An airborne ocean laser radar layer and water bottom synchronous three-dimensional reconstruction method

Abstract

The application discloses an airborne ocean laser radar layer and water bottom synchronous three-dimensional reconstruction method, which comprises the following steps: obtaining three-dimensional point clouds of laser on the water surface according to airborne laser radar data; carrying out gridding on the three-dimensional point clouds of laser on the water surface, carrying out multi-pulse averaging of spatial aggregation, and obtaining signals after gridding and aggregation; acquiring water surface peak position, layer peak position and water bottom peak position; finally, three-dimensional point clouds of the water bottom and the layer are acquired at the same time, and high-precision three-dimensional reconstruction is realized. The application combines the idea of voxelization grid, avoids resolution sacrifice caused by multi-pulse averaging in a large space range, realizes high-resolution three-dimensional reconstruction with adjustable resolution, and designs an algorithm architecture for multi-target differentiation, so that the effect of simultaneous detection of multiple targets is realized. The application has reference significance for shallow sea environment detection and shallow sea carbon cycle analysis, and has wide applicability.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of laser radar, in particular to an airborne marine laser radar level and water bottom synchronous three-dimensional reconstruction method. BACKGROUND

[0002] The marine ecosystem is a complex whole, containing a large number of species that play a role in a wide range of space-time. Phytoplankton is the basis of most marine ecosystems, and its annual net photosynthetic carbon fixation content is roughly equivalent to that of all terrestrial plants. The phytoplankton thin layer is a common feature of phytoplankton aggregation in the marine environment, which has attracted widespread attention from oceanographers. Its concentration is much higher than that of the surrounding water, and the thickness is only a few centimeters to a few meters, and the horizontal range reaches several kilometers. The thin layer supports the entire food chain from microorganisms to higher trophic levels, and is an important primary productivity (NPP) for shallow marine ecosystem and carbon assessment. However, if it contains toxic phytoplankton species, it may trigger the occurrence of harmful algal blooms.

[0003] Phytoplankton thin layers often occur in coastal waters. As a key factor in regulating water flow, affecting nutrient supply and dynamic distribution of layers, topography becomes an important factor affecting the characteristics of thin layers in coastal waters. Therefore, simultaneously obtaining the spatial position of the phytoplankton layer and the three-dimensional structure of the marine topography in the water body is of great significance to explore the response mechanism of the layer to the topography. At present, the main means of detecting chlorophyll are biochemical methods, in-situ instrument measurement, passive remote sensing and active remote sensing. Laser radar, as an active optical remote sensing device, can be used for detecting the biological optical property profile of the water body, and for remote sensing measurement of the vertical distribution structure of the upper ocean, with advantages of high spatiotemporal resolution, continuous observation day and night, etc. On the other hand, it can be used for bathymetry of shallow sea topography, making up for the detection defects of sonar and other instruments on the topography of the blind area of shallow sea.

[0004] The Chinese patent document with publication number CN115980774A discloses a marine laser radar level detection method based on differential threshold evaluation, which can effectively solve the position, intensity, thickness and other information of the phytoplankton layer in the ocean according to the laser radar echo signal. The Chinese patent document with publication number CN116400322A discloses a marine subsurface detection and identification method based on airborne laser radar, which uses multi-pulse averaging and background noise removal technology to improve the measurement signal-to-noise ratio. Both of them are based on profile echo signal for multi-pulse averaging to improve the signal-to-noise ratio, but the three-dimensional attitude of the layer is not obtained. The Chinese patent document with publication number CN119805405A discloses an airborne marine laser radar water bottom weak echo signal detection method and system, which constructs a three-dimensional model of the water bottom by scanning. However, it also does not realize the simultaneous three-dimensional reconstruction of the thin layer and the topography. Therefore, there is an urgent need to provide a method for simultaneously detecting the three-dimensional structure of the phytoplankton thin layer and the topography. SUMMARY

[0005] The application provides an airborne marine laser radar layer and water bottom synchronous three-dimensional reconstruction method, which can improve the detection effect of weak layer signals and realize simultaneous three-dimensional reconstruction of the water bottom and the layer.

