Improved method for calculating grazing incidence sea surface back scattering through small slope approximation method

Abstract

The invention discloses an improved method for calculating grazing incidence sea surface back scattering through a small slope approximation method, and belongs to the technical field of sea surface electromagnetic scattering calculation, and the method comprises the following steps: S1, determining the wind speed of each stage of sea condition, and calculating the seawater dielectric constant; s2, generating sea surface geometry by using a linear filtering method based on a sea wave spectrum according to the determined wind speed; s3, introducing a conical incident wave; s4, introducing an edge geometric attenuation function; and S5, calculating sea surface back scattering by using an approximate integral formula of a small slope approximation method. According to the improved method for calculating grazing incidence sea surface back scattering through the small-slope approximation method, the edge geometric height is attenuated to 0 by applying the edge geometric attenuation function, so that the situation that the height fluctuation of the sea surface edge is close to an incident wave energy central axis is avoided, the problem that the calculation result is large under grazing incidence is solved, and the calculation efficiency is improved. And meanwhile, the calculation result is more accurate.

Description

Technical Field

[0001] The invention relates to the technical field of sea surface electromagnetic scattering calculation, and in particular to an improved method for calculating grazing incidence sea surface backscattering using a small slope approximation method. Background Art

[0002] The calculation methods of electromagnetic scattering of the sea surface mainly include two categories: numerical simulation method and analytical approximation method. The numerical simulation method is a numerical calculation method derived from Maxwell's equations, which generally has the problem of excessive calculation. The analytical approximation method makes physical approximations through certain assumptions to simplify the calculation process. Common analytical approximation methods include Kirchhoff approximation, integral equation method, two-scale composite model and small slope approximation method. Among them, the small slope approximation method has a wider range of use and better accuracy in the small ground-grabbing angle range.

[0003] However, the small slope approximation method has the problem of overstating the calculation results under grazing incidence, that is, when the grazing angle is <5°. The reason is that when the incident grazing angle is close to 0°, the energy center axis of the incident wave is closer to the horizontal plane, and the energy distribution width becomes narrower and narrower. As for the height fluctuation of the sea surface edge, when the fluctuation height is close to the energy center axis of the incident wave, its energy cannot be attenuated normally, resulting in abnormal edge energy. This abnormal edge energy causes the calculation result of the sea surface backscattering coefficient under grazing incidence to be too large. Summary of the invention

[0004] The purpose of the present invention is to provide an improved method for calculating grazing incidence sea surface backscattering using a small slope approximation method. By applying an edge geometry attenuation function, the edge geometry height is attenuated to 0 to avoid the height fluctuation of the sea surface edge approaching the central axis of the incident wave energy, thereby improving the problem of large calculation results under grazing incidence and making the calculation results more accurate.

[0005] To achieve the above object, the present invention provides an improved method for calculating grazing incidence sea surface backscattering using a small slope approximation method, comprising the following steps:

[0006] Step S1, determining the wind speed of each sea state and calculating the dielectric constant of seawater;

[0007] Step S2: Generate sea surface geometry using a linear filtering method based on sea wave spectrum according to the determined wind speed;

[0008] Step S3, introducing a conical incident wave;

[0009] Step S4, introducing edge geometry attenuation function;

[0010] Step S5: Use the small slope approximation method to approximate the integral formula to calculate the sea surface backscatter.

[0011] Preferably, in step S1, the X-band sea surface backscatter is calculated, and the average wind speed of sea conditions of levels 1-5 is determined according to the international standard sea condition level and wind force level and the corresponding wave height relationship, where level 1 is 0.9 m / s, level 2 is 2.45 m / s, level 3 is 5.05 m / s, level 4 is 8.7 m / s, and level 5 is 12.3 m / s. Under the conditions of average seawater temperature T=15°C, average salinity S=35‰, and irradiation frequency f=10 GHz, the dielectric constant of seawater is calculated according to the double Debye model as ε=53.4770-j38.6646, where j represents an imaginary number.

