A light scattering pendant drop shape parameter measurement system and method

Abstract

The application discloses a light scattering suspended drop shape parameter measurement system and method, and belongs to the technical field of fluid characteristic research. The method comprises the following steps: using a monochromatic coherent laser beam, expanding the laser beam into an incident light with a beam width of 3-5 times of the diameter of the suspended drop to uniformly irradiate the suspended drop; adopting a combined bilinear CCD detector to respectively collect first-order rainbow signals and second-order rainbow signals generated by the suspended drop scattering; performing fast Fourier transform filtering on the collected signals, reconstructing a scattering angle distribution diagram after filtering out high-frequency components; extracting the positions and intensities of multiple groups of scattering peak values in the scattering angle distribution diagram, calculating the radius of the suspended drop through the position interval of the multiple groups of peak values, and calculating the vertical direction curvature radius of the suspended drop through the ratio of the multiple groups of peak values of the first-order rainbow and the second-order rainbow. The method breaks through the limitation that the existing light scattering measurement method can only be applied to spherical liquid drops / circular liquid columns, and successfully expands the light scattering measurement technology to the shape parameter measurement of non-spherical liquid drops.

Description

Technical Field

[0001] This invention belongs to the field of fluid property research technology, and relates to a system and method for measuring the shape parameters of a light-scattering pendant droplet. Background Technology

[0002] Hanging droplets, as a typical non-spherical droplet shape, are a core experimental object for studying liquid evaporation kinetics, surface tension coefficients, interfacial rheological properties, and combustion processes. For example... Figure 1 As shown, in the field of fluid physics, the equatorial radius R1 and the vertical radius of curvature R2 of a pendant drop directly determine the droplet's evaporation rate, internal flow field distribution, and surface stress evolution. In industrial applications, the accurate measurement of these two parameters provides crucial information for optimizing processes such as spray cooling, inkjet printing, and fuel atomization. Therefore, achieving rapid and high-precision measurement of pendant drop geometric parameters is of great significance for both basic research and engineering applications. Currently, methods for measuring pendant drop geometric parameters are mainly divided into the following two categories: I. Photographic Method Photographic methods are currently the most widely used technique for pendant drop measurement. Their core principle involves capturing images of the droplet's morphology with a camera (or CCD), then using image processing algorithms to extract the droplet's contour, and finally calculating geometric parameters such as R1 and R2. The advantages of this method are its intuitive principle and ability to obtain multi-dimensional droplet contour information; however, it suffers from significant technical bottlenecks. (1) The contradiction between accuracy and speed: If high accuracy is pursued, a high-pixel camera is required, which will greatly increase the computational load of image processing and reduce the measurement speed (usually the processing time of a single frame is hundreds of milliseconds), which cannot meet the real-time measurement requirements of transient processes such as rapid evaporation and dynamic deformation of droplets; if the pixel is reduced in order to improve speed, the resolution of contour extraction is insufficient, and the measurement accuracy is difficult to break through the micrometer level.

[0003] (2) Sensitive to environmental interference: uneven illumination, background noise and droplet transparency can cause blurring of the outline edge. Especially for semi-transparent or dynamically vibrating droplets, the outline extraction error can reach more than 5%, which cannot meet the requirements of high-precision research.

[0004] (3) Poor adaptability to dynamic scenes: For droplets that move at high speed or deform rapidly (such as droplets in combustion), the camera is prone to producing motion blur, which leads to distortion of contour information and further reduces the reliability of measurement.

[0005] II. Light Scattering Intensity Measurement Method (1) Light scattering measurement methods (such as rainbow measurement and diffraction measurement) invert geometric parameters by analyzing the intensity angular distribution of scattered light from a droplet, theoretically offering advantages such as high measurement speed and high accuracy. However, existing technologies have fundamental limitations: (2) Limitations of theoretical models: Traditional Airy and Mie theories can only accurately describe the scattering characteristics of spherical or cylindrical particles and cannot handle the scattering process of non-spherical droplets. Due to the lack of an effective theory for non-spherical particle scattering, existing light scattering methods cannot establish the relationship between the vertical curvature radius R2 of the droplet and the intensity distribution of scattered light. They can only measure the radius R1 of spherical droplets and cannot meet the needs of multi-parameter measurement of droplets.

[0006] (3) Insufficient signal processing capability: Existing rainbow measurement techniques do not perform efficient filtering and peak extraction for the first and second order rainbow signals of pendant droplets. The original scattering signal contains a large amount of high-frequency noise, resulting in low extraction accuracy of peak position and intensity, and difficulty in ensuring measurement stability.

[0007] (4) Limited application scenarios: Due to the limitations of theoretical models, the existing light scattering method is only applicable to the measurement of spherical droplets or cylindrical liquid columns and cannot be extended to non-spherical suspended droplets. However, the non-spherical characteristics of suspended droplets (such as the curvature change in the vertical direction) are the core of studying physical processes such as evaporation and deformation.

