CN110568449B - Wind-borne rough sea surface laser reflection and transmission matrix calculation method - Google Patents

Abstract

The invention discloses a method for calculating a laser reflection and transmission matrix on a wind-generated rough sea surface. The method first calculates the mean square error of the ocean wave slope under the wind speed, calculates the scattering angle from given incident light and outgoing light, and then calculates the wave surface normal vector The zenith angle and the incident angle in the scattering plane, the shadow function, and the probability distribution function, and then the specular reflection matrix and the transmission matrix are calculated. Then use the coordinate transformation to calculate the rotation matrix. Finally, by multiplying the probability distribution function, the rotation matrix and the specular reflection transmission matrix, the reflection and transmission matrix of the incident light and the outgoing light at the wind speed can be obtained. By multiplying the Stokes vector of the laser with the reflection and transmission matrices, the radiation transmission of the polarized laser on the wind-generated rough sea surface can be obtained. The invention adopts the rough sea surface model, which can take into account the laser polarization state and the rough sea surface, and simulate the reflection and transmission matrix of the polarized laser on the wind-generated rough sea surface under the real environment.

Description

A calculation method of laser reflection and transmission matrix for wind-induced rough sea surface

technical field

The invention belongs to the technical field of marine laser detection, in particular to a method for calculating a laser reflection and transmission matrix on a wind-generated rough sea surface.

Background technique

Lidar has been widely used in the detection of the atmosphere, but due to the energy loss at the air-sea interface, the random influence of waves and suspended objects on the signal direction and intensity, and the rapid attenuation of laser light in water, all of which lead to the detection of lidar in the ocean. The application is not as good as the atmosphere. However, compared with passive remote sensing, ocean lidar detection technology has the advantages of not relying on solar radiation, can work day and night, and can provide depth profile information. Airborne or spaceborne lidar can quickly, effectively and widely detect three-dimensional information of the ocean, and can be used as an effective supplement to conventional remote sensing methods.

Marine lidar is an active remote sensing detection technology that emits laser light into seawater and receives echo signals to invert water parameters. The laser will reflect and refract at the air-sea interface, which requires special treatment. For simplicity, the existing processing methods assume that the sea surface is flat and do not consider the polarization characteristics of the laser. However, the sea surface under natural conditions will generate waves under the action of wind, and the roughness of the sea surface will also vary under different wind speeds. If the polarization characteristics are not considered, a large error will be introduced in the inversion of the laser echo signal.

SUMMARY OF THE INVENTION

In view of the deficiencies of the prior art, the present invention proposes a method for calculating the laser reflection and transmission matrix of the wind-generated rough sea surface, which takes into account the situation that the laser enters the atmosphere from the water body through the sea surface, and comprehensively analyzes the interaction between the laser and the air-sea interface. The sea surface model is used to simulate the roughness of the sea surface, and the reflection-transmission law is used to calculate the laser reflection and transmission matrix of the rough sea surface at any wind speed.

The object of the present invention is achieved through the following technical solutions:

A method for calculating a laser reflection and transmission matrix on a wind-generated rough sea surface, characterized in that the method comprises the following steps:

S1: According to the rough sea surface model, the mean square deviation of the slope of the waves under a certain wind speed is obtained;

σ ² =0.003+0.00512×W (1)

Among them, W is the sea surface wind speed, σ ² is the mean square deviation of the wave slope;

S2: Calculate the scattering angle Θ between the incident light and the outgoing light:

与

分别为入射光和出射光的天顶角、方位角；in,

and

are the zenith angle and azimuth angle of the incident light and the outgoing light, respectively;

S3: Calculate the cosine value of the zenith angle μ _n of the wavefront normal vector and the incident angle θ _i in the scattering plane:

Among them, μ′ and μ are the cosine values of the zenith angle of the incident light and the outgoing light, respectively;

S4: Calculate the shadow function that the light is blocked by the wave:

erfc(η)为互补误差函数；in,

erfc(η) is the complementary error function;