[0012] Preferably, in step S2, the Apel wave spectrum is selected to generate the sea surface geometry, and its two-dimensional directional spectrum W Apel (K,φ) is as follows:

[0013]

[0014] Among them, a1 = 0.00195, which is a constant; K is the spatial wave number of the wave; U 10 is the wind speed at a height of 10m above the sea surface; g0 is the acceleration due to gravity; φ is the direction angle; φ m is the wind direction angle; K P is the main wave number, that is, the wave number corresponding to the peak position; D(K, φ) is the directional expansion function, which is specifically:

[0015]

[0016] Preferably, a conical incident wave is introduced in step S3, and at the space R=(x, y, z), the conical incident field E i (R) is expressed as:

[0017] E i (R) = T(R)exp(-jk i ·R);

[0018] T(R)=exp[-j(k i ·R)w]exp(-t x -t y );

[0019]

[0020] Among them, k i is the incident wave vector; θ i is the incident angle; φ i is the incident wave azimuth; g c is the cone control parameter, and its commonly used value is:

[0021]

[0022] Preferably, in step S4, an edge geometry attenuation function F is introduced z (x, y) is as follows:

[0023]

[0024] Among them, g z As the control parameter, g z =L / 2.3;

[0025] The actual sea surface geometry for electromagnetic scattering calculation is as follows:

[0026] z′(x, y)=F z (x, y)z(x, y).

[0027] Preferably, in step S5, the electromagnetic scattering calculation is performed on the sea surface geometry z′(x, y) after edge geometry attenuation using a small slope approximation method. The small slope approximation method regards the sea surface as a rough surface and uses the translation invariance of the mean scattering amplitude to obtain the following scattering amplitude expression:

[0028] S(k s , k i )=∫φ[k s , k i ,z(r)]exp[-j(k s -k i )·rj(q s1 +q i1 )z(r)]dr;

[0029] Among them, k s is the horizontal component of the scattered wave vector; k i is the horizontal component of the incident wave vector; φ is the function of the sea surface height; r is the horizontal coordinate vector r = (x, y); q i1 is the vertical component of the incident wave number vector; q s1 is the vertical component of the scattered wave number vector; z(r) represents the sea surface height at the coordinate r = (x, y), z(r) = z(x, y);

[0030] The integral of the vector r satisfies the following transformation:

[0031] ∫dr=∫∫dxdy;

[0032] Expand φ in an integral power series and after a series of derivations, the first term of its expansion is:

[0033]

[0034] Among them, B1(k s , k i ) According to the different polarization modes, there are the following expressions:

[0035]

[0036] Among them, N = (0, 0, 1) is the unit normal vector of the horizontal plane; the first letter of polarization represents the receiving polarization mode, and the second letter represents the transmitting polarization mode.

[0037] Preferably, the function φ0 is substituted into s(k s , k i ) expression, and adding the amplitude factor T(R) of the cone wave, the scattering amplitude expression of the first-order small slope approximation is obtained:

[0038]

[0039] For sea surface backscattering, consider the far-field scattering amplitude S far (k s , k i ), which is defined as:

[0040]

[0041] The far-field scattering amplitude is determined by the near-field scattering amplitude at a distance The asymptotic field at is:

[0042]

[0043] in, The factor is due to the fact that in S1(k s , k i ) is corrected by normalizing the incident wave and scattered wave used in the derivation of ) relative to the vertical energy flux.

[0044] Preferably, the scattering coefficient σ is substituted 0 The expression of the scattering coefficient of the first-order small slope approximation is as follows:

[0045]

[0046] Among them, P inc is the incident wave energy normalization factor, defined as:

[0047]

[0048] Where A represents the illuminated sea surface area; considering that the energy of the cone wave decays to 0 at the edge, x =L y =L is approximately equal to the energy integral in the square with diameter L, so:

[0049]

[0050] Under the same sea condition, the average of multiple randomly generated sea surface backscatter coefficients is taken to obtain the sea surface backscatter coefficient under the sea condition:

[0051]

[0052] The symbol <·> indicates that the calculation results of multiple sea surfaces are averaged.

[0053] Therefore, the present invention adopts the above-mentioned improved method of calculating grazing incidence sea surface backscattering using the small slope approximation method. By introducing the edge geometry attenuation function in the process of calculating sea surface backscattering using the small slope approximation method, the problem of large calculation results under grazing incidence, that is, when the ground grazing angle is <5°, is improved.

[0054] At the same time, after introducing the edge geometry attenuation function, the abnormal energy at the edge of the sea surface in the simulation calculation is eliminated, making the result more accurate, while not changing the calculation results under non-abnormal conditions.