[0008] In the prior art, the closest to this invention is the rainbow measurement technique, but this method can only measure the radius of spherical or cylindrical droplets. Its fundamental defect is the lack of a theoretical model that can describe the scattering characteristics of non-spherical pendant droplets. It cannot correlate the vertical curvature radius R2 of the pendant droplet with the distribution of scattered light intensity, and therefore cannot meet the needs of multi-parameter measurement of pendant droplets. Summary of the Invention

[0009] The purpose of this invention is to solve the technical problems that existing photographic methods cannot simultaneously meet the dual requirements of rapid and high-precision measurement, and that current light scattering intensity measurement methods cannot be used for measuring non-circular / spherical droplets due to theoretical model limitations. This invention provides a light scattering pendant drop shape parameter measurement system and method.

[0010] To achieve the above objectives, the present invention employs the following technical solution: In a first aspect, the present invention discloses a light scattering pendant drop shape parameter measurement system, comprising: A laser emitting module includes a monochromatic laser and a beam expander unit disposed on the output path of the monochromatic laser; The pendant droplet carrying and control module includes a droplet generation and control turntable for carrying the pendant droplet and placing it in the irradiation area of ​​the incident light; The scattered light detection module, including a combined bilinear CCD detector, is set on the path of the scattered light emitted from the pendant drop to collect the first-order rainbow signal and the second-order rainbow signal after the pendant drop is scattered. The data processing module, electrically connected to the combined bilinear CCD detector, is used to receive the scattered signal and reconstruct the scattering angle distribution map after filtering by fast Fourier transform, extract the position and intensity of the scattering peak, and then calculate the radius and vertical curvature radius of the pendant droplet.

[0011] Further improvements are made in the following aspects: The combined bilinear CCD detector can be fixed or have adjustable spacing.

[0012] A fixed bilinear CCD detector is used when measuring pendant drops of a specific liquid; an adjustable-pitch bilinear CCD detector is used when measuring pendant drops of different liquids.

[0013] The monochromatic laser is a helium-neon laser, and the coherence length of its output laser is greater than the diameter of the droplet.

[0014] Secondly, this invention discloses a method for measuring the shape parameters of a light-scattering pendant droplet based on the above-mentioned system, comprising: A monochromatic coherent laser beam is used to expand the laser beam into an incident light with a beamwidth of 3-5 times the diameter of the droplet, so as to uniformly irradiate the droplet. A combined bilinear CCD detector was used to collect the first-order rainbow signal and the second-order rainbow signal generated by pendant droplet scattering, respectively. The first-order and second-order rainbow signals were subjected to fast Fourier transform filtering to remove high-frequency components and then the scattering angle distribution map was reconstructed. The positions and intensities of multiple scattering peaks in the scattering angle distribution map are extracted. The radius of the droplet is calculated by the positional spacing of the multiple peaks. The vertical radius of curvature of the droplet is calculated by the ratio of the intensities of the multiple peaks in the first-order rainbow to those in the second-order rainbow.

[0015] The coherence length of the monochromatic coherent laser beam is greater than the diameter of the droplet.

[0016] After the Fast Fourier Transform (FFT) filtering, the reconstructed scattering angle distribution map is smoothed to further reduce noise interference and improve the accuracy of peak extraction.

[0017] Before uniformly irradiating the droplet, the droplet is kept stationary or rotated at a constant speed to avoid interference from droplet swaying on the acquisition of the scattering signal.

[0018] Specifically, the positions and intensities of multiple scattering peaks in the scattering angle distribution map are extracted as follows: The complex amplitude and total field intensity of the first-order and second-order rainbow signals are calculated based on the vector complex ray model to determine the location and intensity of the scattering peaks.

[0019] The complex amplitude and total field intensity of the first-order and second-order rainbow signals are calculated based on the vector complex ray model to determine the location and intensity of the scattering peaks. First-order rainbow and second-order rainbow Amplitude of scattered light and Calculated by the following formula:

[0020] in, Let Fi be the Fresnel factor, where vertical Peaceful Reflection coefficient during polarization Calculated using Fresnel's formula; As a divergence factor, and Calculated using the following two formulas respectively:

[0021]

[0022] in:

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] in:

[0032]

[0033]

[0034] in, Let be the angle of incidence of light on the surface of the pendant drop. For the corresponding angle of refraction, The refractive index of the pendant drop; the phase of the outgoing ray. Calculated by the following formula:

[0035] The exit angle of the emitted ray It can be determined based on the angle of incidence of the incident light. and angle of refraction It can be obtained from the following formula:

[0036] The angle of incidence of the incident ray corresponding to the geometric optics rainbow angle is: and angle of refraction Calculated using the following formulas respectively:

[0037]

[0038] The angle of incidence of the geometrical optical incident rays corresponding to the first and second order rainbows can be calculated from the above formula. Then calculate the range of incident angles corresponding to the rays on both sides of the rainbow ray's incident angle. Amplitude of the emitted light rays inside , and phase , The total field is calculated from this. and total strength Since the incident light rays corresponding to the geometric rainbow angle exit on the same side of the geometric rainbow angle, interference is generated to form secondary rainbow peaks. The position and intensity of these peaks are related to the geometry of the pendant drop and are used for rapid and accurate measurement.

