Airborne photon laser background noise modeling method based on bidirectional reflection model

Abstract

The invention discloses an airborne photon laser background noise modeling method based on a bidirectional reflection model, and belongs to the technical field of radar imaging. Comprising the following steps: constructing a surface reflection function based on a dynamic BRDF; respectively calculating an atmospheric energy influence function and a receiver energy conversion function; and according to the atmospheric energy influence function, the receiver energy conversion function and the surface reflection function constructed based on the dynamic BRDF, modeling to obtain an airborne photon counting laser radar background noise model. According to the dynamic geometric coupling noise field modeling method based on the bidirectional reflectance distribution function, the zenith angle and the azimuth angle in the incident direction of the sun and the observation direction of a receiver are coupled in real time, the space-time propagation mechanism of noise photons is accurately described, the limitation of a traditional Lambertian hypothesis on directivity is effectively broken through, and the method has the advantages of being high in practicability and high in practicability. The precision of dynamic noise field modeling is remarkably improved, and a solid theoretical basis is provided for design optimization and data processing of an airborne laser radar system.

Description

Technical Field

[0001] The present invention relates to the field of radar imaging technology, and in particular to an airborne photon laser background noise modeling method based on a bidirectional reflection model. Background Art

[0002] Photon-counting lidar, with its single-photon detection sensitivity, has become a core technology for high-precision island mapping and coastal monitoring, playing a key role in underwater terrain detection. However, in dynamic flight environments, the interference of solar background noise on the lidar signal-to-noise ratio remains a significant factor affecting accuracy. Solar noise is primarily caused by the uneven incidence of light due to changes in the solar zenith angle and azimuth. During rapid UAV maneuvers, the instantaneous optical path changes make it difficult for traditional static noise models to capture its spatiotemporal modulation effects, resulting in missing point cloud data and accumulated depth measurement errors.

[0003] Existing solar noise modeling methods have three limitations: 1. Traditional models based on the Lambert assumption simplify surface scattering as an isotropic process, failing to reflect the significant influence of the solar zenith angle and azimuth angle on the scattering process; 2. Although existing layered noise analysis methods can achieve a quantitative assessment of the contribution of water and land noise, they have difficulty in reflecting in real time the impact of the dynamic posture of the UAV and changes in solar geometric parameters (especially the zenith angle and azimuth angle) on the noise field; 3. Although the latest research attempts to construct an ocean background noise model, the mismatch between the static geometric assumption and the dynamic flight scenario makes the prediction accuracy of the spatiotemporal distribution of the noise field still insufficient. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this paper proposes a dynamic geometrically coupled noise field modeling method (BNR-B) within the theoretical framework of the bidirectional reflectance distribution function (BRDF). This model accurately depicts the spatiotemporal propagation mechanism of noise photons by real-time coupling the zenith angle and azimuth angle of the solar incidence direction, as well as the receiver observation direction. This effectively overcomes the directional limitations of the traditional Lambertian assumption, significantly improves the accuracy of dynamic noise field modeling, and provides a solid theoretical basis for airborne lidar system design optimization and data processing.

[0005] In order to achieve the above object, the present invention proposes an airborne photon laser background noise modeling method based on a bidirectional reflection model, comprising the following steps:

[0006] Construct surface reflection function based on dynamic BRDF;

[0007] Calculate the atmospheric energy impact function and receiver energy conversion function respectively;

[0008] The background noise model of airborne photon counting lidar is obtained based on the atmospheric energy impact function, the receiver energy conversion function and the surface reflection function constructed based on the dynamic BRDF.

[0009] f=[Atmospheric Effects]·[System Constants]·[Dynamic BRDF]

[0010] Where: f represents the noise rate; Atmospheric Effects represents the atmospheric energy impact function, SystemConstants represents the receiver energy conversion function, and Dynamic BRDF represents the surface reflection function.

[0011] Furthermore, the surface reflection function constructed based on the dynamic BRDF only considers the specular reflection component, specifically:

[0012]

[0013] Where: i is the incident direction, ω o is the emission direction, n is the surface normal vector; D(α) is the normal distribution function; F(F0) is the Fresnel reflection coefficient; G(k) is the geometric shadow function GSF.