[0055] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 It is a flow chart of an embodiment of an improved method for calculating grazing-incidence sea surface backscattering using a small slope approximation method of the present invention;

[0057] Figure 2 It is a schematic diagram of sea surface space domain and frequency domain discretization in an embodiment of an improved method for calculating grazing incidence sea surface backscattering using a small slope approximation method of the present invention;

[0058] Figure 3 It is a geometrical schematic diagram of two-dimensional sea surface electromagnetic scattering in an embodiment of an improved method for calculating grazing incidence sea surface backscattering using a small slope approximation method of the present invention;

[0059] Figure 4 It is a diagram of cone wave energy distribution and geometric height attenuation function in an improved method for calculating grazing incidence sea surface backscattering using a small slope approximation method of the present invention;

[0060] Figure 5 1 is a graph showing the calculation results of the sea surface backscattering coefficient by comparing the original method with the improved method in an embodiment of an improved method for calculating grazing incidence sea surface backscattering using a small slope approximation method of the present invention. Figure 5 (a) is a comparison chart of the sea surface backscatter coefficients of the original method and the improved method for level 1 sea conditions; Figure 5 (b) is a comparison chart of the sea surface backscatter coefficients of the original method and the improved method for level 2 sea conditions; Figure 5(c) is a comparison chart of the sea surface backscatter coefficients of the original method and the improved method for level 3 sea conditions; Figure 5 (d) is a comparison chart of the sea surface backscatter coefficients of the original method and the improved method for level 4 sea conditions; Figure 5 (e) is a comparison chart of the sea surface backscatter coefficients of the original method and the improved method for level 5 sea conditions. DETAILED DESCRIPTION

[0061] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0062] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0063] Embodiment 1

[0064] like Figure 1 As shown, the present invention provides an improved method for calculating grazing incidence sea surface backscattering using a small slope approximation method, comprising the following steps:

[0065] Step S1, determining the wind speed of each sea state and calculating the dielectric constant of seawater;

[0066] Step S2: Generate sea surface geometry using a linear filtering method based on sea wave spectrum according to the determined wind speed;

[0067] Step S3, introducing a conical incident wave;

[0068] Step S4, introducing edge geometry attenuation function;

[0069] Step S5: Use the small slope approximation method to approximate the integral formula to calculate the sea surface backscatter.

[0070] In step S1, the X-band sea surface backscatter is calculated, and the average wind speed of sea conditions of levels 1-5 is determined according to the international standard sea condition level and wind force level and the corresponding wave height relationship. Level 1 is 0.9 m / s, level 2 is 2.45 m / s, level 3 is 5.05 m / s, level 4 is 8.7 m / s, and level 5 is 12.3 m / s. Under the conditions of average seawater temperature T = 15°C, average salinity S = 35‰, and irradiation frequency f = 10 GHz, the seawater dielectric constant is calculated according to the double Debye model as ε = 53.4770-j38.6646, where j represents an imaginary number.

[0071] In step S2, the Apel wave spectrum is selected to generate the sea surface geometry, and its two-dimensional directional spectrum W Apel (K,φ) is as follows:

[0072]

[0073] Among them, a1 = 0.00195, which is a constant; K is the spatial wave number of the wave; U 10 is the wind speed at a height of 10m above the sea surface; g0 is the acceleration due to gravity; φ is the direction angle; φ m is the wind direction angle; K P is the main wave number, that is, the wave number corresponding to the peak position; D(K, φ) is the directional expansion function, which is specifically:

[0074]

[0075] To generate the sea surface geometry using the linear filtering method, we first need to discretize the sea surface geometry space and frequency domain space symmetrically about the coordinate origin. x ×L y The sea surface, the discrete numbers in the x and y directions are M and N respectively (M and N must be odd numbers, take M = N = 17501, then the lengths in the two directions are equal, that is, L x =L y =L), such as Figure 2 shown.

[0076] The space discretization is:

[0077] dx=L x / (M-1);

[0078] dy=L y / (N-1);

[0079] x m =mdx;

[0080] y n =ndy;

[0081] In order to ensure the simulation accuracy, the spatial discrete interval is dx=dy=λ / 8, where λ is the wavelength of the incident wave.

