derivation process and specific embodiments:

[0125] The experimental apparatus used in this invention is as follows: Figure 1 As shown: The liquid core lens measuring device comprises: "a semiconductor laser, an attenuator, a spatial filter, a converging lens, a width-limiting slit, a dual-pool interference type liquid core lens, an imaging system (CMOS), and a host computer (not shown in the figure)".

[0126] In this example, after a monochromatic light beam is emitted by the light source system, it is attenuated by an attenuation sheet. The attenuated light intensity enters a spatial filter to eliminate some stray light. A converging lens is adjusted to expand the point light source into parallel light, and the parallel light passes through a width-limiting slit and then enters an interference-type liquid-core cylindrical lens. After interference imaging by the interference-type liquid-core cylindrical lens, it is saved in real time by an image acquisition system.

[0127] The interference-type liquid-core cylindrical lens is composed of a meniscus cylindrical lens glued together. In the middle, the lens is divided into two parts, a reference cell and a diffusion cell, by a separator plate ( Figure 2 The left is a physical diagram, Figure 2 and the right is a model diagram). It not only serves as the core imaging element. At the same time, it also serves as the diffusion cell for the binary liquid and the reference cell for the reference liquid.

[0128] When a liquid with a refractive index of n2 is injected into the reference cell of the interference-type liquid-core cylindrical lens, by injecting solutions with different concentrations, different refractive indices will also correspond. When the parallel light passes through the interference-type liquid-core cylindrical lens and is imaged, different-width images will be imaged on the image acquisition system (CMOS) (such as Figure 3 shown, different refractive indices correspond to different image widths). When the image acquisition system (CMOS) moves to the focal plane position of the interference-type liquid-core cylindrical lens, at this time, the CMOS acquisition plane receives a thin and sharp straight line with the same width, that is, the collimated light converges into a thin straight line after passing through the interference-type liquid-core cylindrical lens. When diffusion occurs between two liquids with refractive indices of n1 and n3 (n3 > n2 > n1) respectively in the diffusion cell of the interference-type liquid-core cylindrical lens, as the binary solution continuously diffuses and is imaged, different diffusion images will be formed. The concentration is relatively large near the lower interface, corresponding to corresponding diffusion images (such as Figure 4 shown, the converging image of the reference cell and the diffusion and diffusion images of the diffusion cell coincide and intersect). During the diffusion process, a concentration gradient will be formed, and the corresponding refractive indices will also be different. Each interface of the diffusion cell will correspond to a refractive index distribution according to the concentration distribution. The light with different refractive indices at different interfaces of the diffusion cell and the light with a fixed refractive index of the single liquid in the reference cell interfere with each other as the lens converges, forming interference fringes corresponding to the refractive index distribution (such as Figure 5 shown interference fringes).

[0129] (II) Method for accurately measuring the liquid-phase diffusion coefficient based on a double-cell interference-type liquid-core cylindrical lens

[0130] Experimental operation: First, according to the refractive index of the solution to be measured, select a reference liquid with a suitable refractive index. The selection of the solution refractive index should follow the rule that the upper diffusion liquid n1, the reference liquid n2, and the lower diffusion liquid n3 increase in order, that is, n1 < n2 < n3. Inject the reference liquid into the reference cell. Then adjust the positions of the lens and the CMOS so that the reference cell is imaged on the focal plane of the reference liquid. At this time, the image is a slender straight line.

[0131] A solution with a refractive index of n3 is injected into the diffusion cell; this is the lower diffusion solution. Due to underfocusing, the lower diffusion solution produces a diffuse image on one side of the reference solution image. After standing for 15-20 minutes to allow the solution to stabilize, a higher diffusion solution with a refractive index of n1 is slowly injected into the diffusion cell using a syringe pump, causing diffusion between the upper and lower diffusion solutions. Due to overfocusing, the image of the upper diffusion solution is diffused on the other side of the lower diffusion solution image. Furthermore, due to diffusion, numerous refractive index distributions appear near the diffusion interface, causing the width and boundary of the diffused image to transition from the lower to the upper diffusion solution. The reference solution intersects the diffused image in the middle, forming a reference intersection point. After waiting 20 minutes for the diffusion to stabilize, image acquisition begins.

[0132] Image Analysis and Calculation: The image displays a fixed number of interference fringes from top to bottom. The interference is caused by the optical path difference resulting from the difference in refractive indices between the reference cell and the diffusion cell. The refractive index is distributed from n1 to n3 from top to bottom as diffusion progresses. The number of fringes from the diffusion layer to the reference point satisfies:

[0133]

[0134] The number of streaks from the reference point to the diffused liquid satisfies:

[0135]

[0136] Adding the two equations together, we get:

[0137]

[0138] d is the thickness of the liquid core column, and m is the number of stripes from the upper liquid to the lower liquid.