[0006] An airborne marine laser radar layer and water bottom synchronous three-dimensional reconstruction method comprises the following steps:

[0007] (1) Obtain airborne laser radar data, and obtain the distance between the water surface and the laser radar according to the echo signal flight time;

[0008] (2) Obtain the position data of the aircraft through GPS, obtain the attitude data of the aircraft through IMU, and obtain the angle data of the scanning motor through the scanning galvanometer;

[0009] (3) Obtain the three-dimensional point cloud of the laser emitted by the laser radar on the water surface through the distance between the water surface and the laser radar, the position data of the aircraft, the attitude data of the aircraft, and the angle data of the scanning motor;

[0010] (4) Divide the grid according to the three-dimensional point cloud of the laser on the water surface, record the profile serial number in the grid, and obtain the profile set containing the serial number label;

[0011] (5) Perform multi-pulse average processing on the profiles with the same serial number label to obtain the grid aggregation signal;

[0012] (6) Based on the grid aggregation signal, first find the first peak value of the water surface echo signal as the water surface peak position, and then use the peak value judgment algorithm to find the water bottom peak position;

[0013] (7) Use the layer algorithm to obtain the layer peak position and the corresponding relative intensity and thickness information, with the water surface peak position as the starting point and the water bottom peak position as the ending point;

[0014] (8) Calculate the distance information of the water bottom and the layer according to the obtained water surface peak position, layer peak position and water bottom peak position, and further perform three-dimensional reconstruction on the water bottom and the layer.

[0015] The specific process of step (1) is as follows:

[0016] Record the light-emitting waveform of the laser radar emitted laser to obtain the peak position ; the water surface echo signal is obtained through the water surface reflection, and the water surface peak position ; the distance between the water surface and the laser radar is:

[0017] ;

[0018] In the formula, is the speed of light.

[0019] In step (2), the position data of the aircraft, the attitude data of the aircraft, and the angle data of the scanning motor need to be interpolated according to the laser radar data to ensure one-to-one correspondence between the data.

[0020] The specific process of step (3) is as follows:

[0021] The attitude data of the aircraft is used to convert the aircraft coordinate system into the world coordinate system; the angle data of the scanning motor and the distance between the water surface and the laser radar are combined to obtain the landing position of the laser on the water surface; and the position data of the aircraft is used to obtain the position information of the landing position in the world coordinate system, thereby obtaining the three-dimensional point cloud on the water surface.

[0022] In step (4), the grid is divided according to the density and range of the three-dimensional point cloud of the laser on the water surface. Different resolution grids can be divided according to the different point cloud densities.

[0023] In step (6), when using the peak value judgment algorithm to find the water bottom peak value position, the half-height full-width and peak height restrictions need to be added, and the profile after the peak value should be lower than the set noise threshold. The specific operation of the water bottom peak value judgment algorithm is as follows:

[0024] First, the water bottom peak value has a higher peak value and a smaller half-height full-width, so the ratio of the half-height full-width to the peak height is used as a threshold to distinguish levels and water bottom;

[0025] Second, there is no deeper water body signal after the water bottom signal, so the signal intensity after the water bottom peak value should be at the noise level. Set the signal intensity of 2-5 times the noise level as the noise threshold to perform secondary verification on the water bottom signal, thereby determining the water bottom peak value position.

[0026] In step (7), the original signal of the laser radar is first used to calculate the relative intensity of the echo signal and the water body background signal .

[0027] ;

[0028] Then, the difference threshold method is used as a level algorithm to determine the level peak value position and the corresponding thickness information according to the relative intensity of the echo signal .

[0029] In step (8), the distance information of the water bottom and the levels is calculated, and the formula is as follows:

[0030] ;

[0031] ;

[0032] ​In the formula, Indicates the distance between the layer and the water surface. Indicates the distance between the bottom of the water and the surface of the water. Represents the speed of light. Represents the refractive index of water; This is the peak position of the water level. The peak position of the layer. This represents the peak position at the bottom of the water.