[0039] Compared with the prior art, the present invention has the following beneficial effects: This invention discloses a light-scattering pendant drop shape parameter measurement system. The system's overall structure is scientifically and rationally designed, with clearly defined functions and coordinated cooperation among modules. From incident light control, stable droplet support, scattering signal acquisition to data processing, a complete and precise measurement chain is formed, effectively solving the technical pain points of existing pendant drop measurement systems, such as insufficient accuracy, inability to simultaneously and reliably measure two core shape parameters, and low signal acquisition efficiency. Specifically, the laser emission module consists of a monochromatic laser and a beam expander unit positioned along its output path. It emits a stable monochromatic coherent beam, and the beam expander unit precisely controls the laser to ensure uniform illumination of the droplet surface, providing a fundamental guarantee for accurate acquisition of subsequent scattering signals and avoiding distortion caused by uneven illumination, thus improving the reliability of measurement data from the source. The droplet support and control module includes a droplet generation and control turntable that stably generates and supports the droplet while precisely controlling its position to ensure it remains within the incident light's illumination area. This effectively reduces interference from droplet movement and displacement on scattering signal acquisition, ensuring the stability and repeatability of the measurement process, guaranteeing consistency across multiple measurements, and improving the system's measurement reliability. The scattered light detection module employs a combined bilinear CCD detector, positioned along the scattered light emission path of the pendant droplet. It is specifically designed to separately acquire the first-order and second-order rainbow signals scattered by the droplet. Compared to traditional single-CCD detectors, this design ensures consistency in intensity and angle measurements of both types of rainbow signals, avoiding deviations during signal acquisition. It also allows for targeted acquisition of effective signals, preventing resource waste caused by invalid signal areas. This significantly improves the targeting and efficiency of scattered signal acquisition, providing a high-quality signal foundation for subsequent data processing and parameter calculation. The data processing module is stably electrically connected to the combined bilinear CCD detector, enabling rapid reception of the acquired scattered signals. Through Fast Fourier Transform (FFT), the signal is filtered to effectively remove high-frequency noise, thereby accurately reconstructing the scattering angle distribution map, precisely extracting the position and intensity of the scattering peaks, and ultimately reliably calculating the droplet's radius and vertical radius of curvature. This solves the problems of low data processing accuracy, inaccurate peak extraction, and large parameter calculation errors in existing systems. The entire system does not rely on complex imaging equipment and cumbersome contour extraction processes. Through the synergistic effect of various modules, it achieves synchronous, rapid, and high-precision measurement of the two core shape parameters of a pendant drop. The measurement process is stable and efficient, and the system has a simple structure and strong practicality. It can adapt to the pendant drop measurement needs in different scenarios, providing reliable system support for the study of pendant drop-related fluid properties and evaporation processes. At the same time, compared with existing measurement systems, its overall design is more targeted, easy to operate, and highly stable, which can effectively reduce interference factors in the measurement process and further improve the accuracy and reliability of measurement data.

[0040] This invention discloses a method for measuring the shape parameters of a light-scattering pendant droplet. The method first expands a monochromatic coherent laser beam into an incident light beam with a beamwidth 3-5 times the droplet diameter, ensuring that the incident light uniformly covers and illuminates the droplet surface. This avoids the distortion of the scattering signal caused by uneven illumination from the initial measurement stage, laying a solid foundation for the accurate acquisition of subsequent scattering signals. Simultaneously, the monochromatic coherence of the laser further enhances the stability of the scattering signal, facilitating subsequent signal filtering and feature extraction, thus ensuring the original reliability of the measurement data from the source. In the scattering signal acquisition stage, the method employs a combined bilinear CCD detector to acquire the first-order and second-order rainbow signals generated by the droplet scattering. This design is highly targeted: on the one hand, it ensures consistency in the intensity and angle measurements of the two types of rainbow signals, effectively avoiding measurement deviations that easily occur when acquiring two types of signals with a single CCD detector, significantly improving the accuracy of signal acquisition; on the other hand, it accurately captures the effective scattering signal, effectively avoiding areas in the Alexandria dark region where there are no useful signals, avoiding resource waste during signal acquisition, significantly improving the targeting and efficiency of scattering signal acquisition, and providing high-quality signal support for subsequent data processing and parameter calculation. In the signal processing and parameter calculation stages, this method performs fast Fourier transform filtering on the acquired first-order and second-order rainbow signals, which can efficiently filter out high-frequency noise in the signal and accurately reconstruct the scattering angle distribution map, ensuring the integrity and clarity of the scattering angle distribution map, and providing a clear signal foundation for the subsequent accurate extraction of scattering peaks. By extracting the position and intensity of multiple sets of scattering peaks in the scattering angle distribution map, the droplet radius is calculated by using the position spacing of multiple sets of peaks and the vertical radius of curvature is calculated by the ratio of the intensity of multiple sets of peaks. Compared with the single peak calculation method, this method significantly improves the accuracy and stability of the measurement, realizes the synchronous and accurate measurement of the two core shape parameters of the droplet, eliminates the need for additional measurement steps, simplifies the measurement process, and improves measurement efficiency. Compared to traditional photographic methods, this method eliminates the need for high-resolution imaging equipment and cumbersome contour extraction algorithms, thus avoiding complex image processing procedures. This significantly improves measurement speed while avoiding accuracy loss caused by contour blurring and noise interference during image processing, truly achieving a dual improvement in measurement speed and accuracy. Even when applied to the measurement of spherical droplets / circular liquid columns, this method outperforms existing rainbow measurement techniques. Thanks to the consistency of dual CCD signal acquisition and the efficient filtering processing of Fast Fourier Transform, both measurement efficiency and accuracy are significantly optimized. More importantly, this method overcomes the limitation of existing light scattering measurement methods that are only applicable to spherical droplets / circular liquid columns, successfully extending light scattering measurement technology to the measurement of shape parameters of non-spherical droplets. This effectively fills the technological gap in the measurement of light scattering from non-spherical pendant droplets, providing a reliable and efficient measurement method for basic research and engineering applications in related fields such as pendant drop evaporation and fluid surface tension coefficient measurement.Meanwhile, the method has a simple and easy-to-operate design, can adapt to the needs of pendant drop measurement in different scenarios, has outstanding practicality, does not require complicated operation procedures and professional maintenance personnel, and is easy to promote and apply. Attached Figure Description

