CN117113789A - Laser beam scattering calculation method based on JONSWAP spectrum sea surface modeling - Google Patents
Laser beam scattering calculation method based on JONSWAP spectrum sea surface modeling Download PDFInfo
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Abstract
The invention discloses a laser beam scattering calculation method based on JONSWAP spectrum sea surface modeling, which is implemented according to the following steps: setting a simulation scene, determining a JONSWAP spectrum and a direction distribution function, and calculating a two-dimensional sea wave frequency direction spectrum; based on a two-dimensional sea wave frequency direction spectrum, a complex sea surface model is established and discretized through a linear superposition method, and a discretized model is obtained; obtaining a coordinate transformation formula between the sea surface and the laser beam based on coordinate transformation according to the post-discrete model; deriving a kirchhoff approximation formula, and completing calculation of a scattering cross section of the laser beam by the sea surface according to a coordinate transformation formula between the sea surface and the laser beam; the random complex sea surface model is obtained based on the JONSWAP spectrum and the linear superposition method, meets the natural development rule of the sea surface, and can be used for analyzing the influence of the complex sea surface on the scattering cross section of a typical laser beam, in particular the influence of the beam incidence angle, the beam waist radius and the beam self parameters on the scattering cross section.
Description
Technical Field
The invention belongs to the technical field of ocean microwave remote sensing methods, and particularly relates to a laser beam scattering calculation method based on JONSWAP spectrum sea surface modeling.
Background
Compared with the traditional radio guidance, the laser guidance has the advantages of high precision, good distance cut-off characteristic, strong electromagnetic interference resistance, strong directivity of detection view fields and the like, but the laser guidance technology has the defect of being greatly influenced by the meteorological environment, particularly the complex marine environment due to the working wave band. When a laser beam propagates in the ocean atmosphere, atmospheric turbulence caused by random fluctuation of the refractive index of the atmosphere causes phenomena such as laser beam jitter, light intensity fluctuation, light spot drift, beam expansion and the like, and the effects of the atmospheric turbulence can lead to laser signal fading. Moreover, when the laser beam is transmitted in the ocean atmosphere, various gas molecules and ocean aerosol particles in the atmosphere can absorb and scatter the laser beam, so that the energy distribution of the laser beam in the ocean atmosphere is affected, and among various factors causing laser attenuation, the scattering, absorption and attenuation effects of the ocean aerosol particles are the most intense on the transmission energy loss and transmission characteristics of the laser beam. In addition, the complex dynamic sea surface may cause a decrease in the accuracy of detection and identification of targets based on laser guidance. In summary, the complex marine environment has become a bottleneck problem restricting the development and application of laser guidance technology.
In recent years, along with the progress of laser regulation technology, a plurality of laser beams with special amplitude, phase and polarization state distribution are sequentially proposed and realized, and the typical laser beams show a series of novel physical effects and phenomena, for example, the laser beams with special amplitude can inhibit the influence of ocean atmospheric turbulence on the transmission of the laser beams, the laser beams with vortex phase carry orbital angular momentum, more information can be modulated in the same frequency band and the vector beams with polarization state dependent spatial distribution can be realized, so that the possibility of improving the identification capability of the laser guidance on an offshore target is provided, due to the sensitivity of the polarization degree of the scattered polarized light of the target to the scattering effect of a scattering medium and the material of the target, the information provided by the polarization state can effectively distinguish scattering bodies with different materials and different surface forms, and the scattered polarized light imaging has the advantages of improving the target contrast and distinguishing the material compared with the traditional light intensity imaging, and the target information resolution capability under all weather and complex environments is greatly improved.
Thus, research on electromagnetic scattering of plane waves by sea surfaces has become a hotspot field for physical ocean research; however, the prior art does not address the research and calculation of scattering of laser beams from the sea surface, especially complex laser beam scattering.
Disclosure of Invention
The invention aims to provide a laser beam scattering calculation method based on JONSWAP spectrum sea surface modeling, which has the characteristics of analyzing the changes of reflection and scattering of a sea surface on laser beam along with the parameters of the light beam incidence height, polarization mode and beam waist radius from the construction of a complex sea surface model, and realizing the effective calculation of the sea surface on the laser beam scattering.
The technical scheme of the invention is that the laser beam scattering calculation method based on JONSWAP spectrum sea surface modeling is implemented according to the following steps:
step 1, setting a simulation scene, determining a JONSWAP spectrum and a direction distribution function, and calculating a two-dimensional sea wave frequency direction spectrum; step 2, based on a two-dimensional sea wave frequency direction spectrum, a complex sea surface model is established and discretized through a linear superposition method, and a discretized model is obtained; step 3, obtaining a coordinate transformation formula between the sea surface and the laser beam based on coordinate transformation according to the discretized model; and 4, deducing a kirchhoff approximation formula, and completing calculation of a scattering cross section of the laser beam by the sea surface according to a coordinate transformation formula between the sea surface and the laser beam.
The invention is also characterized in that: the step 1 is specifically implemented according to the following steps: step 1.1, setting a simulation scene, and selecting a JONSWAP spectrum to perform initial sea surface fitting, wherein the expression of the JONSWAP spectrum is as follows
Wherein a is dimensionless energy scale parameter, g is local gravitational acceleration, ω p Is peak frequency, gamma is spectral peak factor, F is wind area, U 10 The average wind speed of the sea surface over 10 meters is shown, and sigma is a peak shape parameter;
step 1.2, introducing a direction distribution function to describe the energy distribution of sea waves relative to a direction angle, and combining different sea spectrum functions with the direction distribution function, namely the JONSWAP two-dimensional sea spectrum is
S(ω,θ)＝S(ω)G(θ) (2)
Wherein G (θ) is a directional distribution function, and S (ω, θ) is a directional spectrum function;
step 1.3, aiming at the JONSWAP two-dimensional sea spectrum, adopting a light-sensitive distribution function, namely
Wherein θ sea Is the main direction of wave propagation, D 0 (s) is a coefficient determined by the direction distribution concentration parameter s; d (D) 0 The calculation formula of(s) is
Wherein Γ is a gamma function;
step 1.4, obtaining a two-dimensional wave frequency direction spectrum according to the formula (2)
The step 2 is specifically implemented according to the following steps:
step 2.1, defining a sea surface with three-dimensional height by a linear superposition method, and simulating by using a computer and MATLAB software according to a two-dimensional sea wave frequency direction spectrum S (omega, theta), so as to establish a complex sea surface model effectively reflecting the actual motion condition of sea waves, wherein the sea surface with three-dimensional height is defined as
Wherein M and N are angular frequency and direction respectivelyThe discrete number of angles, ω being the angular frequency, θ n For the nth direction angle, a mn And b mn For the mth angular frequency, the amplitude and phase angle at the nth direction angle, b mn Is the wave phase angle;
and 2.2, discretizing the complex sea surface model according to the complex sea surface model, and reconstructing a sea surface model which has small error with the actual sea surface and can be subjected to numerical calculation, namely a discretized model.
