A variable-beam SAR region of interest sea surface imaging simulation method

Abstract

The application discloses a simulation method for imaging sea surface in a region of interest of variable-beam SAR, and belongs to the technical field of radar signal simulation processing. In order to solve the problem of improving the fidelity of echo signal simulation, the application comprises the following steps: constructing a sea surface movement model of a coastal zone; constructing a Kirchhoff mirror reflection model; constructing a Bragg resonance scattering model; performing echo simulation and simulation of the sea surface of the variable-beam SAR, including updating the space-varying scattering grid by using the sea surface movement model of the coastal zone and updating the instantaneous sea surface movement state, calculating the backscattering intensity of each scattering facet in the time domain by using the Kirchhoff mirror reflection model and the Bragg resonance scattering model, then calculating the space-varying azimuth two-way pattern at each distance unit of the scattering facet at the same azimuth position, weighting the echo of each scattering facet, and then traversing the non-uniform sampling time to obtain an echo matrix of the variable-beam high-resolution wide-width SAR. The application can significantly improve the fidelity of echo signal simulation.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of radar signal simulation processing, and particularly relates to a variable-beam SAR interested region sea surface imaging simulation method. BACKGROUND

[0002] As a high two-dimensional resolution and active microwave sensor, space-borne synthetic aperture radar (SAR) has unique advantages in coastal zone remote sensing. Compared with land-based fixed monitoring equipment and sea-based buoy platforms, space-borne SAR has a larger coverage range. Space-borne SAR generally operates in a near-polar orbit, and can realize global coastal zone coverage by relying on the movement of the platform along the orbit. However, land-based and buoy platforms can only observe and record a region, and increasing the observation range inevitably requires increasing the number of sensors, which is costly. In the space-borne platform, compared with passive microwave radiometers, visible light and hyperspectral ocean color remote sensors, space-borne SARs usually operate in the L to X band, have the ability to penetrate clouds, are not affected by the weather above, and can continuously perform remote sensing of the coastal zone region at all times and in all weather, avoiding data gaps and missing. Compared with other active sensors such as microwave altimeters and microwave scatterometers, space-borne SARs have two-dimensional imaging capability in the azimuth and range directions, and compared with other active microwave sensors that only have one-dimensional observation capability, the information obtained by a single pass is richer.

[0003] Coastal zone disasters spread quickly and have a wide range of influence, and require flexible high-resolution wide swath imaging capabilities for timely monitoring. The coastal zone has a wide width and is not parallel to the satellite orbit, but the existing space-borne SAR high-resolution wide swath imaging modes are mostly based on normal side-looking strip configurations, and the imaging strips are parallel to the satellite orbit. In the case of constant orbital height, the effective observation range of the space-borne SAR depends on the downward viewing angle. Since the coastal zone extends from the coastline to both the land and the sea, the width of the sea side is more than 300 km, and the width of the land side can reach 100 km, and the strike of the coastal zone is often not parallel to the satellite orbit, so normal side-looking strip high-resolution wide swath SAR cannot cover the entire coastal zone region in a single pass, and can only be based on time-interrupted data from multiple passes to stitch the images. Variable-beam strip high-resolution wide swath SAR can flexibly adjust the azimuth and elevation pointing of the beam, so that the imaging strips are no longer parallel to the satellite orbit, but match the target interested region, and fully utilize the effective downward viewing angle range of the satellite according to the actual observation requirements. While avoiding time discontinuity caused by repeated orbit observations, the effective observation number of the interested region can also be increased. In addition, the flexible imaging geometry of the variable-beam strip high-resolution wide swath SAR makes the allocation of the effective width more reasonable, and can increase the information acquisition tolerance of the interested region. Therefore, variable-beam high-resolution wide swath SAR has important research significance in the field of sea surface monitoring of interested regions.

[0004] The imaging principle of spaceborne SAR for various ocean phenomena is mainly based on the change of sea surface roughness caused by sea surface movement. Compared with a static sea surface, a rough sea surface can reflect part of the incident radar wave energy back to the SAR receiver, thereby showing corresponding light and dark changes on the SAR image. In addition to the SAR image amplitude change caused by the change of sea surface roughness, the spaceborne SAR radar echo irradiated to the moving sea surface contains the Doppler shift caused by the sea water movement, and by extracting the Doppler phase information in the SAR image, the movement parameters of the sea surface can be inverted, and the movement state of the sea surface can be quantitatively analyzed. Compared with a microwave scatterometer, the spaceborne SAR image has high-resolution two-dimensional imaging capability, and the SAR image of the ocean surface is comprehensively affected by various factors such as the ocean surface wind field, ocean current, ocean front, climate front, etc. It is necessary to analyze and model the imaging mechanism and imaging parameters of various factors in the SAR image, and study the space-variant and time-variant phenomena between the amplitude and phase of each factor component in the SAR image, so as to identify, classify and parameterize various ocean phenomena.

[0005] Sea surface echo modeling is a key technology for analyzing the imaging performance of spaceborne SAR in the coastal zone. The existing spaceborne SAR echo model can be divided into two key links: dynamic sea surface modeling, the beam domain direction spectrum on the sea surface corresponds to the height field and normal direction of each scattering facet; radar backscattering model, according to the microwave scattering mechanism, an empirical model is established to analyze the backscattering components under different scattering mechanisms, such as specular reflection component, Bragg resonance scattering component, broken wave scattering component, high-order reflection component, etc. Finally, the backscattering intensity of each sea surface scattering facet is mapped to the slant range coordinate system to generate the corresponding radar echo. Under the variable-beam strip SAR observation configuration, the antenna beam is not parallel to the strip region of the satellite orbit, and the facet element corresponding to the distance scattering grid is severely distorted with the azimuth position, and there is non-uniform sampling in the azimuth direction, which is a new problem that does not exist under the forward-looking imaging geometry. SUMMARY

[0006] The problem to be solved by the present application is based on the existing sea surface echo simulation method under the variable-beam strip SAR observation configuration, the distance scattering grid facet element is severely distorted with the azimuth position, and the azimuth direction is non-uniformly sampled. In order to improve the fidelity of echo signal simulation, a variable-beam SAR interested region sea surface imaging simulation method is proposed.

[0007] To achieve the above purpose, the technical scheme is as follows:

[0008] A variable-beam SAR interested region sea surface imaging simulation method, comprising the following steps:

[0009] S1. Construct a coastal zone sea surface movement model, including a physical ocean equation and an Elfouhaily wave spectrum;

[0010] S2. Constructing the Kirchhoff specular reflection model, including constructing the target scattering electric field, the scattering facet center scattering intensity, and the scattering facet mirror scattering component;

[0011] S3. Constructing the Bragg resonance scattering model, including constructing the Bragg scattering component of the sea surface facet, establishing a numerical model for the sea surface height spectrum, and calculating the instantaneous slant range of the scattering facet;

[0012] S4. Based on the models constructed in steps S1-S3, performing echo simulation and modeling for the variable-beam SAR sea surface, including updating the space-varying scattering grid using the coastal sea surface motion model obtained in step S1 and updating the instantaneous sea surface motion state, calculating the backscattering intensity of each scattering facet in the time domain using the Kirchhoff specular reflection model obtained in step S2 and the Bragg resonance scattering model obtained in step S3, then calculating the space-varying azimuthal two-way pattern at each distance unit for the scattering facets at the same azimuthal position, weighting the echoes of the scattering facets, and then traversing the non-uniform sampling time to obtain the echo matrix of the variable-beam high-resolution wide-swath SAR.