[0041] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 This is a pendant drop profile diagram from an embodiment of the present invention; Figure 2 This is a schematic diagram of a light scattering pendant drop shape parameter measurement system according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the first-order rainbow signal of a spherical particle with a radius of 500 micrometers, used in a light scattering droplet shape parameter measurement method according to an embodiment of the present invention. Figure 4 This is a schematic diagram of the second-order rainbow signal of a spherical particle with a radius of 500 micrometers, as described in an embodiment of the present invention for measuring the shape parameters of a light-scattering pendant droplet. Figure 5 This is a rainbow scattering intensity diagram of a spherical particle with a radius of 500 micrometers after filtering the first-order rainbow signal, according to a method for measuring the shape parameters of a light-scattering pendant droplet in an embodiment of the present invention. Figure 6 This is a rainbow scattering intensity diagram of a spherical particle with a radius of 500 micrometers after second-order rainbow signal filtering, as described in an embodiment of the present invention for measuring the shape parameters of a light-scattering pendant droplet. Figure 7 This is a rainbow scattering intensity diagram of a spherical particle with a radius of 600 micrometers after first-order rainbow signal filtering, as described in an embodiment of the present invention for measuring the shape parameters of a light-scattering pendant droplet. Figure 8 This is a rainbow scattering intensity diagram of a spherical particle with a radius of 600 micrometers after second-order rainbow signal filtering, as described in an embodiment of the present invention for measuring the shape parameters of a light-scattering pendant droplet. Figure 9 This is a rainbow scattering intensity diagram after filtering the first-order rainbow signal of a light scattering droplet with R1=500 μm and R2=600 μm, according to an embodiment of the present invention. Figure 10 This is a rainbow scattering intensity diagram of a second-order rainbow signal filtered from a light scattering droplet with R1=500 μm and R2=600 μm, according to an embodiment of the present invention. Figure 11 This is a flowchart of a method for measuring the shape parameters of a light-scattering pendant droplet in an embodiment of the present invention; Figure 12 This is a block diagram of a light scattering pendant drop shape parameter measurement system according to an embodiment of the present invention.

[0043] Among them: 1-monochromatic laser; 2-beam expander unit; 3-droplet generation and control turntable; 4-combined bilinear CCD detector. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0045] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0046] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0047] The present invention will now be described in further detail with reference to the accompanying drawings: See Figure 12 This invention discloses a light scattering pendant drop shape parameter measurement system, comprising: The laser emitting module includes a monochromatic laser 1 and a beam expander unit 2 disposed on the output path of the monochromatic laser; the monochromatic laser 1 is a helium-neon laser, and the coherence length of its output laser is greater than the diameter of the droplet.

[0048] The pendant droplet carrying and control module includes a droplet generation and control turntable 3, which is used to carry the pendant droplet and place the pendant droplet in the irradiation area of ​​the incident light; The scattered light detection module includes a combined bilinear CCD detector 4, which is set on the path of the scattered light emitted by the pendant drop to collect the first-order rainbow signal and the second-order rainbow signal after the pendant drop is scattered. The combined bilinear CCD detector 4 can be fixed or adjustable in spacing. When it is used for pendant drop measurement of a specific liquid, the fixed type is used, and when it is used for pendant drop measurement of different liquids, the adjustable type is used.

[0049] The data processing module, electrically connected to the combined bilinear CCD detector, is used to receive the scattered signal and reconstruct the scattering angle distribution map after filtering by fast Fourier transform, extract the position and intensity of the scattering peak, and then calculate the radius and vertical curvature radius of the pendant droplet.

