Small-footprint Laser Scanning Simulator for System Validation, Error Assessment, and Algorithm Development

Transcription

1 Small-footprint Laser Scanning Simulator for System Validation, Error Assessment, and Algorithm Development Antero Kukko and Juha Hyyppä Abstract Airborne lidar systems have come to be extensively used in photogrammetry and mapping sciences. In this paper, a high-quality simulation approach and methods of smallfootprint lidar processing are presented and discussed, validated for tree height estimation, and demonstrated for scanning geometry effects analysis and mobile mapping. The simulation method implemented combines both spatial and radiometric components to produce realistic waveform and point cloud data for system performance analysis and for algorithm development for lidar data processing and mapping purposes. Waveform data generated by the simulator were shown to demonstrate the possibilities of such an approach in system and data verification. As the related empirical data are insufficient for effective research and exploitation in mapping purposes at the moment, the simulated waveform data are needed. A tree location accuracy of 15 cm and tree height underestimation of 0.33 m was found using the simulation model for the TopEye Mk II laser scanner, compared to the artificial forest model reference data. Modeling of light interaction on object surfaces and characteristics of scanning systems provide an opportunity to simulate laser data acquisition of well-defined objects under controlled conditions. By eliminating different sources of error case-by-case, we can improve the knowledge obtained merely from the experimental studies. Data validation in the scanning geometry simulations was carried out by comparing the simulated first echo data to the environment model and, separately, to the first echo data from an independent TopoSys II flight strip that was not used for the environment model computation. The mean differences reveal that the simulator slightly overestimates the object elevations. Deviation between the real TopoSys point cloud and the environmental model was 2 to 3 times larger than that obtained for the simulated Optech and TopoSys data sets. We believe that the developed simulation and modeling is an efficient tool for determining the most reasonable set of flight parameters for any current mapping task, for analyzing change detection possibilities of repeated laser surveys, and for studying and verifying future lidar systems and concepts. However, this requires high-quality modeling of the system and extensive knowledge of the interaction between the laser beam and the object, which should be further developed in the coming years. Finnish Geodetic Institute, P.O. Box 15, FI MASALA, FINLAND (Antero.Kukko@fgi.fi). Introduction Airborne lidar systems have been widely adopted for mapping purposes in recent years. Laser scanning is used in digital elevation model (DEM) production (e.g., Kraus and Pfeifer, 1998; Huising and Pereira, 1998; Pereira and Janssen, 1999; Petzold et al., 1999; Axelsson, 2000; Artuso et al., 2003; Reutebuch et al., 2003), building extraction (e.g., Brenner, 2003; Brenner, 2005; Haala et al., 1998; Maas and Vosselman, 1999; Maas, 2001; Rottensteiner, 2003; Rottensteiner et al., 2005; Vosselman, 2002; Vosselman and Dijkman, 2001; Vosselman and Süveg, 2001; Kaartinen and Hyyppä, 2006), forest management (e.g., Naesset, 1997; Naesset, 2002; Hyyppä et al., 2001; Persson et al., 2002; Yu et al., 2004), and map updating (Matikainen et al., 2003). In the references cited above, the algorithm development was adapted to data obtained from small-footprint commercial lidars. In addition to airborne systems, there is also an increasing market for terrestrial scanners, especially terrestrial scanners mounted on vehicle-borne platforms that provide 3D data on the road and built environments (Talaya et al., 2004; Kukko et al., 2007) and for autonomous vehicle guidance systems (e.g., Montemerlo et al., 2006). Terrestrial scanners are beyond the scope of this paper, but a special case for mobile mapping is verified and discussed. There are two major types of scanning lidars: large- and small-footprint systems. Large-footprint systems typically have beam size between five and 25 m and full-waveform recording capability. They are also restricted to experimental systems. Experimental studies using large-footprint systems include Anderson et al. (2006), Blair et al. (1999), Brenner et al. (2000), Carabajal and Harding (2001), Harding et al. (2001), Hyde et al. (2005), and Lefsky et al. (1999). Significant simulation and modeling work has been done previously for large-footprint lidar systems (e.g., Sun and Ranson, 2000; Ni-Meister et al., 2001 and Koetz et al., 2006). Widely used for DTM, city modeling, and forest inventory, smallfootprint systems use footprints of less than 1 m and mainly record the backscatter as discrete points (x, y, z, and intensity) for multiple echoes. Simulation and modeling for smallfootprint systems is more rare, even though the same largefootprint system knowledge can be applied. Earlier attempts at three-dimensional simulations in forests using smallfootprint airborne laser scanner include modeling of the Photogrammetric Engineering & Remote Sensing Vol. 75, No. 9, October 2009, pp /09/ /$3.00/ American Society for Photogrammetry and Remote Sensing PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING October