[0033] In step (8), a three-dimensional reconstruction of the water bottom and layers is performed, using the following formula:

[0034] ;

[0035] ;

[0036] ;

[0037] ;

[0038] ;

[0039] ;

[0040] ;

[0041] ;

[0042] In the formula, represent The position of the laser beam on the water surface along the axial direction. With the aircraft position The difference, represent The position of the laser beam on the water surface along the axial direction. With the aircraft position The difference, Represents the height of the laser's impact point on the water surface. At the altitude of the aircraft The difference, Represents the angle between the underwater laser beam path and the horizontal plane. The line formed by the projection of the aircraft's position onto the horizontal plane and the point where the laser light falls on the water surface, and... The angle formed by the axial direction; , , These represent the three-dimensional spatial coordinates obtained from the layer or underwater reconstruction, respectively, under the index. When representing levels, This indicates the distance between the layer and the landing point of the lidar on the water surface, under the subscript. When representing the bottom of the water, Indicates the distance between the water bottom and the landing point of the laser radar on the water surface.

[0043] Compared with the prior art, the present application has the following beneficial effects:

[0044] 1. The present application adopts a scanning airborne laser radar system, which can obtain three-dimensional distributed hierarchical signals and terrain signals, and realizes large-range shallow sea three-dimensional detection of the laser radar, and the analysis of the shallow sea environment is not limited to a profile.

[0045] 2. The present application designs an algorithm architecture for distinguishing multiple targets, which is different from the traditional single-target detection algorithm, and realizes the effect of simultaneous detection of multiple targets.

[0046] 3. The present application combines the idea of grid voxelization, avoids the resolution sacrifice caused by multi-pulse averaging in a large space range, controls the reconstruction resolution by the grid resolution, and realizes high-resolution three-dimensional reconstruction with adjustable resolution.

[0047] 4. The present application has reference significance for shallow sea environment detection and shallow sea carbon cycle analysis, and has wide applicability. BRIEF DESCRIPTION OF DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiment description. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0049] Figure 1 A scanning airborne laser radar simultaneously detects the water bottom and the hierarchical conceptual diagram in the embodiment of the present application.

[0050] Figure 2 A flow chart of a three-dimensional reconstruction method of an airborne marine laser radar hierarchy and water bottom simultaneously in an embodiment of the present application.

[0051] Figure 3 A hierarchical algorithm detection result diagram in an embodiment of the present application.

[0052] Figure 4 A water bottom and hierarchical three-dimensional reconstruction result diagram in an embodiment of the present application. DETAILED DESCRIPTION

[0053] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0054] It should be noted that the features in the following examples and embodiments can be combined with each other without conflict.

[0055] The application is based on a scanning airborne laser radar, and a multi-target distinguishing method of echo signals is used to simultaneously distinguish various targets such as water surface, layers, and water bottom. A spatial grid aggregation method is used to realize multi-pulse averaging and weak layer signal detection without sacrificing spatial resolution, so that the water bottom and layer signals can be accurately detected while maintaining high resolution, thereby realizing simultaneous detection of high-precision three-dimensional layers and terrain.

[0056] In the embodiment of the application, Figure 1 The concept diagram of the scanning airborne laser radar for simultaneously detecting the water bottom and layers is shown. The outgoing light spots of the laser radar are uniformly scattered in an elliptical shape on the sea level by the scanning motor, and the speed of the aircraft is superimposed, so that the laser is uniformly distributed. A single laser passes through the water surface, reaches the phytoplankton thin layer in the water body, generates backscattering to obtain layer signals, and penetrates through a part of the laser to reach the water bottom to obtain water bottom position signals.

[0057] As Figure 2 shown, a method for synchronously reconstructing layers and water bottoms of an airborne marine laser radar in three dimensions is provided, and the specific process is as follows:

[0058] Step S1: The laser radar data format is 100000 (pieces) * 300 (ns) outgoing light signals and 100000 (pieces) * 800 (ns) marine echo signals, wherein 300 ns is used to store the waveform of the outgoing light, and 800 ns is used to store the marine echo signals. The data points representing a group of profiles have 100000, and the profile of each data point lasts for 800 ns, that is, the maximum detectable distance is about 88 m. The peak position at the time of outgoing can be obtained from the 300 ns outgoing signal At the same time, the laser radar passing through the water surface reflection brings obvious sea surface echo, and the sea surface peak position is obtained is the speed of light, so the distance between the sea surface and the laser radar is :

[0059] ;

[0060] The distance is the slant range distance between the laser radar and its landing point on the sea surface, and the corresponding three-dimensional position information also needs to be calculated.

