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Abstract
The identification of raindrops and hailstones is of great significance to the study of precipitation characteristics from the aspect of microphysics and can provide important data support for weather modification. In this paper, an identification method of raindrops and hailstones based on digital holographic interference is proposed. The grayscale gradient variance method is used to obtain the focus position of the particles. By means of binarization and morphological processing, digital holograms are processed to obtain clear profiles of the particles. Then the contour parameters of the particles are used to obtain the equivalent volume diameter and roundness. Finally, according to the equivalent volume diameter, roundness and lens-like effect of the particles, the phase states of the raindrop and hailstone are identified by the algorithm. Experiments show that the method proposed in this paper has a good identification effect on raindrops and hailstones. The research results can provide reference for the research of the identification method of raindrops and hailstones and the acquisition of accurate characteristic parameters.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Hailstone, with spherical, conical or irregular shapes, is a kind of solid water condensate with diameter of 5 - 50 mm [1]. Hailstone weather often occurs in spring and summer and is of great harm to social production, because it will damage crops and threaten the safety of people and animals [2]. Raindrop, with diameter of 0.2–5 mm (when the equivalent volume diameter is greater than 5 mm, raindrops are easily broken into smaller particles), often falls with hailstone, which has adverse effects on the accurate identification of hailstone, like other kinds of hydrometeor [3–5]. Therefore, accurate identification of raindrop and hailstone in the mixed phase flow of the two is of great importance for hailstones cloud and artificial hailstones suppression research. The research on the identification of raindrop and hailstone belongs to hydrometeor phase identification (HPI), which refers to the classification of different hydrometeors [6]. At present, dual polarization radar is the main equipment for phase identification of hydrometeors. Dual polarization radar provides radar parameters reflecting physical properties of water condensates for phase identification. The identification methods applied to dual polarization radar include traditional fuzzy logic hydrometeor classification (FHC) based on fuzzy logic method, FHC based on neural network model, FHC based on clustering model and its improved version, and FHC based on clustering model combined with other physical parameters. The above method uses FHC as the core algorithm, and calculates the particle size, shape, phase state and other information based on radar wave parameters [6–20]. The classification results of FHC on raindrop and ice phase particle largely depend on the use of radar wave parameters such as differential reflectance ZDR, which is very accurate for raindrop measurement, however, the measurement of mixed raindrop and ice phase particle may need to be improved [9,10,12,13]. Moreover, the objectivity of FHC is not very good, because the classification effect depends on the parameter setting of membership function, which is determined by artificial experience.
Since the charge coupled device (CCD) or complementary metal oxide semiconductor (CMOS) devices are used instead of dry board to record holograms, digital holographic interferometry (DHI) enables rapid, real-time, non-destructive, full-field optical measurement [21–24]. Compared with the above method, DHI can directly reflect the optical and morphological characteristics of particles. Hydrometeor measurement and identification methods based on DHI include the combination of DHI and interference imaging technology, as well as the combination of DHI and artificial intelligence algorithms (such as naive Bayes, Support Vector Machine, decision tree) [25,26]. At present, researchers have synchronously completed the measurement and identification of micron level raindrop and ice phase particle by using the first kind of method, but the identification of larger size ice phase particle remains to be studied. The second method needs to be improved in the droplet type classification of a single precipitation particle as a sample. In this paper, coaxial DHI is used to record the contour boundary and optical information of particles, and then the optical characteristics, equivalent volume diameter and roundness of particles are obtained. Finally, the phase identification algorithm is used to identify the phase states of raindrop and hailstone. This method can be used to accurately identify raindrop and hailstone, and provides a powerful research method for raindrop and hailstone identification and artificial hailstone suppression.
