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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

As LADAR systems applications gradually become more diverse, new types of systems are being developed. When developing new systems, simulation studies are an essential prerequisite. A simulator enables performance predictions and optimal system parameters at the design level, as well as providing sample data for developing and validating application algorithms. The purpose of the study is to propose a method for simulating a Geiger-mode imaging LADAR system. We develop simulation software to assess system performance and generate sample data for the applications. The simulation is based on three aspects of modeling—the geometry, radiometry and detection. The geometric model computes the ranges to the reflection points of the laser pulses. The radiometric model generates the return signals, including the noises. The detection model determines the flight times of the laser pulses based on the nature of the Geiger-mode detector. We generated sample data using the simulator with the system parameters and analyzed the detection performance by comparing the simulated points to the reference points. The proportion of the outliers in the simulated points reached 25.53%, indicating the need for efficient outlier elimination algorithms. In addition, the false alarm rate and dropout rate of the designed system were computed as 1.76% and 1.06%, respectively.

LADAR (Laser Detection and Ranging) calculates target distance ranges by measuring the flight times of the laser pulses transmitted to and reflected from the target surfaces. These ranges can be further converted into a 3D point cloud or a range-image in a local coordinate system by their integration with the position and attitude data acquired from Global Positioning System (GPS)/Integrated Navigation System (INS) sensors mounted with the laser ranging unit.

As an emerging technology, it provides densely sampled 3D points with reliable and consistent quality in an automatic and prompt way. Thus LADAR systems have been widely utilized for various applications in diverse fields. According to their specific applications, various kinds of LADAR systems have been developed with different components and mechanisms (e.g., scanning mechanisms, detector types and sizes, and output data types) [

In topographic mapping, many applications to derive geospatial information from 3D point clouds have been developed, such as noise reduction [

Most systems used in topographic mapping employ a single detector with a scanning system [

In the defense sector, LADAR with Focal Plane Array (FPA) is more widely used for surveillance and reconnaissance in order to detect obstacles for safety guidance of ground or aerial vehicles [

For a high sensitivity detector, a Geiger-mode avalanche photodiode (GmAPD) has been recently employed. When the number of incident photons exceeds a predefined threshold, the APD becomes saturated [

As various kinds of LADAR systems have been developed for diverse applications, simulations of such systems have also been studied. Simulation studies are an essential prerequisite for the development of a new LADAR system [

Topographic mapping applications have predominantly used airborne LADAR systems, including a laser scanner with a linear mode single detector and a scanning mirror, GPS and IMU. Most simulation studies on such systems have focused on the geometric aspects. For example, the precise modeling of the systematic error of an airborne mapping LADAR system was performed by Schenk [

The previous studies related to FPA are as follows: the Center for Advanced Imaging LADAR (CAIL) in the University of Utah, USA, performed a modeling simulation for linear mode imaging LADAR to develop LadarSIM, implemented in Matlab [

In this study, we developed a method of comprehensive modeling and simulation for Geiger-mode imaging LADAR with a gate ranging and scanning mechanism. We then predicted and modeled its performance. For high fidelity models, we analyzed previous works and then integrated the rigorous models into a comprehensive method. Our simulator is composed of three main modules: geometry, radiometry, and detection modules. The geometry module defines the rays of laser beams and then determines the locations at which the rays intersect with the target surfaces. The radiometry module computes the powers of the return pulses and generates the waveforms. The detection module finally generates the time when each pixels in a detector perceives the first photon. Using the proposed simulation of three modules, the reference data, as well as the corresponding simulated point cloud, are generated. Finally, we evaluated the sensor performance based on the simulation by comparing the simulated points with the reference points.

This research reliably verifies the data from a new type of LADAR system with given parameters and assesses its performance using indicators, such as the amount of noise and false alarms in advance of developing hardware. Our simulator also provides a diversity of simulated data for the development of application algorithms that should be optimized for a real system.

The paper is organized as follows: Section 2 describes the modeling principles and simulation processes. Section 3 presents the experimental results with the implemented simulator and our analysis of the performance assessment with the given system parameters. Finally, we present our conclusions and future research directions.