[0061] Step S2, obtain attitude information through IMU, obtain position information through GPS, and obtain motor angle information through scanning galvanometer feedback. Interpolate the IMU, GPS, and scanning galvanometer angle data according to the laser radar data to ensure one-to-one correspondence between the data.

[0062] After interpolation, the following arrays are obtained: the attitude array POS (10000*3) stores the head, roll, and pitch attitude angles; the position array Gcoordinates (10000*2) stores the longitude and latitude information; the height array Height (10000*1) stores the height information; and the motor angle array Motorangle (10000*1) stores the motor angle information.

[0063] Since the aircraft moves mainly in a straight line during flight, the aircraft's jolt can also be approximated as a linear change, so the interpolation method is linear interpolation. In this step, the aircraft position parameters are obtained from the position array and the height array: Axis direction coordinates , Axis direction coordinates , height coordinates .

[0064] Step S3, the IMU attitude information can be used to convert the aircraft coordinate system to the world coordinate system, and the scanning galvanometer angle information can be used to obtain the laser emission angle information, thereby obtaining the relative position of the laser radar landing point, and then obtaining the absolute position information of the point cloud according to the GPS geographic position information. Thus, the landing point of the laser radar on the water surface is obtained: Axis direction coordinates , Axis direction coordinates , height coordinates .

[0065] Step S4, divide the grid according to the density and range of the three-dimensional point cloud of the laser on the water surface. Different resolution grids can be divided according to the point cloud density. In this experiment, 5m*5m*5m grid division is performed according to the point cloud density and accuracy requirements. Based on the range of the sea surface point cloud, the minimum value of the position (X, Y, Z) is set as the starting point, the interval distance is 5m, and the grid is divided until the maximum value of the point cloud position. Set the water surface position solving method as a judgment condition to determine which grid the solved position is located in and add a grid number tag to it. ,

[0066] For example: ​​​​​+5 and +5, it is considered to fall in the grid of (x, y) and is labeled. Finally, a set of profiles containing labels is formed.

[0067] Step S5, the same number of label profile is processed by multi-pulse average, and the gridding aggregated signal is obtained.

[0068] Step S6, based on the gridding aggregated signal, first find the first peak of the water surface echo signal as the water surface peak position, and then use the peak value judgment algorithm to find the water bottom peak position.

[0069] First, use the findpeak() function to find the peak value existing in the profile, set enough peak threshold to exclude the influence of noise, at this time there may be multiple peaks, which are water surface peak, water bottom peak and multiple level peaks. First find the first peak as the water surface peak, but the last peak cannot be determined. The existence of peak values in different situations is analyzed as follows:

[0070] 1. There is water bottom and there is level: at this time the last peak is certainly water bottom, after the water bottom judgment program, take it as the end point, take the water surface as the starting point, find the level peak value in this range, which can be found by setting multiple peaks. There may be multiple levels.

[0071] 2. There is water bottom and there is no level: at this time the last peak is certainly water bottom, after the water bottom judgment program, take it as the end point, take the water surface as the starting point, find the level peak value in this range. It is found that there is no level.

[0072] 3. There is no water bottom, but there is level: at this time the last peak is certainly level, after the water bottom judgment program, it is determined that the point is not water bottom, so this profile takes the water surface as the starting point and the last data point as the end point to find the level.

[0073] 4. Both do not exist: no second peak value will be found except the water surface peak.

[0074] ​​​​The method for judging the water bottom peak value is as follows: since the water bottom peak value does not necessarily exist and can be confused with the hierarchy, the judgment of the water bottom peak value is added when the water bottom peak value is obtained, and the signals with the water bottom peak value are selected to calculate the threshold value. Since the water bottom peak value and the hierarchy peak value have different waveform characteristics: the water bottom peak value has a higher peak value and a smaller full width at half maximum, the ratio of the full width at half maximum to the peak value is used as the threshold value to distinguish the hierarchy and the water bottom. Secondly, there is no deeper water body signal after the water bottom signal, so the signal intensity after the water bottom peak value should be at the noise level, and the signal intensity of 2-5 times the noise level is set as the threshold value to verify the water bottom signal twice. Thus, the water bottom and the hierarchy signal can be accurately distinguished.

