Real-time simulation of laser beam scanning of small target complexes

Abstract

The invention relates to a device for real-time simulation of a laser beam scan of a small target complex, such as a grain field, comprising a virtual environment with an overall 3D model of the small target complex and further comprising a sensor simulation for simulating a sensor for measuring a distance by means of a laser beam. The sensor simulation includes a ray casting routine and a noise adding routine for simulating the laser beam. A noise addition routine design is used to determine an angle of incidence of the laser beam on the surface of the 3D model and to select an intensity distribution from a database comprising a plurality of intensity distributions that is assigned to the determined angle of incidence. The intensity component reflected by the laser beam can be read out from each intensity distribution according to the invasion depth of the laser beam into the small target complex. A noisy routine design is used to calculate noisy distance measurements taking into account the selected intensity distribution to simulate multiple reflections of the laser beam on multiple small targets, such as ears of a grain field.

Description

Background Art

[0001] A LiDAR sensor (LIDAR = Light Detection and Ranging) is a sensor for scanning the environment with the aid of short-wavelength light signals, usually in the near-infrared range. By detecting the reflections of the light signals and by measuring their round-trip time, a LiDAR sensor can create a three-dimensional image of its environment with high resolution. This property makes LiDAR interesting for use in highly automated vehicles, which can travel in unknown environments without human control and for this purpose must sense their environment. To scan the environment, many LiDAR sensors use a directed laser beam that is emitted at high frequency in alternating spatial directions in order to calculate a point cloud representing the environment from the reflections.

[0002] For many years, it has been customary to test safety-critical electronic control systems in a virtual environment before they are put into series production. Depending on the design of the device under test, this testing method is referred to as software-in-the-loop (SIL), hardware-in-the-loop (HIL) or vehicle-in-the-loop (VIL), for example. The virtual environment is calculated in real time on a simulation computer and includes a sensor simulation, which calculates sensor signals that match the virtual environment and feeds them into the device under test, i.e. the control system under test, in order to check whether the control system correctly evaluates the sensor signals and reacts appropriately to them.

[0003] For testing lidar systems, corresponding sensor simulations are available on the market that mimic the functionality of a lidar and synthetically generate sensor signals for a given lidar sensor. In particular, for simulating lidar sensors that operate with a directed laser beam, it is suitable to use a ray casting method for this purpose, since this method corresponds to the natural operating mode of a real sensor to a certain extent. In this case, the laser beam can be modeled in the virtual environment by a single straight line that emanates from the simulated sensor in the virtual environment, in order to calculate the point of incidence of the laser beam on a virtual target surface in the virtual environment. The point of incidence is then modeled as a simulated reflection source for the laser beam.

[0004] This method provides satisfactory results as long as the laser beam can be approximated as an ideal geometric beam with no beam cross section. This is usually the case when the laser beam interacts with a target that exceeds the beam cross section by at least one order of magnitude. Examples of such targets are buildings, signs, vehicles, people and the ground. This method is problematic when the virtual environment is to include a complex of small targets (Komplex). "Complex of small targets" refers to a close localized collection of targets, each of which has a similar or smaller order of magnitude than the beam diameter of the laser beam in at least one spatial direction. In particular, vegetation elements usually form such complexes. Thus, for example, a grain field is a complex of ears of grain, a meadow is a complex of grass (possibly other plants), and leafy plants, bushes or conifers are a complex of leaves. When the laser beam collides with such a small target, the beam cross section cannot be ignored. Usually, the small target only reflects a part of the beam intensity, while another part of the laser beam passes through the small target. Therefore, the laser beam that hits the small target complex penetrates into the complex and - due to multiple collisions with different small targets - loses intensity as the penetration depth increases. In this case, the lidar sensor does not record a single, clearly defined reflection, but a time-distorted reflection signal consisting of multiple reflections with different round-trip times at different small objects.

[0005] To simulate this reflection process physically plausibly by conventional ray casting or ray tracing, a high-resolution 3D model of a single small target is required in detail, combined with a ray casting model that takes into account thousands of beams in order to adequately resolve the extended laser beam. Such simulations cannot be performed fast enough in hard real time at a reasonable cost.