[0050] This invention discloses a light-scattering pendant drop shape parameter measurement system. The system's overall structure is scientifically and rationally designed, with clearly defined functions and coordinated cooperation among modules. From incident light control, stable droplet support, scattering signal acquisition to data processing, a complete and precise measurement chain is formed, effectively solving the technical pain points of existing pendant drop measurement systems, such as insufficient accuracy, inability to simultaneously and reliably measure two core shape parameters, and low signal acquisition efficiency. Specifically, the laser emission module consists of a monochromatic laser and a beam expander unit positioned along its output path. It emits a stable monochromatic coherent beam, and the beam expander unit precisely controls the laser to ensure uniform illumination of the droplet surface, providing a fundamental guarantee for accurate acquisition of subsequent scattering signals and avoiding distortion caused by uneven illumination, thus improving the reliability of measurement data from the source. The droplet support and control module includes a droplet generation and control turntable that stably generates and supports the droplet while precisely controlling its position to ensure it remains within the incident light's illumination area. This effectively reduces interference from droplet movement and displacement on scattering signal acquisition, ensuring the stability and repeatability of the measurement process, guaranteeing consistency across multiple measurements, and improving the system's measurement reliability. The scattered light detection module employs a combined bilinear CCD detector, positioned along the scattered light emission path of the pendant droplet. It is specifically designed to separately acquire the first-order and second-order rainbow signals scattered by the droplet. Compared to traditional single-CCD detectors, this design ensures consistency in intensity and angle measurements of both types of rainbow signals, avoiding deviations during signal acquisition. It also allows for targeted acquisition of effective signals, preventing resource waste caused by invalid signal areas. This significantly improves the targeting and efficiency of scattered signal acquisition, providing a high-quality signal foundation for subsequent data processing and parameter calculation. The data processing module is stably electrically connected to the combined bilinear CCD detector, enabling rapid reception of the acquired scattered signals. Through Fast Fourier Transform (FFT), the signal is filtered to effectively remove high-frequency noise, thereby accurately reconstructing the scattering angle distribution map, precisely extracting the position and intensity of the scattering peaks, and ultimately reliably calculating the droplet's radius and vertical radius of curvature. This solves the problems of low data processing accuracy, inaccurate peak extraction, and large parameter calculation errors in existing systems. The entire system does not rely on complex imaging equipment and cumbersome contour extraction processes. Through the synergistic effect of various modules, it achieves synchronous, rapid, and high-precision measurement of the two core shape parameters of a pendant drop. The measurement process is stable and efficient, and the system has a simple structure and strong practicality. It can adapt to the pendant drop measurement needs in different scenarios, providing reliable system support for the study of pendant drop-related fluid properties and evaporation processes. At the same time, compared with existing measurement systems, its overall design is more targeted, easy to operate, and highly stable, which can effectively reduce interference factors in the measurement process and further improve the accuracy and reliability of measurement data.

[0051] See Figure 11This invention discloses a method for measuring the shape parameters of a light-scattering pendant droplet, comprising: S1, using a monochromatic coherent laser beam, the laser beam is expanded into an incident light with a beamwidth of 3-5 times the diameter of the droplet, so as to uniformly irradiate the droplet; The coherence length of the monochromatic coherent laser beam is greater than the diameter of the droplet. Before uniformly irradiating the droplet, the droplet is kept stationary or rotating at a constant speed to avoid interference from droplet swaying on the acquisition of the scattered signal.

[0052] S2 uses a combined bilinear CCD detector 4 to collect the first-order rainbow signal and the second-order rainbow signal generated by pendant droplet scattering, respectively; S3, perform fast Fourier transform filtering on the collected first-order rainbow signal and second-order rainbow signal, filter out high-frequency components, and reconstruct the scattering angle distribution map; After the Fast Fourier Transform (FFT) filtering, the reconstructed scattering angle distribution map is smoothed to further reduce noise interference and improve the accuracy of peak extraction.

[0053] S4. Extract the positions and intensities of multiple scattering peaks from the scattering angle distribution map, calculate the radius of the droplet by the positional spacing of the multiple peaks, and calculate the vertical radius of curvature of the droplet by the ratio of the intensities of the multiple peaks of the first-order rainbow to those of the second-order rainbow.

[0054] The complex amplitude and total field intensity of the first-order and second-order rainbow signals are calculated based on the vector complex ray model to determine the location and intensity of the scattering peaks.