[0014] Furthermore, the atmospheric energy influence function is specifically:

[0015]

[0016] in: is the extraterrestrial solar spectrum irradiance, θ s is the solar zenith angle, T0 is the one-way atmospheric transmittance, h is Planck's constant, and v is the frequency of light.

[0017] Furthermore, the receiver energy conversion function is specifically:

[0018]

[0019] Where: Δλ is the filter bandpass, θ r is the receiver half field of view FOV, η d is the quantum detection efficiency, η r To detect the receiving efficiency, A r is the effective aperture area of ​​the receiver.

[0020] Beneficial effects of the present invention:

[0021] The dynamic geometric coupled noise field modeling method based on the bidirectional reflectance distribution function proposed in this paper accurately depicts the spatiotemporal propagation mechanism of noise photons by real-time coupling the zenith angle and azimuth angle in the solar incidence direction and the receiver observation direction. It effectively breaks through the directional limitations of the traditional Lambertian hypothesis, significantly improves the accuracy of dynamic noise field modeling, and provides a solid theoretical basis for the design optimization and data processing of airborne lidar systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 The figure is a flow chart of a method for modeling background noise of airborne photon laser based on a bidirectional reflection model according to an embodiment of the present invention.

[0023] Figure 2 Schematic diagram of experimental data of an embodiment of the present invention.

[0024] Figure 3 This is the half space of the laser receiving direction vector and its top view according to an embodiment of the present invention.

[0025] Figure 4 This is a schematic diagram of the model calculation results of the zenith angle change diagram extracted along the transverse line according to an embodiment of the present invention.

[0026] Figure 5 Schematic diagram of reflection field statistics for noise rates at different zenith angles according to an embodiment of the present invention.

[0027] Figure 6 Schematic diagram of model results under different solar azimuth angles according to an embodiment of the present invention.

[0028] Figure 7 This is a schematic diagram of the model calculation results of the azimuth angle change diagram extracted along the cross-section according to an embodiment of the present invention.

[0029] Figure 8 Schematic diagram of the comparison between the theoretical values ​​and measured values ​​of the invention example model and the Lambertian model. DETAILED DESCRIPTION

[0030] The present invention will be further explained and illustrated below with reference to the accompanying drawings and embodiments.

[0031] The core of solar background noise modeling lies in quantifying the distribution characteristics of noise photons caused by solar radiation in photon-counting lidars. Its theoretical framework is based on the photon energy propagation equation. By establishing a coupled relationship between incident energy, surface reflection characteristics, and receiver response, it achieves a parameterized representation of the noise rate.

[0032] Compared to dark noise, which is typically only a few hundred hertz or even negligible, solar background noise caused by solar radiation is one of the main noise sources. Measurements show that the vertical distribution of noise photons is relatively uniform, covering a range of tens to hundreds of meters near the ground. However, due to the influence of surface environmental characteristics, its horizontal distribution varies. To more accurately assess changes in noise levels, the noise rate f is defined here: the ratio of the average number of noise photons N to the time interval τ, that is, the noise photon level per unit time. Its expression is as follows:

[0033] N=τ*f (1)

[0034] The total number of noise photons generated during the measurement process can be expressed as:

[0035] N rec =N s +N other ≈N s (2)

[0036] Where: N s is the number of noise photons generated by solar radiation, N other is the number of noise photons generated by other noise sources, N s >>N other .

[0037] Since single-photon lidar can capture energy changes at the photon level, the amount of measurement noise will increase significantly as the solar radiation level increases. Generally speaking, from the perspective of the energy propagation process, the energy ultimately received by the receiver can be simply expressed as:

[0038] E rec =E inc G rec Rτ b (3)

[0039] The formula consists of the product of four parts, namely the incident energy E determined by the sun inc , surface reflection function R and receiver energy conversion function G rec and short time interval τ b Although this representation is simple, it is the basis for most current research. Combining formula (1), from the photon energy equation E0 = hv, the basic concept formula of the theoretical noise rate can be derived as:

[0040]

[0041] Among them, f recis the received noise rate, E0 represents the energy of the photon, h is Planck's constant, and v is the frequency of light. The above formula only retains the noise source caused by surface reflection of the medium, while ignoring the atmospheric diffuse reflection noise, which is orders of magnitude lower.