[0006] It is known in principle from computer graphics that if physically correct simulations based on ray casting or ray tracing are too computationally intensive, stochastic methods can be used to simulate distorted light reflections in a credible and real-time manner. For example, the professional paper "Simulation of Realistic Water on 3D Game Scene" (Xiang Xu, Kun Zou, Procedia Engineering 29, 2012) describes a method for real-time simulation of reflections on a rippled water surface.

[0007] Another example from the specialized field of sensor simulation can be found in the specialized paper “A 3-D Model for Millimeter-Wave Propagation ThroughVegetation Media Using Ray-Tracing” (Nuno R. Leonor et al., IEEE Antennas and Propagation Journal, 67(6), 2019). The paper describes the problem of properly simulating radar returns from vegetation elements against the background of a fine structure formed by leaves. However, the proposed solution based on fixed-position point scattering centers cannot be applied to the simulation of lidars operating with the aid of a directional and strongly collimated laser beam.

[0008] A general introduction to the prior art for simulation of imaging vehicle sensors for stimulating control systems in a test manner can be found in the professional paper "Development of Full Speed ​​Range ACC with SiVIC, a virtual platform for ADAS Prototyping, Test and Evaluation" (Dominique Gruyer et al., IEEE Intelligent Vehicles Symposium, 2013). Summary of the invention

[0009] Against this background, the object of the present invention is to accelerate, in particular sufficiently accelerate, the computer simulation of laser beam scanning of small object complexes in order to enable a hard real-time simulation at the operating speed of a sensor for measuring distances by means of a laser beam.

[0010] In order to solve this problem, a device for real-time simulation of laser beam scanning of a small object complex is proposed. The device comprises a virtual environment and an overall 3D model of the small object complex as part of the virtual environment.

[0011] Advantageously, the overall 3D model is designed so that it does not have a structure of the order of magnitude of a small object and in particular does not include the modeling of a single small object. Particularly advantageously, the 3D model of a complex only models the complex by a surface surrounding the complex. For example, a corn field (which is a complex composed of ears of corn in the physical world) can be modeled by only a rectangular parallelepiped bounding box surrounding the corn field. The bounding box can certainly be provided with a texture matching the corn field for visualization, but does not include a three-dimensional structure for simulating a single ear of corn.

[0012] Furthermore, the device comprises a sensor simulation which is designed to simulate a sensor for measuring distances by means of a laser beam. The sensor simulation comprises a raycasting routine which is configured to calculate the point of incidence of a laser beam emitted by the sensor with a surface in the virtual environment, calculate the Euclidean distance of the sensor from the point of incidence and simulate the distance measurement by the sensor based on the Euclidean distance, in particular to generate a synthetic sensor signal. The synthetic sensor signal can be fed into a control system under test for evaluating the sensor signal, for example a lidar system, in order to disguise the presence of the sensor to the control system in a test manner.

[0013] Furthermore, part of the sensor simulation is a database in which a plurality of intensity profiles are stored. Each of the plurality of intensity profiles is assigned to an angle of incidence of the laser beam. The intensity profiles are designed so that an intensity component of the reflection of the laser beam can be read from each of the plurality of intensity profiles as a function of the penetration depth of the laser beam into the small target complex.

[0014] Furthermore, the sensor simulation includes a noise adding routine, which is designed to determine the angle of incidence of the laser beam on the surface of the 3D model and to select an intensity distribution assigned to the determined angle of incidence from the plurality of intensity distributions. The noise adding routine calculates a noisy distance measurement taking into account the Euclidean distance and the selected intensity distribution. In other words, the noise adding routine accesses the data stored in the intensity distribution in order to simulate, based on the data, a plurality of reflections with different round trip times of the laser beam penetrating into the composite body at a plurality of small targets in the composite body.

[0015] The sensor simulation is designed to record the collision of a simulated laser beam with the surface of the 3D model of the small target complex and to call a noise addition routine if the impact point of the laser beam is located on the surface of the 3D model.

[0016] The number of possible angles of incidence of a laser beam is infinite. Therefore, it is of course impossible to assign an intensity distribution to each possible angle of incidence. Therefore, the feature of the present invention "selecting an intensity distribution assigned to the determined angle of incidence from the plurality of intensity distributions" should be understood as selecting an intensity distribution from a finite number of intensity distributions stored in a database, the angle of incidence assigned to the intensity distribution being sufficiently similar to the determined angle of incidence, in particular as similar as possible. In an extension of the present invention, the selected intensity distribution can also be adapted to the determined angle of incidence by interpolating the selected intensity distribution to another adjacent intensity distribution in the database.