[0055] The complex amplitude and total field intensity of the first-order and second-order rainbow signals are calculated based on the vector complex ray model to determine the location and intensity of the scattering peaks. First-order rainbow and second-order rainbow Amplitude of scattered light and Calculated by the following formula:

[0056] in, Let Fi be the Fresnel factor, where vertical Peaceful Reflection coefficient during polarization Calculated using Fresnel's formula; As a divergence factor, and The calculations are performed using the following two formulas:

[0057]

[0058] in:

[0059]

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067] in:

[0068]

[0069]

[0070] in, Let be the angle of incidence of light on the surface of the pendant drop. For the corresponding angle of refraction, The refractive index of the pendant drop; the phase of the outgoing ray. Calculated by the following formula:

[0071] The exit angle of the emitted ray It can be determined based on the angle of incidence of the incident light. and angle of refraction It can be obtained from the following formula:

[0072] The angle of incidence of the incident ray corresponding to the geometric optics rainbow angle is: and angle of refraction Calculated using the following formulas respectively:

[0073]

[0074] The angle of incidence of the geometrical optical incident rays corresponding to the first and second order rainbows can be calculated from the above formula. Then calculate the range of incident angles corresponding to the rays on both sides of the rainbow ray's incident angle. Amplitude of the emitted light rays inside , and phase , The total field is calculated from this. and total strength Since the incident light rays corresponding to the geometric rainbow angle exit on the same side of the geometric rainbow angle, interference is generated to form secondary rainbow peaks. The position and intensity of these peaks are related to the geometry of the pendant drop and are used for rapid and accurate measurement.

[0075] This invention discloses a method for measuring the shape parameters of a light-scattering pendant droplet. The method first expands a monochromatic coherent laser beam into an incident light beam with a beamwidth 3-5 times the droplet diameter, ensuring that the incident light uniformly covers and illuminates the droplet surface. This avoids the distortion of the scattering signal caused by uneven illumination from the initial measurement stage, laying a solid foundation for the accurate acquisition of subsequent scattering signals. Simultaneously, the monochromatic coherence of the laser further enhances the stability of the scattering signal, facilitating subsequent signal filtering and feature extraction, thus ensuring the original reliability of the measurement data from the source. In the scattering signal acquisition stage, the method employs a combined bilinear CCD detector to acquire the first-order and second-order rainbow signals generated by the droplet scattering. This design is highly targeted: on the one hand, it ensures consistency in the intensity and angle measurements of the two types of rainbow signals, effectively avoiding measurement deviations that easily occur when acquiring two types of signals with a single CCD detector, significantly improving the accuracy of signal acquisition; on the other hand, it accurately captures the effective scattering signal, effectively avoiding areas in the Alexandria dark region where there are no useful signals, avoiding resource waste during signal acquisition, significantly improving the targeting and efficiency of scattering signal acquisition, and providing high-quality signal support for subsequent data processing and parameter calculation. In the signal processing and parameter calculation stages, this method performs fast Fourier transform filtering on the acquired first-order and second-order rainbow signals, which can efficiently filter out high-frequency noise in the signal and accurately reconstruct the scattering angle distribution map, ensuring the integrity and clarity of the scattering angle distribution map, and providing a clear signal foundation for the subsequent accurate extraction of scattering peaks. By extracting the position and intensity of multiple sets of scattering peaks in the scattering angle distribution map, the droplet radius is calculated by using the position spacing of multiple sets of peaks and the vertical radius of curvature is calculated by the ratio of the intensity of multiple sets of peaks. Compared with the single peak calculation method, this method significantly improves the accuracy and stability of the measurement, realizes the synchronous and accurate measurement of the two core shape parameters of the droplet, eliminates the need for additional measurement steps, simplifies the measurement process, and improves measurement efficiency. Compared to traditional photographic methods, this method eliminates the need for high-resolution imaging equipment and cumbersome contour extraction algorithms, thus avoiding complex image processing procedures. This significantly improves measurement speed while avoiding accuracy loss caused by contour blurring and noise interference during image processing, truly achieving a dual improvement in measurement speed and accuracy. Even when applied to the measurement of spherical droplets / circular liquid columns, this method outperforms existing rainbow measurement techniques. Thanks to the consistency of dual CCD signal acquisition and the efficient filtering processing of Fast Fourier Transform, both measurement efficiency and accuracy are significantly optimized. More importantly, this method overcomes the limitation of existing light scattering measurement methods that are only applicable to spherical droplets / circular liquid columns, successfully extending light scattering measurement technology to the measurement of shape parameters of non-spherical droplets. This effectively fills the technological gap in the measurement of light scattering from non-spherical pendant droplets, providing a reliable and efficient measurement method for basic research and engineering applications in related fields such as pendant drop evaporation and fluid surface tension coefficient measurement.Meanwhile, the method has a simple and easy-to-operate design, can adapt to the needs of pendant drop measurement in different scenarios, has outstanding practicality, does not require complicated operation procedures and professional maintenance personnel, and is easy to promote and apply.

[0076] The working principle of this invention is as follows: The principle of the measurement system of this invention is as follows: Figure 2 As shown, a monochromatic coherent beam, such as a helium-neon laser, is expanded by a beam expander system and then irradiates a pendant drop. The laser coherence length is required to be much larger than the droplet diameter, and the beamwidth after expansion is three to five times the droplet diameter to ensure uniform irradiation. After being scattered by the pendant drop, the incident light is acquired by a combined bilinear CCD. The two CCDs measure the first-order and second-order rainbow signals, respectively. The measured signals are shown in the figure. Figure 3 and Figure 4 As shown. After filtering, the result is as follows. Figure 5 and Figure 6 The scattering angle distribution diagram shows the angular positions of each peak and the spacing between them relative to the droplet diameter. R 1. Related to this. Figure 5 , Figure 6 , Figure 7 and Figure 8 The scattering peak positions of pendant droplets with radii of 500 μm and 600 μm are shown respectively. Table 1 compares the scattering peak positions of the two pendant droplets of different sizes. Table 1 shows the variation of peak position with droplet size.