2. Theory
Coaxial DHI is widely used in the measurement of multiphase flow particles due to its features such as simple optical path, high information density, high spatial bandwidth utilization, large recording range, and small interference of particle twin images recorded in far-field conditions [27–31]. When a particle is irradiated by plane wave, the diffracted light (scattered wave) of the particle interferes with the direct light that is not interfered, forming a hologram, which is recorded by CCD or CMOS [32–34]. Fresnel-kirchhoff diffraction formula is used to reconstruct holograms. When particles exist in the measurement space, the complex amplitude distribution of the hologram reconstruction plane can be expressed as [32]
The reconstructed hologram is reconstructed by Eq. (1), which contains particle and background information. The two-dimensional centroid coordinates (x, y) of a particle can be realized by obtaining the first moment of the binary image of the reconstructed hologram. In the connected domain of particles, firstly, the sum of grayscales of all pixels (first moment) M00 is obtained, and then the sum of x-axis coordinates of all pixels M10 and the sum of y-axis coordinates of all pixels M01 are obtained, as shown below [31]
In order to ensure the accuracy of particle phase identification, particles need to be identified at the position with the clearest profile, namely the focusing position. Therefore, in this paper, reconstruction distance and grayscale gradient variance method of fusion hologram are combined to determine the z-axis position of particles with high precision [31]. The grayscale gradient variance k is shown below [31]
where, G is the total grayscale gradient, $\overline G$ is the average grayscale gradient, N is the total number of pixels in each particle area of the hologram. Considering the difference in the size of raindrop and hailstone, the reconstruction range and the spacing between each reconstruction plane are needed to be set separately. For raindrop identification, the sampling length is 23.44 mm, and the numerical reconstruction range of each small segment is 0.23 mm. For hailstone identification, the sampling length is set to 200 mm, and the numerical reconstruction range of each small segment is 2 mm. Therefore, the z-axis position accuracy in this paper is 0.01–2 mm.After the particle focusing position is determined, the two-dimensional particle centroid coordinates, circumference, area and equivalent volume diameter of the location are extracted. Since raindrops in the digital hologram are two-dimensional, the deformation of the bottom during falling has little influence on the calculation of roundness of raindrops in the digital hologram. Therefore, according to the contour observation, the two-dimensional plane shape of raindrops is approximately a circle, and its roundness is close to 1, while the two-dimensional plane shape of hailstones is much different from the circle. The circumference and area of the particle are used to calculate roundness, and the formula is shown below [25]
Since the diameter of hailstone is not less than 5 mm, and the diameter of raindrop is usually not more than 5 mm, the equivalent volume diameter is used as the second feature to identify raindrop and hailstone. The formula of equivalent volume diameter Deq is as follows [35]
where, a represents half of the longest chord length of the particle, b represents half of the shortest chord length of a particle [35–37].Considering the optical properties of the particles themselves, raindrop, due to high transparency, spherical shape and deformation, usually has a converging effect on laser called lens-like effect. On the other hand, due to low transparency and usually irregular shape, hailstone does not easily converge laser [38]. The difference between raindrop and hailstone is particularly obvious in the grayscale distribution of the particle region. Therefore, whether the particles have lens-like effect is the last feature required for the algorithm in this paper to identify raindrop and hailstone.
3. Experimental setup
Figure 1 shows the experimental setup for identification of raindrop and hailstone based on coaxial DHI. In the experiment, a light beam from the pulsed laser with the wavelength of 532 nm and average power of 100 mW, is turned into linearly polarized light by a polarizer P. The light beam is expanded and collimated by lens L1 and L2, respectively. Then the beam passes through microform objective lens L3 into CMOS. Below the optical path is the process of recording particle information by digital holographic technology. In this process, because the propagation of electromagnetic waves does not depend on the medium, the incident wave (plane wave), taken as the object light, still exists after irradiating the particles. The incident wave interferes with the scattered wave (spherical wave of constant phase), generated by the incident wave irradiation of the particle, taken as the reference light, thus changing the energy field distribution near the particle and forming a ring-structure (interference ring). In this way, information about the particles, such as size and shape, is recorded. L3 (0.16× magnification, 24 mm depth of field, 494.50 mm working object distance) is used to scale down three-dimensional coordinates and contour information of raindrop and hailstone and phase information of transmitted light. The CMOS sensor (79 fps maximum sampling rate, 2448 W × 2048H pixels, 3.45 µm × 3.45 µm pixel size) is used to record the reduced digital hologram. The smallest particle size that can be detected by the experimental system is 43 µm, depending on the magnification of L3.