Step 2.2 is specifically implemented according to the following steps:
step 2.2.1, equally dividing the transverse dimension into equal parts, marking the points according to a mode of firstly traversing the axis and then longitudinal the axis, and recording the space coordinate information of the points according to the format of each point (x, y, z);
2.2.2, forming a triangle surface element by every three points, recording the number of the points of each surface element in a anticlockwise sequence, and acquiring two data files by the operation, wherein one records the node number of the triangle surface element and the other records the coordinate information of the node;
and 2.2.3, reconstructing a sea surface model which has small sea surface error with the actual sea surface and can perform numerical calculation according to the two data files.
The step 3 is specifically implemented according to the following steps:
step 3.1, establishing a sea surface coordinate system, obtaining the node numbers and the node coordinates of the triangular surface elements through data files, and then establishing a local coordinate system to obtain the reflection condition of any one triangular surface element under any incident light ray:
step 3.2, introducing an interaction probability density function, which is defined as the product of a shadow function of whether a light source illuminates a surface element and a hiding function of whether reflected light of the surface element can be received;
and 3.3, calculating the light field intensity of the light beam emitted by the given laser position on the surface element, and carrying out coordinate transformation to meet the condition of a sea surface global coordinate system.
The specific calculation formula of the step 3.1 is that three nodes of the triangular surface element are N according to a anticlockwise method 1 (x 1 ,y 1 ,z 1 )，N 2 (x 2 ,y 2 ,z 2 ) And N 3 (x 3 ,y 3 ,z 3 )，U n (x n ,y n ,z n ) Is the normal unit vector of the surface element, U i (x i ,y i ,z i ) Is the incident direction unit vector of the light,u is the zenith angle and azimuth angle of incident light r (x r ,y r ,z r ) Is the reflection direction unit vector of the light ray, +.>For zenith and azimuth angles, θ, of reflected light ω The included angle between the incident direction vector or the reflecting direction vector and the normal vector of the surface element is the incident angle or the reflecting angle; the parameters satisfy the following relationship:
the method for calculating the normal vector of the bin and the direction vector of the incident light under the global coordinate system is provided, and the corresponding direction vector of the reflected light can be calculated through the law of specular reflection, and the specific formula is as follows:
U i ＝2(U r ·U n )U n -U r (9)
the reflection condition of any triangular surface element under any incident light can be obtained through a formula and node coordinate information of the surface element.
The specific calculation formula of the step 3.2 is that the interaction probability density function Q is q=s·h, and the specific expression form of the function is:
wherein S is a shadow function, U i As unit direction vector, U n Is a unit normal vector, theta is a diffusion angle of a laser beam, A is a laser coordinate under a global coordinate system, B is a center coordinate of a face element, C is a position coordinate of a main axis of the laser beam irradiated to the sea surface, A' is a vertical projection of the laser on the sea surface, AC is a main axis ray of the laser beam, and an included angle between the main axis ray and a z axis is theta i The location of BC is at sea level, i.e. z b ＝z c =0, AB represents the diffuse light, the angle between AB and AC is the angle θ between the diffuse light and the principal axis of the beam c The coordinate information of A and B is a known quantity, and the specific forms of the other parameters are as follows:
A'C＝z a /tan(90°-θ i ) (13)
cosθ c ＝(AC 2 +AB 2 -BC 2 )/(2AC·AB) (19)
when theta is as c <At θ, the binSince the irradiation range of the laser beam is within, the function S is rewritten as follows:
step 3.3 the specific steps are as follows:
step 3.3.1, introducing a light field coordinate system Ou ' v ' w ' with the same origin of coordinates as the sea surface coordinate system, rotating the coordinate system to coincide with the sea surface coordinate system, and defining the rotation angle as the included angle with the positive direction of the coordinate axis
Step 3.3.2 rotating the rotation axis by an angle alpha with the w 'axis as the center to make the v' axis in the xoy plane
Step 3.3.3 rotating the rotation axis by an angle beta with the v 'axis as the center to make the w' axis coincide with the z axis
Step 3.3.4 rotating the rotation axis by an angle gamma with w ' as the center, so that the Ou ' v ' w ' coordinate system coincides with the Oxyz coordinate system, wherein alpha, beta and gamma are referred to as rotating Euler angles, and the conversion relationship between the Ou ' v ' w ' coordinate system and the Oxyz coordinate system can be expressed in a matrix form
In equation (21), the transformation matrix T may be expressed as the Euler angle
The conversion relationship between the Ouvw coordinate system and the Oxyz coordinate system satisfies
The specific steps of the step 4 are as follows: step 4.1, introducing kirchhoff approximation, and introducing a second theorem of vector green;
let vector F exist in two forms:respectively substituting them into the formula (24), and simplifying them into
Let vector A be electric field E and vector B be the vector of the parallel vector Green function point multiplied by any constant vectorSubstituting the electric field and the parallel green's function into the formula (25) to simplify
Step 4.2, solving a vertical polarization component and a horizontal polarization component of the incident electromagnetic field in a local coordinate system;
order theIs a unit vector facing outwards perpendicular to the incident plane, < >>Is a unit vector parallel to the incident plane, +.>Is a vector of normal units of the face element, < >>Is incident direction unit vector, +.>Is a reflection direction unit vector, then->And->An orthogonal coordinate system is formed, and the following relation is satisfied
Let the incident electric field be E i The incident magnetic field is H i The step of solving the vertical polarization component of the incident electromagnetic field in the local coordinate system is to solve the polarization of the incident electromagnetic field in the global coordinate system, and then to obtain the vertical component in the local coordinate system and solve the horizontal polarization component;
let E ρ For polarized electric field, the incident electric field has a vertical polarization component ofIts horizontal polarization component isThe perpendicular polarization component of the incident magnetic field is +.>Its horizontal polarization component is
Step 4.3, obtaining a total tangential electromagnetic field according to a vertical polarization component expression and a horizontal polarization component expression of the incident electric field and the reflected electric field;