S5: Calculate the probability distribution function of waves under the sea surface wind speed W:

S6: Calculate the specular reflection matrix RF(θi) and the refraction matrix TF( _θi ) according to the reflection-transmission law

Among them, n _i and n _t are the refractive indices of the medium where the incident light and refracted light are located, respectively, θ _t is the refraction angle in the scattering plane, Re is the real part, Im is the imaginary part, * represents the conjugate, and r _⊥ is the reflected light The reflection coefficient of the vertical component, r _|| is the reflection coefficient of the parallel component in the reflected light, t _⊥ is the reflection coefficient of the vertical component of the refracted light, and t _|| is the reflection coefficient of the parallel component of the refracted light;

S7: Calculate the angle χ _{1 between the scattering plane and the incident photon meridian plane, and the angle χ 2 between} the scattering plane and the outgoing photon meridian plane, and substitute them into formula (9) to obtain two rotation matrices R(χ) respectively;

S8: Obtain the reflection matrix r and the transmission matrix t at the wind speed by formulas (10) and (11)

Further, the rough sea surface model is a Cox-Munk model.

Further, the reflection-transmission law is Fresnel's law.

Further, the rotation matrix is obtained by three-dimensional coordinate transformation.

The beneficial effects of the present invention are as follows:

The calculation method of the invention combines the rough sea surface model with the reflection-transmission law, and can calculate the reflection and transmission matrix of the air-sea interface under different wind speeds. Compared with the previous method that simplifies the sea surface as a flat surface and does not consider the polarization characteristics of the laser, the method of the present invention considers the situation that the laser enters the atmosphere from the water body through the sea surface, and comprehensively analyzes the interaction between the laser and the air-sea interface. The sea surface model is used to simulate the roughness of the sea surface, and combined with the law of transmission-reflection, the laser reflection and transmission matrix of the rough sea surface at any wind speed can be calculated. Simulation and inversion accuracy.

Description of drawings

Fig. 1 is a geometric schematic diagram of laser transmission on rough sea surface;

分别为入射光、反射光和透射光，θ_i、θ_r、θ_t分别为入射角、反射角和折射角，

为入射光的天顶角和方位角，

为出射光的天顶角和方位角，

为海浪波面法向量，θ_n为波面法向量天顶角，

为透射光的方位角。In the picture:

are the incident light, reflected light and transmitted light, respectively, θ _i , θ _r , and θ _t are the incident angle, reflection angle, and refraction angle, respectively,

are the zenith and azimuth angles of the incident light,

are the zenith and azimuth angles of the outgoing light,

is the wave surface normal vector, θ _n is the wave surface normal vector zenith angle,

is the azimuth angle of the transmitted light.

Fig. 2 is a geometric schematic diagram of coordinate system rotation transformation;

为入射光的天顶角和方位角，

为出射光的天顶角和方位角，OP₁P₂为散射平面，OP₁Z为入射光子午平面，OP₂Z为出射光子午平面，χ₁、χ₂分别为OP₁P₂与OP₁Z、OP₂Z的夹角。In the picture:

are the zenith and azimuth angles of the incident light,

are the zenith angle and azimuth angle of the outgoing light, OP ₁ P ₂ is the scattering plane, OP ₁ Z is the incident photonic meridian plane, OP ₂ Z is the outgoing photonic meridian plane, χ ₁ and χ ₂ are OP ₁ P ₂ and OP respectively ₁ Z, OP ₂ Z angle.

Fig. 3 is the reflected light spherical energy distribution diagram when the wind speed W=10m/s, (130°, 0°) atmospheric incident light;

In the figure: a, b, c, and d are the total light intensity, the linearly polarized light in the x-axis direction, the linearly polarized light in the 45° direction, and the energy distribution of the right-handed circularly polarized light, respectively.