LADAR (or laser radar) generates 3D point cloud and range images by measuring the flight times of laser pulses.

Ideally, a detector senses only the pulse energy emitted by the transmitter. However, internal and external noise energies are also detected by the receiver along with the return pulse. The main causes of noise are the backscattered solar radiation and dark count due to thermal effects.

For the simulation of a LADAR system, three models were required (

In the second step, the radiometric model computes how much energy strikes the pixels, including noise energies. First, the transmitted energy of each pixel is calculated using the predefined beam profile. The return energy is computed using the laser equation with the radiometric and optical parameters and ranges calculated from the geometric model. Using the radiometric model, we can compute the number of incident photons according to time.

The detection model generates the simulated time when the first photon is detected based on a probability function. It includes the effect of APD timing jitter—statistical time interval between the pulse arrival and the signal output of APD. But afterpulsing effect, causing the noise, is not considered in this paper. According to earlier research, the saturation of a Geiger-mode detector from all light sources follows Poisson statistics under several assumptions [

The purpose of the geometric modeling is to identify the source of each pixel's information, or the point at which the transmitted laser pulse is reflected on a target surface. To find this point, the geometry of the laser pulse needs to be determined, both the direction and origin. Geometric modeling can then establish the ray model of the laser pulse and compute the intersection point. We can determine the range from the origin to the intersection point and the reflectance of the intersected surface, which are used for the radiometric modeling described in Section 2.2.

The ray model can be defined by the geometric integration of the sub-modules in the LADAR system. The sub-modules are a GPS/INS and a scanning mechanism, each of which has its own coordinate system. Therefore, they should be redefined in a common coordinate system using a geometric transformation based on the geometric relationships between the sub-modules.

An FPA detector system has N × N pixels. The acquired information for each pixel originates from the target point on the ray passing the pixel and the perspective center. The pixel location, the perspective center and the target point are collinear. The line equation of the pixel ray can be established with three points. To define the ray, we defined the sensor coordinate system of the detector as shown in _{0}, and the range _{0} is a unit vector from the location of pixel _{r,c} to the origin

A LADAR system employs the scanning mechanism to increase its coverage. There are a variety of scanning mechanisms and each has its own scanning pattern (

The horizontal and vertical angular positions (_{h}_{v}

We then transformed the line-equation in

All sub-modules in LADAR systems, such as GPS/INS and laser scanners, possess some systematic and random errors. There are two kinds of errors in LADAR systems. The first comprises the individual sensor errors, and the second the integration errors [

The direction and origin of the pixel rays can be represented as follows. The true range of the pixel ray can be calculated by searching the intersecting surface. However, a real LADAR system handles tens of thousands of laser pulses per second. Furthermore, LADAR simulation executes a tremendous number of geometric operations to search for the intersecting points between the pixel rays and the target surfaces [

The particular details of the ray-tracing used are as follows [

The purpose of radiometric modeling is to calculate the number of incident photons that enter the detector pixels. The radiometric model uses the range computed in the geometric simulation, the radiometric and optical parameters of the system.

Ideally, the photons that strike the pixels of the detector are from the laser energy emitted from the transmitter. However, the detector collects not only the reflected laser energy, but also the energy caused from the backscattered solar radiation. Furthermore, the dark count can also cause false alarms. The radiometric model deals with the reflected pulse energy and these noise sources [

The intensity of the laser beam across the range is not uniform, but varies in the spatial and temporal domains [_{0} is the maximum irradiance of the beam; and _{0}/^{2}) at

In the temporal domain, the laser signal is modeled as a pulse. There are several pulse models with different shapes. The pulse model used in this study was suggested in [

The returned laser energy is calculated using a LADAR range equation [_{t}_{s}_{s}_{sys}_{atm}_{atm}_{sys}_{FF}_{BPF}_{ND}_{T}_{R}

The main sources of the noises occurring in the detector are reflected sunlight and dark count. They contribute to false alarms by arriving at the detector before the returned laser pulse. The sunlight (solar radiation) is collected by the receiver, although it does not originate from the transmitter. The incident energy of the backscattered solar radiation is given in _{si}^{2}/nm; _{λ}_{t}^{2} and is calculated as in

The expected number of photoelectrons created by the dark count due to the thermal effects within the detector is determined using _{dc}

FPA imaging systems have a detector consisting of an N × N arrayed pixel. The simulation of an imaging system requires the computation of the incident energy for each pixel, including the noise. For this, we derived an equation to compute the incident energy for each pixel under the following assumptions. The first assumption is that N × N laser beams, which we call sub-beams, are independently transmitted from the arrayed pixels and return to the pixel after reflecting off the target surfaces. The other is that the incident noises of each pixel are the same. Under these assumptions, we can calculate the incident energy per pixel.