The experimental optical path is placed on the optical experimental platform of 600 mm × 900 mm. The experimental temperature is 298.15 ± 2 K, the relative humidity is 50%, and the air pressure is standard atmosphere. The sampling space is set at the working object distance of 494.50 mm, with a width of 52.79 mm and a height of 39.98 mm, and the sampling depth is set to be 11.72 mm (D = 2 × 11.72 mm) each before and after the working object distance point. In the experiment, the CMOS sampling rate is set to 50 frames per second and the exposure time is set to 20 µs.
A digital hologram, with no particles, is subtracted by a digital hologram with particles behind it to remove noise such as background light. The reconstruction range of the digital hologram is 0.30 mm each before and after the working object distance point of the image square, which is obtained from the sampling space and magnification of the microform objective. On one side of reconstruction range, 51 reconstructed holograms are obtained through numerical reconstruction, so the corresponding reconstruction distance of two adjacent reconstructed holograms is 0.06 × 10−1 mm. Within these 51 reconstructed holograms, another set of reconstructed holograms is taken at intervals of 5 reconstructed holograms. Therefore, the reconstruction distance interval is reset to 0.03 mm, so that the range of 0 mm - 0.3 mm is evenly divided into 9 reconstruction distances, that is, 0.03 mm - 0.27 mm, as shown in Fig. 2. Then, the 9 reconstruction holograms corresponding to the reconstruction distance are processed.
In the experiment, under a reasonable grayscale threshold setting, the corrosion template and expansion template are adjusted to the appropriate size to obtain a clear and complete particle edge. The holes and weak joints inside the particle are filled by the closed operation, and the burrs at the edge of the particle are removed by the open operation. After these steps, a clear, complete particle edge is obtained.
As shown in Fig. 2, the reconstructed hologram with a reconstruction distance of l, one of the 9 selected reconstruction images, is extracted along with its first 5 and last 5 reconstructed graphs. According to Eq. (3), the grayscale gradient variance of the particles in these reconstructed holograms is obtained successively and summarized into a matrix by column, where the maximum value of each column is converted into the z-axis coordinate of the corresponding particle in the reconstructed graph with a reconstructed distance of l. After the 9 reconstructed holograms with a reconstruction distance of 0.03 mm are processed successively, the accurate z-axis coordinates of the particles in the corresponding digital hologram can be obtained by removing duplicate particles.
Since diameter (equivalent volume diameter) is one of the significant characteristics that distinguish hailstone from raindrop, diameter correction is needed to obtain accurate diameter data. Under natural circumstances, when the diameter reaches 5 mm, under the multiple action of air resistance, surface tension and other forces, raindrop will split, and the diameter of hailstone is not less than 5 mm, so the diameter of 5 mm is regarded as one of the characteristics to distinguish raindrop and hailstone. Standard glass beads of 5 mm diameter are released and measured. Ten digital holograms containing particles are processed and a total of 10 clear and complete beads are recorded. Figure 3(a) shows 10 digital holograms, and Fig. 3(b) shows the statistical situation of the error between the measured diameter and 5 mm after the bad data is removed. As shown in Fig. 3(b), the error fluctuates around the mean value -0.63 × 10−3 mm, so the final result of diameter is set as Deq + 0.63 × 10−3 mm.
Fig. 3. Correction of diameter. (a) 10 digital holograms containing only 5 mm standard glass beads. (b) Diameter errors of 5 mm standard glass beads in 10 digital holograms.