[0139] Let m = 1, then the refractive index difference between every two fringes can be obtained as:

[0140]

[0141] Thus, given the refractive index of either the upper or lower liquid layer, the refractive index corresponding to each fringe level can be calculated. Based on the fitted relationship between refractive index and concentration, the concentration corresponding to each fringe level can be calculated. According to the diffusion equation for a binary solution, combined with the initial and boundary conditions, a concentration distribution function can be obtained.

[0142]

[0143] C represents the solution concentration; D represents the liquid-phase diffusion coefficient of the binary solution. The initial and boundary conditions satisfied by equation (5) are as follows:

[0144]

[0145] The solution to equation (5), combining the initial and boundary conditions, can be expressed as a Gaussian error function:

[0146]

[0147] Equation (8) represents the positional relationship between concentration and time after diffusion of a binary solution over a certain period of time, where erf is the error function. Let "erfinv" be the inverse error function. Then equation (8) can be rewritten as:

[0148]

[0149] By selecting the concentration C(Z,t) corresponding to the stripe; the boundary concentration between C1 and C2; and Z as the selected stripe, the data is fitted to Z and... Based on equation (9), the diffusion coefficient D can be expressed as equation (10):

[0150]

[0151] It is understood that this invention employs a lens imaging method to obtain an interference image of binary solution diffusion. Parallel light, after passing through the reference cell and diffusion cell of the interference-type liquid-core lens, converges at the focal plane of the reference cell, and the light from the reference cell interferes with the light from the diffusion cell. This invention simplifies experimental operations and improves calculation results through the analysis and calculation of the interference image formed by the diffusion and reference cells. This not only improves the stability of the measurement but also expands the range for measuring solution concentration differences.

[0152] This embodiment uses the measurement of potassium chloride aqueous solution by a "double-cell interference liquid core lens" as an example to calculate the diffusion coefficient between them (refer to...). Figure 5 ).

[0153] 1. Set up the experimental system

[0154] The interferometric liquid core lens measuring device used in this implementation is as follows: Figure 1 As shown, the experimental setup consists of five parts: (a) a light source system comprising a low-power semiconductor laser with a wavelength λ = 589 nm and a maximum power of 20 mW, an attenuator, and a light source system. (b) a collimation and beam-expanding system consisting of a 40x microscope objective, a spatial filter with a 15 μm aperture pinhole, and a convex lens with a focal length of 500 mm, used to collimate and expand the monochromatic laser beam. (c) an adjustable-width limiting slit serving as a limiting element for collimating the beam. (d) an interference-type liquid-core lens serving as an imaging element, a liquid-phase diffusion cell, and an interference element. (e) an imaging system based on a CMOS chip, with a resolution of 4090 × 3072 pixels and a pixel size of 5.5 × 5.5 micrometers.

[0155] 2. Prepare the required solution

[0156] The test solution was prepared at room temperature (25℃) using 99.9% analytical grade potassium chloride solid granules and pure water. The refractive index n of the test solution was measured using an Abbe refractometer with an accuracy of 0.0002. The relationship between the prepared solution and the refractive index is shown in Table 1.

[0157] Table 1 shows the relationship between the prepared solutions and refractive indices.

[0158]

[0159] In this embodiment, the test solutions are binary solutions consisting of a 0.33 mol / L potassium chloride upper solution and a 3 mol / L potassium chloride lower solution, with a 0.487 mol / L potassium chloride solution as the reference solution. The corresponding upper solution concentration is 0.33 mol / L potassium chloride solution, and the lower solution concentration is 3 mol / L potassium chloride solution.

[0160] Before injecting the diffusion solution, we need to inject the reference solution and adjust it to the focal plane position. At room temperature (25℃), we add the reference solution to the reference cell of the dual-cell interference liquid-core lens and adjust the CMOS position to form a bright and sharp line. For the diffusion system of "0.33 (mol / L) potassium chloride solution and 3 (mol / L) potassium chloride solution", we choose 0.487 (mol / L) potassium chloride solution as the reference solution. We first inject 3 (mol / L) potassium chloride solution into the diffusion cell, and then slowly inject 0.33 (mol / L) potassium chloride solution at a rate of 0.17 ml / min using a syringe pump to start the diffusion process.

[0161] As the binary diffusion and interference process proceeds, we extract the position of the fringe corresponding to the selected refractive index to obtain the functional relationship between the position and time. According to formula (9), the liquid phase diffusion coefficient of the binary solution can be calculated.