[0017] The distance measurement with noise added by analog calculation of the sensor based on the intensity distribution can be designed in different ways. In a simple embodiment of the invention, the intensity components of the reflections at different penetration depths are simply read out from the intensity distribution and used directly. The response signal detected by the analog sensor then therefore consists of a plurality of reflections, the spatial distance of each individual reflection being the sum of the determined Euclidean distance and its penetration depth stored in the intensity distribution.

[0018] The disadvantage of this design approach is that it can lead to unrealistic sensor simulations, since the response signal will repeat when its angle of incidence is consistent. This disadvantage is particularly problematic in simulation scenarios where the angle of incidence of the laser beam does not change. An example is the simulation of highly automated agricultural machinery that sweeps the laser beam of a lidar system across a grain field in a circular trajectory without changing the elevation angle. In this case, if the 3D model of the grain field is modeled as a bounding box, there is a constant angle of incidence, so that the simulated sensor will detect exactly the same response signal with each sweep.

[0019] Therefore, in an advantageous embodiment, the noise adding routine is designed to use a random number generator when calculating the noisy distance measurement in order to vary the noisy distance measurements relative to one another. It is particularly advantageous if the noise adding routine is designed to interpret the intensity distribution as a probability distribution from which the probabilities of different penetration depths into the composite body can be read for each reflection of the laser beam and the noisy distance measurement is calculated based on this probability distribution. For example, the noise adding routine can be designed to simulate a fixed or variable predetermined number of reflections of the laser beam. The noise adding routine then accesses the intensity distribution assigned to the angle of incidence and configures the random number generator in such a way that the random number generator generates random numbers whose statistical distribution corresponds to the pre-determination of the intensity distribution. The noise adding routine then uses the configured random number generator in order to assign a penetration depth into the composite body to each reflection of the predetermined number of reflections and simulates the noisy distance measurement generated from the reflections of the laser beam calculated in this way.

[0020] The creation of the intensity distribution can be based on measurements made in reality, but is advantageously carried out with the aid of a fine-grained 3D model of the complex of small objects, which resolves the individual small objects, so that the fine-grained 3D model enables the position calculation of the point of incidence of the laser beam penetrating into the complex with the aid of ray casting. High-resolution ray casting of the laser beam impinging on the complex at different angles of incidence is repeated on the fine-grained 3D model. The laser beam is modeled by a plurality of beams, which as a whole simulate a fan-out laser beam with an extended beam diameter, i.e. different from zero.

[0021] For each incident angle to which an intensity distribution is to be assigned, a corresponding ray casting is performed and the points of incidence of a plurality of light beams on the small target surface in the fine-grained 3D model are calculated according to the ray casting. Each intensity distribution is then created by counting the points of incidence according to the penetration depth of the light beam into the fine-grained 3D model. In other words, the intensity distribution is designed such that intervals of penetration depth are plotted on its abscissa and a parameter characterizing the number of light beams of the corresponding ray casting which hit the small target surface within the penetration depth located in the corresponding interval and cause reflection at the point of incidence.

[0022] In the simplest case, if a uniform brightness is assumed for all reflections, the reflection intensity of the laser beam corresponding to the penetration depth is proportional to the respective number of impact points. However, in a development of the invention, each reflection can also be assigned an individual brightness, for example taking into account material properties or the size of the surface on which the impact point is located or the point of action.

[0023]

[0024] In one embodiment of the invention, each of the plurality of intensity distributions is assigned to at least one further parameter in addition to the angle of incidence. The further parameter represents a further physical variable that influences the reflection of the laser beam and can be, for example, the type of vegetation, the divergence angle of the laser beam, the plant density, the row spacing, the height of the vegetation or the maturity. The noise addition routine is designed to select the intensity distribution assigned to the determined angle of incidence and the at least one further parameter from the plurality of intensity distributions. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The invention is explained in detail below with reference to the drawings. The drawings are shown highly schematically. For the sake of better illustration, the geometrical dimensions and numbers of the elements are sometimes not shown realistically.