[0013] Further, the specific implementation method of step S1 includes the following steps:

[0014] S1.1. Based on the one-dimensional approximate solution of the physical ocean equation, assuming that the coordinates of a point on the sea surface are x=(x, y) and the height is z=0, x is the x-axis coordinate point, y is the y-axis coordinate point, when a single-frequency sea wave passes through a point on the sea surface, the expression of the vertical motion vector ξ(x, t) and the horizontal motion vector D(x, t) of the point on the sea surface is:

[0015]

[0016] where φ i is the initial phase of the i-th sea wave, k i is the wave vector of the i-th sea wave, k i is the wave number, ω i is the frequency of the i-th sea wave, t is time, A i is the amplitude of the i-th sea wave, and N is the total number of sea waves.

[0017] k i =||k i || = 2π / λ

[0018] where λ is the wavelength.

[0019] S1.2. Setting the open boundary sea surface as a linear superposition of a finite number of plane waves, where A i and k i are independent of the sea surface position, and φ iIf the sea surface is uniformly distributed in the interval [0, 2π), the mean value of the vertical direction of the motion vector of the point on the sea surface is <ζ(x, t)> = 0, and the variance of the vertical direction of the motion vector of the point on the sea surface is

[0020] S1.3. Based on the fact that the sea surface wave is a superposition of infinite plane waves, the variance of the vertical direction of the motion vector of the point on the sea surface is transformed into an integral form, and the expression is:

[0021]

[0022] Wherein, Ψ(k) and Ψ(k, θ) are the sea surface directional spectrum in the Cartesian coordinate system and the sea surface directional spectrum in the polar coordinate system respectively, and θ is the propagation direction of the beam;

[0023] S1.4. The sea surface directional spectrum in the polar coordinate system is divided into two components, including the sea wave spectrum S(k) and the angular spread function Φ(k, θ), and the expression is:

[0024]

[0025] Then the sea wave spectrum is defined as the Elfouhaily sea wave spectrum, and the expression is:

[0026] S(k) = k -3 [B l +B h ] (4)

[0027] Wherein, B l and B h represent the long sea wave curvature spectrum and the short sea wave curvature spectrum respectively;

[0028] S1.5. B l is defined as follows:

[0029]

[0030] Wherein, c p is the sea wave phase velocity of the spectral peak, c p = c(k p ), k p is the spectral peak wave number, α p is the long wave equalization parameter, F p is the long wave function, and c is the phase velocity corresponding to the current beam;

[0031]

[0032] Wherein, Ω is a dimensionless parameter, used to adjust the decay rate of the exponential term, Ω = U 10 / c p , U 10 is the 10m high wind speed of the sea surface, and LPM , J p are the PM spectrum and the peak enhancement function of JONSWAP, respectively;

[0033] L PM , J p are defined as follows:

[0034]

[0035] where γ is the peak enhancement factor, Γ is the Gaussian-type weight function, and σ is the spectral width parameter;

[0036] S1.6.B h are defined as follows:

[0037]

[0038] where c m is the phase speed corresponding to the minimum wave number, F m and α m are the first and second dimensionless parameters, respectively;

[0039]

[0040] where u * is the friction velocity of the sea surface;

[0041] S1.7. The angular spreading function Φ(k, θ) is defined as follows:

[0042]

[0043] where Δ(k) is the upwind-crosswind ratio, which is used to describe the directivity of sea waves of different wavelengths;

[0044] Δ(k) is defined as:

[0045] Δ(k) = tanh{a0 + a p (c / c p ) 2.5 + a m (c m / c) 2.5} (12)

[0046] where a0 is the first constant, a p , a m are parameters corresponding to U 10 / c p , u * / c m , respectively.

[0047] Further, the specific implementation method of step S2 includes the following steps:

[0048] S2.1. Set the applicable conditions of the Kirchhoff's mirror reflection model as:

[0049] (k0r c ) 1 / 3 cosθ>>1 (13)

[0050] wherein, r c is the radius of the curved surface;

[0051] S2.2. Set the expression of the target scattering electric field E s constructed based on the Kirchhoff's mirror reflection model as:

[0052]

[0053] wherein, K s is the central scattering intensity of the scattering surface element, p is the distribution function, k s is the scattering signal wave number of the scattering surface element, is the mirror scattering component of the scattering surface element, S is the integral of the sea surface to the scattering surface element, and j is the imaginary unit;

[0054] The expression of p is as follows:

[0055]

[0056] wherein, × represents the vector cross product, E is the electric field in the propagation medium, is the surface normal unit vector of the scattering surface element, H is the magnetic field in the propagation medium, and η is the medium dielectric constant;

[0057] The expression of K s is as follows:

[0058]

[0059] wherein, R s is the distance between the center of the irradiation area and the incident point;

[0060] The expression of p is as follows:

[0061]

[0062] wherein, φ s is the azimuth angle, θ s is the elevation angle, represents the vector in three directions of the rectangular coordinate system;

[0063] S2.3. Assuming that the incident wave is a spherical wave, the expression of the incident field intensity E inc is as follows:

[0064]

[0065] where R inc is the distance from the illumination source to the scattering center, is the unit vector of the polarization direction of the incident wave, is the unit vector of the incident direction;

[0066]

[0067] The normalized scattering intensity is given by:

[0068]

[0069] where pq represents the polarization mode of the incident and scattered waves, and <·> denotes the average.

[0070] Further, the specific implementation method of step S3 includes the following steps:

[0071] S3.1. Constructing the Bragg scattering component of the sea surface facet according to the Bragg resonance scattering model The expression is:

[0072]

[0073] where Ψ(k) is the sea surface height spectrum, k0 is the radar wave number (2.1 appears), k b is the Bragg wave vector, s p is the tilt angle parallel to the viewing direction, s n is the tilt angle perpendicular to the viewing direction, θ l is the equivalent incident angle at the facet, and θ l = arccos [cos(θ-s p )coss n ], b pp is the complex scattering coefficient of horizontal polarization, and b qq is the complex scattering coefficient of vertical polarization;

[0074] The amplitude and direction are defined as follows, respectively:

[0075]

[0076] where φ0 is the radar azimuth angle, k b is the Bragg wave number, and φ b is the Bragg beam direction;

[0077] Then, the equivalent scattering coefficient correction of the Bragg scattering component of the sea surface facet relative to the radar is obtained, and the expression is:

[0078]

[0079] where H0 is the height of the radar relative to sea level, and ζ is the height of the facet;

[0080] S3.2. A numerical model is established for the sea surface height spectrum, and the expression of the omnidirectional spectrum S(k) is as follows:

[0081]

[0082] where P L is a function of wind speed, U n is the sea surface reference wind speed, and W H is a high-frequency correction function;

[0083] The low wave number roll-off and the peak of JONSWAP are modeled, and the expression is as follows:

[0084]

[0085] where, g is the acceleration of gravity;

[0086] W H The Bragg wave is modeled, and the expression is as follows:

[0087]

[0088] where k6=280 rad / m, k7=75 rad / m, k8=1300 rad / m, and k9=8885 rad / m;

[0089] U n =1 m / s, and β is the corresponding wind power index, and the expression is as follows:

[0090]

[0091] where k1=183 rad / m, k2=3333 rad / m, k3=33 rad / m, k4=140 rad / m, and k5=220 rad / m;

[0092] The diffusion function is obtained as follows:

[0093]

[0094] where δ is a distribution width control parameter;

[0095]

[0096] where c1=400 rad / m, U n =1 m / s, and k n =1 rad / m.