[0075] Step S7, using the hierarchy algorithm, the hierarchy peak value position and the corresponding relative intensity and thickness information are obtained from the water surface peak value position as the starting point and the water bottom peak value position as the ending point.

[0076] First, the raw signal of the laser radar is used and the water body background signal The relative intensity of the echo signal is calculated :

[0077] ;

[0078] Then, the difference threshold method is used as the hierarchy algorithm, and the hierarchy peak value position and the corresponding thickness information are determined according to the relative intensity of the echo signal .

[0079] Figure 3 The profile of the echo signal in logarithmic coordinates shows the detection results of the hierarchy algorithm. At 11 m, a hierarchy with a relative intensity of 1.6 and a thickness of 2.5 m is detected, and at 15 m, a water bottom signal is found.

[0080] Step S8, according to the obtained water surface peak value position, hierarchy peak value position and water bottom peak value position, the distance information of the water bottom and the hierarchy is calculated; further, the water bottom and the hierarchy are three-dimensionally reconstructed.

[0081] The distance information of the water bottom and the hierarchy is calculated, and the formula is as follows:

[0082] ;

[0083] ;

[0084] In the formula, represents the distance of the hierarchy from the water surface, represents the distance of the water bottom from the water surface, represents the speed of light, represents the refractive index of the water body; is the water surface peak value position, is the hierarchy peak value position, This represents the peak position at the bottom of the water.

[0085] The formula for 3D reconstruction of the water bottom and layers is as follows:

[0086] ;

[0087] ;

[0088] ;

[0089] ;

[0090] ;

[0091] ;

[0092] ;

[0093] ;

[0094] In the formula, represent The position of the laser beam on the water surface along the axial direction. With the aircraft position The difference, represent The position of the laser beam on the water surface along the axial direction. With the aircraft position The difference, Represents the height of the laser's impact point on the water surface. At the altitude of the aircraft The difference, Represents the angle between the underwater laser beam path and the horizontal plane. The line formed by the projection of the aircraft's position onto the horizontal plane and the point where the laser light falls on the water surface, and... The angle formed by the axial direction; , , These represent the three-dimensional spatial coordinates obtained from the layer or underwater reconstruction, respectively, under the index. When representing levels, This indicates the distance between the layer and the landing point of the lidar on the water surface, under the subscript. When representing the bottom of the water, This indicates the distance between the underwater surface and the point where the lidar lands on the water surface.

[0095] Figure 4 Two case studies showcasing synchronous 3D reconstruction of layers and the seabed based on the above methods are presented. Both achieve meter-level accuracy in 3D space for layer and seabed reconstruction.

[0096] The above-described embodiments illustrate the technical solutions and beneficial effects of the present application. It should be understood that the above-described embodiments are only specific embodiments of the present application and are not intended to limit the present application. Any modifications, supplements and equivalent replacements made within the principle range of the present application shall be included in the protection range of the present application.

Claims

1. An airborne ocean laser radar layer and water bottom synchronous three-dimensional reconstruction method, characterized in that, The method comprises the following steps: (1) obtaining airborne laser radar data, and obtaining the distance between the water surface and the laser radar according to the time of flight of the echo signal; (2) obtaining the position data of the aircraft through GPS, obtaining the attitude data of the aircraft through IMU, and obtaining the angle data of the scanning motor through the scanning galvanometer; (3) obtaining the three-dimensional point cloud of the laser radar emitted laser on the water surface through the distance between the water surface and the laser radar, the position data of the aircraft, the attitude data of the aircraft, and the angle data of the scanning motor; (4) dividing the grid according to the range of the three-dimensional point cloud of the laser on the water surface, recording the profile number in the grid, and obtaining the profile set containing the serial number label; (5) performing multi-pulse average processing on the profiles with the same serial number label to obtain the grid aggregation signal; (6) based on the grid aggregation signal, first find the first peak value of the water surface echo signal as the water surface peak position, and then find the water bottom peak position by using the water bottom peak value judgment algorithm; (7) using the hierarchical algorithm, taking the water surface peak position as the starting point and the water bottom peak position as the ending point, obtaining the hierarchical peak position and the corresponding relative intensity and thickness information; (8) calculating the distance information of the water bottom and the hierarchy according to the obtained water surface peak position, hierarchical peak position and water bottom peak position; further three-dimensional reconstruction of the water bottom and the hierarchy.