[0042] This equation provides the general definition of the noise rate, where the first term Represents the atmospheric energy influence function, the second term G rec represents the receiver energy transfer function, and the third term R(ω, ρ) represents the surface reflection function, usually based on the Lambert assumption.

[0043]

[0044] Where: Δλ is the filter bandpass, θ r is the receiver half FOV (field of view), η d is the quantum detection efficiency, η r To detect the receiving efficiency, A r is the effective aperture area of ​​the receiver, is the extraterrestrial solar spectrum irradiance, θ s is the solar zenith angle, T0 is the one-way atmospheric transmittance, h is the Planck constant, v is the frequency of light. β is the surface reflectivity, θ s is the solar zenith angle, σ is θ s The local surface slope at is the azimuth of the slope.

[0045] The parameter E in the above formula inc and G rec Neither of these variables is significant during the measurement process. Therefore, only the medium properties ρ, caused by the random distribution of ground species, and the optical propagation path ω, which varies with the measurement process, have extremely high uncertainties. However, based on the Lambert isotropy assumption, the incident direction of light is of primary concern, but changes at the receiving end are imperceptible. This is the direct cause of significant changes in the surface reflection component R, and it also greatly increases the complexity of description and modeling.

[0046] Considering that the dynamic changes in the incident direction (sunlight) and the outgoing direction (lidar reception) are the main factors affecting the background noise, the traditional surface reflection function based on the Lambert assumption cannot describe how the surface reflection energy changes with the geometric relationship. Therefore, the embodiment of the present invention introduces the BRDF model, establishes the connection between the light propagation process and the surface reflection function, and constructs a transient noise rate model reflecting the dynamic measurement light path, thereby revealing the temporal and spatial evolution mechanism of the noise.

[0047] like Figure 1 As shown, an embodiment of the present invention provides an airborne photon laser background noise modeling method based on a bidirectional reflection model, comprising:

[0048] First, a surface reflection function is constructed based on the dynamic BRDF.

[0049] The Cook-Torrance model is a widely recognized BRDF model, which is expressed as

[0050] R r =k d R lambert +k s R cook-torrance , k d +k s =1 (8)

[0051] This model divides reflection into diffuse reflection (R lambert ) and specular reflection (R cook-torrance ) two parts, of which k d and k s Represent their respective energy contribution coefficients. The diffuse reflection part still follows the Lambert assumption, which is consistent with formula (7):

[0052]

[0053] Here, β is the surface reflectivity, θ s is the solar zenith angle, σ is θ s The local surface slope at is the azimuth of the slope.

[0054] Although the Cook-Torrance model includes diffuse and specular reflection, the sun's position remains virtually unchanged over short periods of time. This indicates that changes in the diffuse reflection component are minimal, and therefore its influence can be largely ignored. On the other hand, the specular reflection component in the model is more sensitive to dynamic changes in the measurement light path. Furthermore, the direction of the reflected light exhibits strong regularity and is closely correlated with the measurement results. This is the primary reason for the discrepancies in the model results. Therefore, the embodiments of the present invention focus on modeling the specular reflection component.

[0055]

[0056] Where: i is the incident direction, ω ois the outgoing direction, n is the surface normal vector; D(α) is the Normal Distribution Function (NDF), which describes the roughness of the surface and defines the number of microplanes with the normal direction in a certain direction; F(F0) is the Fresnel Reflection Coefficient, which describes the surface's ability to reflect incident light; G(k) is the Geometry Shadowing Function, which describes the occlusion and reflection characteristics of the microscopic surface. Roughness is used as the input parameter. The higher the surface roughness, the higher the probability of mutual occlusion between microplanes.

[0057] Then, the atmospheric energy impact function and the receiver energy conversion function are calculated according to formulas (5) and (6) respectively.

[0058] Finally, based on the atmospheric energy impact function, the receiver energy conversion function, and the surface reflection function constructed based on the dynamic BRDF, the background noise model of the airborne photon counting lidar is obtained:

[0059] f=[Atmospheric Effects]·[System Constants]·[Dynamic BRDF]

[0060]

[0061] Among them: Atmospheric Effects represents the atmospheric energy impact function, System Constants represents the receiver energy conversion function, and Dynamic BRDF represents the surface reflection function.