[0026] The attached pictures are as follows:

[0027] Figure 1 A schematic diagram showing creation of an intensity distribution from a fine-grained 3D model;

[0028] Figure 2 The method of operation of a sensor simulation for simulating a plurality of reflections based on an intensity distribution is shown. DETAILED DESCRIPTION

[0029] Figure 1The diagram of schematically shows the creation of an intensity distribution 2 assigned to an angle of incidence θ. The virtual environment for testing the lidar system, which runs on a computer-based simulation device, comprises a simulated lidar sensor 4 and a fine-grained 3D model 6 of a complex of small targets 8. The fine-grained 3D model 6 resolves individual small targets 8, i.e. comprises detailed 3D modeling of individual small targets 8 and comprises a surface 10 surrounding the complex, which defines the outer boundary of the complex.

[0030] The sensor simulation for simulating a lidar sensor comprises a raycasting routine. The raycasting routine performs a high-resolution modeling of a laser beam by means of a plurality of beams 12, which as a whole result in a high-resolution simulation of a fanned-out laser beam with an extended beam diameter. Each beam 12 is a straight line directed through the three-dimensional space of the virtual environment. The beams 12 are fanned out from a common origin, which is identical to the coordinate position of the simulated lidar sensor 4 in the virtual environment. The optical axis 14 of the laser beam abuts the envelope surface 10 of the complex 6 at an angle of incidence θ, and the sensor simulation is designed to determine the angle of incidence θ. For each beam 12, the raycasting routine checks for the presence of an incidence point 16 on a surface in the virtual environment.

[0031] Each light beam 12 whose point of incidence 16 lies on the surface of the small object 8 is assigned a penetration depth D which is defined as the distance between the respective point of incidence 16 and the penetration point of the respective associated light beam 12 on the envelope surface 10 .

[0032] To create the intensity distribution 2, after a one-time calculation of all the incident points 16, all the incident points 16 located within the complex, i.e., all the incident points 16 surrounded by the surface 10, are determined and the penetration depth D is calculated for each incident point 16 surrounded by the surface 10. The distribution of the penetration depth D is plotted in a histogram 18. The created histogram 18 plots a plurality of penetration depth intervals D1, D2, D3, ..., DN on its abscissa and the number of the incident points 16 whose penetration depth D lies within the respective interval on its ordinate. The histogram 18 is converted into an intensity distribution 2 by interpolating the numbers plotted in the histogram 18 and the intensity distribution 2 is stored in the database 20 in such a way that the intensity distribution 2 is uniquely assigned to the incident angle θ in the database 20. This process is repeated with different incident angles θ in order to fill the database 20 with a plurality of intensity distributions 2, which are each assigned to a different incident angle θ and the parameter space of the possible incident angles θ is gridded with sufficient density. The parameter space to be gridded by the intensity distribution 2 can also include, in addition to the angle of incidence θ, other parameters that influence the reflection of the laser beam, which are changed accordingly when the intensity distribution 2 is created and to which the intensity distribution 2 is assigned in the database 20 .

[0033] In a three-dimensional virtual environment, θ is the angle θH and the elevation angle θ V The solid angles of the components and the intensity distribution 2 are assigned accordingly in the database 20. In the creation of the intensity distribution 2 described above, for simplicity, it has been assumed that each incident point 16 has a predetermined and identical contribution to the temporal distribution intensity of the response signal measured by the analog sensor 4 for all incident points 16. However, it is of course also possible to assign a separate intensity to each incident point 16. In this case, when creating the histogram 18, the individual incident points 16 are weighted differently according to the intensity respectively assigned to them.

[0034] Figure 2 The diagram shows the working mode of the sensor simulation during the real-time simulation run after the database 20 has been completed. Instead of calculating a high-resolution light beam, the ray casting routine of the sensor simulation only calculates a single light beam 12 from the simulated sensor 4, which represents the laser beam of the lidar sensor, but does not take into account the beam diameter of the laser beam. The fine-grained 3D model 6 of the small target 8 complex is replaced by a simple overall 3D model 5, which only includes the envelope surface 10. Therefore, the small target 8 complex is modeled by a polyhedron, such as a bounding box, during the real-time simulation and the small target 8 is not resolved.