[0097] Further, the specific implementation method of step S4 includes the following steps:

[0098] S4.1. Input radar and sea surface simulation parameters:

[0099] According to the simulation scene, set the radar parameters and sea surface environment parameters, the radar parameters include center frequency, pulse width, signal bandwidth, sampling frequency, orbital height, azimuth resolution, center downward angle, variable beam strip angle, antenna type and antenna size, antenna beam width; the sea surface environment parameters include sea surface area size, wind speed and wind direction;

[0100] S4.2. Generation of range-dependent coordinate system scattering grid:

[0101] The range-dependent coordinate system is defined as a rectangular coordinate system, and the range-dependent scattering grid step is set to satisfy the Nyquist sampling theorem, and the range-dependent scattering grid point set is generated for scattering calculation and sea wave dynamic simulation;

[0102] S4.3. Initialization simulation of sea surface motion state:

[0103] According to the physical ocean equation constructed in step S1, generate time-varying sea surface according to the sea wave spectrum, generate initial sea surface state according to the Elfouhaily sea wave spectrum, and generate real-time sea surface motion state by using the Fourier superposition method;

[0104] S4.4. Update non-uniform azimuth time:

[0105] According to the antenna size, the synthetic aperture is divided into several time slices, each time slice corresponds to a position of the radar in the synthetic aperture, and the non-uniform sampling time of each azimuth is updated;

[0106] S4.5. Update of sea surface motion state:

[0107] Including intercepting the range-dependent scattering grid within the beam irradiation range, and updating the instantaneous sea surface motion state within the beam irradiation range, calculating the sea surface motion state of all observation angles in the current time slice;

[0108] S4.6. Update slant distance scattering network:

[0109] Calculate the backscattering intensity of each scattering facet in the time domain, calculate the specular scattering component and Bragg scattering component of the scattering facet according to formula (19) and formula (20), and calculate the instantaneous slant distance of the scattering facet;

[0110] S4.7. Time domain antenna two-way directional diagram weighting:

[0111] The space-variant azimuth two-way directional diagram at each distance unit of the scattering facet in the same azimuth position is calculated, whether the traversal of all scattering facets in the current beam range is completed is judged, the scattering facet echo in the current azimuth time beam irradiation range is superimposed if the judgment is yes, and step S4.4 is returned to update the non-uniform azimuth time if the judgment is no.

[0112] S4.8. A variable-beam high-resolution wide swath SAR sea surface echo matrix is generated:

[0113] The scattering facet echo in the current azimuth time beam irradiation range obtained in step S4.7 is judged whether the azimuth end point is reached, the non-uniform azimuth time is updated if the judgment is no, and the variable-beam high-resolution wide swath SAR sea surface echo matrix is output if the judgment is yes.

[0114] Further, the instantaneous slant range calculation method of the scattering facet in step S4.6 is:

[0115] Suppose that the satellite platform moves at a uniform speed in the horizontal direction and linearly relative to the observed scene, the azimuth width of the target observation region is S az , and the ground distance width is S rg . The expression of the instantaneous slant range R s (t; S) of the scattering facet is:

[0116]

[0117] Wherein, is the ground distance from the scattering point S to the satellite foot point, V is the satellite platform speed, t S is the time used for irradiation to the center of the azimuth aperture of the scattering point.

[0118] The beneficial effects of the present application are:

[0119] The variable-beam SAR sea surface imaging simulation method of the present application solves the problems of the existing sea surface echo simulation method, such as the serious distortion of the distance scattering grid facet with the azimuth position and the azimuth non-uniform sampling under the variable-beam strip SAR observation configuration. A dynamic sea surface physical model is established, a corresponding scattering intensity model is analyzed based on the sea surface echo scattering mechanism, and then a variable-beam strip SAR time-varying sea surface echo simulation method is proposed based on the variable-beam strip SAR imaging geometry and the azimuth non-uniform time slice and slant range space-variant scattering grid mapping, so as to realize the high-fidelity sea surface echo signal simulation of the region of interest.

[0120] The variable-beam SAR sea surface imaging simulation method of the application realizes matching between imaging strips and target regions of interest which are not parallel to the satellite orbit, solves the problems of serious distortion of the distance scattering grid facet with the azimuth position and non-uniform sampling in the azimuth direction under the variable-beam strip SAR observation configuration, realizes high-fidelity sea surface echo signal simulation, the simulation result is matched with the real sea surface height, and the fidelity of the echo signal simulation can be significantly improved. BRIEF DESCRIPTION OF DRAWINGS

[0121] Figure 1 For the sea surface roughness and radar echo condition;

[0122] Figure 2 For the Kirchhoff approximation (KA) scattering geometry model;

[0123] Figure 3 For the prior art strip SAR sea surface echo simulation algorithm flowchart;

[0124] Figure 4 For the variable-beam SAR sea surface echo simulation algorithm flowchart of the application;

[0125] Figure 5 For the sea surface height field, sea surface height map and sea surface scattering intensity at the azimuth center simulated by the application under the wind speed of 15 m / s and the wind vector angle of 0°, wherein (a) is the sea surface height field, (b) is the sea surface height map, and (c) is the ocean surface NRCS;

[0126] Figure 6 For the sea surface height and scattering intensity under different sea winds, wherein (a) is the sea surface height map under the 5 m / s sea wind, (b) is the sea surface scattering intensity map under the 5 m / s sea wind, (c) is the sea surface height map under the 30 m / s sea wind, and (d) is the sea surface scattering intensity map under the 30 m / s sea wind;

[0127] Figure 7 For the sea surface height and scattering intensity under different wind directions, wherein (a) is the sea surface height map under the wind vector angle of 45°, (b) is the sea surface scattering intensity map under the wind vector angle of 45°, (c) is the sea surface height map under the wind vector angle of 90°, and (d) is the sea surface scattering intensity map under the wind vector angle of 90°;

[0128] Figure 8 For the echo simulation sea wave spectrum and sea surface height map, wherein (a) is the sea wave spectrum, and (b) is the sea surface height map;

[0129] Figure 9The sea surface echo focusing imaging result map of the prior art echo simulation method based on a uniform sampling azimuth shift-invariant grid and the non-uniform time slice space-variant scattering grid echo simulation method proposed in the present application, wherein (a) is a simulation variable beam high-resolution wide swath SAR image of the prior art, (b) is a simulation variable beam high-resolution wide swath SAR image spectrum of the prior art, (c) is a simulation variable beam high-resolution wide swath SAR image of the method of the present application, and (d) is a simulation variable beam high-resolution wide swath SAR image spectrum of the method of the present application.