[0082] The frequency domain discretization is:

[0083]

[0084] K x，m =mdK x ;

[0085] K y，n =ndK y ;

[0086] The sea surface height function can be expressed as:

[0087] z(x,y,t)=∑∑A(K,t)exp(jK·r);

[0088]

[0089] Among them, the vector wave number K is defined as:

[0090] K=(K,φ)=(K x , K y );

[0091] K x =Kcosφ;

[0092] K y =Kcosφ;

[0093] Where G(K) is a two-dimensional complex Gaussian random number sequence with a mean of 0 and a variance of 1. G*(-K) is the reverse conjugate of G(K). t is time. For the study of the stealth performance of UAVs under the background of sea clutter, the sea surface can be regarded as static at each moment, that is, t = 0. A(K, t) has the following conjugate symmetry properties to ensure that the sea surface height after inverse Fourier transform is a real number.

[0094] A(K x , K y )=A * (-K x , -K y );

[0095] A(K x , -K y )=A * (-K x , K y );

[0096] Since the generated frequency domain matrix contains negative frequency parts, the negative frequencies need to be moved to positive frequencies to use the inverse fast Fourier transform, that is, the two-dimensional matrix A(K, t) is reconstructed as follows:

[0097]

[0098] Compare to the MATLAB standard two-dimensional inverse Fourier transform:

[0099]

[0100] Then the sea surface height function can be expressed by two-dimensional inverse Fourier transform as:

[0101] z(x, y, t) = F -1 (A(K, t))MN;

[0102] The sea surface geometry can be obtained by calculating the above formula. For a static sea surface, take t=0 and obtain the sea surface geometry z(x, y).

[0103] Electromagnetic scattering calculation is performed based on the sea surface geometry z(x, y), assuming that a plane wave is incident on the two-dimensional rough sea surface z(x, y), θ i and θ s are the incident angle and scattering angle, respectively, i and φ s are the incident wave azimuth and the scattered wave azimuth, respectively. The geometric relationship is as follows: Figure 3 shown.

[0104] The incident wave number vector and the scattered wave number vector are:

[0105]

[0106] The horizontal components of the incident and scattered wave number vectors are:

[0107]

[0108] The perpendicular components of the incident and scattered wave number vectors are:

[0109] q i1 =K cosθ i ;

[0110] q s1 =K cosθ s ;

[0111] The vertical components of the incident wave number vector and the scattered wave number vector in the medium are:

[0112]

[0113] Where ε is the dielectric constant of the medium and K is the wave number of the irradiated electromagnetic wave.

[0114] In order to eliminate the sudden change of edge current, a conical incident wave is introduced in step S3. At the space R = (x, y, z), the conical incident field E i (R) is expressed as:

[0115] E i (R) = T(R)exp(-jk i ·R);

[0116] T(R)=exp[-j(k i ·R)w]exp(-t x -t y );

[0117]

[0118] Among them, k i is the incident wave vector; θ i is the incident angle; φi is the incident wave azimuth; g c is the cone control parameter, and its commonly used value is:

[0119]

[0120] In order to eliminate the abnormal energy of the edge under grazing incidence, the edge geometry attenuation function F is introduced in step S4. z (x, y) is as follows:

[0121]

[0122] Among them, g z As the control parameter, g z =L / 2.3.

[0123] In fact, due to the incident cone wave, the scattered energy at the edge of the sea surface tends to 0, that is, the geometry of the edge of the sea surface contributes little to the calculation of the scattering coefficient. Therefore, although the geometric height attenuation changes the geometry of the sea surface, it has no effect on the scattering of the energy center. The cone wave energy distribution and geometric height attenuation function are as follows: Figure 4 shown.

[0124] The energy distribution of the conical incident wave in the z=0 plane is:

[0125]

[0126] The geometric height attenuation function hardly changes the geometric height within the energy center, but attenuates the height to 0 near the edge. The actual sea surface geometry for electromagnetic scattering calculation is as follows:

[0127] z′(x, y)=F z (x, y)z(x, y).

