Underwater two-way optical transmission simulation method based on turbulent phase screen and vector Monte Carlo

Abstract

The invention discloses an underwater two-way optical transmission simulation method based on a turbulent phase screen and vector Monte Carlo, and the method comprises the steps: building a three-dimensional coordinate system, and initializing parameters; generating a multi-layer turbulence phase screen; generating a random rough surface to simulate a target rough surface; sequentially judging whether the photons intersect with the phase screen, arrive at a target surface and arrive at a receiving surface; if the photon intersects with the phase screen, calculating an intersection coordinate, and updating the photon coordinate and direction; if not, whether a target surface is reached is judged, and if the target surface is reached, a return transmission process is triggered; if the photon does not arrive at the target surface, judging whether the photon arrives at a receiving surface, and if the photon arrives at the receiving surface, recording information of the current photon on the receiving surface; if the receiving surface is not reached, updating photon information, and judging the survival state of photons; and repeating the process until the photons arrive at the receiving surface or the weight is lower than a survival threshold value, and accumulating the number of the received photons and a polarization state statistical result. According to the invention, a theoretical basis is provided for underwater light transmission and optical communication experiment research of blue-green polarized light.

Description

Technical Field

[0001] The present invention relates to application fields such as underwater laser communication, polarization imaging and laser radar, and is particularly suitable for high-precision simulation of polarized light transmission characteristics in complex seawater environments with strong turbulence and high scattering coupling. Background Art

[0002] Since the discovery of the blue-green light transmission window in the 1960s, underwater optical detection technology has become a key means of marine resource exploration due to its strong directionality and high positioning accuracy. Blue-green lasers are widely used in fields such as water depth measurement, seabed topography inversion, and target identification due to their high penetration and anti-interference capabilities. However, the complex interference effect of seawater on light transmission has always been the core bottleneck restricting detection performance: on the one hand, the absorption-scattering effect caused by suspended particles and plankton in the water body will lead to light intensity attenuation, signal time delay broadening, and random fluctuations in polarization state; on the other hand, turbulent disturbances driven by salinity and temperature gradients will cause random fluctuations in the refractive index in time and space, resulting in beam expansion, drift, and phase distortion.

[0003] Existing simulation models are mostly based on the scalar Monte Carlo method, which simplifies turbulence effects into equivalent refractive index changes under the generalized law of refraction and couples them with absorption-scattering effects. While these methods can simulate light intensity distribution and transmission loss, they suffer from significant drawbacks: First, they ignore the vector modeling of target scattering characteristics. The models primarily focus on water effects and neglect the vector characteristics of polarization. Especially when the target surface is made of metal, its surface roughness causes diffuse reflection of polarized laser light, resulting in depolarization. Existing models cannot effectively analyze the depolarization of backscattered light caused by these target characteristics, nor can they fully describe the dynamic changes in the polarization state of the beam along the propagation path. This leads to severe inaccuracies in simulations for technologies such as polarization-multiplexed detection and coherent imaging. Second, there is a mismatch between the physical mechanisms of the two-way optical path: the assumptions of traditional single-pass transmission modeling do not match the physical mechanisms of the two-way optical path (transmitter-target reflection-receiver) in active detection scenarios. Especially when there is a significant depolarization mechanism on the target surface (such as a rough metal surface), the model cannot accurately capture the complex coupling between the turbulence and the target depolarization scattering effect of the target echo signal in the reverse transmission path, resulting in distortion of the echo signal modeling. Summary of the Invention

[0004] In order to overcome the above problems existing in the prior art, the present invention proposes an underwater two-way optical transmission simulation method based on turbulence phase screen and vector Monte Carlo.

[0005] The technical solution adopted by the present invention to solve the technical problem is: an underwater two-way optical transmission simulation method based on turbulence phase screen and vector Monte Carlo, comprising the following steps: Step 1: Establish a three-dimensional coordinate system, initialize parameters, and sample the initial position coordinates and initial direction cosines of the photons. Step 2: Initialize the photon Stokes vector according to the polarization state of the incident light and calculate the new Stokes vector of the photon; Step 3: Based on the ocean turbulence power spectrum model, a multi-layer turbulence phase screen is generated by the fast Fourier transform inversion method; a random rough surface is generated to simulate the target rough surface; Step 4: Calculate the free path of the photon. Based on the photon coordinates, direction cosines, and random step length, determine whether the photon intersects the phase screen, reaches the target surface, and reaches the receiving surface. Step 5: If the photon intersects the phase screen, the intersection coordinates are calculated and the photon coordinates and direction are updated; if the photon does not intersect the phase screen, it is determined whether the photon has reached the target surface. If it has reached the target surface, the return transmission process is triggered, and the photon transmission direction, photon coordinates, Stokes vector and photon weight are updated according to the target surface properties, and the photon weight is judged against the predetermined threshold; if it has not reached the target surface, it is determined whether it has reached the receiving surface. If it has reached the receiving surface, the coordinate position, Stokes vector and weight information of the current photon on the receiving surface are recorded; if it has not reached the receiving surface, the photon coordinates, direction cosines, Stokes vector and weight are updated to determine the photon survival status; Step 6: Loop through steps 4-5 until the photon reaches the receiving surface or the weight is lower than the survival threshold, and accumulate the number of received photons and the polarization state statistics.