[0062] This model accurately captures the spatiotemporal characteristics of solar background noise under dynamic light path changes, providing a theoretical basis for analysis and discussion.

[0063] By introducing the BRDF model, a dynamically changing light path propagation process is established in the laser measurement scenario. It is used to assist in calculating the surface reflection function and construct a transient noise rate model that can reflect the dynamic change of the measurement light path. This helps to understand the formation mechanism and action process of noise.

[0064] In order to verify the modeling method of the embodiment of the present invention, the embodiment of the present invention uses the measurement experimental data from a reef island coastal zone. At 10:00 a.m. local time on August 8, 2020, a drone-mounted lightweight single-photon counting lidar measurement was conducted near Jiaji Island (coordinates: 110°17′24″E, 18°00′N) located on the south side of Shimei Bay, Wanning City, Hainan Province, China. The survey area is as follows: Figure 2 shown.

[0065] The solar background noise model based on BRDF can flexibly cope with various light path changes. In the actual measurement process, the position changes of the sun and the laser are as follows: Figure 3 As shown. The position of the sun is marked at point S, and there will not be much deviation in a short time. The sunlight propagates in the direction of SO, radiates outward at the measuring point O, and is finally received by the laser at O'. Therefore, for the propagation light path SOO', the direction of the sun's position and the direction of the laser's position can be recorded as OS and OO' respectively. The receiving direction of the laser under elliptical orbit scanning will continue to change. Ideally, all possible positions and receiving directions of the laser can be simplified to a hemispherical space Ω for description, and O' is also a point on the sphere. Simply traverse the laser receiving direction in the entire space to obtain Figure 3 The top view on the right side allows you to see the situation in all receiving directions more intuitively. Figure 3 The right-hand side cross-section is used to better compare the model differences at different receiving locations.

[0066] To quantify the coupling effect between azimuth and zenith angles, Figure 3 Extract two orthogonal transversals: the main plane transversal L1 that is consistent with the sun's position and its perpendicular orthogonal plane transversal L2. Figure 4 As shown, for the L1 cross section (main plane), the peak position shifts outward as the zenith angle increases, consistent with specular reflection geometry. At high zenith angles (>48°), the noise rate largely drops to a low-intensity plateau, excluding some outliers, reflecting the suppression of directional sensitivity under grazing illumination conditions. For the L2 cross section (orthogonal plane), the peak position remains stable at different zenith angles, but the peak amplitude drops sharply from 28.64 kHz (0° zenith angle) to 4.60 kHz (72° zenith angle), indicating that non-specular scattering is reduced under oblique incidence.

[0067] Figure 5The violin plots in Figure 1 statistically quantify the zenith angle dependence of the noise rate across the entire hemispherical field (zenith angles 0° to 80°). The results show: 1. The median noise rate (black curve) decreases continuously with increasing zenith angle, driven by the weakening of specular reflection intensity. 2. As the zenith angle increases, the noise rate becomes concentrated within a narrow range (the interquartile range decreases by 68%), with a long tail indicating the presence of residual specular reflection hotspots. 3. Spatial heterogeneity decreases above 60°, indicating the emergence of a quasi-uniform noise field, where noise levels are similar in most directions. This also means that zenith angle determines the trade-off between noise intensity and directional uniformity. At low zenith angles (when the Sun is near the zenith), high-intensity noise is concentrated in specular reflection regions, necessitating trajectory planning to avoid critical angles. At high zenith angles (when the Sun is near the horizon), uniform, low-intensity noise simplifies system calibration but places higher demands on detector sensitivity.

[0068] These results highlight the importance of understanding the sun geometry to optimize airborne lidar operations in coastal or mountainous terrain under dynamic lighting conditions.