2 scanning angle effect in the measurement of tree height and canopy closure (Holmgren et al., 2003) and the establishment of optimal lidar acquisition parameters for forest height retrieval (Lovell et al., 2005). In these cases, two assumptions are made: the simulated laser pulse is assumed to be a single ray without any divergence, and the coarse objects simulated are assumed to be solid. In general, such simulation methods were useful, but the implementation was relatively simple. It is thus no wonder that the results obtained with the simulation method in Holmgren et al. (2003) systematically overestimated the laser height percentiles by 2.25 m. Beam interaction, waveform, and threshold detection were not simulated. Even though the modeling in Goodwin et al. (2007) was improved in the Lidar Interception and Tree Environment (LITE) model, the model simulations compared to coinciding airborne lidar data indicated that the estimates differed less than 2.4 m in maximum tree height and less than 2.3 m in mean heights of the first return data. Thus, the geometry of the modeling and the interaction between the lidar pulses and forest canopies should be further improved. There are possible applications in which simulation, together with good models for the sensors, target, and beam interaction could provide further insights and answers. Optimization of the laser acquisition parameters is one feasible application area; an example is tree height estimation, in which it is not precisely known why a bias in tree height is found to be 1.3 m in one study and 0.5 m in another (see e.g., Rönnholm et al., 2004). Furthermore, it is not properly known how much the repeatability of laser surveys affects object extraction (building or tree extraction) and discovery of certain small targets. Opportunities for the use of small-footprintwaveform data will be long delayed due to the lack of experimental data. Even the capabilities of future laser instruments can be estimated with simulation and good models. This article presents a small-footprint laser simulator developed at the Finnish Geodetic Institute (FGI) in which the models of interaction between the laser pulse and objects have been derived in the hyperspectral laser laboratory of the FGI. In this paper, the simulation system is depicted; the system is verified with a simple individual tree extraction case and validated against true laser scanning data over an urban test area. Furthermore, several new applications are discussed. Since the accuracy of the lidarderived attributes is dependent on sensor configuration and object properties and structure, it is expected that the simulator can be used together with experimental laser data to further optimize the lidar acquisition parameters of several applications in the future. The Laser Scanning Principle An airborne laser scanner transmits a short laser pulse, typically 3 to 10 ns. This laser pulse is transmitted from a known location (computed in post-processing on the basis of GPS-INS observations) in a certain direction, determined by the deflection unit of the scanner, to reach the object surface. The beam diverges from its nominal direction and creates a narrow conic shape, and thus the transmitted energy spreads over a footprint area and its intensity decreases towards the edges of the beam. The pulse reflections return from this footprint area. Within the footprint, a variable amount of surface material at variable ranges and orientations is encountered. This affects the power and shape of the backscattered time-space echo, or waveform, of the received signal. This situation is illustrated in Figure 1, which schematically depicts one laser beam and its reflection from a building. The different orientations and locations of the building and ground surfaces cause sequential reflections, which integrate into a time-space waveform. Figure 1. Principle of lidar observation. Beam divergence causes the spread of a beam over the footprint area, from which multiple echoes are collected. The nominal beam direction determines the final 3D position for the detected point (x f, y f, z f and x l, y l, z l ). Multiple reflections from the object are schematically illustrated along the center line of the shifted beam. The amount of beam divergence from the nominal beam direction causes a decrease in ranging accuracy in both the planar and height directions (first and last echo points extracted from the waveform are denoted by x f, y f, z f, and x l,y l, z l in Figure 1, respectively), since during data processing all echoes are assumed to have been reflected from the axis of the nominal beam direction. (Baltsavias, 1999.) One of the most crucial factors for exact range determination from the returned echo is the echo detection algorithm applied (Wagner et al., 2004). Since the