[0006] The above-mentioned underwater two-way optical transmission simulation method based on turbulence phase screen and vector Monte Carlo, the step 1 is specifically: establishing a three-dimensional coordinate system, setting the positive direction of the Z axis as the main direction of light transmission, Z=0 as the light source emission plane, initializing the light source parameters, receiver position, ocean turbulence parameters, water body scattering coefficient and absorption coefficient; and according to the spatial distribution characteristics of the light source, sampling the initial position coordinates of the photons through Gaussian distribution, and generating the initial direction cosines of the photons based on the light source divergence angle distribution.

[0007] The above-mentioned underwater two-way optical transmission simulation method based on turbulent phase screen and vector Monte Carlo, the step 2 is specifically: initialize the photon Stokes vector according to the polarization state of the incident light, and use the Henyey-Greenstein scattering model to randomly sample the scattering angle θ and azimuth , generating a new transmission direction to continue transmission and obtain the new Stokes vector of the photon.

[0008] In the above-mentioned underwater two-way optical transmission simulation method based on turbulence phase screen and vector Monte Carlo, step 3 specifically includes: Step 3.1: Select the ocean turbulence power spectrum model : is the spatial wave number; is the Kolmogorov inner scale; ; It represents the turbulent kinetic energy dissipation rate per unit mass of seawater; is the mean square temperature dissipation rate; It represents the ratio of the contribution of refractive index changes caused by temperature and salinity fluctuations in the ocean turbulence power spectrum; Step 3.2: Use the turbulent refractive index spectrum and the complex Gaussian random number matrix to generate the phase space complex random field, and perform inverse Fourier transform to obtain the spatial distribution of the two-dimensional phase. ; Step 3.3: Repeat steps 3.1-3.2 to generate all phase screens.

[0009] In the above-mentioned underwater two-way optical transmission simulation method based on turbulent phase screen and vector Monte Carlo, the Monte Carlo method is used in step 3 to generate a random rough surface to simulate the target rough surface. The specific method is: The Monte Carlo method is used to express the height of a point on the rough surface as: in, Represents a two-dimensional rough surface x , y The correlation length in the direction is used to characterize the variation period of the rough surface; M , N express x , y The number of pixels in the direction; 、 express x , y spatial frequency of the direction; , represents the coordinates on the two-dimensional rough surface, and is the distance between two adjacent points; and are Fourier transform pairs, Power density through a two-dimensional rough surface Obtain: In the formula represents a normally distributed random number with mean 0 and variance 1. The expression is: ; Represents the root mean square height of a two-dimensional rough surface.

[0010] In the above-mentioned underwater two-way light transmission simulation method based on turbulent phase screen and vector Monte Carlo, if the photon intersects with the target rough surface in step 5, then the photon and the target rough surface are calculated. The coordinates of the target rough surface intersection for: ; in and are the coordinates and directions of the photons incident in front of the target, respectively; Direction of the photon after reflection: in, is the target surface gradient field, is the surface height, and the normal vector is: ; When the target surface is made of metal, the polarized laser reflection s 、 p The expressions for component reflectance and phase angle changes are: Where: The asterisk in denotes the complex conjugate of the variable; l and m The expression is: Where: n is the refractive index of the metal; nk is the loss rate, n、k are all functions of the incident angle, and the expressions are: 、 They are The principal refractive index and principal loss rate under the conditions of the incident angle, 、 is the refractive index of seawater and the angle of incidence; 、 is the complex refractive index and complex refraction angle of the metal material, i represents the imaginary part; then the coordinates of the photon before the next scattering occurs after being reflected by the target surface Expressed as: in, L R is the random step size in the scattering event by the target reflecting surface; The Stokes vector after reflection is updated as: in, and They are s 、 p Component reflection coefficient.