step 4.4, according to the total tangential electromagnetic field, solving a scattered field at any position above the sea surface, wherein in a specific direction, the mathematical expression of a scattered section is defined as
Step 4.3 the specific steps are
When the specular reflection is satisfied, the incident directionAnd reflection direction->The following relationships are satisfied: />The vertical polarization component of the reflected electric field is +.>Its horizontal polarization component isThe vertical polarization component of the reflected magnetic field isIts horizontal polarization component is +.>
According to the vertical polarization component expression and the horizontal polarization component expression of the incident electric field and the reflected electric field, the total tangential electromagnetic field can be obtained as follows:
the beneficial effects of the invention are as follows: the invention starts from a basic method for constructing a complex sea surface model, carries out two-dimensional random sea surface simulation by taking a JONSWAP sea spectrum function and a light-sensitive direction distribution function as models, then gives out the steps of establishing and discretizing the complex sea surface on the basis, carries out discretization treatment on the two-dimensional random sea surface after interpolation fitting by adopting a linear superposition method, and gives out a coordinate transformation formula between the sea surface and a laser beam on the basis of a coordinate transformation theory; meanwhile, a kirchhoff approximation formula is deduced, and calculation of a laser beam scattering cross section by the sea surface is realized; the random complex sea surface model based on the JONSWAP spectrum and the linear superposition method adopted by the invention meets the natural development rule of the sea surface, has physical feasibility, and can be used for analyzing the influence of the complex sea surface on the scattering cross section of a typical laser beam, in particular the influence of the beam incidence angle, the beam waist radius and the beam self parameters on the scattering cross section; the method of the invention realizes the scattering of the typical laser beam by the complex sea surface, and has important application value in the fields of ocean remote sensing, ocean resource detection, sea surface target detection and identification and the like.
Drawings
FIG. 1 is a flow chart of a laser beam scattering calculation method based on JONSWAP spectrum sea surface modeling of the present invention;
FIG. 2 is a two-dimensional sea surface simulation diagram generated by a linear superposition method in the calculation method of the invention;
FIG. 3 is a schematic diagram of a two-dimensional sea surface discrete plot in the calculation method of the present invention;
FIG. 4 is a data file format of discrete storage node information in the computing method of the present invention;
FIG. 5 is a data file format of discrete encoded bin information in the computing method of the invention;
FIG. 6 is a discrete plot of random two-dimensional sea surfaces at different wind speeds in the calculation method of the present invention, where the wind speed is U 10 ＝5m/s；
FIG. 7 is a discrete plot of random two-dimensional sea surfaces at different wind speeds in the calculation method of the present invention, where the wind speed is U 10 ＝10m/s；
FIG. 8 is a schematic representation of a triangular bin coordinate system and various parameters in the computing method of the invention;
FIG. 9 is a schematic diagram of three-dimensional spatial distribution of lasers and bins in the calculation method of the present invention;
FIG. 10 is a schematic diagram of a light field coordinate system in the computing method of the present invention;
FIG. 11 is a schematic diagram of a sea surface coordinate system in the calculation method of the present invention;
FIG. 12 is a first step flow chart of the conversion of the coordinate system Ou ' v ' w ' to Oxyz in the calculation method of the present invention;
FIG. 13 is a second step flow chart of the conversion of the coordinate system Ou ' v ' w ' to Oxyz in the calculation method of the present invention;
FIG. 14 is a flow chart of a third step of conversion of the coordinate system Ou ' v ' w ' to Oxyz in the calculation method of the present invention;
FIG. 15 is a fourth step flow chart of the conversion of the coordinate system Ou ' v ' w ' to Oxyz in the calculation method of the present invention;
FIG. 16 is a schematic diagram of the sea surface coordinate system geometry in the calculation method of the present invention;
FIG. 17 is a scattering plot of the fundamental Gaussian beam in the calculation method of the invention at a sufficient distance from the sea surface;
FIG. 18 is a schematic view of scattering cross sections of sea-side light beams on E-side and H-side respectively in the calculation method of the present invention;
FIG. 19 shows the change of the incident zenith angle θ of the fundamental mode Gaussian beam in the calculation method of the invention i An effect simulation diagram on sea surface scattering;
FIG. 20 is a simulation of the effect of a fundamental mode Gaussian beam change in beam polarization on sea surface scattering in the calculation method of the present invention;
FIG. 21 is a simulation of the effect of a fundamental mode Gaussian beam change in the height h of the beam incidence on sea surface scattering in the calculation method of the invention;
FIG. 22A illustrates a fundamental mode Gaussian beam changing beam waist radius w in the method of the present invention 0 An effect simulation diagram on sea surface scattering;
FIG. 23 is a simulation of the scattering cross-section distribution of a complex sea surface to hermite beam in the calculation method of the present invention;
FIG. 24 is a simulation of the scattering cross-section distribution of a complex sea-facing Laguerre-Gaussian beam in the computational method of the present invention.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
Example 1
As shown in FIG. 1, the invention provides a laser beam scattering calculation method based on JONSWAP spectrum sea surface modeling, which is implemented according to the following steps:
step 1, setting a simulation scene, determining a JONSWAP spectrum and a direction distribution function, and calculating a two-dimensional sea wave frequency direction spectrum; step 1.1, setting a simulation scene, selecting a JONSWAP spectrum to perform initial sea surface fitting, wherein the expression of the JONSWAP spectrum is as follows,
where a is the dimensionless energy scale parameter and g is the local gravitational acceleration, typically 9.8m/s 2 ，ω p The peak frequency is gamma, the spectrum peak factor is gamma, and the value is the spectrum peak E under the same wind speed max Spectral peak value of PM spectrumThe ratio of gamma is in the range of 1.5 to 6.0, and the average value is usually 3.3, according to the data measured in the JONSWAP experiment.ω p ＝22(U 10 F/g 2 ) -0.33 F is a wind area, which refers to a sea surface area blown by sea wind at a constant speed, and is in units of km and U 10 Mean wind speed in m/s at 10 meters above the sea surface. Sigma is the peak shape parameter, and the value of the sigma is omega and omega p Commonly determining that when ω is less than or equal to ω p When σ=0.07, when ω>ω p When σ=0.09.