The transmitted energy of the pulse _{pulse}_{t}_{pulse}_{r,c}, can be represented as

The returned energy of the sub-beam collected by a pixel can be derived using _{r}

Consequently, the expected number of photoelectrons sensed by the (^{dc}

The detection simulation determines the simulated time when each pixel detects the first photon. A Geiger mode detector can only perceive the primary photon, because it takes a few microseconds to recover from the saturation by the photon. The saturation of the detector by the laser pulse and noise follows Poisson statistics [

In a certain time interval (time bin), the probability

Using the detection probability of one pixel at each time bin, we can generate the simulated time when each pixel detects the photons as follows [

Compute the incident photons for each time bin within the range gate using

By computing the probabilities that the pixel detects at least one photon for each time bin using

Convert the PDF into a CDF (Cumulative Distribution Function) using

Generate a random number Y from 0 to 1 that follows the uniform distribution. Then, search for the bin

We performed an experiment to verify the proposed methods for LADAR simulation. Based on the simulation results, we also assessed the performance of the LADAR system with the designed system parameters and mission scenario.

The simulation program was implemented using C++ language. The simulator is mainly composed of three parts: geometry, radiometry, and detection, as shown in

The developed simulator employs 3D polyhedral models expressed in B-rep. As the input data of the LADAR simulator, B-rep models retain some advantages. They simplify the geometric operations in simulations without the need for interpolation. Moreover, they are very flexible in varying the given system parameters according to the mission scenario. For example, if the simulator uses range images as the input data instead of the B-rep models, many different images are needed to account for the various positions and orientations of the sensors based on the given mission scenario.

A LADAR system has three sub-modules, such as a GPS/INS and laser scanner. The laser scanner consists of various components, such as a laser transmitter, optics, a receiver, a detector, and a scanning device. Their system parameters need to be determined for each simulation.

The dark count is the noise generated on the circuit board due to thermal activity. The occurrence rate was 20 kHz, which is the average number of saturation counts per second even in complete darkness.

Most of the parameters listed in ^{2}/nm approximately, which is the value corresponding to 1,560 nm wavelength of the laser in the solar radiance spectrum curve for direct light at sea level [

Having the system and platform parameters established, we were able to perform the LADAR simulation. The coverage of the simulated data with these parameters overlapped with the target models in

As a result of the whole simulation—geometry, radiometry and detection, 44,136 points were generated. The simulated point cloud generated by the entire simulation from the geometric to detection simulation is presented in ^{2}; the range of its x-coordinate value was 77.619∼122.230 m, and the range of its y-coordinate value was 140.620∼175.061 m. Unlike a linear mode system known to retain only a few outliers, we can confirm from the simulation results that the Geiger mode system produces significantly large number of outliers. Most outliers are caused from the dark count and the backscattered sunlight. It also includes points backscattered from target surfaces with more high density than that of outlier as shown in the middle of

As shown in

The method to assess the detection performance of the LADAR system by using the simulated data with the given system parameters is as follows. As mentioned in Section 2, in general, it is difficult to identify the corresponding point pairs in two data sets of point clouds acquired by a real LADAR system. However, the pair of points between the simulated point cloud and the reference point cloud can be easily determined, because the simulated point is generated point by point from the reference data.

As seen in

G1 and G2 are the cases where in the detection process worked correctly. E1 and E2 are cases where it did not. E1 is the dropout case in which a pixel fails to detect the return photons mainly due to a low received energy. E2 is a false alarm wherein the pixels are saturated by the noise, though there is no target in the range gate. In the Case E0, there was a target in the gate range, and the pixel was saturated similarly to G1; however, the pixels in E0 were saturated not by the laser pulse, but by the noise. In this study, we can calculate E0 by comparing the ranges between the reference and the simulated data.