4. Algorithm and verification
4.1 Phase identification algorithm
The complete process of identification algorithm of raindrop and hailstone is shown in Fig. 4. First, the number of processing holograms is set to 10, then the numerical reconstruction, binarization and parameter acquisition operations are carried out, and finally recorded particles are classified into phase states. 7 parameters correspond to the x-axis coordinate, y-axis coordinate, z-axis coordinate, length of minor axis b and major axis a, Deq and particle circumference C of the camera coordinate system, respectively. The x-axis coordinate and y-axis coordinate are calculated by using Eq. (2), and the Deq is calculated by using Eq. (5). The unit of tilt Angle of b is degree.
In this paper, the roundness threshold, equivalent volume diameter, and lens-like effect are used together to determine whether a particle is a raindrop or a hailstone. The component of phase identification in the above phase identification algorithm is as follows:
- (1) Firstly, the particles with an equivalent diameter of more than 200 µm are divided into the particles with lens-like effect and the particles without lens-like effect.
- (2) Then, in the particles with lens-like effect, considering that the irregular particles may be misjudged to have lens-like effect, the particles are divided into raindrop and particles of other types based on whether the roundness (calculated by Eq. (4)) is close to 1.
- (3) After that, in the particles without lens-like effect, the particles are divided into hailstone and other particles according to whether the diameter is greater than or equal to 5 mm.
- (4) Finally, other particles with diameter less than 5 mm and without lens-like effect phenomenon can be divided into ice particles covered by water and particles of other types based on whether the roundness is close to 1.
4.2 Lens-like effect
Raindrop of a certain diameter acts as lenses to focus, while hailstone does not. This lens-like effect makes the grayscale of a certain area in the center of the raindrop significantly higher than other areas in the digital hologram. Raindrops and hailstones to be processed are marked in Fig. 5 and Fig. 12 respectively. In order to observe the grayscale distribution of particles, that is, the phase distribution of light, a square range is selected with the size of half of the short axis b at the two-dimensional centroid coordinates of particles (calculated by Eq. (1)). Figure 6 shows the grayscale distribution around the two-dimensional coordinates of three raindrops, named as Raindrop (a), Raindrop (b) and Raindrop (c) respectively, with lens-like effect.
Fig. 5. Digital holograms to be processed, containing only raindrops. Raindrops to be processed are marked in three holograms respectively.
Fig. 6. Grayscale distribution of raindrops with lens-like effect. (a), (b) and (c) are three raindrops with lens-like effect, respectively. (a) shows the grayscale distribution of the central area of the raindrop (a).
As can be seen in Fig. 6, the grayscale of the central area of raindrop with lens-like effect is significantly higher than that of the surrounding region. In order to detect lens-like effect, the grayscale distribution in the central area of the particle needs to be extracted. As shown in Figs. 7(a), 7(b) and 7(c), the grayscale vectors are located in the same column of the x-axis coordinate and the same row of the y-axis coordinate of the particle. Along the x-axis and y-axis, starting from the x-axis and y-axis coordinates of the particle, the length of both vectors is set to a quarter of the short axis b.
Fig. 7. Detection of lens-like effect of raindrop. (a), (b) and (c) show the grayscale distribution of the central area of three raindrops with lens-like effect respectively. (d) and (e) show the grayscale distribution curves of three groups of grayscale vectors respectively.