Fig. 4 is the spherical energy distribution diagram of transmitted light when the wind speed W=10m/s, (130°, 0°) atmospheric incident light;

In the figure: a, b, c, and d are the total light intensity, the linearly polarized light in the x-axis direction, the linearly polarized light in the 45° direction, and the energy distribution of the right-handed circularly polarized light, respectively.

Fig. 5 is the spherical energy distribution diagram of reflected light when the water body with wind speed W=10m/s and (50°, 0°) incident light;

In the figure: a, b, c, and d are the total light intensity, the linearly polarized light in the x-axis direction, the linearly polarized light in the 45° direction, and the energy distribution of the right-handed circularly polarized light, respectively.

Fig. 6 is the spherical energy distribution diagram of transmitted light when the water body with wind speed W=10m/s and (50°, 0°) incident light;

In the figure: a, b, c, and d are the total light intensity, the linearly polarized light in the x-axis direction, the linearly polarized light in the 45° direction, and the energy distribution of the right-handed circularly polarized light, respectively.

Detailed ways

The present invention will be described in detail below according to the accompanying drawings and preferred embodiments, and the purpose and effects of the present invention will become clearer. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

A method for calculating a laser reflection and transmission matrix on a wind-generated rough sea surface, characterized in that the method comprises the following steps:

S1: According to the rough sea surface model, the mean square deviation of the slope of the waves under a certain wind speed is obtained;

σ ² =0.003+0.00512×W (1)

Among them, W is the sea surface wind speed, σ ² is the mean square deviation of the wave slope;

S2: Calculate the scattering angle Θ between the incident light and the outgoing light:

与

分别为入射光和出射光的天顶角、方位角；in,

and

are the zenith angle and azimuth angle of the incident light and the outgoing light, respectively;

S3: Calculate the cosine value of the zenith angle μ _n of the wavefront normal vector and the incident angle θ _i in the scattering plane:

Among them, μ′ and μ are the cosine values of the zenith angle of the incident light and the outgoing light, respectively;

S4: Calculate the shadow function that the light is blocked by the wave:

erfc(η)为互补误差函数；in,

erfc(η) is the complementary error function;

S5: Calculate the probability distribution function of waves under the sea surface wind speed W:

S6: Calculate the specular reflection matrix RF(θ _i ) and the refraction matrix TF(θ _i ) according to the reflection-transmission law

Among them, n _i and n _t are the refractive indices of the medium where the incident light and refracted light are located, respectively, θ _t is the refraction angle in the scattering plane, Re is the real part, Im is the imaginary part, * represents the conjugate, and r _⊥ is the reflected light The reflection coefficient of the vertical component, r _|| is the reflection coefficient of the parallel component in the reflected light, t _⊥ is the reflection coefficient of the vertical component of the refracted light, and t _|| is the reflection coefficient of the parallel component of the refracted light;

S7: Calculate the angle χ _{1 between the scattering plane and the incident photon meridian plane, and the angle χ 2 between} the scattering plane and the outgoing photon meridian plane, and substitute them into formula (9) to obtain two rotation matrices R(χ) respectively;

S8: Obtain the reflection matrix r and the transmission matrix t at the wind speed by formulas (10) and (11)

Taking the wind speed W=10m/s and the incident light at (130°, 0°) as an example, when _ni = 1 and _nt = 1.333, the laser enters the water body from the atmosphere, and the geometric schematic diagram of the laser transmission on the rough sea surface is shown in Figure 1. Assuming that the incident laser S ₀ =[1 1 0 0]′, the rough sea surface model is the Cox-Munk model, and the reflection-transmission law is Fresnel's law, which is obtained by three-dimensional coordinate transformation, and calculates the reflection matrix, transmission matrix, and coordinates of different orientations. The system rotation transformation is specifically shown in Figure 2. The reflection matrix and the transmission matrix are multiplied by S ₀ to obtain the spherical energy distribution diagrams of the reflected light and the transmitted light (shown in Figure 3 and Figure 4 ), and the transmittance is 99.3%. Traditionally, only the zenith angle of incident light is considered, and the sea surface is simplified as a flat surface, and the three-dimensional distribution of reflected light cannot be obtained. The transmittance of the sea to the laser obtained by the traditional scalar calculation method is 96.4%, while the transmittance of the parallel polarized light by the calculation method of the present invention is 99.3%, and it will be different with the change of the polarization state of the laser, which is more different from the actual situation. To comply, laser polarization information can be used to invert water parameters.