length of the typical laser pulse is longer than the accuracy needed (a few meters versus a few centimeters), a specific timing of the return pulse needs to be defined. In a non-waveform ranging system, analogue detectors are used to derive discrete, time-stamped trigger pulses from the received signal in real time during the acquisition process (Wagner et al., 2004). The timing event should not change when the level of signal varies, which is an important requirement in the design of analog detections, as discussed by Palojärvi (2003). For full-waveform digitizing ALS systems, several algorithms can be used at the postprocessing stage (e.g., leading edge discriminator/threshold, center of gravity, maximum, zero crossing of the second derivative, and constant fraction) (Wagner et al., 2004). The mandatory echo waveform parameters affecting the range measurement in an ideal case of even, bright Lambertian surface at right angle to beam direction are: shape, power and duration of the pulse, sampling frequency of the waveform and detector sensitivity, and as mentioned above, 1178 October 2009 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

3 the scanner type (non-waveform, waveform), and the applied point discrimination method. To further complicate the system, the object reflectivity, orientation, and structure within the footprint affect the shape of the received waveform, along with the atmospheric effects of transmission and refraction during the round-trip of the transmitted pulse. Three basic scanning geometries are most commonly implemented for commercial airborne lidars. These operate mainly in line, oscillating and conic geometries, all of which form a different measuring pattern on the ground. These general patterns are illustrated in Figure 2. The point density on the ground surface is determined by the scanning angle of the scanner, pulse repetition frequency and scanning frequency, and the velocity, altitude, attitude, and drift of the sensor. Table 1 summarizes some principal parameters of commercial airborne laser scanning systems which are implemented in the simulation software. The main operational differences for the listed sensors are in the pulse and scanning frequency, the scanning angle, the beam divergence, and the pulse length. On top of these, the pulse shape and detector sensitivities, as well as the system noise, may not be identical. In addition to these basic functional parameters, there are a number of factors affecting the quality of the acquired laser scanning data: pulse shape and stability, physical errors in the construct of the sensor, e.g. scan angle error and mirror misalignments, timing errors, and aircraft navigation and bore-sight errors. However, these factors were left out of this study for further investigation in future works. Therefore, in the test cases to be described in the Tests and Results Section, the sensor trajectory (i.e., the navigation data) and sensor mechanics were assumed to be Figure 2. Scanning patterns for three basic measuring principles: (a) Line, (b) Oscillating, and (c) Conic. without error. We must bear in mind that by adjusting some parameter values provided by the real scanners (e.g., scanning angle, pulse frequency and power, different waveform recording modes, etc.), one can broaden the possibilities for simulation studies. Simulation System This section describes the basic implementation of the simulation software. The methodology includes implementation of the geometric properties of the scanner system, laser radiation and scattering on the target surface, and the signal waveform processing. A complete lidar simulator covers platform and beam orientation, pulse transmission, beam interaction with the target surface, computation of waveform prototype, and eventually digitization of the waveform: Beam deflection and platform orientation: Controls platform movements and scanner operation according to the system and flight parameters. Pulse transmission: Deals with the laser beam properties according to the beam angular divergence and the spatial distribution of the transmitted energy. Beam interaction: Laser beam division into sub-beams and their interaction with the target surface are computed. Elevation, surface orientation, reflectivity, and distance from the beam center are considered. Waveform: The echo waveform prototype is created by summing up the energy returned from different parts of the laser beam according to the range and surface-orientationdependent reflectivity. Returned energy is collected by a telescope aperture. Threshold detection and waveform digitizing In this phase the echoes exceeding a given power threshold are detected. Recorded output echo waveform is created in digitization of the simulated echo prototype using system-dependent sampling interval and detection parameters. The following sections discuss each of these simulation components separately. Scanning Geometries Airborne laser scanners typically have three basic scanning geometries, or modes: line, oscillating, and conic as shown in Figure 2. These have been implemented into the simulation system. The other relevant