[0077] Table 1

[0078] for R 1 and R For two identical droplets, the ratio of their peak intensities is constant. However, when... R 1 and R When the two peaks are not in the same position, the ratio of their intensities will change with the shape of the pendant drop, and the ratio will be related to the radius of curvature of the pendant drop in the vertical direction. R 2 and the radius of the pendant drop R 1 ratio R 2 / R 1. Related to this. Figure 9 , Figure 10 , Figure 5 and Figure 6 radius R 1. Same as R 2. Comparison of scattering intensities from two different pendant drops. It can be seen that when... R 1 and R When the values ​​of 2 are the same, the ratio of the peak intensities of the first-order rainbow to those of the second-order rainbow is close to 10, while when... R 1 is 500 micrometers. RAt a wavelength of 600 micrometers, the peak intensities of a first-order rainbow and a second-order rainbow are almost equal. Therefore, the radius of the pendant drop can be measured simultaneously based on the ratio of the peak position to the intensity of the pendant drop's scattering intensity. R 1 and vertical radius of curvature R 2. In principle, the distance between any two peaks can be used to measure the droplet diameter. However, this invention uses multi-peak positioning to measure the droplet radius, which greatly improves the measurement accuracy and stability. The ratio of the intensities of the first-order and second-order rainbow main peaks is related to the deformation of the pendant drop, and therefore can be used to determine the vertical radius of curvature of the pendant drop. R 2. This invention also employs the ratio of multiple secondary peak intensities to improve measurement accuracy. This invention can be used for the measurement of droplets with circular symmetry, such as ultrasonically suspended droplets, pendant droplets, and seated droplets.

[0079] The main theoretical basis of this invention is the vector complex ray model, and all algorithms used are ray tracing algorithms. That is, using the basic equations of the vector complex ray model, the propagation direction, phase, wavefront curvature, and amplitude of the wave represented by each ray interacting with the object surface are calculated step by step. Finally, the total scattered field is calculated based on the amplitude and phase of the wave represented by the outgoing ray. The calculation formulas in this patent are analytical expressions derived from the vector complex ray model, which can directly calculate the complex amplitude and total field of the wave represented by the outgoing ray. These formulas require specific derivation. The specific derived calculation formulas are given below.

[0080] This section uses R The radius of curvature of the wavefront is represented by ρ1 and ρ2, which represent the pendant drop radius and the vertical radius of curvature, respectively.

[0081] First-order rainbow and second-order rainbow Amplitude of scattered light and Calculated by the following formula: (A1) In the formula Let Fi be the Fresnel factor, where vertical Peaceful Reflection coefficient during polarization Calculated using Fresnel's formula. As a divergence factor, and The following two formulas are used for calculation.

[0082]

[0083] In the formula

[0084]

[0085]

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092] in

[0093]

[0094]

[0095] Let be the angle of incidence of light on the surface of the pendant drop. For the corresponding angle of refraction, The refractive index of the pendant drop. Phase of the outgoing ray. Calculated by the following formula: (A2) The exit angle of the emitted ray It can be determined based on the angle of incidence of the incident light. and angle of refraction It can be obtained from the following formula:

[0096] The angle of incidence of the incident ray corresponding to the geometric optics rainbow angle is: and angle of refraction Calculated using the following formulas respectively: , (A3) In the specific calculation, based on the refractive index of the suspended drop liquid, the angle of incidence of the geometrical optical incident rays corresponding to the first and second order rainbows is calculated using equation (A3). Then, using equations (A1) and (A2), the range of incident angles corresponding to the rays on both sides of the rainbow ray's incident angle is calculated. Amplitude of the emitted light rays inside , and phase , The total field is calculated from this. and total strength Because the incident light rays corresponding to the geometric rainbow angle exit on the same side of the geometric rainbow angle, interference occurs, forming secondary rainbow peaks. The position and intensity of these peaks are related to the geometry of the pendant drop and can be used for rapid and accurate measurements.

[0097] 1. Traditional Airy theory can calculate the intensity angular distribution and peak positions near the rainbow angle of a spherical particle, but it has two problems: 1) The calculated secondary rainbow peak ( , , (etc.) The position is inaccurate, and the deviation increases with the distance from the rainbow corner; 2) The angular distribution of scattering intensity of non-spherical particles cannot be calculated.

[0098] 2. Classical theories such as Mie and Debye can rigorously calculate the angular distribution of scattering intensity for spherical particles, but they cannot be applied to non-spherical particles. Currently, there are no theoretical or numerical methods for calculating the scattering of large (particle size much larger than wavelength) non-spherical particles.