In the step 1.2, in a practical situation, the sea wave is a three-dimensional multidirectional irregular wave, the geometric characteristics of the sea wave cannot be fully described by the one-dimensional sea spectrum, and a direction distribution function is required to be introduced to describe the energy distribution of the sea wave relative to a direction angle. The influence of frequency and direction angle on energy distribution is considered to be independent, so that different sea spectrum functions and direction distribution functions can be combined, the direction distribution functions are introduced to describe the energy distribution of sea waves relative to the direction angle, different sea spectrum functions and direction distribution functions are combined, namely the JONSWAP two-dimensional sea spectrum is,
S(ω,θ)＝S(ω)G(θ) (2)
wherein G (θ) is a directional distribution function, and S (ω, θ) is a directional spectrum function; is determined by the angular frequency ω and the direction angle θ together.
Step 1.3, aiming at the JONSWAP two-dimensional sea spectrum, adopting a light-sensitive distribution function, namely
Wherein θ sea Is the main direction of wave propagation, D 0 (s) is a coefficient determined by the direction distribution concentration parameter s; d (D) 0 The calculation formula of(s) is
Wherein Γ is a gamma function;
step 1.4, obtaining a two-dimensional wave frequency direction spectrum according to the formula (2)
Step 2, based on a two-dimensional sea wave frequency direction spectrum, a complex sea surface model is established and discretized through a linear superposition method, and a discretized model is obtained; and 2.1, establishing a complex sea surface model and discretizing the complex sea surface model. The sea surface has randomness under stable sea conditions, and a geometric model of the random sea surface can be established through a two-dimensional sea spectrum function. By a linear superposition method, a computer and MATLAB software are adopted for simulation, and a sea surface model for effectively reflecting the actual motion condition of sea waves is established.
The linear superposition method is a double superposition method, and the method regards a random sea surface as cosine wave superposition with infinite wave heights, different periods, different phases and different movement directions. Let the sea surface height at any time t and coordinates (x, y) be H (x, y, t), according to the principle of linear superposition method, the sea surface with three-dimensional height can be defined as
Where M and N represent the angular frequency and the discrete number of direction angles, respectively. For angular frequency omega, let the energy of sea spectrum be concentrated mainly at [ omega ] start ,ω end ]In the spectrum, the high-frequency and low-frequency parts with less energy are ignored, and the interval [ omega ] is calculated start ,ω end ]M aliquots were made, each equal to dω= (ω) in width end -ω start ) M; for a direction angle θ, the principal direction θ will be propagated sea Two sides-pi/2 interval [ -pi/2+theta [ sea ,π/2+θ sea ]N aliquots were made, each equal to dθ=pi/N in width. k (k) m And omega m Represents wave number and frequency, θ, of sea wave at the mth angular frequency n Represents the nth direction angle, a mn And b mn The specific form of each parameter is respectively that the m-th angular frequency, the amplitude and the phase angle under the n-th direction angle are represented b mn =rand (0, 2pi). Sea wave phase angle b mn Is in [0,2 pi ]]Random numbers uniformly distributed over a range can be typically implemented in MATLAB using the rand () function.
The formula and analysis show the principle of generating the three-dimensional sea surface by adopting a linear superposition method, and according to the adopted sea spectrum function and the adopted direction distribution function, the computer is used for dispersing and simulating the related parameters to obtain the height distribution data of the three-dimensional multidirectional irregular sea surface. Selecting a JONSWAP spectrum and a light-sensitive distribution function, and establishing a transverse scale of 100m multiplied by 100m, a spectrum peak factor gamma of 3.3, a wind area of 20km and a wind speed U 10 A three-dimensional sea wave with 5m/s, time t of 0 and concentration parameter s of 25 is shown in figure 2;
and 2.2, discretizing the complex sea surface model according to the complex sea surface model, and reconstructing a sea surface model which has small error with the actual sea surface and can be subjected to numerical calculation, namely a discretized model.
Step 2.2.1, equally dividing the transverse dimension into equal parts, marking the points according to a mode of firstly traversing the axis and then longitudinal the axis, and recording the space coordinate information of the points according to the format of each point (x, y, z);
2.2.2, forming a triangle surface element by every three points, recording the number of the points of each surface element in a anticlockwise sequence, and acquiring two data files by the operation, wherein one records the node number of the triangle surface element and the other records the coordinate information of the node;
and 2.2.3, reconstructing a sea surface model which has small sea surface error with the actual sea surface and can perform numerical calculation according to the two data files.
By the linear superposition method, a true and effective random two-dimensional sea surface can be established. The invention researches the scattering of laser on the sea surface, namely exploring the influence of complex sea on the laser beam based on a numerical method, and knowing the sea wave height at any (x, y) coordinate point of the sea surface, so that discretization treatment is also needed on the two-dimensional random sea surface after interpolation fitting. As shown in fig. 3, 4 and 5, taking a sea area range of 100m×100m as an example, dividing the transverse dimension into 100 equal parts, marking points according to a mode of firstly transverse axis and secondly longitudinal axis, recording space coordinate information of the points according to a format of (x, y and z) for each point, forming a triangle surface element by every three points, and recording the serial numbers of the points in a anticlockwise sequence. Through the operation, two files can be acquired, one records the node number of the triangle surface element, and the other records the coordinate information of the node. From these two data files we can reconstruct a sea surface model with small errors from the actual sea surface and with numerical calculations.
As shown in FIG. 6 and FIG. 7, the wind speed U at 10m above the sea surface is shown 10 In the case of 5m/s and 10m/s, respectively, it is known by comparison that the frequency of sea surface fluctuation becomes more severe with the increase of wind speed. When the wind speed is small, the sea surface state is relatively stable, the fluctuation amplitude is small, the local change is quick, the sea wave attenuation distance is short, the whole height range is below 2m, and along with the increase of the wind speed, the vertical fluctuation of the sea surface is moreThe method is obvious, the number of larger fluctuation is far higher than that of the condition of smaller wind speed, the local change is slow, the attenuation distance of sea waves is long, and the whole height range is below 5 m. In summary, the random complex sea surface obtained by adopting the JONSWAP spectrum and the double superposition method meets the natural development rule of the sea surface, has physical feasibility, and provides a basis for the subsequent calculation of the reflection and scattering of the laser beam on the complex sea surface.