implemented system-specific parameters affecting the achieved scanning pattern, and thus the data coverage on the ground surface, were pulse frequency, scanning frequency, scanning angle, and the along-track velocity of the platform. TABLE 1. CHARACTERISTICS OF SOME COMMERCIAL AIRBORNE LASER SCANNING SYSTEMS Sensor Mode Scan Freq. Pulse Freq. Scanning Angle Beam Div. 1/e 2 Pulse Energy Range Resolution Pulse Length Digitizer Optech 2033 Optech ALTM3100 Oscillating 0 70 Hz 33 khz Oscillating 0 70 Hz khz /1.0 mrad N/A 1.0 cm 8,0 ns N/A 0.3/0.8 mrad 200 mj 1.0 cm 8,0 ns 1 ns TopEye Conic 35 Hz 5 50 khz 14, mrad N/A 4,0 ns 0.5 ns 1.0 cm Mk II TopoSys I Line 653 Hz 83 khz mrad N/A 6.0 cm 5,0 ns N/A TopoSys II Line 630 Hz 83 khz mrad N/A 2.0 cm 5,0 ns 1 ns Leica Oscillating Hz 83 khz 0.33 mrad N/A N/A 10 ns N/A 37.5 ALS50 Leica Oscillating Hz 150 khz 0.22 mrad N/A N/A 10 ns 1 ns 37.5 ALS50-II LMS-Q560 Line 160 Hz 100 khz mrad 8 mj 2.0 cm 4,0 ns 1 ns PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING October

4 One swath produced by the scanner consists of a certain number of beams fired over the scanning angle, depending on the pulse and scanning frequencies of the scanner. The beam distribution within the swath is typically produced by deflecting mirror or fixed-fiber array system in physical sensors. For simulation, the beam distribution within the swath was reproduced computationally by mathematical models to achieve the correct orientation for each beam in the ground coordinate system. Thus, e.g., 127 fixed fibers in the TopoSys II scanner correspond to an equal number of simulated beams with equal angular spacing and orientation in the simulator. The instantaneous scanning angle for line and oscillating scan patterns is determined by Equations 1, 2, and 3. Let us denote the time taken to complete one-fourth of a scan swath by T and the maximum scan angle by u max. We also assume constant mirror speed. During time T, P pulses will be shot towards the ground as defined by the pulse repetition frequency f p. For the i th pulse, which is fired at time t i from the beginning of the scan, the instantaneous scan angle u i will be: u i u max (1) 4P i. This relationship applies for the line and oscillating scanning geometries; only the direction of the oscillation changes at the edge of the swath. For a sinusoidal scanning pattern, the equation becomes: where, u i u max sina p 2T t ib, t i T P i. For the conic palmer scanner, the beam is deflected by a nutating mirror. The mirror rotation axis is at 45 in relation to the laser beam axis, and mirror facet normal is deviated from the rotation axis by an angle h. Thus, the resulting circular distribution is modeled by two angles, as follows: u i 2hsina p 2T t ib f i 2hcosa p 2T t ib where u i and f i are the beam deflection angles for alongtrack and across-track directions, respectively. Scan angle errors due to encoder quantization and galvanometers used in angular measurement are almost negligible for the altitudes of 100 to 1,000 m above ground level typical in aerial laser scanning, and are usually to mrad, corresponding to 2 to 3 cm at a 1,000 m range (Campbell, 2006). By comparison, the beam divergence for small-footprint systems usually ranges from 0.2 to 1 mrad, giving a 0.02 to 0.10 m and 0.2 to 1.0 m footprint diameter at ground level for 100 m and 1,000 m flight altitudes, respectively. In addition, there are some errors which are regarded as constant (e.g., misalignments between the mirror and the encoders, misalignments between facets on multifaceted mirrors, and the accuracy from which the laser steering fibers are aimed), and which are thus not interesting from the simulation point of view. Platform trajectory and the attitude of the sensor, in particular, strongly affect the acquired data. Typically, the, (2) (3) (4) swinging of the aircraft causes deviations of several degrees to the ideal scanning strip, posing a threat of gaps between adjacent data strips. Winds cause the aircraft to drift, which must be compensated for by turning the plane towards the wind, thus narrowing the effective strip width. In the simulation model, the platform trajectory is computed during the simulation. Basic parameters determining the general trajectory are speed and drift of the aircraft, altitude, and the direction of the flight strip. Since the sensor was assumed to follow a flawless trajectory, the navigation errors could be introduced for each computed pulse firing time. Platform accelerations were not introduced to the current version of the simulator. Pulse Transmission The laser scanner creates a short laser pulse transmitted towards the ground. This pulse may vary in shape, duration, and power as a function of time. In many cases, the Gaussian power distribution for the pulse is pursued, but seldom achieved precisely. The deviation of the ideal Gaussian pulse from its real world exemplar is studied, e.g., in Wagner et al. (2006). This has led to problems in the Gaussian decomposition of the waveform laser scanning data. It is also known that increasing the pulse repetition frequency could easily degrade the pulse power