[0128] In step S5, the electromagnetic scattering calculation is performed on the sea surface geometry z′(x, y) after edge geometry attenuation using a small slope approximation method. The small slope approximation method regards the sea surface as a rough surface and uses the translation invariance of the mean scattering amplitude to obtain the following scattering amplitude expression:

[0129] S(k s , k i )=∫φ[k s , k i ,z(r)]exp[-j(k s -k i )·rj(q s1 +q i1 )z(r)]dr;

[0130] Among them, k s is the horizontal component of the scattered wave vector; ki is the horizontal component of the incident wave vector; φ is the function of the sea surface height; r is the horizontal coordinate vector r = (x, y); q i1 is the vertical component of the incident wave number vector; q s1 is the vertical component of the scattered wave number vector; z(r) represents the sea surface height at the coordinate r = (x, y), z(r) = z(x, y);

[0131] The integral of the vector r satisfies the following transformation:

[0132] ∫dr=∫∫dxdy;

[0133] Expand φ in an integral power series and after a series of derivations, the first term of its expansion is:

[0134]

[0135] Among them, B1(k s , k i ) According to the different polarization modes, there are the following expressions:

[0136]

[0137] Among them, N = (0, 0, 1) is the unit normal vector of the horizontal plane; the first letter of polarization represents the receiving polarization mode, and the second letter represents the transmitting polarization mode.

[0138] Substitute the function φ0 into S(k s , k i ) expression, and adding the amplitude factor T(R) of the cone wave, the scattering amplitude expression of the first-order small slope approximation is obtained:

[0139]

[0140] For sea surface backscattering, consider the far-field scattering amplitude S far (k s , k i ), which is defined as:

[0141]

[0142] The far-field scattering amplitude is determined by the near-field scattering amplitude at a distance The asymptotic field at is:

[0143]

[0144] in, The factor is due to the fact that in S1(k s , k i ) is corrected by normalizing the incident wave and scattered wave used in the derivation of ) relative to the vertical energy flux.

[0145] Preferably, the scattering coefficient σ is substituted 0 The expression of the scattering coefficient of the first-order small slope approximation is as follows:

[0146]

[0147] Among them, P inc is the incident wave energy normalization factor, defined as:

[0148]

[0149] Where A represents the illuminated sea surface area; considering that the energy of the cone wave decays to 0 at the edge, x =L y =L is approximately equal to the energy integral in the square with diameter L, so:

[0150]

[0151] Under the same sea condition, the average of multiple randomly generated sea surface backscatter coefficients is taken to obtain the sea surface backscatter coefficient under the sea condition:

[0152]

[0153] The symbol <·> indicates that the calculation results of multiple sea surfaces are averaged.

[0154] For X-band, sea conditions of 1 to 5, and a ground-grazing angle range of 1 to 10°, the calculation results of the sea surface backscatter coefficient by the original method and the improved method are as follows: Figure 5 shown.

[0155] From the comparison of the calculation results, it can be seen that under sea conditions of level 1 to 2, the improved method does not change the calculation results, but for sea conditions of level 3 to 5 under grazing incidence, that is, when the grazing angle is <5°, the problem of the calculation results being too large is improved.

[0156] Therefore, the present invention adopts the above-mentioned small slope approximation method to calculate the improved method of grazing incidence sea surface backscattering. By applying the edge geometry attenuation function, the edge geometry height is attenuated to 0 to avoid the height fluctuation of the sea surface edge approaching the central axis of the incident wave energy, thereby improving the problem of large calculation results under grazing incidence and making the calculation results more accurate.

[0157] It is worth noting that the contents not elaborated in detail in the present invention are all prior art and are well known to those skilled in the art.

[0158] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. An improved method for calculating grazing incidence sea surface backscattering using a small slope approximation method, characterized in that: The following steps are involved: Step S1, determining the wind speed of each sea state and calculating the dielectric constant of seawater; Step S2: Generate sea surface geometry using a linear filtering method based on sea wave spectrum according to the determined wind speed; Step S3, introducing a conical incident wave; Step S4, introducing edge geometry attenuation function; Step S5: Use the small slope approximation method to approximate the integral formula to calculate the sea surface backscatter.

2. The improved method for calculating grazing incidence sea surface backscattering using a small slope approximation method according to claim 1, characterized in that: In step S1, the X-band sea surface backscatter is calculated, and the average wind speed of sea conditions of levels 1-5 is determined according to the international standard sea condition level and wind force level and the corresponding wave height relationship. Level 1 is 0.9 m / s, level 2 is 2.45 m / s, level 3 is 5.05 m / s, level 4 is 8.7 m / s, and level 5 is 12.3 m / s. Under the conditions of average seawater temperature T = 15°C, average salinity S = 35‰, and irradiation frequency f = 10 GHz, the seawater dielectric constant is calculated according to the double Debye model as ε = 53.4770-j38.6646, where j represents an imaginary number.