[0162] The boundary concentrations C1 and C2 are 0.33 (mol / L) and 3 (mol / L), respectively. The fitted relationship between potassium chloride concentration and refractive index is C = n 2 The correlation coefficient R is 0.9996, calculated as *(-2283.3)+n*6175.1-4174.1. The diffusion coefficients of the two binary solutions are shown in Table 2.

[0163] Table 2 Measurement results of potassium chloride solution

[0164]

[0165] An experimental setup was constructed using an "interferometric liquid-core lens," comprising: a semiconductor laser, an attenuator, a spatial filter, a converging lens, a width-limiting slit, an interferometric liquid-core lens, an imaging system (CMOS), and a host computer. The necessary solutions were also prepared. Real-time acquisition of diffusion images was then performed.

[0166] For diffusion systems using 0.33 mol / L and 3 mol / L potassium chloride solutions, a 0.487 mol / L potassium chloride solution was used as a reference. One fringe near the upper layer of solution was randomly selected, and its position at different times was recorded. Multiple diffusion images needed to be processed during the measurement process.

[0167] The diffusion coefficient is calculated by considering the relationship between the position of the fringes and time, as well as the refractive index and concentration corresponding to the fringes.

[0168] As shown in Example 3, by measuring the diffusion coefficients of "0.33 (mol / L) potassium chloride solution and 3 (mol / L) potassium chloride solution", their relative errors were within 0.56%. This demonstrates the accuracy of the measurement method.

[0169] Furthermore, based on the above method steps, the fringe drift method measurement data of different stripes of pure water-0.3mol / L potassium chloride were obtained as shown in Table 3.

[0170] Table 3. Measurement data of different fringes of pure water with 0.3 mol / L potassium chloride using the equal refractive index fringe drift method.

[0171]

[0172] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An interferometric liquid phase diffusion parameter measurement system, characterized in that, The system includes a semiconductor laser, a beam adjustment module, an interferometric liquid-core lens, an imaging system, and a control device arranged sequentially. The semiconductor laser is used to emit a monochromatic collimated beam. The beam adjustment module is used to adjust the monochromatic collimated beam to obtain an incident beam with a target width. The interferometric liquid-core lens is formed by combining two opposing meniscus lenses. Two solution cavities are formed between the two meniscus lenses by a partition. The partition is provided in the solution cavity and extends from the middle of the arc segment of one meniscus lens to the middle of the arc segment of the other meniscus lens. The partition divides the solution cavity into a reference cell and a diffusion cell. The reference cell is used to place a reference liquid with a refractive index of n2, and the diffusion cell is used to place an upper diffusion liquid with a refractive index of n1 and a lower diffusion liquid with a refractive index of n3. The interferometric liquid-core lens is used to transmit an incident beam of the target width onto the imaging system, enabling the imaging system to acquire multiple consecutive interferometric images during the diffusion process. Each interferometric image is formed by the interference of the diffused images of the upper and lower diffusing liquids during the diffusion process with a reference image formed by the reference liquid. Each interferometric image includes multiple interference fringes from the current frame's diffused image and the current frame's reference image, as well as a reference intersection point. The reference intersection point is the point where the diffused image intersects with the reference image of the reference liquid when the diffusion transitions from the lower to the upper diffusing liquid. The control device is used to analyze each interferometric image to obtain the diffusion parameters of the upper and lower diffusing liquids at the time of the interferometric image frame. The refractive indices n1, n2, and n3 are related as follows: n1 <n2<n3。 2. The interferometric liquid phase diffusion parameter measurement system according to claim 1, characterized in that, The beam adjustment module includes an attenuator, a spatial filter, a converging lens, and a width-limiting slit arranged sequentially. The attenuator is used to attenuate the light intensity of the monochromatic collimated beam to obtain an attenuated beam. The spatial filter is used to filter the attenuated beam to obtain a filtered beam. The converging lens is used to converge the filtered beam to obtain a parallel beam. The width-limiting slit is used to limit the width of the parallel beam to obtain the incident beam of the target width.

3. An interferometric method for measuring liquid-phase diffusion parameters, characterized in that, The method is performed based on the interferometric liquid phase diffusion parameter measurement system according to any one of claims 1-2, and the method includes: Obtain the target refractive index of the target diffusion liquid, wherein the target diffusion liquid is an upper diffusion liquid or a lower diffusion liquid, and the target refractive index is the upper liquid refractive index corresponding to the upper diffusion liquid or the lower liquid refractive index corresponding to the lower diffusion liquid; Acquire the target dispersion image at the target time; Extract the number of upper interference fringes, the number of lower interference fringes, and the target reference point from the target diffusion image; The target refractive index of the target interference fringes is determined based on the target refractive index, the number of upper interference fringes, the number of lower interference fringes, and the target reference point. Obtain a fitting function, which characterizes the functional relationship between refractive index and concentration; Based on the target refractive index of the target interference fringes and the fitting function, the target concentration of the target interference fringes is determined; Obtain initial and boundary conditions; Based on the target concentration of the target interference fringes, the initial conditions, and the boundary conditions, a concentration-time function is constructed. Based on the concentration-time function, the liquid phase diffusion target coefficient of the target interference fringes is obtained.