2. The airborne ocean laser radar bathymetry and water bottom synchronous three-dimensional reconstruction method according to claim 1, characterized in that, The specific process of step (1) is as follows: The laser radar records the light-emitting waveform when emitting laser light, and obtains a peak position The water surface echo signal is brought by water surface reflection, and a water surface peak position is obtained The distance between the water surface and the laser radar is : ； In the formula, c is the speed of light.

3. The airborne ocean laser radar bathymetry and seafloor synchronization three-dimensional reconstruction method according to claim 1, characterized in that, In step (2), the position data of the aircraft, the attitude data of the aircraft, and the angle data of the scanning motor need to be interpolated according to the laser radar data to ensure one-to-one correspondence between the data.

4. The airborne ocean laser radar bathymetry and water bottom synchronous three-dimensional reconstruction method according to claim 1, characterized in that, The specific process of step (3) is as follows: The aircraft coordinate system is converted into the world coordinate system using the attitude data of the aircraft; the drop point position of the laser on the water surface is obtained by combining the angle data of the scanning motor and the distance between the water surface and the laser radar; and the position information of the drop point position in the world coordinate system is obtained according to the position data of the aircraft, thereby obtaining the three-dimensional point cloud on the water surface. In step (4), the grid is divided according to the density and range of the three-dimensional point cloud of the laser on the water surface.

5. The airborne ocean laser radar bathymetry and seafloor synchronization three- dimensional reconstruction method according to claim 1, characterized in that, In step (6), when using the water bottom peak value judgment algorithm to find the water bottom peak position, the half-height full-width and peak height restrictions need to be added, and the profile after the peak value should be lower than the set noise threshold; the water bottom peak value judgment algorithm specifically operates as follows:

6. The airborne ocean laser radar bathymetry and seafloor synchronization three-dimensional reconstruction method according to claim 1, characterized in that, First, the water bottom peak value has a higher peak value and a smaller half-height full-width, so the ratio of the half-height full-width to the peak height is used as a threshold to distinguish the hierarchy and the water bottom; Second, there is no deeper water body signal after the water bottom signal, so the signal intensity after the water bottom peak value should be at the noise level, and the signal intensity of 2-5 times the noise level is set as the noise threshold to verify the water bottom signal twice, thereby determining the water bottom peak position. In step (8), the distance information of the water bottom and the hierarchy is calculated, and the formula is as follows:

7. The airborne ocean laser radar bathymetry and seafloor synchronization three-dimensional reconstruction method according to claim 1, characterized in that, In step (7), the raw signal of the laser radar is first used to calculate the relative intensity of the echo signal with the background signal of the water body The relative intensity of the echo signal is calculated : ； Then, the differential thresholding method is used as a hierarchical algorithm, based on the relative intensity of the echo signal. Determine the location of the layer peak and the corresponding thickness information.

8. The airborne ocean laser radar bathymetry and seafloor synchronization three- dimensional reconstruction method according to claim 1, characterized in that, In step (8), the three-dimensional reconstruction of the water bottom and the hierarchy is performed, and the formula is as follows: ； ； wherein, represents the distance of the level from the water surface, represents the distance of the water bottom from the water surface, represents the speed of light, represents the refractive index of the water body; is the water surface peak position, is the level peak position, is the water bottom peak position.

9. The airborne ocean laser radar bathymetry and seafloor synchronization three- dimensional reconstruction method according to claim 1, characterized in that, ​ ； ； ； ； ； ； ； ； wherein represents the position of the laser on the water surface in the axial direction and the position of the aircraft, represents the position of the laser on the water surface in the axial direction and the position of the aircraft, represents the difference between the height of the laser on the water surface and the height of the aircraft, represents the angle between the horizontal plane and the laser path under water, represents the angle between the line formed by the projection of the position of the aircraft on the horizontal plane and the position of the laser on the water surface and the axial direction; , , , respectively represent the three-dimensional spatial coordinates obtained by the reconstruction of the layers or the bottom, when the subscript represents the layers, represents the distance between the layers and the position of the laser on the water surface, when the subscript represents the bottom, represents the distance between the bottom and the position of the laser on the water surface.​​​

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