[0130] Figure 10 The flow chart of the variable beam SAR sea surface imaging simulation method of the present application. DETAILED DESCRIPTION

[0131] In order to make the objectives, technical solutions and advantages of the present application clearer, the present application is further described in detail below in combination with the drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application, that is, the specific embodiments described are only a part of the embodiments of the present application, but not all the specific embodiments. The components of the specific embodiments of the present application generally described and shown in the drawings can be arranged and designed in various different configurations, and the present application can also have other embodiments.

[0132] Therefore, the detailed description of the specific embodiments of the present application provided below in the drawings is not intended to limit the scope of the claimed present application, but only represents selected specific embodiments of the present application. All other specific embodiments obtained by those skilled in the art based on the specific embodiments of the present application without making creative efforts are within the scope of the present application.

[0133] In order to further understand the inventive content, characteristics and effects of the present application, the following specific embodiments are exemplified, and the drawings are used for reference Figure 1 - the drawings Figure 10 The detailed description is as follows:

[0134] Embodiment 1:

[0135] A variable beam SAR sea surface imaging simulation method, comprising the following steps:

[0136] S1. Constructing a coastal sea surface motion model, including a physical ocean equation and an Elfouhaily sea wave spectrum;

[0137] Based on the analysis and interpretation of a large number of marine SAR images, research shows that SAR backscattering is largely affected by sea surface roughness. Sea surface roughness is a physical quantity reflecting the roughness of the sea surface, and its value is not only related to the roughness of the sea surface, but also different under different radar wavelengths and incident angles, such asFigure 1 To quantitatively describe the sea surface roughness, a bisection method of Rayleigh criterion can be used. That is, if the condition h r cosθ < λ R is satisfied, the sea surface is a smooth sea surface, otherwise, it is a rough sea surface. Where, h r is the vertical height of the sea surface fluctuation.

[0138] The electromagnetic wave emitted by the satellite propagates downward, encounters the sea surface, and undergoes reflection and scattering and other physical processes. The returned electromagnetic wave carries the information of the sea surface, which is received by the radar together with noise. For a calm and windless sea surface, specular reflection is the main process of the electromagnetic wave energy returning to the radar sensor, and the sea surface can basically reflect the energy to the receiver in the nadir direction (the direction perpendicular to the sea surface, i.e., the incident angle is 0°), and the microwave signal energy of other incident angles cannot be reflected back to the receiver. However, an ideal calm sea surface is difficult to appear in the natural environment. The sea surface is affected by the sea surface wind, and with the appearance of the wind-induced surface tension wave and capillary gravity wave (collectively referred to as microscale wave), the sea surface becomes smooth and rough, which is equivalent to the generation of many small reflection surfaces with random distribution in the normal direction on the sea surface, resulting in a significant reduction of the return wave to the nadir direction, and the receiver deviating from the nadir direction also has corresponding scattering signal energy.

[0139] For a microwave remote sensor carried by a satellite platform, the inclination of the facet element of the rough sea surface compared to the horizontal plane is mainly distributed within 25°, and therefore, when analyzing the backscattering component of the microwave sensor, the specular reflection component is only important at the down-view angle of 0°-15°. When the down-view angle is greater than 15°, the main component of the return signal is the scattering component based on the roughness, and the strength of the return signal is largely dependent on the roughness of the sea surface. For a relatively calm sea surface, the sea surface fluctuation amplitude is small, and the inclination of each facet element relative to the horizontal plane changes little, which will produce a reflection effect similar to a mirror, and basically no backscattering, so it appears very dark on the SAR image; for a moderately rough sea surface, the number of facet elements that can form scattering conditions increases significantly, and a part of the radar wave energy incident to the sea surface can be scattered back to the receiver, and the backscattering energy is higher than that of a calm sea surface; and for a rough sea surface, not only the sea wave amplitude of the sea surface becomes large, but also the inclination range of each facet element becomes larger, and therefore, the backscattering energy to the radar increases. Generally, the backscattering is proportional to the sea surface roughness, and in the SAR remote sensing image, the rough surface has a larger brightness than the smooth surface for the same scattering characteristic material.

[0140] Accurate modeling of the ocean surface is a fluid dynamics problem, often involving solving nonlinear fluid dynamics equations of the physical ocean. For sea surface echo simulations of spaceborne SAR systems, the sea surface modeling accuracy typically reaches the meter level. The physical ocean equations fully account for various internal and external components. However, due to their complex time domain form and the nonlinear coupling relationship between various parameters, they are not applicable to actual engineering. In this case, linear approximate solutions of the physical ocean equations can be used to obtain an engineering-realizable sea surface motion model at the expense of a certain degree of accuracy. Under natural conditions, the energy of the sea surface is mainly concentrated in wind-induced surface waves and capillary gravity waves. Therefore, existing empirical and theoretical models mainly consider the accurate modeling of these two types of waves.

[0141] Furthermore, the specific implementation method of step S1 includes the following steps:

[0142] S1.1. Based on the one-dimensional approximate solution of the physical ocean equation, assuming that the coordinates of a point on the sea surface are x = (x, y), and the height z = 0, where x is the x-axis coordinate point and y is the y-axis coordinate point, when a single-frequency sea wave passes through the point on the sea surface, the vertical motion vector ξ(x, t) and the horizontal motion vector D(x, t) of the point on the sea surface are expressed as follows:

[0143]

[0144] Among them, φ i is the initial phase of the i-th wave, k i is the wave vector of the ith sea wave, k i is the wave number, ω i is the frequency of the ith sea wave, t is the time, A i is the amplitude of the ith sea wave, and N is the total number of sea waves;

[0145] k i =||k i ||=2π / λ

[0146] Where λ is the wavelength;

[0147] S1.2. Assume that the open boundary sea surface is a linear superposition of a finite number of plane waves, where A i With k i Independent of the sea surface position, φ i If the independent points are evenly distributed in the interval [0,2π), then the mean of the vertical motion vector of the point on the sea surface <ζ(x,t)>=0, and the variance of the vertical motion vector of the point on the sea surface is

[0148] S1.3. Based on the fact that sea surface waves are the superposition of an infinite number of plane waves, the variance of the vertical motion vector of a point on the sea surface is transformed into an integral form, expressed as:

[0149]

[0150] where Ψ(k) and Ψ(k, θ) are the sea surface directional spectrum in Cartesian coordinate system and polar coordinate system respectively, and θ is the propagation direction of the beam;

[0151] S1.4. The sea surface directional spectrum in polar coordinate system is divided into two components, including the sea wave spectrum S(k) and the angular spreading function Φ(k, θ), and the expression is:

[0152]

[0153] The main component of the radar signal scattered by the sea surface comes from the short wave region, so it is necessary to select a sea surface directional spectrum model that can accurately describe the energy of the short wave. According to the test data, the JONSWAP model is better in modeling the distribution of long waves on the sea surface under the condition of limited wind area, and the Elfouhaily model considers both the long wave region and the short wave region of the sea surface. Therefore, for the modeling of the sea surface for microwave remote sensing, the Elfouhaily model or other improved models based on Elfouhaily are usually used.