4. The method for measuring interferometric liquid phase diffusion parameters according to claim 3, characterized in that, The determination of the target refractive index of the target interference fringes based on the refractive index of the upper liquid or the refractive index of the lower liquid, the number of upper interference fringes, the number of lower interference fringes, and the target reference point includes: A reference interference fringe is determined, wherein the reference interference fringe is the interference fringe corresponding to the target diffusion liquid, and the reference interference fringe has a reference refractive index; Obtain the number of fringe intervals between the target interference fringes and the reference interference fringes; The fringe refractive index difference is determined based on the number of upper interference fringes, the number of lower interference fringes, the thickness of the interferometric liquid-core lens, and the wavelength of the incident beam. Based on the reference interference fringe, the number of fringe intervals, and the fringe refractive index difference, the target refractive index of the target interference fringe is determined, wherein the target interference fringe is one of the upper interference fringe or the lower interference fringe.

5. The method for measuring interferometric liquid phase diffusion parameters according to claim 1, characterized in that, The determination of the fringe refractive index difference includes: Determine the number of fringes from the diffused liquid to the reference point, where the number satisfies: Determine the number of streaks from the reference point to the diffused liquid, such that the number satisfies: Adding the two equations together, we get: Let m = 1, then the refractive index difference between every two fringes can be obtained as: In the formula, n1 is the refractive index of the upper liquid corresponding to the diffusion upper liquid, n2 is the reference refractive index corresponding to the reference liquid, n3 is the refractive index of the lower liquid corresponding to the diffusion lower liquid, d is the maximum thickness at the center of the solution cavity, and m u m represents the number of upper interference fringes from the diffused liquid to the reference point. d λ represents the number of lower interference fringes from the reference point to the lower diffuser; m represents the number of fringes from the upper diffuser to the lower diffuser; and λ represents the wavelength of the incident beam.

6. The method for measuring interferometric liquid phase diffusion parameters according to claim 5, characterized in that, The determination of the target refractive index of the target interference fringe based on the reference interference fringe, the number of fringe intervals, and the fringe refractive index difference includes: When the reference refractive index is the upper refractive index corresponding to the upper diffusing liquid, the target refractive index is: n k = n1+k×Δn; When the reference refractive index is the lower refractive index corresponding to the lower diffusing liquid, the target refractive index is: n k =n3-k×Δn; In the formula, n k Let be the target refractive index of the target interference fringes. When the reference refractive index is the upper refractive index corresponding to the upper diffuser, the downward k is positive and the upward k is negative. When the reference refractive index is the lower refractive index corresponding to the lower diffuser, the upward k is positive and the downward k is negative.

7. The method for measuring interferometric liquid phase diffusion parameters according to claim 3, characterized in that, Determining the target concentration of the target interference fringes based on the target refractive index and the fitting function includes: Based on the known target refractive index of the target interference fringes, the fitting function is solved to obtain the target concentration of the target interference fringes.

8. The method for measuring interferometric liquid phase diffusion parameters according to claim 3, characterized in that, The construction of the concentration-time function based on the target concentration of the target interference fringes, the initial conditions, and the boundary conditions includes: Obtain the diffusion equation for the binary solution and construct the concentration distribution function; By combining the concentration distribution function, initial conditions, and boundary conditions, a concentration-time function is constructed. The concentration distribution function is: The initial conditions are: The boundary conditions are: The concentration-time function is: In the formula, C(Z,t) represents the target concentration corresponding to the target interference fringe Z at time t, Z is the target interference fringe, and C1 and C2 are the boundary concentrations.

9. The method for measuring interferometric liquid phase diffusion parameters according to claim 3, characterized in that, The liquid-phase diffusion coefficient of the target interference fringes, obtained based on the concentration-time function, includes: Based on the concentration-time function, the target liquid phase diffusion coefficient function of the target interference fringes is derived; Solving the target liquid phase diffusion coefficient function yields the target liquid phase diffusion coefficient corresponding to the target interference fringes, wherein the expression for the target liquid phase diffusion coefficient is: In the formula, D is the liquid phase diffusion target coefficient of the target interference fringe Z at the target concentration C at time t.

Images