[0099] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A system for measuring the shape parameters of a light-scattering pendant droplet, characterized in that, include: The laser emitting module includes a monochromatic laser (1) and a beam expander (2) disposed on the output path of the monochromatic laser. The droplet carrying and control module includes a droplet generation and control turntable (3) for carrying the droplet and placing the droplet in the irradiation area of ​​the incident light; The scattered light detection module includes a combined bilinear CCD detector (4), which is set on the scattered light emission path of the droplet to collect the first-order rainbow signal and the second-order rainbow signal after the droplet is scattered. The data processing module, electrically connected to the combined bilinear CCD detector, is used to receive the scattered signal and reconstruct the scattering angle distribution map after filtering by fast Fourier transform, extract the position and intensity of the scattering peak, and then calculate the radius and vertical curvature radius of the pendant droplet.

2. The light scattering pendant drop shape parameter measurement system according to claim 1, characterized in that, The combined bilinear CCD detector (4) is either fixed or has an adjustable spacing.

3. The light scattering pendant drop shape parameter measurement system according to claim 2, characterized in that, A fixed bilinear CCD detector (4) is used when measuring pendant drops of a specific liquid; an adjustable-pitch bilinear CCD detector (4) is used when measuring pendant drops of different liquids.

4. The light scattering pendant drop shape parameter measurement system according to claim 1, characterized in that, The monochromatic laser (1) is a helium-neon laser, and the coherence length of its output laser is greater than the diameter of the droplet.

5. A method for measuring the shape parameters of a light-scattering pendant droplet based on the system described in any one of claims 1-4, characterized in that, include: A monochromatic coherent laser beam is used to expand the laser beam into an incident light with a beamwidth of 3-5 times the diameter of the droplet, so as to uniformly irradiate the droplet. A combined bilinear CCD detector (4) was used to collect the first-order rainbow signal and the second-order rainbow signal generated by the droplet scattering, respectively; The first-order and second-order rainbow signals were subjected to fast Fourier transform filtering to remove high-frequency components and then the scattering angle distribution map was reconstructed. The positions and intensities of multiple scattering peaks in the scattering angle distribution map are extracted. The radius of the droplet is calculated by the positional spacing of the multiple peaks. The vertical radius of curvature of the droplet is calculated by the ratio of the intensities of the multiple peaks in the first-order rainbow to those in the second-order rainbow.

6. The method for measuring the shape parameters of a light-scattering pendant droplet according to claim 5, characterized in that, The coherence length of the monochromatic coherent laser beam is greater than the diameter of the droplet.

7. The method for measuring the shape parameters of a light-scattering pendant droplet according to claim 5, characterized in that, After the Fast Fourier Transform (FFT) filtering, the reconstructed scattering angle distribution map is smoothed to further reduce noise interference and improve the accuracy of peak extraction.

8. The method for measuring the shape parameters of a light-scattering pendant droplet according to claim 5, characterized in that, Before uniformly irradiating the droplet, the droplet is kept stationary or rotated at a constant speed to avoid interference from droplet swaying on the acquisition of the scattering signal.

9. The method for measuring the shape parameters of a light-scattering pendant droplet according to claim 5, characterized in that, Specifically, the positions and intensities of multiple scattering peaks in the scattering angle distribution map are extracted as follows: The complex amplitude and total field intensity of the first-order and second-order rainbow signals are calculated based on the vector complex ray model to determine the location and intensity of the scattering peaks.

10. The method for measuring the shape parameters of a light-scattering pendant droplet according to claim 9, characterized in that, The complex amplitude and total field intensity of the first-order and second-order rainbow signals are calculated based on the vector complex ray model to determine the location and intensity of the scattering peaks. First-order rainbow and second-order rainbow Amplitude of scattered light and Calculated by the following formula: in, Let Fi be the Fresnel factor, where vertical Peaceful Reflection coefficient during polarization Calculated using Fresnel's formula; As a divergence factor, and Calculated using the following two formulas respectively: in: in: in, Let be the angle of incidence of light on the surface of the pendant drop. For the corresponding angle of refraction, The refractive index of the pendant drop; the phase of the outgoing ray. Calculated by the following formula: The exit angle of the emitted ray It can be determined based on the angle of incidence of the incident light. and angle of refraction It can be obtained from the following formula: The angle of incidence of the incident ray corresponding to the geometric optics rainbow angle is: and angle of refraction Calculated using the following formulas respectively: The angle of incidence of the geometrical optical incident rays corresponding to the first and second order rainbows can be calculated from the above formula. Then calculate the range of incident angles corresponding to the rays on both sides of the rainbow ray's incident angle. Amplitude of the emitted light rays inside , and phase , The total field is calculated from this. and total strength Since the incident light rays corresponding to the geometric rainbow angle exit on the same side of the geometric rainbow angle, interference is generated to form secondary rainbow peaks. The position and intensity of these peaks are related to the geometry of the pendant drop and are used for rapid and accurate measurement.

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