[0035] The sensor simulation simulates the working mode of the lidar sensor in that during the simulation, the sensor simulation periodically calls the raycasting routine and places the light beam 12 in a changing spatial orientation in the virtual environment, for example to simulate scanning the environment by a circling laser beam. Whenever the point of incidence of the light beam 12 is on the envelope surface 10, the sensor simulation calls the noise addition routine. The noise addition routine determines the angle of incidence θ of the light beam 12 on the envelope surface 10 and calls up a suitable intensity distribution 2 from the database 20, which is the intensity distribution at its azimuth angle θ. H and its elevation angle θ V The noise adding routine corrects the called intensity distribution 2 by interpolating the called intensity distribution 2 with at least one adjacent intensity distribution in the database so that the called intensity distribution 2 is adapted to the determined angle of incidence θ. The noise adding routine interprets the intensity distribution 2 corrected in this way as a probability distribution of the penetration depth D of a single given reflection of the laser beam hitting the complex of small targets 8 at the angle of incidence θ. The noise adding routine assigns a penetration depth D to a predetermined number of reflections to be simulated of the laser beam in each case by calling a random number generator for each reflection to be simulated, which, using the intensity distribution 2, assigns a penetration depth to the corresponding reflection, thereby generating a statistical distribution of the penetration depths D corresponding to the intensity distribution 2 for the number of reflections.

[0036] The virtual environment in which the simulated sensor 4 operates includes two categories of 3D targets, and the sensor simulation is designed to distinguish between these two categories of targets. The first category describes compact targets that the laser beam cannot penetrate. Examples are buildings, vehicles, road signs and people. If the incident point of the beam 12 is on the first category of targets, the sensor simulation does not call the noise addition routine, but only simulates the distance measurement based on the Euclidean distance from the simulated sensor 4 to the incident point and uses the Euclidean distance (which may be slightly distorted to simulate the measurement error of the sensor 4) as the measured distance of the simulated sensor 4.

[0037] The second category describes a complex of small targets that can be penetrated by the laser beam. If the entry point 16 is located on a target of the second category, the sensor simulation calculates the Euclidean distance of the entry point 16 to the sensor 4 in the same way as described above, but does not use the Euclidean distance as the measured distance. Instead, the sensor simulation calls the noise addition routine in order to calculate a plurality of entry points with different penetration depths D as described above. Based on the plurality of penetration depths, the noise addition routine calculates a noisy distance measurement, which consists of a plurality of distance measurements corresponding to a plurality of reflections of the laser beam on different small targets 8. For each entry point 16 calculated by the noise addition routine according to the random number generator, its own measured distance is calculated, which is respectively generated from the sum of the Euclidean distance of the corresponding entry point 16 and the individual penetration depths D. The noise addition routine generates a noisy distance measurement from the sum of all distance measurements calculated in this way. When calculating the noisy distance measurement, the noise addition function in particular also takes into account the different round trip times resulting from the different penetration depths D and simulates the time-distorted response signal of the laser beam.

[0038] The noise adding routine outputs the noisy distance measurement to the sensor simulation. The sensor simulation calculates a synthetic sensor signal based on the noisy distance measurement, the synthetic sensor signal simulating a real sensor signal, just like the sensor signal output by a physical lidar sensor based on the corresponding noisy distance measurement, and outputs the synthetic sensor signal to an interface of the simulation device. A control system under test can be connected to the interface, the control system being designed to process the sensor signal.

[0039] The invention makes it possible to simulate nearly realistically multiple reflections of a laser beam on a small target complex using a simple ray casting method using only a single beam 12 and a simple 3D model 5 comprising only one envelope surface 10. Due to this simplification, the simulation can be carried out in hard real time at reasonable cost and at the operating speed of a physical lidar sensor and can therefore be used for testing and developing control systems.

Claims

1. A device for real-time simulation of laser beam scanning of a complex of small targets (8), There is a virtual environment, the virtual environment including an overall 3D model (5) of the small target (8) complex; A sensor simulation is provided, which is designed to simulate a sensor for measuring distances by means of a laser beam, the sensor simulation comprising: a ray casting routine arranged to calculate the point of incidence (16) of a laser beam emitted from the sensor on a surface in the virtual environment and to simulate distance measurements made by the sensor based on determining the Euclidean distance from the sensor to the point of incidence; a database (20) comprising a plurality of intensity distributions (2), each of which is assigned to an angle of incidence θ of the laser beam and from which an intensity component of the laser beam reflection can be read out as a function of the penetration depth D of the laser beam into the small target complex; and a noise adding routine designed to determine an angle of incidence θ of the laser beam on the surface (10) of the 3D model, to select an intensity distribution (2) assigned to the determined angle of incidence θ from the plurality of intensity distributions (2) and to calculate a noisy distance measurement taking into account the Euclidean distance and the selected intensity distribution (2); The sensor simulation design is used to call a noise adding routine when the incident point (16) of the laser beam is located on the surface of the 3D model (5) to simulate multiple reflections (16) of the laser beam on multiple small targets (8).