For an accurate assessment of the performance of the LADAR system with the given system parameters, multiple experimental analyses with various target models must be performed. Therefore, further studies focusing on performance assessment will be undertaken. Also, it seems to require a new method to remove outliers. There are few studies about eliminating outliers with high outlier ratio, whereas there are many studies detecting outliers from point cloud generated by linear mode LADAR with low level noise.

By using the performance assessment process based on simulation, we can easily analyze the impact of the main system parameters to the system performance. We can perform this analysis by evaluating the system performance derived from simulation while changing the system parameters used as the input to the simulator. For example, we performed the analysis on the impact of pulse repetition rate, as shown in

When developing a new LADAR system, a simulation study can be useful to assess its performance. In this paper, we propose a method for creating a simulation for a Geiger-mode imaging LADAR system and its performance assessment. The proposed simulation technique has three main parts—geometry, radiometry and detection simulations. In the geometric simulation, the sub-beam rays of the pixels are defined, and the intersection points between the rays and the target surfaces are computed using ray-tracing. Then, the radiometric simulation calculates the incident energy of the transmitted sub-beams and the noise in time domain. Finally, the detection part performs a simulation for the responses of the detector based on the probability function used by the Geiger mode detector. We confirmed that the simulated point cloud was well generated on the object surfaces and verified the range image generated using the point cloud.

Furthermore, we attempted to evaluate the detection performance. For this, we used the reference data as a result of geometric simulation. Then, we compared the simulated point cloud point by point with the reference data. The results were represented in the error matrix. The proportion of outliers in the simulated point cloud was 25.53%, and the false alarm rate of the LADAR system was approximately 1.76%. The proposed method can be applied to various applications with diverse platform and sensor systems and will be useful for such processes as system comprehension, data provision, and performance prediction.

This research was supported by the Defense Acquisition Program Administration and Agency for Defense Development, Korea, under the contract UD100028GD.

The authors declare no conflict of interest.

Principle of a LADAR sensor. The transmitter emits pulsed laser repetitively with a constant rate. The laser pulses are then backscattered on the surfaces of targets or background. Each pixel of the detector measures the travel time of the laser pulse by collecting the return pulse. The collected incident energy also includes noises such as sunlight and dark count due to thermal effects.

Simulation process of Geiger-mode imaging LADAR. Geometric model finds where the information of each pixel comes from. Radiometric model computes how much energy strikes the pixels, including noise energies. Detection model generates the simulated time when the first photon is detected based on a probability function. Simulated point cloud was compared point by point to the reference data generated in the geometric simulation.

Sensor coordinate system and a pixel ray model. The left one is 2D view of the detector and the right figure shows 3D view. Subscript (

Scanning mechanisms and resulting ground patterns [

Geometric deflection by a wedge prism. The horizontal and vertical angular positions (_{h}_{v}

Scan pattern by the wedge prisms with deflection angle of 0.256° at 1 km (

Geometric relationships among sub-modules [

Concept of the ray-tracing algorithm [

Intensity distribution of a simulated Gaussian beam profile with the array of 16 × 16, pulse energy of 0.4 mJ and 4.8 mrad beam divergence. Normalizing by the sum of Gaussian model and multiplying the pulse energy, we considered the energy loss due to the difference between array size of detector and beam width.

Pulse model used in this study.

Simulation of the time at which the pixel detects the primary photon ((

Main modules in the LADAR simulation program and their relationships. Geometric module outputs the range from the perspective center to the intersection point. Radiometric module computes the incident energy of each pixel from both the transmitted laser pulse and the noise and generates the number of incident photons on each pixel per time bin. Detection module calculated the simulated time at which the pixel perceives the incident photons based on the probability model.

City model of the test area. The test area is a part of Yeongdeungpo-gu in Seoul, South Korea ((

Scenario of the LADAR system for simulation. The aerial platform is assumed to be in the midair at 1 km with the speed of 0 m/s. Besides, the LADAR sensor is mounted obliquely to look targets and background slantingly.