[0154] Then the sea wave spectrum is defined as the Elfouhaily sea wave spectrum, and the expression is:

[0155] S(k) = k -3 [B l +B h ] (4)

[0156] where B l and B h represent the long sea wave curvature spectrum and the short sea wave curvature spectrum respectively;

[0157] S1.5. B l is defined as follows:

[0158]

[0159] where c p is the sea wave phase velocity of the spectrum peak, c p = c(k p ), k p is the wave number of the spectrum peak, α p is the long wave equilibrium parameter, F p is the long wave function, and c is the phase velocity corresponding to the current beam;

[0160]

[0161] where Ω is a dimensionless parameter used to adjust the decay rate of the exponential term, and Ω = U 10 / cp , U 10 is the 10m height wind speed over sea surface, L PM , J p are the PM spectrum and the peak enhancement function of JONSWAP, respectively;

[0162] L PM , J p are defined as follows:

[0163]

[0164] where γ is the peak enhancement factor, Γ is the Gaussian-type weight function, and σ is the spectral width parameter;

[0165] S1.6.B h are defined as follows:

[0166]

[0167] where c m is the phase speed corresponding to the minimum wave number, F m and α m are the first and second dimensionless parameters, respectively;

[0168]

[0169] where u * is the friction velocity over sea surface;

[0170] S1.7. The angular spreading function Φ(k, θ) is defined as follows:

[0171]

[0172] where Δ(k) is the upwind-crosswind ratio, which is used to describe the directivity of sea waves with different wavelengths;

[0173] Δ(k) is defined as:

[0174] Δ(k) = tanh{a0 + a p (c / c p ) 2.5 + a m (c m / c) 2.5} (12)

[0175] where a0 is the first constant, a p , a m are the parameters corresponding to U 10 / c p , u * / c m , respectively.

[0176] S2. Constructing the Kirchhoff mirror reflection model, including constructing the target scattering electric field, the center scattering intensity of the scattering facet, and the mirror scattering component of the scattering facet;

[0177] When the curvature radius of the scatterer or scattering facet is much larger than the radar wavelength, the surface field can be represented by the tangent plane approximation at each point on the surface. The process of obtaining the scattering field according to this approximation method is called the Kirchhoff approximation (KA) or the physical optics method, as shown in Figure 2 .

[0178] Further, the specific implementation method of step S2 includes the following steps:

[0179] S2.1. Setting the applicable condition of the Kirchhoff mirror reflection model as:

[0180] (k0r c ) 1 / 3 cosθ>>1 (13)

[0181] wherein r c is the curvature radius of the surface;

[0182] S2.2. Setting the expression of the target scattering electric field E s constructed based on the Kirchhoff mirror reflection model as:

[0183]

[0184] wherein K s is the center scattering intensity of the scattering facet, p is a distribution function, k s is the scattering signal wave number of the scattering facet, is the mirror scattering component of the scattering facet, S is the integral of the sea surface to the scattering facet, and j is the imaginary unit;

[0185] The expression of p is as follows:

[0186]

[0187] wherein × represents the vector cross product, E is the electric field in the propagation medium, is the unit normal vector of the surface of the scattering facet, H is the magnetic field in the propagation medium, and η is the dielectric constant of the medium;

[0188] The expression of K s is as follows:

[0189]

[0190] wherein R s is the distance between the center of the irradiation area and the incident point;

[0191] The expression of E

[0192]

[0193] where φ s is the azimuth angle, θ s is the elevation angle, represents the vector of three directions of the rectangular coordinate system;

[0194] S2.3. Assuming that the incident wave is a spherical wave, the incident field intensity E inc The expression of E

[0195]

[0196] where R inc is the distance from the illumination source to the scattering center, is the unit vector of the polarization direction of the incident wave, is the unit vector of the incident direction;

[0197]

[0198] The expression of the normalized scattering intensity I is as follows:

[0199]

[0200] where pq represents the polarization mode of the incident and scattered waves, and <·> represents the average.

[0201] Further, due to the large amount of direct integration calculation, in the application of the actual sea surface scattering model, some approximate algorithms are generally used, among which the Stationary-Phase Approximation (SPA) and the Facet Approach (FA) method are commonly used in the calculation of the sea surface scattering model.

[0202] S3. Constructing the Bragg resonance scattering model, including constructing the Bragg scattering component of the sea surface facet, establishing a numerical model for the sea surface height spectrum, and calculating the instantaneous slant range of the scattering facet;

[0203] According to the Bragg resonance scattering model, the normalized scattering coefficient of the rough sea surface is proportional to the Bragg wave spectrum intensity of the sea surface, so the scattering intensity of each facet of the ocean surface is mainly contributed by the small-scale wave close to the radar wave scale, and the larger-scale sea surface wave makes the incident angle and the incident plane of each facet change randomly, playing a role of random modulation, so the sea surface spectrum is modeled as two scales: the small-scale wave k>k d and the large-scale wave k<k d, where k d = d k0, d is a constant less than 1. Consider a facet on the sea surface with a small tilt in the direction parallel to the radar look direction;

[0204] Further, the specific implementation method of step S3 comprises the following steps:

[0205] S3.1. Constructing the Bragg scattering component of the sea surface facet according to the Bragg resonance scattering model The expression is:

[0206]

[0207] where Ψ(k) is the sea surface height spectrum, k0 is the radar wave number (2.1 has appeared), k b is the Bragg wave vector, s p is the tilt angle parallel to the look direction, s n is the tilt angle perpendicular to the look direction, θ l is the equivalent incident angle at the facet and θ l = arccos [cos(θ-s p )coss n ], b pp is the complex scattering coefficient of horizontal polarization, b qq is the complex scattering coefficient of vertical polarization;

[0208] The amplitude and direction are defined as follows, respectively:

[0209]

[0210] where φ0 is the radar azimuth angle, k b is the Bragg wave number, and φ b is the Bragg beam direction;

[0211] Then, the equivalent scattering coefficient correction of the Bragg scattering component of the sea surface facet relative to the radar is obtained, and the expression is:

[0212]

[0213] where H0 is the height of the radar relative to the sea level, and ζ is the height of the facet;

[0214] S3.2. Numerical model is established for the sea surface height spectrum, and the expression of the omnidirectional spectrum S(k) is as follows:

[0215]

[0216] where P L is a function of wind speed, U n is the reference wind speed of the sea surface, and W H is a high-frequency correction function;

[0217] The low wave number roll-off and the peak of JONSWAP are modeled, and the expression is as follows:

[0218]

[0219] wherein, g is the acceleration of gravity;

[0220] W H The Bragg wave is modeled, and the expression is as follows:

[0221]

[0222] wherein, k6=280 rad / m, k7=75 rad / m, k8=1300 rad / m, k9=8885 rad / m;

[0223] U n =1 m / s, and β is the corresponding wind force index, and the expression is as follows:

[0224]

[0225] wherein, k1=183 rad / m, k2=3333 rad / m, k3=33 rad / m, k4=140 rad / m, and k5=220 rad / m;

[0226] The diffusion function is obtained as follows:

[0227]

[0228] wherein, δ is a distribution width control parameter;

[0229]

[0230] wherein, c1=400 rad / m, U n =1 m / s, and k n =1 rad / m.