Step 3, obtaining a coordinate transformation formula between the sea surface and the laser beam based on coordinate transformation according to the discretized model;
taking a basic mode Gaussian beam as an example, the light beam is scattered into a huge number of light sets, the direction and the light intensity of the light reflected by the surface element at the incidence position of the light are calculated according to the geometrical position of each light transmitted to the sea surface by using a geometrical optics principle and a Fresnel law, and a mathematical model of the basic mode Gaussian beam on complex sea surface reflection is established. The spatial distribution of the reflected light above the complex sea surface can be obtained by counting the direction and the light intensity of the reflected light in the three-dimensional space and superposing the directions and the light intensity.
The invention disperses the simulated random sea surface into a plurality of triangular small surface elements, when the surface elements are small enough, the surface elements can be regarded as ideal planes, and then the sea surface reflection of the laser beam is calculated by taking the mutually independent surface elements as reflection surfaces.
Step 3.1, establishing a sea surface coordinate system, obtaining the node numbers and the node coordinates of the triangular surface elements through data files, and then establishing a local coordinate system to obtain the reflection condition of any one triangular surface element under any incident light ray:
as shown in fig. 7, three nodes of the triangle primitive are N according to the counterclockwise method 1 (x 1 ,y 1 ,z 1 )，N 2 (x 2 ,y 2 ,z 2 ) And N 3 (x 3 ,y 3 ,z 3 )，U n (x n ,y n ,z n ) Is the normal unit vector of the surface element, U i (x i ,y i ,z i ) Is the incident direction unit vector of the light,u is the zenith angle and azimuth angle of incident light r (x r ,y r ,z r ) Is the reflection direction unit vector of the light ray, +.>For zenith and azimuth angles, θ, of reflected light ω The included angle between the incident direction vector or the reflecting direction vector and the normal vector of the surface element is the incident angle or the reflecting angle; the parameters satisfy the following relationship:
the method for calculating the normal vector of the bin and the direction vector of the incident light under the global coordinate system is provided, and the corresponding direction vector of the reflected light can be calculated through the law of specular reflection, and the specific formula is as follows:
the reflection condition of any triangular surface element under any incident light can be obtained through a formula and node coordinate information of the surface element.
When the laser emits light beams to the complex sea surface, only discrete surface elements of a part of areas can be illuminated under the influence of the divergence angle of the light beams, and in practical situations, the complex sea surface has the condition that incident light rays cannot strike the surface elements or reflected light rays cannot be transmitted to the upper space of the sea surface due to the height difference between sea waves, and the triangular surface elements which cannot contribute to the light intensity distribution of the final three-dimensional space are omitted in calculation, so that an interaction probability density function Q is introduced.
Step 3.2, introducing an interaction probability density function, which is defined as the product of a shadow function of whether a light source illuminates a surface element and a hiding function of whether reflected light of the surface element can be received;
the specific calculation formula is that the interaction probability density function Q is Q=S.H, and the specific expression form of the function is:
the shading function S is not just the unit direction vector U of the incident ray i Unit normal vector U of sum surface element n Also related to the spread angle θ of the laser beam, θ is used to determine whether a bin is within the irradiation range of the laser beam. As shown in fig. 9, the laser coordinates a in the global coordinate system, the center coordinates B of the surface elements and the coordinates C of the position of the laser beam main axis irradiated to the sea surface form a triangle, a' is the vertical projection of the laser on the sea surface, AC is the laser beam main axis ray, and the included angle between the laser beam main axis ray and the z axis is θ i The location of BC is at sea level, i.e. z b ＝z c =0, AB represents the diffuse light, the angle between AB and AC is the angle θ between the diffuse light and the principal axis of the beam c . The coordinate information of A and B is a known quantity, and the specific forms of the other parameters are as follows:
A'C＝z a /tan(90°-θ i ) (13)
/>
when theta is as c <In θ, the bin is within the irradiation range of the laser beam, and therefore the form of the function S is rewritten, and the correction is as follows:
in summary, the geometric ray reflection problem of any one effective triangular bin has been solved, and the light field intensity of the fundamental mode gaussian beam emitted by a given laser position on the bin needs to be calculated. The coordinate system where the Gaussian beam of the fundamental mode is located is the light field coordinate system of the fundamental mode, and the propagation direction is along the positive direction of the z axis, so that coordinate transformation is needed to meet the condition of the sea surface global coordinate system.
As shown in fig. 10, the light field coordinate system Ouvw of the fundamental mode gaussian beam is the center of the beam waist, which is the coordinate O (x 0 ,y 0 ,z 0 ) As shown in fig. 11, the sea surface coordinate system Oxyz has a center coordinate of O (0, 0), and it is now necessary to convert the coordinates in any sea surface coordinate system into values in the light field coordinate system.
And 3.3, calculating the light field intensity of the light beam emitted by the given laser position on the surface element, and carrying out coordinate transformation to meet the condition of a sea surface global coordinate system. As shown in figures 12, 13, 14 and 15,
step 3.3.1, introducing a light field coordinate system Ou ' v ' w ' with the same origin of coordinates as the sea surface coordinate system, rotating the coordinate system to coincide with the sea surface coordinate system, and defining the rotation angle as the included angle with the positive direction of the coordinate axis
Step 3.3.2 rotating the rotation axis by an angle alpha with the w 'axis as the center to make the v' axis in the xoy plane
Step 3.3.3 rotating the rotation axis by an angle beta with the v 'axis as the center to make the w' axis coincide with the z axis
Step 3.3.4 rotating the rotation axis by an angle gamma with w ' as the center, so that the Ou ' v ' w ' coordinate system coincides with the Oxyz coordinate system, wherein alpha, beta and gamma are referred to as rotating Euler angles, and the conversion relationship between the Ou ' v ' w ' coordinate system and the Oxyz coordinate system can be expressed in a matrix form
In equation (21), the transformation matrix T may be expressed as the Euler angle
The conversion relationship between the Ouvw coordinate system and the Oxyz coordinate system satisfies
And 4, deducing a kirchhoff approximation formula, and completing calculation of a scattering cross section of the laser beam by the sea surface according to a coordinate transformation formula between the sea surface and the laser beam.