[0011] The beneficial effect of the present invention is that, based on the random phase screen method to simulate ocean turbulence and the Monte Carlo method to generate random rough target surfaces, the present invention analyzes the changes in the number of received photons and polarization degree after the polarized light beam is transmitted two-way underwater at different distances, providing a theoretical basis for the experimental research on underwater optical transmission and optical communication of blue-green polarized light. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 This is a schematic diagram of a polarized light underwater two-way transmission model according to the present invention; Figure 2 This is an overall flow chart of the polarized light underwater two-way transmission model of the present invention; Figure 3 The number of photons received after two-way underwater transmission of a polarized light beam at different distances according to an embodiment of the present invention; Figure 4 This is the change in polarization degree of a polarized light beam after underwater two-way transmission at different distances according to the transmission distance of the embodiment of the present invention. DETAILED DESCRIPTION

[0013] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0014] like Figure 1 As shown, the present invention provides a technical solution: an underwater two-way optical transmission simulation method based on turbulent phase screen and vector Monte Carlo, such as Figure 2 As shown, the following steps are included: Step 1: Take the positive direction of the Z axis as the positive direction of light transmission, the plane where the emitting light source is located and the plane where the receiving plane is located are both at Z = 0, the wavelength λ is 532nm, and the number of photons N is 10 4 , the photon weight threshold is 10 -4 , initial beam width The phase screen spacing in the Z-axis direction is Δz=5m, and the phase screen size is 2m×2m; the azimuth angle The angle between the projection of the photon scattering direction on the XOY plane and the positive half axis of the X axis; the scattering angle θ is the angle between the photon propagation direction and the positive half axis of the X axis; sets the absorption coefficient of seawater =0.1m -1, scattering coefficient b =0.5m -1 , single scattering transmittance c=b / (a+b); the initial weight of the photon is W0=1, the refractive index of seawater n=1.33, the material property of the target rough surface is metallic copper, and the complex refractive index is 0.62+ i 3.03, albedo 0.3, receiving aperture r =5m.

[0015] Step 2: If the Stokes vector of the incident photon is expressed as ,in is the total intensity of the incident wave, is the phase difference between the x and y directions of the incident wave; ± 45° linearly polarized light component; Indicates the proportion of circular polarization in polarized light. Set the initial Stokes vector , for mie scattering, the phase function is approximated by the HG function, in, θ is the scattering angle, g is the asymmetry factor; Photon scattering azimuth 0 to A random number between and is the Mie scattering matrix The elements are: The parameters 、 、 、 The scattering amplitude can be and get: in, and The size of is related to the photon radius and the photon complex refractive index.

[0016] New directions for photon transmission as follows: when hour, in, is the direction of the photon before scattering; when hour, The Stokes parameters after scattering are expressed as: in 、 is the rotation matrix, the rotation angle Expressed as represents the Stokes parameter before scattering; the final state of the total polarized light is: ; Where N0 is the number of photons; The total degree of polarization Dop of polarized light is: .

[0017] Step 3: Generate the ocean turbulence phase screen and target rough surface as follows: Step 3.1: Select the ocean turbulence power spectrum model : is the spatial wave number; is the Kolmogorov inner scale; ; It represents the turbulent kinetic energy dissipation rate per unit mass of seawater; is the mean square temperature dissipation rate; It represents the ratio of the contribution of refractive index changes caused by temperature and salinity fluctuations in the ocean turbulence power spectrum; Step 3.2: Use the turbulent refractive index spectrum and the complex Gaussian random number matrix to generate the phase space complex random field, and perform inverse Fourier transform to obtain the spatial distribution of the two-dimensional phase. : Where, and Respectively represent x Direction and y The discrete spatial frequencies of the directions, , ,in and Respectively represent x Direction and y Grid size in direction; represents a complex random matrix with Gaussian random distribution and mean zero; is the interval of the phase screen on the z axis, is the spatial wave number; Step 3.3: Repeat steps 3.1-3.2 to generate all phase screens.

[0018] Step 3.4: Use the Monte Carlo method to generate random rough surfaces to simulate the target rough surface. The specific method is as follows: The Monte Carlo method is used to express the height of a point on the rough surface as: in, Represents a two-dimensional rough surface x , y The correlation length in the direction (the following order ), which is used to characterize the variation period of the rough surface; M , N express x , y The number of pixels in the direction; , Description x , y spatial frequency of the direction; and is the distance between two adjacent points; , Represents the coordinates on the two-dimensional rough surface; and are Fourier transform pairs. Power density that can be achieved through a two-dimensional rough surface Obtain: In the formula Represents a normally distributed random number with mean 0 and variance 1. The expression is , Represents the root mean square height of a two-dimensional rough surface.