stability, directly deteriorating the ranging accuracy. Even though the pulse model could be chosen freely (e.g., to reflect empirical measurements), for simulations (described later in this paper) the power distribution of the transmitted pulse was approximated by a Gaussian pulse. A thorough investigation of the effects of pulse power instability on the data quality will have to be addressed in a future paper. The second element in the transmission sub-system controls the laser beam divergence, i.e., the laser footprint size at ground level. The size of the footprint on the ground is a simple function of the divergence angle and the flight altitude, or more precisely, the range: D 2 z tan u/2, (5) where D is the beam footprint diameter, u is the beam divergence angle, and z the distance to the ground surface. The intensity of a laser pulse was modeled using a transverse mode TEM 00, which gives one centralized Gaussian spot on the target surface. As it travels in the air, the laser beam wavefront acquires curvature and begins to spread as follows: w1z2 w 0 c1 a lz 2 1/2 (6) pw b d, 2 0 where z is the distance propagated from the plane where the wavefront was flat, l is the wavelength of light, w 0 is the radius of the 1/e 2 irradiance contour at the plane where the wavefront is flat, w(z) is the radius of the 1/e 2 contour after the wave has propagated a distance z. The energy per unit area that was eventually attained was calculated with: I1r2 2P 2r2 expa (7) 2 pw1z2 w(z) b, 2 where I(r) is the intensity function, P the total energy, w(z) the laser footprint radius measured between 2s points at range z, and r the distance (perpendicular to the beam direction) from the center of the laser beam at range z from the aperture. Thus, the energy decreases as a function of the distance from the beam center leading to less energy returning from the outer parts of the beam than from the center. The intensity pattern of a typical airborne laser scanner pulse is illustrated with a 1/e 2 contour in Figure October 2009 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

5 Figure 4. Backscattering of 1,064 nm laser light from a concrete sample as a function of the angle of incidence. Figure 3. Intensity of an 8.0 mj pulse with a beam divergence angle of 1.0 mrad (1/e 2, contour emphasized in yellow), at a range of 400 m. The resulting footprint diameter is approximately 40 cm. In the simulation model, the transmitted laser pulse was modeled by a predefined number of discrete rays. The returned energy was calculated using the intensity of the transmitted pulse at the range in question, the surface reflectivity and the area of interaction, which here depends on the beam sub-division parameters as follows E ret 1r2 tr1u2i 0 1r2A, where E ret is the returned energy, t is atmospheric transmission, R anisotropic surface reflectance at given angle of incidence u, I 0 pulse intensity at range r from the scanner, and A the receiving area of the scatterer. Surface reflectance R depends on the angle of incidence u and the type of the surface. The scatterer area A was calculated using angular distribution of sub-beam rays. Each scatterer (ray intersection) is then integrated to an echo waveform prototype. Finally, the recorded intensity was affected by the aperture of the receiver telescope. Scattering and Attenuation The wavelength of the laser used affects the scattering from the object surface. This scattering can be assumed to be isotropic, but the anisotropy could be taken into account for better precision. Scattering anisotropy depends greatly on the surface orientation relative to the light source, and on the surface properties (Nicodemus et al., 1977; Hapke et al., 1996; Sandmeier and Itten, 1999). Variation in the light scattering from different surfaces can be carried out by introducing different object types and incidence angle dependent scattering functions. Models introducing multiple scattering could also be considered. In this paper, the scattering was assumed to conform to the cosine of the angle (8) of incidence (i.e., Lambertian surface). Laboratory measurements of backscattered intensity as a function of the angle of incidence using 1,064 nm laser light have been performed for a set of natural and artificial surface types, and is depicted in detail in (Kukko et al., 2008). The laboratory system allows us to measure calibrated backscatter intensity as a function of incidence angle. Papers featuring the system include (Kaasalainen et al., 2005; Kaasalainen et al., 2008). As an example of the laboratory results, a backscatter from a concrete sample is shown in Figure 4. Concrete is one of the most used materials in the construction industry and is thus present at every urban site all over the world. The sample shows approximately 35 percent decrease for 1,064 nm laser light in the backscattered power as the angle of incidence increases from zero to 70 degrees. This knowledge is built into the FGI lidar simulator for various natural and manmade targets. Atmospheric transmission is considered as constant per unit length and can be given by atmospheric models such as MODTRAN. The