Taking the wind speed W=10m/s and the incident light at (50°, 0°) as an example, at _ni = 1.333, n _t =1, the laser enters the atmosphere from the water body, assuming the initial laser S ₀ =[1 1 0 0]′ , calculate the reflection matrix and transmission matrix in different directions, and multiply by S ₀ to obtain the spherical energy distribution diagram of reflected light and transmitted light (shown in Figure 5 and Figure 6), and the transmittance is 44%. Without considering the roughness of the sea surface, 50° is already greater than the critical angle of total reflection of sea water, and the transmission is 0 in this case by the traditional method. However, in actual situations, due to the wind-generated waves, some light will still escape into the air, and the transmittance obtained by the calculation method of the present invention is 44%, so as to better reflect the real situation.

Those of ordinary skill in the art can understand that the above are only preferred examples of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still Modifications are made to the technical solutions described in the foregoing examples, or equivalent replacements are made to some of the technical features. All modifications and equivalent replacements made within the spirit and principle of the invention shall be included within the protection scope of the invention.

Claims (4)

1. a wind-generated rough sea surface laser reflection, transmission matrix calculation method, is characterized in that, this method comprises the steps: S1: According to the rough sea surface model, the mean square deviation of the slope of the waves under a certain wind speed is obtained; σ ² =0.003+0.00512×W (1) Among them, W is the sea surface wind speed, σ ² is the mean square deviation of the wave slope; S2: Calculate the scattering angle Θ between the incident light and the outgoing light:

in,

and

are the zenith angle and azimuth angle of the incident light and the outgoing light, respectively; S3: Calculate the cosine value of the zenith angle μ _n of the wavefront normal vector and the incident angle θ _i in the scattering plane:

Among them, μ′ and μ are the cosine values of the zenith angle of the incident light and the outgoing light, respectively; S4: Calculate the shadow function that the light is blocked by the wave:

in,

erfc(η) is the complementary error function; S5: Calculate the probability distribution function of waves under the sea surface wind speed W:

S6: Calculate the specular reflection matrix RF(θ _i ) and the refraction matrix TF(θ _i ) according to the reflection-transmission law

Among them, n _i and n _t are the refractive indices of the medium where the incident light and refracted light are located, respectively, θ _t is the refraction angle in the scattering plane, Re is the real part, Im is the imaginary part, * represents the conjugate, and r _⊥ is the reflected light The reflection coefficient of the vertical component, r _|| is the reflection coefficient of the parallel component in the reflected light, t _⊥ is the reflection coefficient of the vertical component of the refracted light, and t _|| is the reflection coefficient of the parallel component of the refracted light;

S7: Calculate the angle χ _{1 between the scattering plane and the incident photon meridian plane, and the angle χ 2 between} the scattering plane and the outgoing photon meridian plane, and substitute them into formula (9) to obtain two rotation matrices R(χ) respectively;

S8: Obtain the reflection matrix r and the transmission matrix t at the wind speed by formulas (10) and (11)

2 . The method for calculating the laser reflection and transmission matrix of a wind-generated rough sea surface according to claim 1 , wherein the rough sea surface model is a Cox-Munk model. 3 . 3 . The method for calculating a laser reflection and transmission matrix on a wind-generated rough sea surface according to claim 1 , wherein the reflection-transmission law is Fresnel's law. 4 . 4 . The method for calculating a laser reflection and transmission matrix on a wind-generated rough sea surface according to claim 1 , wherein the rotation matrix is obtained by three-dimensional coordinate transformation. 5 .

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