3. The improved method for calculating grazing incidence sea surface backscattering using a small slope approximation method according to claim 2, characterized in that: In step S2, the Apel wave spectrum is selected to generate the sea surface geometry, and its two-dimensional directional spectrum W Apel (K,φ) is as follows: Among them, a1 = 0.00195, which is a constant; K is the spatial wave number of the wave; U 10 is the wind speed at a height of 10m above the sea surface; g0 is the acceleration due to gravity; φ is the direction angle; φ m is the wind direction angle; K P is the main wave number, that is, the wave number corresponding to the peak position; D(K, φ) is the directional expansion function, which is specifically:

4. The improved method for calculating grazing incidence sea surface backscattering using a small slope approximation method according to claim 3, characterized in that: In step S3, a conical incident wave is introduced. At the space R = (x, y, z), the conical incident field E i (R) is expressed as: E i (R)=T(R)exp(-jk i ·R); T(R)=exp[-j(k i ·R)w]exp(-t x -t y ); Among them, k i is the horizontal component of the incident wave vector; θ i is the incident angle; φ i is the incident wave azimuth; g c is the cone control parameter, specifically: Wherein, L represents the side length of the simulated sea surface, and the simulated sea surface is a square.

5. The improved method for calculating grazing incidence sea surface backscattering using a small slope approximation method according to claim 4, characterized in that: In step S4, the edge geometry attenuation function F is introduced z (x, y) is as follows: Among them, g z As the control parameter, g z =L / 2.3; The actual sea surface geometry for electromagnetic scattering calculation is as follows: z′(x,y)=F z (x,y)z(x,y)。 6. The improved method for calculating grazing incidence sea surface backscattering using a small slope approximation method according to claim 5, characterized in that: In step S5, the electromagnetic scattering calculation is performed on the sea surface geometry z′(x, y) after edge geometry attenuation using a small slope approximation method. The small slope approximation method regards the sea surface as a rough surface and uses the translation invariance of the mean scattering amplitude to obtain the following scattering amplitude expression: S(k s ,k i )=∫φ[k s ,k i ,z(r)]exp[-j(k s -k i )·r-j(q s1 +q i1 )z(r)]dr; Among them, k s is the horizontal component of the scattered wave vector; k i is the horizontal component of the incident wave vector; φ is the function of the sea surface height; r is the horizontal coordinate vector, r = (x, y); q i1 is the vertical component of the incident wave number vector; q s1 is the vertical component of the scattered wave number vector; z(r) represents the sea surface height at the coordinate r = (x, y), z(r) = z(x, y); The integral of the vector r satisfies the following transformation: ∫dr=∫∫dxdy; Expand φ in an integral power series and after a series of derivations, the first term of its expansion is: Among them, B1(k s , k i ) According to the different polarization modes, there are the following expressions: Among them, N = (0, 0, 1) is the unit normal vector of the horizontal plane; the first letter of polarization represents the receiving polarization mode, and the second letter represents the transmitting polarization mode.

7. The improved method for calculating grazing incidence sea surface backscattering using a small slope approximation method according to claim 6, characterized in that: Substitute the function φ0 into S(k s , k i ) expression, and adding the amplitude factor T(R) of the cone wave, the scattering amplitude expression of the first-order small slope approximation is obtained: For sea surface backscattering, consider the far-field scattering amplitude S far (k s , k i ), which is defined as: The far-field scattering amplitude is determined by the near-field scattering amplitude at a distance The asymptotic field at is: in, The factor is due to the fact that in S1(k s , k i ) is corrected by normalizing the incident wave and scattered wave used in the derivation of ) relative to the vertical energy flux.

8. The improved method for calculating grazing incidence sea surface backscattering using a small slope approximation method according to claim 7, characterized in that: Substitute the scattering coefficient σ 0 The expression of the scattering coefficient of the first-order small slope approximation is as follows: Among them, P inc is the incident wave energy normalization factor, defined as: Where A represents the illuminated sea surface area; considering that the energy of the cone wave decays to 0 at the edge, x =L y =L is approximately equal to the energy integral in the square with diameter L, so: Under the same sea condition, the backscatter coefficients of multiple randomly generated sea surfaces are averaged to obtain the sea surface backscatter coefficient under the sea condition: The symbol <·> indicates that the calculation results of multiple sea surfaces are averaged.

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