[0231] S4. On the basis of the model constructed in steps S1-S3, echo simulation of the variable-beam SAR sea surface is performed, including updating the space-varying scattering grid by using the coastal sea surface motion model obtained in step S1 and updating the instantaneous sea surface motion state, calculating the backscattering intensity of each scattering facet in the time domain by using the Kirchhoff mirror reflection model obtained in step S2 and the Bragg resonance scattering model obtained in step S3, then calculating the space-varying azimuth two-way pattern at each distance unit of the scattering facet at the same azimuth position, weighting the echoes of each scattering facet, and then traversing the non-uniform sampling time to obtain the echo matrix of the variable-beam high-resolution wide-width SAR;

[0232] Due to the complex and fast-changing sea surface, the force source of the sea surface change is complex, and is related to the terrain, weather and other aspects of the sea area, and the microwave scattering characteristics of the sea surface are complex. The existing sea surface scattering intensity model is a numerical approximation under a specific scenario, and there is no scattering model that can completely describe all the characteristics of sea surface scattering. The existing microwave scattering model is mainly aimed at the normal side view strip or scanning SAR. In the synthetic aperture time, the radar incidence angle of each azimuth direction is unchanged. Therefore, by modeling the height field of the sea surface, according to the sea surface height field and the radar incidence angle, the radar polarization mode, the sea surface microwave scattering model is input, the normalized radar scattering cross section of each grid on the sea surface is obtained, and the slant range of each point to the radar is combined to simulate the SAR echo. The algorithm flow is as shown in Figure 3

[0233] In the imaging mode of variable-beam strip high-resolution wide swath SAR, the incidence angle changes along the azimuth direction, the slant range has a high-order motion component of azimuth-range coupling, and the radar echo has a non-equidistant azimuth slow time in the variable PRI mode. The traditional simulation method is invalid, and it is necessary to analyze the space variation and signal non-uniform sampling of the scattering facet in the new imaging mode to realize accurate modeling. The flow of the variable-beam high-resolution wide swath SAR sea surface echo simulation method is as shown in Figure 4 The existing strip SAR echo simulation method is based on the Fourier transform relationship between the wave number domain wave spectrum and the spatial domain sea surface motion state of the uniform scattering grid. The beam coverage range of each azimuth time is the same, and the number of observable scattering points at each time is constant. Based on the fast Fourier algorithm and the parallel computing, the dynamic sea surface in the SAR synthetic aperture time is obtained. The backscattering intensity of each distance unit facet is directly calculated in the range compression domain. Then, the first antenna pattern is superimposed in the azimuth Doppler domain, and the strip SAR echo matrix of the sea surface is quickly generated. In the variable-beam high-resolution wide swath mode, the distance center of the radar beam is always away from the subsatellite point, and the interested region not parallel to the orbital direction can be observed continuously in space and time. Due to the non-uniform time-domain sampling caused by variable PRI and the azimuth space variation of the beam footprint caused by variable-beam pointing, the existing strip SAR fast simulation method is not applicable. It is necessary to update the space-varying scattering grid at each azimuth sampling time, and calculate the backscattering intensity of each scattering facet in the time domain. Then, the space-varying azimuth two-way pattern at each distance unit of the scattering facet at the same azimuth position is calculated, the scattering facet echo is weighted, and then the non-uniform sampling time is traversed to obtain the echo matrix of the variable-beam high-resolution wide swath SAR.

[0234] Further, the specific implementation method of step S4 includes the following steps:

[0235] S4.1. Input radar and sea surface simulation parameters:

[0236] ​According to the simulation scene, the radar parameter and the sea surface environment parameter are set, the radar parameter includes center frequency, pulse width, signal bandwidth, sampling frequency, orbit height, azimuth resolution, center downward angle, variable beam strip angle, antenna type and antenna size, antenna beam width; the sea surface environment parameter includes sea surface area size, wind speed and wind direction;

[0237] S4.2. The generation of the ground distance coordinate system variable scattering grid:

[0238] The ground distance coordinate system is defined as a rectangular coordinate system, the variable scattering grid step is set to meet the Nyquist sampling theorem, and the variable scattering grid point set is generated for scattering calculation and sea wave dynamic simulation;

[0239] S4.3. Initialization simulation of sea surface motion state:

[0240] According to the physical ocean equation constructed in step S1, the time-varying sea surface is generated through the sea wave spectrum, the initial sea surface state is generated according to the Elfouhaily sea wave spectrum, and the real-time sea surface motion state is generated by using the Fourier superposition method;

[0241] S4.4. Update non-uniform azimuth time:

[0242] According to the antenna size, the synthetic aperture is divided into several time slices, each time slice corresponds to a position of the radar in the synthetic aperture, and the non-uniform sampling time of each azimuth is updated;

[0243] S4.5. Sea surface motion state update:

[0244] Including intercepting the variable scattering grid in the beam irradiation range, updating the instantaneous sea surface motion state in the beam irradiation range, and calculating the sea surface motion state of all observation angles in the current time slice;

[0245] S4.6. Update slant distance scattering network:

[0246] The backscattering intensity of each scattering facet is calculated in the time domain, the mirror scattering component and the Bragg scattering component of the scattering facet are calculated according to formula (19) and formula (20), and the instantaneous slant distance of the scattering facet is calculated;

[0247] Further, the instantaneous slant distance calculation method of the scattering facet in step S4.6 is:

[0248] Suppose that the satellite platform moves at a uniform speed in the horizontal direction, the azimuth amplitude width of the target observation area is S az , the ground distance amplitude width is S rg , then for the instantaneous slant distance of any scattering point to the satellite platform in the observation scene, the expression of the instantaneous slant distance R s (t;S) of the scattering facet is:

[0249]

[0250] wherein, is the slant range from the scatterer S to the satellite foot point, V is the satellite platform velocity, t S is the time used for illuminating the center of the azimuth aperture of the scatterer;

[0251] S4.7. Time-domain antenna two-way pattern weighting:

[0252] The time-domain antenna two-way pattern weighting is calculated for each distance unit of the scatterer in the same azimuth position, it is judged whether all scatterers in the current beam range are traversed, if yes, the echo of the scatterer in the current azimuth time beam illumination range is superimposed, and if no, step S4.4 is returned to update the non-uniform azimuth time.