[0019] The specific implementation of step 4 is as follows: Calculate the random step size of the photon: in, For Pseudo-random numbers uniformly distributed between; c is the attenuation coefficient; Furthermore, if the position of the photon before collision is The cosine of the angle in the propagation direction z is , the update method of the photon position is: .

[0020] Furthermore, according to the photon coordinates , photon direction cosines With random step size L , determine whether the photon intersects the phase screen and reaches the target surface; The specific implementation of step 5 is as follows: If the photon intersects the phase screen, calculate the coordinates of the intersection of the photon and the phase screen for: in, and are the coordinates and directions before passing through the photon phase screen, is the position of the phase screen in the z-axis direction; When a photon passes through a phase screen, its transmission direction changes. According to the generalized Snell's law, the new direction of the photon is Expressed as: Where, is the light wave number; is the spatial phase function of the phase screen.

[0021] After a photon passes through the phase screen, the photon coordinates before the next scattering occurs Expressed as: ; If photons and If the target surface intersects at , then calculate the coordinates where the photon intersects the target surface for: in and are the coordinates and directions of the photons incident on the target; update the direction of the photons after reflection: in, is the target surface gradient field, is the surface height, and the normal vector is: .

[0022] When the target surface is made of metal, the polarized laser reflection s 、 p The expressions for component reflectance and phase angle changes are: Where: The asterisk in denotes the complex conjugate of the variable; l and m The expression is Where: n is the refractive index of the metal; nk is the loss rate, n、k are all functions of the incident angle, and the expressions are: 、 They are The principal refractive index and principal loss rate under the conditions of the incident angle, 、 is the refractive index of seawater and the angle of incidence; 、 are the complex refractive index and complex refraction angle of metal materials.

[0023] The coordinates of the photon before the next scattering occurs after the photon is reflected by the target surface Expressed as: in, L R is the random step size in the scattering events by the target reflecting surface.

[0024] Furthermore, the Stokes vector after reflection is updated: in, in, and They are s 、 p Component reflection coefficient.

[0025] If the photon does not collide with the target surface, it is determined whether the photon reaches the receiving surface. If so, the coordinate position, Stokes vector and weight information of the current photon on the receiving surface are recorded; if it does not reach the receiving surface, the photon coordinates, direction cosines, Stokes vector and weight are updated to determine the survival status of the photon; Step 6: Loop through steps 4 and 5 until the photon reaches the receiving surface or the weight is lower than the survival threshold, and accumulate the statistical results of the light intensity distribution and polarization state at the receiving surface.

[0026] In order to verify the correctness of the underwater two-way optical transmission simulation model constructed by the method of the present invention, the changes in the number of received photons and polarization degree at different distances of the polarized light beam underwater two-way transmission are analyzed.

[0027] Figure 3 for ε =10 -2 m 2 / s 3 , χ T =10 -10 K 2 / s, ω = -3, when the target surface is at Z = 10, 20, 25, 30, 35, and 40 m respectively, the distribution of received photons after the light beam is transmitted underwater at different distances; Figure 4 for ε =10 -2 m 2 / s 3 , χ T =10 -10 K 2 / s, ω = -3, when the target surface is at Z = 10, 20, 25, 30, 35, and 40 m respectively, the polarization degree of the light beam after underwater two-way transmission at different distances; Figure 3 The results show that the longer the beam transmission distance is, the fewer photons the target receives; Figure 4 The results show that the longer the light beam is transmitted, the smaller the polarization degree of the total polarized light at the receiving end.

[0028] The above embodiments are merely exemplary embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art may make various modifications or equivalent substitutions to the present invention within the spirit and scope of protection of the present invention, and such modifications or equivalent substitutions shall also be deemed to fall within the scope of protection of the present invention.

Claims

1. The underwater two-way optical transmission simulation method based on turbulent phase screen and vector Monte Carlo is characterized by: The steps include: Step 1: Establish a three-dimensional coordinate system, initialize parameters, and sample the initial position coordinates and initial direction cosines of the photons. Step 2: Initialize the photon Stokes vector according to the polarization state of the incident light and calculate the new Stokes vector of the photon; Step 3: Based on the ocean turbulence power spectrum model, a multi-layer turbulence phase screen is generated by the fast Fourier transform inversion method; a random rough surface is generated to simulate the target rough surface; Step 4: Calculate the free path of the photon. Based on the photon coordinates, direction cosines, and random step length, determine whether the photon intersects the phase screen, reaches the target surface, and reaches the receiving surface. Step 5: If the photon intersects the phase screen, the intersection coordinates are calculated and the photon coordinates and direction are updated. If the photon does not intersect the phase screen, it is determined whether the photon has reached the target surface. If so, the return transmission process is triggered. The photon transmission direction, photon coordinates, Stokes vector, and photon weight are updated according to the target surface properties, and the photon weight is compared with the predetermined threshold. If it does not reach the target surface, it is determined whether it reaches the receiving surface. If it reaches the receiving surface, the coordinate position, Stokes vector and weight information of the current photon on the receiving surface are recorded; If it does not reach the receiving surface, the photon coordinates, direction cosines, Stokes vector and weight are updated to determine the photon survival status; Step 6: Loop through steps 4-5 until the photon reaches the receiving surface or the weight is lower than the survival threshold, and accumulate the number of received photons and the polarization state statistics.