Step 4.1, introducing kirchhoff approximation, and introducing a second theorem of vector green;
let vector F exist in two forms:respectively substituting them into the formula (24), and simplifying them into
Let vector A be electric field E and vector B be the vector of the parallel vector Green function point multiplied by any constant vectorSubstituting the electric field and the parallel green's function into the formula (25) to simplify
Step 4.2, solving a vertical polarization component and a horizontal polarization component of the incident electromagnetic field in a local coordinate system;
as shown in fig. 16, letIs a unit vector facing outwards perpendicular to the incident plane, < >>Is a unit vector parallel to the incident plane, +.>Is a vector of normal units of the face element, < >>Is incident direction unit vector, +.>Is a reflection direction unit vector, then->Andan orthogonal coordinate system is formed, and the following relation is satisfied
Let the incident electric field be E i The incident magnetic field is H i The step of solving the vertical polarization component of the incident electromagnetic field in the local coordinate system is to solve the polarization of the incident electromagnetic field in the global coordinate system, and then to obtain the vertical component in the local coordinate system and solve the horizontal polarization component;
let E ρ For polarized electric field, the incident electric field has a vertical polarization component ofIts horizontal polarization component isThe perpendicular polarization component of the incident magnetic field is +.>Its horizontal polarization component is
Step 4.3, obtaining a total tangential electromagnetic field according to a vertical polarization component expression and a horizontal polarization component expression of the incident electric field and the reflected electric field;
when the specular reflection is satisfied, the incident directionAnd reflection direction->The following relationships are satisfied: />The vertical polarization component of the reflected electric field is +.>Its horizontal polarization component isThe vertical polarization component of the reflected magnetic field isIts horizontal polarization component is +.>
According to the vertical polarization component expression and the horizontal polarization component expression of the incident electric field and the reflected electric field, the total tangential electromagnetic field can be obtained as follows:
step 4.4, according to the total tangential electromagnetic field, solving a scattered field at any position above the sea surface, wherein in a specific direction, the mathematical expression of a scattered section is defined as
The method has the advantages that the coordinate transformation between the sea surface and the laser beam is researched, and the scattering section of the complex sea surface to the laser beam is calculated numerically based on the coordinate transformation method and the beam vector field expression; the method firstly introduces a sea spectrum function and a direction spectrum function for constructing a complex sea surface, then provides an effective method for establishing and dispersing a complex sea surface model, then sets forth a basic theory of interconversion between a sea surface coordinate system and a light beam coordinate system, and derives a kirchhoff approximation formula, thereby being capable of conveniently calculating a scattering cross section of a laser beam by the sea surface and researching the influence of a light beam incident angle, a beam waist radius, a light beam self parameter and the like on the scattering cross section.
Example 2
The embodiment provides a laser beam scattering calculation method based on JONSWAP spectrum sea surface modeling, which is implemented according to the following steps:
step 1, setting a simulation scene, determining a JONSWAP spectrum and a direction distribution function, and calculating a two-dimensional sea wave frequency direction spectrum;
step 2, based on a two-dimensional sea wave frequency direction spectrum, a complex sea surface model is established and discretized through a linear superposition method, and a discretized model is obtained;
step 3, obtaining a coordinate transformation formula between the sea surface and the laser beam based on coordinate transformation according to the discretized model;
and 4, deducing a kirchhoff approximation formula, and completing calculation of a scattering cross section of the laser beam by the sea surface according to a coordinate transformation formula between the sea surface and the laser beam.
Example 3
The embodiment provides a laser beam scattering calculation method based on JONSWAP spectrum sea surface modeling, wherein parameters are set as follows: the polarization mode of the light beam is x linear polarization, and the beam waist radius w 0 Is 2 lambda, the incident height h is 100 lambda above the sea surface, the incident azimuth angleIncident zenith angle theta i The sea surface model established by the invention is based on a JONSWAP spectrum, and is in the condition of lower wind speed and more gentle sea surface fluctuation, and the sea surface size is 20lambda×20lambda.
As shown in fig. 17 and 18, a simple analysis of the scattering cross section of a complex sea-surface to fundamental mode gaussian beam is given. Fig. 17 shows scattering under the condition that the fundamental mode gaussian beam is far enough from the sea surface, and it is known that when the fundamental mode gaussian beam is far enough from the target, the fundamental mode gaussian beam can be regarded as plane wave, in order to verify the correctness of the program, a blue auxiliary line is added on the red curve obtained by numerical calculation to show the variation trend of the scattering cross section along with the scattering angle, and after comparison, the trend of the blue curve is consistent with the variation of the curve of the scattering of the plane wave by the sea surface in the literature, so as to prove the correctness of the program. Fig. 18 calculates the scattering cross sections of the sea-side beam on the E-side and H-side respectively, and it is easy to see that the scattering cross section of the E-side has a certain regularity for the x-linearly polarized beam, while the scattering cross section of the H-side does not basically see other obvious regularity except for the fluctuation of the value along with the change of the scattering angle.
As shown in fig. 19 and 20, the influence of the parameter variation of the fundamental mode Gaussian beam on sea surface scattering is givenAnd (5) sounding. In FIG. 19, incident zenith angle θ i 0 °, 30 ° and 45 °, respectively, it can be seen that with θ i Is changed, the scattering angle theta corresponding to the scattering cross section peak value s Also changes, e.g. theta i At 0 DEG, the scattering angle theta corresponding to the peak value s The angle is 0 degrees, other incident zenith angles also meet the rule, and the backscattering section is inferred to be the largest in scattering of the fundamental mode gaussian beam by the sea surface. In FIG. 20, the polarization of the laser beam is changed, and it can be seen that at the scattering angle θ s <At 50 DEG, the x linear polarization and the left circular polarization of the fundamental mode Gaussian beam have no difference to the scattering cross section of the sea surface, but have a scattering angle theta s >At 50 DEG, with the scattering angle theta s The difference between the scattering cross section of the left circular polarization and the x linear polarization gradually increases.
As shown in fig. 21, the influence of the beam entrance height h on the scattering cross section was studied, and it was found that when the distance between the beam and the sea surface was relatively short, i.e., h was 10λ and 100deg.λ, respectively, the difference in scattering cross section was not very large as a whole, but the curve of h=100deg.λ fluctuated more severely, but when the beam was relatively far from the sea surface, the value of the scattering cross section was entirely reduced. As shown in FIG. 22, the fundamental mode Gaussian beam waist radius w is given 0 The effect on the scattering cross section is obvious, and as a result, the change of the beam waist radius does not affect the change trend of the curve, but the size of the scattering cross section is increased as the beam waist radius is increased.