Target models (buildings) in the test area (within red boundary).

Coverage of FPAs by the scanning mechanism is the one bounded with red box in

Reference point cloud generated by geometric simulation. They are not affected by the radiometric conditions or the nature of the detector. Therefore, it can be used as a reference for the simulation outputs of the radiometric and detector models.

The simulated point cloud with colors encoded by height (front and side views).

Zoom-in image of the points that are located in height of 20∼40 m to look into inlier points backscattered from target surfaces.

Range image (134 × 76 pixels) generated from the simulated point cloud. To generate this range image, after eliminating the outliers, we grouped the ranges according to the direction of the laser pulses with a constant angular interval.

Overview of performance assessment.

Simulated point cloud color-coded by case—E0: green, E2: magenta and G1: sky blue.

Variations of the number of total points, inliers and outliers (ratio) according to the changes of pulse repetition rate.

Variations of missing and false alarm rate according to the changes of pulse repetition rate.

Variations of point density (inliers) and fill factor according to the changes of pulse repetition rate.

Descriptions of the simulator modules.

Detector module | Define the sensor coordinate system and initial pixel rays |

Scanning module | Compute the rotational matrix for deflection by the scanning mechanism |

Movement module | Compute the position and the attitude of the vehicle at a specific time |

Integration module | Transform the pixel rays from the sensor coordination system into a local coordinate system |

Target module | Input the target and background model as formatted in B-rep |

Ray tracing module | Search the facets intersecting with the laser pulse and compute the range and the intersection point |

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Pulse module | Define the energy distribution in the temporal domain |

Beam profile module | Define the energy distribution in the spatial domain |

Receiver module | Calculate the incident energy using the LADAR range equation with the parameters related to the optical system efficiency |

Noise module | Calculate the expected noise energy due to solar irradiance and the thermal effect of the detector's circuit |

Signal module | Generate a graph representing the numbers of incident photons per time bin by pixel. |

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Detection module | Calculate the simulated times at which the pixels are saturated based on the probabilistic model |

Parameters of the laser pulse (related to

Wavelength | λ | 1,560 nm |

Laser mean power | _{pulse} |
10 W |

Pulse frequency | _{pulse} |
25 kHz |

Pulse width | 1 ns |

Parameters of the scanning mechanism (related to

Deflection angle | _{k} |
0.506 deg | 0.506 deg | 0.256 deg | 0.256 deg |

Rotational speed | _{k} |
45 Hz | −45 Hz | 5 Hz | −5 Hz |

Phase angle | _{k} |
0 deg | 0 deg | 90 deg | 90 deg |

Parameters of the detector (related to

No. of pixels | 16 × 16 | |

No. of sub-pixels | 6 × 6 | |

Pixel pitch | 100 um | |

Dark count rate | _{dc} |
20 kHz |

Photon detection efficiency | 0.3 | |

Gate time | 80 ns | |

Measurement range | 200 m | |

System clock | _{t} |
1 GHz |

Parameters of the optics (related to

Bandpass filter transmittance | _{BPF} |
0.5 |

Bandpass width | _{λ} |
2 nm |

Transmitter optics transmittance | _{T} |
0.8 |

Receiver optics transmittance | _{R} |
0.75 |

Focal length | f | 333 mm |

Solar irradiance | _{si} |
W/m^{2}/nm |

Error matrix for the performance assessment of the target detection.

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Target in the range gate | Exists | 32,867/451 (G1/E0) | 6,791 (E1) |

Does not exist | 10,818 (E2) | 589,073 (G2) |

Descriptions of cases in

G1 | Target exists in gate range, and pixel is saturated by target |

G2 | Target does not exist in gate range, and pixel is not saturated |

E0 | Target exists in gate range, but pixel is saturated due to noise |

E1 | Target exists in gate range, but pixel is not saturated |

E2 | Target does not exist in gate range, but pixel is saturated by noise |

Indicators for the performance assessment of target detection.

Dropout rate | 1.06% | |

False alarm rate | 1.76% | ( |

Outlier ratio | 25.53% | ( |