[0069] Figure 6 The spatial distribution characteristics of the noise rate calculated by the BNR-B model at different solar azimuths are shown. In the experiment, the solar zenith angle is fixed at 20°, and the solar azimuth is sampled every 24° in all circumferential directions (from 0° to 360°). The color mapping in the figure is the intensity of the noise rate, and the XY coordinates represent the projection component of the laser receiving direction in the hemispherical coordinate system. The results show that changes in the solar azimuth will only lead to a rigid rotation of the noise distribution pattern, while the numerical value and distribution shape are exactly the same, verifying the rotational symmetry of the model in the horizontal plane. This feature shows that the calculation results of any azimuth can be mapped to a reference azimuth (such as 0°) through a rotation transformation, and the model itself will not be substantially affected by changes in azimuth.

[0070] Figure 7 The results of the cross-sectional analysis for azimuth angles of 0°, 24°, 48°, and 72° are presented when the solar zenith angle is 20°. The following findings are made: ① Azimuth independence: When the solar azimuth is used as a fixed reference system, the results for different azimuth angles in the L1 and L2 cross-sectional views completely coincide, confirming that changes in azimuth angle only change the observation angle, not the numerical distribution of the noise field. ② Spatial heterogeneity: Although the noise field is rotationally symmetric overall, the significant differences between the L1 and L2 cross-sectional views reveal the non-uniformity of the hemispherical reflection field. This heterogeneity stems from the directional sensitivity of the BRDF model to the incident-receiving geometry.

[0071] During dynamic flight, real-time changes in the laser receiving direction relative to the sun (e.g., flight trajectory deflection) can violate theoretical rotational symmetry assumptions. For example, even if the sun's position remains fixed, attitude perturbations or heading adjustments of the UAV platform can still alter the spatial coupling pattern of the noise rate. Therefore, optimizing flight trajectory design to avoid areas of high noise coupling is key to improving system robustness.

[0072] In order to systematically evaluate the directional resolution capability of the noise model based on BRDF, the flight data of the same coastal zone were selected to perform noise rate inversion using BRDF and Lambertian models respectively, and quantitatively compared with the measured statistical results. Figure 8 shown.

[0073] The figure clearly shows that the noise rate calculated based on the BRDF model is more consistent with the changing trend of the measured data. The BRDF model accurately reproduces the dynamic fluctuation characteristics of the measured noise rate, with an RMSE of 6.61kHz for the first-order difference, significantly better than the 9.26kHz of the Lambertian model, and an accuracy improvement of 28.6%. The model can significantly reflect the impact of laser direction on the noise rate results, which fully demonstrates that the BRDF-based background noise model has greater adaptability and can better cope with various orbital inclination conditions. With this excellent adaptability, the model can provide more accurate guidance for measurement work and effectively reduce the adverse effects of noise on data quality.

[0074] The above specific description further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for modeling airborne photon laser background noise based on a bidirectional reflection model, characterized in that: The steps include: Construct surface reflection function based on dynamic BRDF; Calculate the atmospheric energy impact function and receiver energy conversion function respectively; The background noise model of airborne photon counting lidar is obtained based on the atmospheric energy impact function, the receiver energy conversion function and the surface reflection function constructed based on the dynamic BRDF. f=[Atmospheric Effects]·[System Constamts]·[Dynamic BRDF] Where: f represents the noise rate; Atmospheric Effects represents the atmospheric energy impact function, System Constants represents the receiver energy conversion function, and Dynamic BRDf represents the surface reflection function.

2. The airborne photon laser background noise modeling method based on the bidirectional reflection model according to claim 1 is characterized in that: The surface reflection function constructed based on the dynamic BRDF only considers the specular reflection component, specifically: Where: i is the incident direction, ω o is the emission direction, n is the surface normal vector; D(α) is the normal distribution function; F(F0) is the Fresnel reflection coefficient; G(k) is the geometric shadow function GSF.

3. The airborne photon laser background noise modeling method based on the bidirectional reflection model according to claim 1 is characterized in that: The atmospheric energy influence function is specifically: in: is the extraterrestrial solar spectrum irradiance, θ s is the solar zenith angle, T0 is the one-way atmospheric transmittance, h is Planck's constant, and v is the frequency of light.

4. The airborne photon laser background noise modeling method based on the bidirectional reflection model according to claim 1, characterized in that: The receiver energy conversion function is specifically: Where: Δλ is the filter bandpass, θ r is the receiver half field of view FOV, η d is the quantum detection efficiency, η r To detect the receiving efficiency, A r is the effective aperture area of ​​the receiver.

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