As shown in Figs. 7(d) and 7(e), the raindrop with lens-like effect has a continuous grayscale change trend within the detection range. In vectors, the grayscale of raindrop with lens-like effect has a continuous rise and then a continuous decline, or a constant trend between continuous rise and continuous decline, and the interval of grayscale change is no less than five pixels. The gradient change of the vector is calculated to detect the change trend. In addition, the maximum value of each vector is obviously greater than the minimum value. In Figs. 7(d) and 7(e), the maximum value of grayscale curve is not less than three times of the minimum value. As shown in Table 1, the difference between the maximum and minimum values can be as much as five times. If the curve of the grayscale vector (GV) in either direction has the above characteristics, it can be determined that the particle has lens-like effect. It is worth noting that, under the condition of constant laser intensity, the maximum grayscale of the lens-like effect area (LCA) of the three raindrops in Fig. 7 is inconsistent, as is the size of the square range of the three raindrops. The size of square range reflects the Deq of the particle, so it can be considered that the maximum grayscale of the LCA of raindrop has a certain relationship with Deq. Eleven raindrops with lens-like effect and diameter of 1–5 mm are recorded. Figure 8 shows that the diameter of raindrop with lens-like effect has an obvious increasing trend relative to the maximum grayscale of the LCA. Moreover, it can be seen that the maximum grayscale ranges from 3 to 9, which indicates that the maximum grayscale of raindrop with lens-like effect has upper limit and lower limit when the light intensity is constant.
Table 1. Grayscale distribution of raindrops in GVs
In Fig. 7(d), the curve of GV of raindrop (b) along the x-axis has no fluctuation, and Fig. 11(a) shows that the size of LCA of raindrop with Deq of 3.73 mm is 0 in GV along the x-axis. It indicates that there is a probability that there is no feature described by the determination basis in the GV of a certain direction. According to Fig. 7(b), the reason is that there is a certain offset between the LCA of raindrop (b) and the GV along the x-axis. This is because the raindrop deforms under the influence of falling resistance in the process of falling, which causes the LCA to shift the centroid of raindrop on a two-dimensional plane. In order to determine the influence of the offset on the detection of the lens-like effect, the maximum widths along the x-axis and y-axis of the LCA of 11 selected raindrops were counted, as shown in Fig. 9. As can be seen from Fig. 9, if the offset reaches half of the maximum width in each direction, then the algorithm cannot determine whether lens-like effect occurs. Figure 10 shows that in practice, the offsets of raindrops in each direction will not exceed half of the maximum widths of the LCA, so it is feasible to detect the LCA by GVs.
Figure 10 also shows that with the increase of diameters of raindrops, the offsets of the LCA have an increasing trend, indicating that the larger the diameter, the larger the deformation degree, which is consistent with the actual situation. Since the diameter of raindrop is positively correlated with the velocity, the offset can be used to predict the falling velocity of raindrop.
The grayscale curves in Fig. 7(d) also reflect the size of the LCA in GVs. In the GVs of two directions, the size of the LCA is extracted with grayscale 3 as the limit. The size of the LCA in the GVs and diameters of the three raindrops in Fig. 6 are shown in Table 2. It can be inferred from Table 2 that the larger the Deq is, the larger the size of the LCA detected by the GVs. The size of the LCA in the GVs and diameters of raindrops with lens-like effect in the 10 digital holograms above are obtained, as shown in Fig. 11. Figure 11 shows that the larger the raindrop diameter, the larger the size of the LCA detected by the GVs, that is, easier it is to detect the convergence area.
Table 2. Diameter and width of lens-like effect range of raindrops
Combined with the maximum width of the LCA shown in Fig. 9 and the offset of the LCA shown in Fig. 10, it can be seen that the sizes of the LCA in the GVs in Fig. 11 are determined by the maximum width and the offset. It can be seen from the growth trend of the offset with the diameter and the growth trend of the sizes of the LCA in the GVs with the diameter that the maximum width of the LCA also has a certain positive correlation with the diameter.
Figure 13 shows the grayscale distribution of three hailstones in Fig. 12, named as Hailstone (a), Hailstone (b) and Hailstone (c) respectively, without lens-like effect. It can be seen that the central areas of hailstones are flat compared to raindrops with lens-like effect, and there is no significant difference in the grayscale. The GVs along the x-axis and y-axis are set in the same way to obtain the grayscale distribution near the two-dimensional centroid of the hailstones.