2. The underwater two-way optical transmission simulation method based on turbulence phase screen and vector Monte Carlo according to claim 1 is characterized in that: The step 1 specifically includes: establishing a three-dimensional coordinate system, setting the positive direction of the Z axis as the main direction of light transmission, Z=0 as the light source emission plane, initializing the light source parameters, receiver position, ocean turbulence parameters, water body scattering coefficient and absorption coefficient; and sampling the initial position coordinates of the photons through Gaussian distribution according to the spatial distribution characteristics of the light source, and generating the initial direction cosines of the photons based on the light source divergence angle distribution.

3. The underwater two-way optical transmission simulation method based on turbulence phase screen and vector Monte Carlo according to claim 1 is characterized in that: The step 2 is specifically as follows: initializing the photon Stokes vector according to the polarization state of the incident light, and randomly sampling the scattering angle using the Henyey-Greenstein scattering model. θ and azimuth , generating a new transmission direction to continue transmission and obtain the new Stokes vector of the photon.

4. The underwater two-way optical transmission simulation method based on turbulence phase screen and vector Monte Carlo according to claim 1 is characterized in that: The step 3 of generating a multi-layer turbulence phase screen specifically includes: Step 3.1: Select the ocean turbulence power spectrum model : ； is the spatial wave number; is the Kolmogorov inner scale; ; It represents the turbulent kinetic energy dissipation rate per unit mass of seawater; is the mean square temperature dissipation rate; It represents the ratio of the contribution of refractive index changes caused by temperature and salinity fluctuations in the ocean turbulence power spectrum; Step 3.2: Use the turbulent refractive index spectrum and the complex Gaussian random number matrix to generate the phase space complex random field, and perform inverse Fourier transform to obtain the spatial distribution of the two-dimensional phase. ; Step 3.3: Repeat steps 3.1-3.2 to generate all phase screens.

5. The underwater two-way optical transmission simulation method based on turbulence phase screen and vector Monte Carlo according to claim 1 is characterized in that: In step 3, the Monte Carlo method is used to generate a random rough surface to simulate the target rough surface. The specific method is: The Monte Carlo method is used to express the height of a point on the rough surface as: ； in, Represents a two-dimensional rough surface x , y The correlation length in the direction is used to characterize the variation period of the rough surface; M , N express x , y The number of pixels in the direction; 、 express x , y spatial frequency of the direction; , represents the coordinates on the two-dimensional rough surface, and is the distance between two adjacent points; and are Fourier transform pairs, Power density through a two-dimensional rough surface Obtain: ； In the formula represents a normally distributed random number with mean 0 and variance 1. The expression is: ； Represents the root mean square height of a two-dimensional rough surface.

6. The underwater two-way optical transmission simulation method based on turbulence phase screen and vector Monte Carlo according to claim 1 is characterized in that: If the photon intersects the target rough surface in step 5, then calculate the intersection of the photon and the target rough surface. The coordinates of the target rough surface intersection for: ； in and are the coordinates and directions of the photons incident in front of the target, respectively; Direction of the photon after reflection: ； in, is the target surface gradient field, is the surface height, and the normal vector is: ; When the target surface is made of metal, the polarized laser reflection s 、 p Component reflectance variation 、 and phase angle change 、 The expressions are: ； Where: The asterisk in denotes the complex conjugate of the variable; l and m The expression is: ； ； Where: n is the refractive index of the metal; nk is the loss rate, n、k are all functions of the incident angle, and the expressions are: ； 、 They are The principal refractive index and principal loss rate under the conditions of the incident angle, 、 is the refractive index of seawater and the angle of incidence; 、 is the complex refractive index and complex refraction angle of the metal material, i represents the imaginary part; then the coordinates of the photon before the next scattering occurs after being reflected by the target surface Expressed as: ； in, L R is the random step size in the scattering event by the target reflecting surface; The Stokes vector after reflection is updated as: ； ； in, and They are s 、 p Component reflection coefficient.

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