[0253] S4.8. Generation of variable-beam high-resolution wide swath SAR sea surface echo matrix:

[0254] The echo of the scatterer in the current azimuth time beam illumination range obtained in step S4.7 is judged whether the azimuth end point is reached, if no, step S4.4 is returned to update the non-uniform azimuth time, and if yes, the variable-beam high-resolution wide swath SAR sea surface echo matrix is output.

[0255] The variable-beam SAR sea surface imaging simulation method of the embodiment is specifically implemented as follows:

[0256] Based on the Elfouhaily sea wave direction spectrum model and combined with the combined surface scattering intensity model of specular reflection and Bragg scattering, a certain area of moving sea surface is simulated, and the radar system and sea surface parameter settings are shown in Table 1:

[0257] Table 1:

[0258]

[0259] The radar system works at a center frequency of 5.4 GHz, adopts a pulse width of 20 microseconds and a signal bandwidth of 50 MHz, and a sampling rate of 62.5 MHz. The radar is carried on an orbit of 700 km in height, has an azimuth resolution of 5 m, a central downward angle of 34.7°, and a variable-beam strip angle of 30°. The antenna adopts a flat phased array design, and the size is 8.86 m x 1.67 m, wherein the number of azimuth elements is 12, and the number of elevation elements is 22. The radar has an azimuth coverage width of 200 km, a distance coverage width of 400 km, an imaging range of a sea surface area of 4 km x 4 km, and a wind area length of 500 km. The system adopts a vertical polarization mode for detection.

[0260] The wind speed at the sea surface 10 m is set to 15 m / s, and the wind vector angle is set to 0°, that is, the wind vector direction is opposite to the direction of the ground coordinate system and perpendicular to the distance unit vector. The sea surface height field, sea surface height map and sea surface scattering intensity at the azimuth center are simulated as shown in Figure 5 .

[0261] The wind strength is changed from 15 m / s to 5 m / s and 30 m / s, and the sea surface height map and sea surface scattering intensity are obtained as shown in Figure 6 . Figure 6 It can be seen that as the wind strength increases, the height difference of the wind-induced wave field also increases, the sea waves with longer wavelengths are formed, the sea surface is rougher, and the signal energy reflected back to the SAR receiving antenna is also stronger. When the wind strength is small, the sea surface is mainly composed of sea waves with shorter wavelengths, the scattering intensity is low, and the noise characteristics are obvious.

[0262] The wind strength is set to 23 m / s, and the wind vector angle is changed to 45° and 90°. The sea surface height map and scattering intensity are obtained as shown in Figure 7 . Figure 7 The simulation results show that the propagation direction of the sea surface ripples is consistent with the set conditions, indicating that the motion sea surface model and the sea surface backscattering intensity model can generate dynamic sea surfaces and backscattering intensities of each scattering element consistent with the input simulation parameters.

[0263] Next, according to the proposed non-uniform time slice and space-varying scattering grid sea surface echo simulation method, variable-beam high-resolution wide swath SAR echo data is generated, and based on the correspondence between the imaging results and the input sea wave spectrum, the effectiveness of the proposed echo simulation method is verified. According to the radar parameters, a 4 km×4 km sea surface is simulated, the wind vector angle of the sea surface is 180°, and the wind speed is 23 m / s. The generated sea wave spectrum and the corresponding sea surface height map are shown in Figure 8 .

[0264] The following methods are used to generate SAR echo signals: ① The echo simulation method based on uniform sampling azimuth shift-invariant grid is used to change the incident angle and instantaneous slant range of each scattering element, and the variable-beam high-resolution wide swath SAR echo is generated using the antenna pattern weight at the azimuth center; ② The non-uniform time slice and space-varying scattering grid echo simulation method is used to generate variable-beam high-resolution wide swath SAR echo. Then the generated wave is focused and imaged, and the experimental results are shown in Figure 9 . Figure 9The imaging result of the simulated echo, if the existing echo simulation method is directly applied in the variable-beam high-resolution wide swath SAR imaging mode, the generated SAR image has strong nonlinear components superimposed due to the non-uniform sampling and the azimuth space-varying scattering grid, and the interference is not consistent with the input sea wave spectrum. The sea surface echo simulation method provided in the application generates an image spectrum close to the SAR image spectrum of the existing strip mode, and is closer to the input sea wave spectrum, which indicates that the proposed echo simulation method can solve the problem of the invalidation of the existing method, and can provide coastal zone sea surface image simulation data for subsequent coastal zone imaging technology.

[0265] It should be noted that the relational terms herein such as first and second and the like are used solely to distinguish one from another entity or action, without necessarily requiring or implying any actual relationship or order between such entities or actions. Moreover, the terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by "comprises... a" does not, without more constraints, exclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element.

[0266] Although the present application has been described with reference to specific implementations, various modifications and / or changes in form and details can be made thereto without departing from the scope of the application. In particular, individual features of the implementations disclosed herein can be combined together in any way, provided that there is no structural conflict. The disclosure is not intended to be limited to the specifically disclosed implementations but includes all alternatives falling within the scope of the claims.

Claims

1. A variable beam SAR region of interest sea surface imaging simulation method, characterized in that: The steps include: S1. Construct a coastal sea surface motion model, including physical ocean equations and Elfouhaily wave spectrum; S2. Construct a Kirchhoff specular reflection model, including constructing the target scattered electric field, the scattering intensity at the center of the scattering element, and the specular scattering component of the scattering element; The specific implementation method of step S2 includes the following steps: S2.

1. Set the applicable conditions of Kirchhoff's specular reflection model as follows: (k0r c ) 1 / 3 cosθ>>1 (1)where r c is the radius of the curved surface; k0 is the radar wave number, and θ is the propagation direction of the beam; S2.

2. Set the target scattered electric field E based on Kirchhoff specular reflection model s The expression is: Among them, K s is the central scattering intensity of the scattering surface element, p is the distribution function, k s is the scattered signal wave number of the scattering surface element, is the specular scattering component of the scattering surface element, S is the integration of the scattering surface element by the sea surface, and j is the imaginary unit; The expression of p is as follows: Where × represents vector cross product, E is the electric field in the propagation medium, is the surface normal unit vector of the scattering element, H is the magnetic field in the propagation medium, and η is the dielectric constant of the medium; K s The expression is as follows: Among them, R s is the distance between the center of the irradiated area and the incident point; The expression is as follows: Among them, φ s is the azimuth angle, θ s is the pitch angle, Represents the vectors in three directions of the rectangular coordinate system; S2.

3. Assuming that the incident wave is a spherical wave, the incident field intensity E inc The expression is as follows: Among them, R inc is the distance from the illumination source to the scattering center, is the polarization direction unit vector of the incident wave, is the unit vector of the incident direction; Get the normalized scattering intensity The expression is: Where pq represents the polarization mode of the incident and scattered waves, and <·> means taking the average; S3. Construct a Bragg resonance scattering model, including constructing the Bragg scattering component of the sea surface element, establishing a numerical model for the sea surface height spectrum, and calculating the instantaneous slant range of the scattering element; S4. Based on the model constructed in steps S1-S3, an echo simulation is performed on the variable-beam SAR sea surface, including using the coastal sea surface motion model obtained in step S1 to update the space-variable scattering grid and update the instantaneous sea surface motion state, using the Kirchhoff specular reflection model obtained in step S2 and the Bragg resonance scattering model obtained in step S3 to calculate the backscattering intensity of each scattering surface element in the time domain, then calculating the space-variable azimuth two-way pattern at each distance unit for the scattering surface element at the same azimuth position, weighting the echo of each scattering surface element, and then traversing the non-uniform sampling time to obtain the echo matrix of the variable-beam high-resolution wide-band SAR.