Fig. 12. Digital holograms to be processed, containing only hailstones. Hailstones to be processed are marked in three holograms respectively.
Fig. 13. Grayscale distribution of hailstones without lens-like effect. (a), (b) and (c) are three hailstones without lens-like effect, respectively. (a) shows the grayscale distribution of the central area of Hailstone (a).
It can be seen in Figs. 14(d) and 14(e) that in the GVs in two directions of the three hailstones, there is no grayscale change trend described above, and the grayscale change interval is no more than 5 pixels. As shown in Table 3, the maximum grayscales of the three ice particles are all less than 3 times of the minimum value. According to the above points, it can be determined that the lens-like effect of the hailstones does not occur. The fluctuation of grayscale curves is due to the scattered transparent region of the hailstones, which makes part of the laser pass through.
Fig. 14. Detection of lens-like effect of hailstone. (a), (b) and (c) show the grayscale distribution of the central area of three hailstones without lens-like effect respectively. (d) and (e) show the grayscale distribution curves of three groups of grayscale vectors respectively.
Table 3. Grayscale distribution of ice particles in GV
4.3 Threshold for roundness
According to the diameter range, the stable shapes of raindrop can be divided into spherical (Deq < 1 mm), ellipsoidal (Deq = 1–3 mm) and steamed bun (Deq > 3 mm). However, since the latter two shapes are spherical deformation, their roundness calculated by Eq. (4) is still approximately 1. Experiments are designed and performed to record separate phase flows of raindrops and hailstones. Near the working object distance point of microscopic objective L3, raindrops and hailstones are dropped with a height of about 300 mm and recorded by DHI. Digital holograms that record only raindrops or hailstones are selected and processed with 30 each, resulting in a total of 72 raindrops and 45 hailstones. The comparison results of roundness data between raindrops and hailstones are shown in Fig. 15.
According to Fig. 15, the roundness range of most raindrops is roughly above 0.7, while the roundness range of most hailstones is roughly below 0.7 due to their non-circular contour. The irregular shape of hailstone is due to the following three cases on the way down. The first case is that other ice particles collide with the hailstone and freeze into one, making the hailstone irregularly shaped. In the second case, the frozen droplets collide with the hailstone and freeze into one body, making the hailstone irregular in shape. The third case is that after the collision between the liquid drop (non-frozen drop) and the hailstone, the hailstone is attached to the liquid drop and continues to roll. During the rolling process, the water on the surface of the hailstone freezes, making the hailstone irregular in shape. Raindrop, on the other hand, maintains regular shape as it falls. Therefore, the roundness threshold can be set to 0.7 to distinguish raindrop from hailstone. If experimental conditions change, the roundness threshold may need to be adjusted appropriately.
There are three raindrops with roundness less than 0.7, as shown in Fig. 15. After expansion and collimation, the laser beam is contracted by the microform objective lens, so the optical system in this experiment inevitably has certain aberration. The aberration is more obvious at the edge of digital hologram. Because they are located at the edge of the digital hologram, the images of these three raindrops are distorted by aberrations. Therefore, after the images of these three raindrops underwent binarization, corrosion, expansion and other operations, the shape changed significantly and became irregular. After processing 40 digital holograms containing only raindrops, roundness data of 86 raindrops are obtained, among which 3 raindrops had roundness less than 0.7. The calculation results show that the error of raindrops to be identified as other particles is 3.49%. Therefore, the above factor has little effect on the identification of raindrop and hailstone.
5. Experiment and analysis
By recording raindrops and hailstones at the working object distance, the identification experiment was performed when the two mixed. In addition to the roundness threshold, which has been adjusted to 0.9 due to the adjustment of light intensity, the other experimental settings are consistent with section 3. The CMOS sampling frequency is set at 79 Hz to obtain stable image acquisition effect. Eleven digital holograms are selected, of which the 11th is used as a background image, without particle. According to visual observation, there are 27 raindrops, 20 hailstones and 1 particle of other types in the 10 digital holograms. The actual appearance of hailstone is shown in Fig. 16(a). Considering that there are some small hailstones which melt greatly when falling, there may be some ice particles covered by water.