atmospheric attenuation dampens the amplitude of the recorded waveform, thus reducing the ranging accuracy for some discrimination methods, as described in the Laser Scanning Principals Section and discussed more in the Discussion Section. This has an effect when data acquired using different flight altitudes, scanning angles, and wavelengths are compared. Waveform Digitization The transmitted pulse energy was modeled as a function of time, with known time-interval sampling. For simulation purposes, 100 ps sampling was chosen to obtain the insidesimulator prototype echo waveform. This provided a sampling frequency 5 to 10 times higher than that provided by the scanners available today. Each single laser beam shot was modeled using multiple rays with uniform angular distribution around the centerline of sight of a single laser pulse. The angular difference between adjacent rays, or sub-beams, was chosen according to the flight altitude and surface model grid spacing used. The beam subdivision was implemented since it corresponds to the illumination integral, and it makes it possible to detect small and narrow objects like branches and power cables within the beam, thus allowing the addition of such objects into the artificial models. Every sub-beam of a modeled laser beam results in a distance, or range, from scanner to target surface intersection. Thus, one beam results in a number of distance PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING October

6 measurements depending on the beam size at the target and target opaque and 3D shape. Different ranges were converted into time units and sub-echoes were integrated into a sum echo as a function of time, according to their target and scattering angle dependent reflectance. By integrating all the sub-echoes we obtain a sum waveform at a given (e.g., 100 ps) inside-simulator sampling interval. Side-lope returns were not simulated in the present system; transmitter gain pattern will be modeled in a more careful way in future versions. This provides a high-resolution view of the target, which could be regarded as an approximation of its physical 3D shape. For each of the time bins t i in the echo waveform prototype, random noise was added before the output echo waveform was digitized. The model for waveform noise generates a uniform distribution of random values at a specified interval [a, b] from the distribution: f1x2 1 for a x b, (9) b a where a is the mean and b-a the range of the distribution, and x the random variable for the sampled noise. The limits [a, b] for the additive noise could be chosen arbitrarily, but they should be as realistic as possible. We used a constant fraction, proportional to the peak power of the transmitted pulse, to limit the noise level in our test cases. However, empirical studies on the noise characteristics in true waveform data are proposed to further improve the simulator. The simulated output echo waveform, which corresponds to that of a real system output, is digitized from the higher resolution prototype waveform with a given system dependent sampling interval. There are several possible echo detection possibilities; many of them already implemented in the simulation system. By using the detector threshold, the information exceeding the selected power threshold is found and digitized. This gives the first approximation for the point location, but more importantly, it captures the meaningful waveform signal from the time slot in hand. Furthermore, the recorded waveform is more often analyzed in post-processing and could be used for more exact point extraction (e.g., multiple peak discrimination) and range-detection algorithm development. The most basic technique for pulse detection is to trigger a pulse whenever the rising edge of the signal exceeds a given power threshold (leading edge discriminator), which was also implemented in this first version of the simulation system. In the point discrimination process of the simulator, the detected waveform is scanned with the predetermined fixed detection threshold, fed to the simulator as a steering parameter. The detected point is stored for output. Although it is conceptually simple and easy to implement, this approach has a disadvantage: the timing of the triggered pulse (and thus the distance measurement) is rather sensitive to the amplitude and width of the signal. If the amplitude of the pulse changes, then the timing point also changes. The same applies for the center of gravity when computed over all points above a fixed threshold. The application and analysis of more advanced point discrimination methods in the processing of simulated waveform data were excluded from this issue to be done in future work, but they are presented and discussed in general in the laser Scanning Principles Section and the Discussion Section. Surface and Object Models The basic assumption of the FGI lidar simulator is that there already exists a high-resolution environmental model of the target (e.g., a raster surface), either obtained from the ground truth measurements, created artificially, or generated from the previous laser survey. Environmental