2. The variable beam SAR region of interest sea surface imaging simulation method according to claim 1, characterized in that: The specific implementation method of step S1 includes the following steps: S1.

1. Based on the one-dimensional approximate solution of the physical ocean equation, assuming that the coordinates of a point on the sea surface are x = (x, y), and the height z = 0, where x is the x-axis coordinate point and y is the y-axis coordinate point, when a single-frequency sea wave passes through the point on the sea surface, the vertical motion vector ξ(x, t) and the horizontal motion vector D(x, t) of the point on the sea surface are expressed as follows: Among them, φ i is the initial phase of the i-th wave, k i is the wave vector of the ith sea wave, k i is the wave number, ω i is the frequency of the ith sea wave, t is the time, A i is the amplitude of the ith sea wave, and N is the total number of sea waves; k i =||k i ||=2p / l Where λ is the wavelength; S1.

2. Assume that the open boundary sea surface is a linear superposition of a finite number of plane waves, where A i With k i Independent of the sea surface position, φ i If the independent points are evenly distributed in the interval [0,2π), then the mean value of the vertical motion vector of the point on the sea surface <ζ(x,t)>=0, The variance of the vertical motion vector of a point on the sea surface is S1.

3. Based on the fact that sea surface waves are the superposition of an infinite number of plane waves, the variance of the vertical motion vector of a point on the sea surface is transformed into an integral form, expressed as: Among them, Ψ(k) and Ψ(k,θ) are the sea surface directional spectrum in the Cartesian coordinate system and the sea surface directional spectrum in the polar coordinate system, respectively, and θ is the propagation direction of the beam; S1.

4. The polar coordinate system sea surface directional spectrum is divided into two components, including the wave spectrum S(k) and the angular spread function Φ(k,θ), which can be expressed as: The wave spectrum is then defined as the Elfouhaily wave spectrum, expressed as: S(k)=k -3 [B l +B h ] (11) Among them, B l With B h denote the long and short sea wave curvature spectra, respectively; S1.5.B l The definition is as follows: Among them, c p is the wave phase velocity at the peak of the spectrum, c p =c(k p ), k p is the peak wave number, α p is the long-wave equalization parameter, F p is the long-wave action function, c is the phase velocity corresponding to the current beam; Where Ω is a dimensionless parameter used to adjust the decay rate of the exponential term, Ω = U 10 / c p , U 10 is the wind speed at 10m above the sea surface, L PM 、J p are the peak enhancement functions of PM spectrum and JONSWAP respectively; L PM 、J p The definition is as follows: Where γ is the peak enhancement factor, Γ is the Gaussian weight function, and σ is the spectrum width parameter; S1.6.B h The definition is as follows: Among them, c m is the phase velocity corresponding to the minimum wave number, F m With α m is the first dimensionless parameter and the second dimensionless parameter; Among them, u * is the friction speed of the sea surface; S1.

7. The angular spread function Φ(k,θ) is defined as follows: Where △(k) is the headwind-crosswind ratio, which is used to describe the directionality of sea waves of different wavelengths; △(k) is defined as: △(k)=tanh{a0+a p (c / c p ) 2.5 +a m (c m / c) 2.5 } (19) Where a0 is the first constant, a p 、a m They are respectively 10 / c p 、u * / c m The corresponding parameters.

3. The variable beam SAR region of interest sea surface imaging simulation method according to claim 2, characterized in that: The specific implementation method of step S4 includes the following steps: S4.

1. Input radar and sea surface simulation parameters: Set radar parameters and sea surface environment parameters according to the simulation scenario. Radar parameters include center frequency, pulse width, signal bandwidth, sampling frequency, orbit altitude, azimuth resolution, center-down viewing angle, variable beam strip angle, antenna type and size, and antenna beam width. Sea surface environment parameters include sea surface area, wind speed, and wind direction. S4.

2. Generation of space-variable scattering grid in ground-distance coordinate system: The ground-distance coordinate system is defined as a rectangular coordinate system, the space-variable scattering grid step size is set to satisfy the Nyquist sampling theorem, and a space-variable scattering grid point set is generated for scattering calculation and wave dynamic simulation. S4.

3. Initialization simulation of sea surface motion state: According to the physical ocean equation constructed in step S1, a time-varying sea surface is generated through the wave spectrum, an initial sea surface state is generated according to the Elfouhaily wave spectrum, and a real-time sea surface motion state is generated using the Fourier superposition method; S4.

4. Update non-uniform bearing time: The synthetic aperture is divided into several time slices according to the antenna size. Each time slice corresponds to a position of the radar within the synthetic aperture, and the non-uniform sampling time of each azimuth is updated; S4.

5. Update of sea surface motion status: It includes intercepting the space-variable scattering grid within the beam illumination range, updating the instantaneous sea surface motion state within the beam illumination range, and calculating the sea surface motion state of all observation angles in the current time slice; S4.

6. Update the slant range scatter network: Calculate the backscattering intensity of each scattering surface element in the time domain, calculate the specular scattering component and Bragg scattering component of the scattering surface element, and calculate the instantaneous slant range of the scattering surface element; S4.

7. Time domain antenna two-way pattern weighting: Calculate the space-variant two-way azimuth pattern at each range cell for the scattering bins at the same azimuth position, determine whether all scattering bins within the current beam range have been traversed, and if so, superimpose the scattering bin echoes within the current azimuth time beam illumination range. If not, return to step S4.4 to update the non-uniform azimuth time. S4.

8. Generate variable beam high-resolution wide-swath SAR sea surface echo matrix: For the scattered surface element echoes within the superimposed current azimuth time beam illumination range obtained in step S4.7, determine whether the azimuth end point has been reached. If not, return to step S4.4 to update the non-uniform azimuth time. If yes, output the variable beam high-resolution wide-band SAR sea surface echo matrix.

4. The variable beam SAR region of interest sea surface imaging simulation method according to claim 3, characterized in that: The instantaneous slant range of the scattering surface element in step S4.6 is calculated as follows: Assume that the satellite platform moves horizontally at a uniform speed relative to the observation scene, and the azimuth width of the target observation area is S az , the ground width is S rg , then for the instantaneous slant distance from any scattering point in the observation scene to the satellite platform, the instantaneous slant distance R of the scattering surface element is obtained s The expression of (t; S) is: in, is the ground distance from the scattering point S to the satellite subsatellite point, V is the satellite platform speed, t S It is the time taken for the scattering point to be illuminated to the center of the azimuth aperture.

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