Fig. 16. (a) is a hailstone sample. (b) and (c) are first and fifth of ten digital holograms, respectively, containing only hailstone and raindrop.
The first and fifth of the 10 digital holograms processed are shown in Figs. 16(b) and 16(c). The gray distribution of raindrops marked in Fig. 16(b) and hailstone marked in Fig. 16(c) are respectively shown in Fig. 17 and Fig. 18. The gray distribution characteristics described in Fig. 17 and Fig. 18 are consistent with those described in section 4, which proves that the algorithm can effectively detect whether particles have lens-like effect. Table 4 shows the roundness and diameter data of the raindrop marked in Fig. 16(b) and the hailstone marked in Fig. 16(c), indicating that the roundness and diameter of actual raindrops and hailstones also have significant differences, which can be detected by the algorithm.
Fig. 17. Raindrop marked in Fig. 15(b). (a) shows the grayscale distribution of raindrop in the chosen square range and central area. (b) and (c) show the grayscale distribution curves of raindrop in GVs along x-axis and y-axis respectively.
Fig. 18. Hailstone marked in Fig. 15(c). (a) shows the grayscale distribution of hailstone in the chosen square range and central area. (b) and (c) show the grayscale distribution curves of hailstone in GVs along x-axis and y-axis respectively.
Table 5 shows the identification results of the algorithm, which has a good identification effect on both raindrops and hailstones, and the results show that the algorithm in this paper can also identify ice particles covered by water. Five raindrops are misjudged as particles of other types, because the raindrops are located at the boundary of digital hologram, making the particle incomplete. One case where particles of other types are misjudged is ice particle covered in water, because the outline of the particle is close to a circle after image processing.
Table 5. Identification results of particle phase states
In addition to the central region, the edge difference between raindrop and hailstone can also be observed in the digital hologram. As shown in Fig. 19, the edge of the raindrop has several distinct interference fringes, while the edge of the hailstone does not have so many fringes. It is known that interference fringes are the result of the interaction of reference light and diffracted light, and the higher the transparency of the particle, the stronger the diffracted light and the more the fringes. The transparency of hailstone is much lower than that of raindrop, so the diffracted light produced by hailstone is weak, making the number of interference fringes much less than that of raindrop.
It can also be observed in the experiment that the number of interference fringes on the edge of hailstone is inconsistent, as shown in Fig. 20. The interference fringes on the edge of hailstone are due to the surface adhesion of water, which is generated by the melting of hailstone or obtained by touching raindrops during falling. Presumably, the more water attached to the surface, the more interference fringes along the edge of the hailstone.
Fig. 20. Difference of interference fringes at the edge of hailstone. (a) shows the edge of unmelted hailstone. (b) shows the edge of partially melted hailstone.
6. Conclusion
Based on coaxial DHI method, accurate phase identification of raindrop and hailstone can be realized by using pulsed laser and high-speed sampling camera according to lens-like effect, Deq and roundness of raindrop and hailstone. The spherical volume formula is equivalent to the ellipsoidal volume formula to obtain the Deq used in this paper. Since the stable shape of raindrops varies with the diameter, not necessarily ellipsoidal, there is a certain error between the Deq in this paper and the real Deq. Roundness is an effective way to identify raindrop and hailstone. Since the hailstone with roundness close to 1 and without lens-like effect is not specifically considered, there will be some error between the final identification results and the real situation. In subsequent studies, the equivalent volume formula should be optimized, and the identification ability of the algorithm for hailstone with roundness close to 1 and without lens-like effect should be improved. The research results can provide reference for the identification method of raindrop and hailstone and the research of actual characteristic parameters.
Funding
National Natural Science Foundation of China (41975045, 52127802).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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