As shown in fig. 23, 24, the scattering cross-sectional distributions of the complex sea-side hermite and lager gaussian beams are given. In FIG. 23, incident zenith angle θ of hermite-Gaussian beam i =30° incidence azimuth angleBeam waist radius w 0 =2λ, the polarization mode is x linear polarization. We compared the scattering cross sections in the three cases where m and n of the hermite beam take the values of m=1, n=1, m=0, n=1 and m=1, n=0, respectively, and the results are quite obvious that the scattering cross section corresponding to m=1, n=0 is the largest, which is the same as the result of the differential scattering cross section of the hermite beam by the fourth chapter particle, and the attention is paid toIt is intended that at the scattering angle θ s At =30°, the value of the scattering cross section drops suddenly, unlike the fundamental mode gaussian beam, since the optical field intensity maximum of the hermite beam is not at the beam center, and it is inferred that the lager gaussian beam should also have this characteristic. In FIG. 24, the incident zenith angle θ of the Laguerre-Gaussian beam i =30°, azimuth angle of incidence->Beam waist radius w 0 =2λ, the polarization mode is x linear polarization. Analysis of the scattering cross-section characteristics of the marine aerosol particles for the Laguerre-Gaussian beam scattering, with reference to the parameters of the beam, p=1, l=0 and p=1, l=2, shows that the scattering cross-section with a larger orbital angular momentum l is overall larger, and that, as was hypothesized, the corresponding scattering cross-section of l=2 is at θ s A dip occurs at 30 °, but not at l=0, because there is a bright spot at the lager-gaussian beam center for l=0, but a dark spot at the beam center for l=2, so it can be seen that the parameter variation of the beam plays a decisive role in the beam properties.
The embodiment shows that the complex sea surface has larger influence on the scattering cross section of the typical laser beam, the random complex sea surface obtained based on the JONSWAP spectrum and the double superposition method adopted by the invention meets the natural development rule of the sea surface, has physical feasibility, and can be used for analyzing the influence of the complex sea surface on the scattering cross section of the typical laser beam, in particular the influence of the incident angle of the beam, the beam waist radius and the parameters of the beam on the scattering cross section. The method for realizing the scattering of the typical laser beam by the complex sea surface has important application value in the fields of ocean remote sensing, ocean resource detection, sea surface target detection and identification and the like.
Claims (10)
1. The laser beam scattering calculation method based on JONSWAP spectrum sea surface modeling is characterized by comprising the following steps of:
step 1, setting a simulation scene, determining a JONSWAP spectrum and a direction distribution function, and calculating a two-dimensional sea wave frequency direction spectrum;
step 2, based on the two-dimensional sea wave frequency direction spectrum, a complex sea surface model is established and discretized through a linear superposition method, and a discretized model is obtained;
step 3, obtaining a coordinate transformation formula between the sea surface and the laser beam based on coordinate transformation according to the post-discrete model;
and 4, deducing a kirchhoff approximation formula, and completing calculation of the scattering cross section of the laser beam by the sea surface according to the coordinate transformation formula between the sea surface and the laser beam.
2. The method for calculating the scattering of the laser beam based on the sea surface modeling of the jonsswap spectrum according to claim 1, wherein the step 1 is specifically implemented according to the following steps:
step 1.1, setting a simulation scene, and selecting a JONSWAP spectrum to perform initial sea surface fitting, wherein the expression of the JONSWAP spectrum is as follows
Wherein a is dimensionless energy scale parameter, g is local gravitational acceleration, ω p Is peak frequency, gamma is spectral peak factor, F is wind area, U 10 The average wind speed of the sea surface over 10 meters is shown, and sigma is a peak shape parameter;
step 1.2, introducing a direction distribution function to describe the energy distribution of sea waves relative to a direction angle, and combining different sea spectrum functions with the direction distribution function, namely the JONSWAP two-dimensional sea spectrum is
S(ω,θ)＝S(ω)G(θ) (2)
Wherein G (θ) is a directional distribution function, and S (ω, θ) is a directional spectrum function;
step 1.3, aiming at the JONSWAP two-dimensional sea spectrum, adopting a light-sensitive distribution function, namely
Wherein θ sea Is the main direction of wave propagation, D 0 (s) is a coefficient determined by the direction distribution concentration parameter s; d (D) 0 The calculation formula of(s) is
Wherein Γ is a gamma function;
step 1.4, obtaining a two-dimensional wave frequency direction spectrum according to the formula (2)
3. The method for calculating the scattering of the laser beam based on the sea surface modeling of the jonsswap spectrum according to claim 1, wherein the step 2 is specifically implemented according to the following steps:
step 2.1, defining a sea surface with three-dimensional height by a linear superposition method, and simulating by using a computer and MATLAB software according to the two-dimensional sea wave frequency direction spectrum S (omega, theta), so as to establish a complex sea surface model effectively reflecting the actual motion condition of sea waves, wherein the sea surface with three-dimensional height is defined as
Wherein M and N are the angular frequency and the discrete number of direction angles, ω is the angular frequency, θ n For the nth direction angle, a mn And b mn For the mth angular frequency, the amplitude and phase angle at the nth direction angle, b mn Is the wave phase angle;
and 2.2, discretizing the complex sea surface model according to the complex sea surface model, and reconstructing a sea surface model which has small error with the actual sea surface and can be subjected to numerical calculation, namely a discretized model.
4. A method for calculating the scattering of a laser beam based on sea surface modeling of a jonsswap spectrum according to claim 3, wherein the step 2.2 is specifically performed as follows:
step 2.2.1, equally dividing the transverse dimension into equal parts, marking the points according to a mode of firstly traversing the axis and then longitudinal the axis, and recording the space coordinate information of the points according to the format of each point (x, y, z);
2.2.2, forming a triangle surface element by every three points, recording the number of the points of each surface element in a anticlockwise sequence, and acquiring two data files by the operation, wherein one records the node number of the triangle surface element and the other records the coordinate information of the node;
and 2.2.3, reconstructing a sea surface model which has small error with the actual sea surface and can perform numerical calculation according to the two data files.