2. The device according to claim 1, wherein: The small object (8) complex is a vegetation element, in particular a complex of ears of grain, ie a grain field, a complex of grass, ie a meadow, or a complex of leaves, ie a leafy plant, a bush or a coniferous tree.

3. The device according to claim 1 or 2, wherein: The order of magnitude of the small targets (8) is similar to or smaller than the beam diameter of the laser beam, so that the laser beam penetrates into the complex of small targets (8) and loses intensity as the penetration depth D increases due to reflection on multiple small targets (8).

4. The device according to any one of the preceding claims, wherein: The 3D model (5) of the complex does not include the modeling of individual small objects (8).

5. The device according to claim 4, wherein: The 3D model (5) is a surface (10) surrounding the complex.

6. The device according to claim 1, wherein: Each intensity distribution (2) is assigned a parameter characterizing the number of reflections for different penetration depths (D), each number of reflections corresponding to the number of incidence points (16) of a high-resolution simulated laser beam, which is modeled by multiple beams (12) in a fine-grained 3D model (6) of the complex, and the fine-grained 3D model resolves individual small targets (8).

7. The device according to claim 6, wherein the sensor of the device is designed to determine the intensity component by taking into account the number of incident points (16).

8. The device according to claim 2, wherein: Each intensity distribution (2) is assigned to at least one further parameter in addition to the angle of incidence θ and the noise addition routine is designed to select from the multiple intensity distributions an intensity distribution (2) assigned to the determined angle of incidence θ and the at least one further parameter, in particular the at least one further parameter being one of the following parameters: vegetation type, laser beam divergence angle, plant density, row spacing, vegetation height, maturity.

9. A device according to any of the preceding claims, wherein the sensor simulation of the device is designed to generate a synthetic sensor signal of a sensor in order to disguise the presence of the sensor to a control system under test, in particular a lidar system, for evaluating the sensor signal.

10. A method for real-time simulation of laser beam scanning of a small target (8) complex, comprising the following method steps: A sensor simulation of a sensor for measuring distances by means of a laser beam is performed in a virtual environment, the virtual environment comprising an overall 3D model (5) of a complex of small objects (8), by means of a raycasting routine, the raycasting routine being configured to calculate the points of incidence (16) of a laser beam emitted from the sensor (4) with a surface in the virtual environment and to simulate the distance measurement by the sensor (4) based on the determination of the Euclidean distance of the sensor (4) from the points of incidence (16); determining an incident angle θ of the laser beam on the surface (10) of the 3D model (5); selecting an intensity distribution (2) assigned to an incident angle θ from a database (20), the database comprising a plurality of intensity distributions (2), each of the plurality of intensity distributions (2) being assigned to an incident angle θ of the laser beam and from which an intensity component of the laser beam reflection can be read out according to a penetration depth (D) of the laser beam into a small target (8) complex; A noisy distance measurement is calculated taking into account the Euclidean distance and the intensity distribution (2) selected to simulate multiple reflections (16) of the laser beam on multiple small targets (8).

11. The method according to claim 10, comprising the following method steps: calculating a synthetic sensor signal of the sensor (4) based on the noisy distance measurement; The synthetic sensor signal is fed to a control system under test, in particular a LiDAR system, ie light detection and ranging, for evaluating the sensor signal.

12. The method according to claim 10 or 11, comprising the following method steps: Providing a fine-grained 3D model (6) of a complex of small objects (8) in a virtual environment to distinguish individual small objects; Repeatedly calculating the incident points (16) of a plurality of light beams (12) on the surface of a small target (8) in a fine-grained 3D model (6) for a plurality of incident angles θ, wherein the plurality of light beams (12) as a whole simulate a fan-out laser beam with an expanded beam diameter; The intensity distribution (2) is created by counting the incidence points (16) according to the penetration depth of the beam into the fine-grained 3D model (6).

Images