5. The method for calculating the scattering of the laser beam based on the sea surface modeling of the jonsswap spectrum according to claim 1, wherein the step 3 is specifically implemented according to the following steps:
step 3.1, establishing a sea surface coordinate system, obtaining the node numbers and the node coordinates of the triangular surface elements through data files, and then establishing a local coordinate system to obtain the reflection condition of any one triangular surface element under any incident light ray:
step 3.2, introducing an interaction probability density function, which is defined as the product of a shadow function of whether a light source illuminates a surface element and a hiding function of whether reflected light of the surface element can be received;
and 3.3, calculating the light field intensity of the light beam emitted by the given laser position on the surface element, and carrying out coordinate transformation to meet the condition of a sea surface global coordinate system.
6. The method for calculating the scattering of the laser beam based on the sea surface modeling of the JONSWAP spectrum according to claim 5, wherein the specific calculation formula in the step 3.1 is that three nodes of the triangular surface element are N according to a counterclockwise method 1 (x 1 ,y 1 ,z 1 )，N 2 (x 2 ,y 2 ,z 2 ) And N 3 (x 3 ,y 3 ,z 3 )，U n (x n ,y n ,z n ) Is the normal unit vector of the surface element, U i (x i ,y i ,z i ) Is the incident direction unit vector of the light,u is the zenith angle and azimuth angle of incident light r (x r ,y r ,z r ) Is the reflection direction unit vector of the light ray, +.>For zenith and azimuth angles, θ, of reflected light ω The included angle between the incident direction vector or the reflecting direction vector and the normal vector of the surface element is the incident angle or the reflecting angle; the parameters satisfy the following relationship:
the method for calculating the normal vector of the bin and the direction vector of the incident light under the global coordinate system is provided, and the corresponding direction vector of the reflected light can be calculated through the law of specular reflection, and the specific formula is as follows:
U i ＝2(U r ·U n )U n -U r (9)
the reflection condition of any triangular surface element under any incident light can be obtained through a formula and node coordinate information of the surface element.
7. The method for calculating the scattering of the laser beam based on the sea surface modeling of the jonsswap spectrum according to claim 5, wherein the specific calculation formula in the step 3.2 is that the interaction probability density function Q is q=s·h, and the specific expression form of the function is:
wherein S is a shadow function, U i As unit direction vector, U n Is a unit normal vector, theta is a diffusion angle of a laser beam, A is a laser coordinate under a global coordinate system, B is a center coordinate of a face element, C is a position coordinate of a main axis of the laser beam irradiated to the sea surface, A' is a vertical projection of the laser on the sea surface, AC is a main axis ray of the laser beam, and an included angle between the main axis ray and a z axis is theta i The location of BC is at sea level, i.e. z b ＝z c =0, AB represents the diffuse light, the angle between AB and AC is the angle θ between the diffuse light and the principal axis of the beam c The coordinate information of A and B is a known quantity, and the specific forms of the other parameters are as follows:
A'C＝z a /tan(90°-θ i ) (13)
cosθ c ＝(AC 2 +AB 2 -BC 2 )/(2AC·AB) (19)
when theta is as c <In θ, the bin is within the irradiation range of the laser beam, and therefore the form of the function S is rewritten, and the correction is as follows:
8. the method for calculating the scattering of the laser beam based on the sea surface modeling of the jonsswap spectrum according to claim 5, wherein the step 3.3 specifically comprises the following steps:
step 3.3.1, introducing a light field coordinate system Ou ' v ' w ' with the same origin of coordinates as the sea surface coordinate system, rotating the coordinate system to coincide with the sea surface coordinate system, and defining the rotation angle as the included angle with the positive direction of the coordinate axis
Step 3.3.2 rotating the rotation axis by an angle alpha with the w 'axis as the center to make the v' axis in the xoy plane
Step 3.3.3 rotating the rotation axis by an angle beta with the v 'axis as the center to make the w' axis coincide with the z axis
Step 3.3.4 rotating the rotation axis by an angle gamma with w ' as the center, so that the Ou ' v ' w ' coordinate system coincides with the Oxyz coordinate system, wherein alpha, beta and gamma are referred to as rotating Euler angles, and the conversion relationship between the Ou ' v ' w ' coordinate system and the Oxyz coordinate system can be expressed in a matrix form
In equation (21), the transformation matrix T may be expressed as the Euler angle
The conversion relationship between the Ouvw coordinate system and the Oxyz coordinate system satisfies
9. The method for calculating the scattering of the laser beam based on the sea surface modeling of the jonsswap spectrum according to claim 1, wherein the specific steps of the step 4 are as follows:
step 4.1, introducing kirchhoff approximation, and introducing a second theorem of vector green;
let vector F exist in two forms:respectively substituting them into the formula (24), and simplifying them into
Let vector A be electric field E and vector B be the vector of the parallel vector Green function point multiplied by any constant vectorSubstituting the electric field and the parallel green's function into the formula (25) to simplify
Step 4.2, solving a vertical polarization component and a horizontal polarization component of the incident electromagnetic field in a local coordinate system;
order theIs a unit vector facing outwards perpendicular to the incident plane, < >>Is a unit vector parallel to the incident plane, +.>Is a vector of normal units of the face element, < >>Is incident direction unit vector, +.>Is a reflection direction unit vector, then->And->An orthogonal coordinate system is formed, and the following relation is satisfied
Let the incident electric field be E i The incident magnetic field is H i The step of solving the vertical polarization component of the incident electromagnetic field in the local coordinate system is to solve the polarization of the incident electromagnetic field in the global coordinate system, and then to obtain the vertical component in the local coordinate system and solve the horizontal polarization component;
let E ρ For polarizing the electric field, incident electric fieldThe vertical polarization component isIts horizontal polarization component isThe perpendicular polarization component of the incident magnetic field is +.>Its horizontal polarization component is
Step 4.3, obtaining a total tangential electromagnetic field according to a vertical polarization component expression and a horizontal polarization component expression of the incident electric field and the reflected electric field;
step 4.4, according to the total tangential electromagnetic field, solving a scattered field at any position above the sea surface, wherein in a specific direction, the mathematical expression of a scattered section is defined as
10. The method for calculating the scattering of the laser beam based on the sea surface modeling of the JONSWAP spectrum according to claim 9, wherein the specific step of the step 4.3 is that
When the specular reflection is satisfied, the incident directionAnd reflection direction->The following relationships are satisfied: />The vertical polarization component of the reflected electric field is +.>Its horizontal polarization component isThe vertical polarization component of the reflected magnetic field isIts horizontal polarization component is +.>
According to the vertical polarization component expression and the horizontal polarization component expression of the incident electric field and the reflected electric field, the total tangential electromagnetic field can be obtained as follows:
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