models employed in this paper were created using multiple overlapping laser scanning strips, or they were artificially created for small areas. Environment models based on laser surveys were typically hundreds of meters in size, and were generated in the following way. First, the area of interest was delineated from the data, and appropriate grid cell size was chosen. Next, the grid cells (i.e., pixels) were populated by elevation of the highest data point within the cell. The elevation values were stored at one-centimeter resolution as 16-bit signed integer data format, so in the simulation computations, the metric values were obtained by multiplying the grid cell value by a factor of The artificial environment models were small in size, for example, single buildings or a randomly generated forest stand, as seen in Figure 5, which presents a forest canopy model expressing a spruce-dominated coniferous forest 150 m 150 m in total area. The grid location and cell size for the artificial surface model generation were chosen similarly. Trees (on top of the ground surface) in the artificial models were generated according to input parameters for number of trees within the stand, tree and canopy heights, and crown diameter with random variation within the specified ranges. Trees were added as data blocks on top of the model ground defined by a mathematical surface or an existing ground surface, as seen in Figure 5. The tree locations were chosen randomly, and overlap of the canopies was allowed. For each tree, the location, tree and canopy height, and crown diameter were stored to be used in the validation of the simulated point data in tree height estimation. Tests and Results Here, we demonstrate the versatility of the developed simulator in several cases. In the beginning, we introduce and discuss the waveform simulation sub-system of the proposed simulator in the next subsection. In the first test case in the Airborne Laser Scanning Sub-section, examining the tree height estimation, the quality of the simulation is analyzed and compared to previously published lidar forest simulators. The second test case in the Mobile Mapping Sub-section considering the scanning geometry effect, the test simulation for mobile mapping purposes demonstrate that it is possible to use the Figure 5. High resolution random forest model with sinusoidal canopy shape October 2009 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

7 Figure 6. Simulated waveforms of a laser pulse using pulse lengths of (a) 4.0 ns, (b) 10.0 ns and (c) 4.0 ns. In (a) and (b), transmitted pulse energy was 50 mj, in (c) 8 mj. Additive random noise with J maximum amplitude for echo recording was used, and 10 percent object reflectivity was assumed. In (a) and (b), 128 last mode samples, and in (c), 256 first mode samples were recorded, using a 1.0 ns sampling interval. simulator in a wide variety of application areas. The validation of these cases was carried out using the environment model built on true laser scanning data, and in the first case, an independent reference laser scanning data acquired with the TopoSys II laser scanner was also used. Waveform Processing and Mapping Applications A laser scanning simulator and simulated waveform and point data provide a research platform for algorithm development to improve object classification and recognition, and to develop automatic mapping tools for detection of buildings and other structures, and natural targets such as trees. Figure 6 demonstrates simulated echo waveforms of a laser pulse with varying pulse lengths and power, and sampling mode and interval of the waveform digitizer. The object, a 20 m high tree with three distinct branch layers in the crown, low undergrowth and ground surface, and the measuring geometry were the same for all waveforms. Three layers of branches are seen in Figure 6a for the 4.0 nm pulse length, but they become blended for the pulse length of 10 nm as shown in Figure 6b. It is clear that the pulse length affects the separation of individual scatterers close to each other. In addition, degradation in the ranging accuracy could be expected, due to visible spreading of the last echo peak. However, the echo peak power seems to slightly increase as the pulse length is extended. The shortening of the sampling interval, i.e., increasing the resolution of the waveform recording, enhance the discrimination of close objects, similar to the decreased pulse length. Furthermore, the number of recorded samples improves the achievable depth range of the sensor. The effect of different parameters (e.g., pulse width, power and shape, detector sensitivity, sampling interval, and target properties) on waveform detection can be studied, as repetitive simulations can be performed while the spatial (especially trajectory component) and radiometric conditions remain unchanged. This leads to better understanding of the beam interaction with different target surfaces and provides insight into system behavior. The fact that waveform decomposition procedures could be tested and verified using simulated waveform data is also emphasized, since the measuring conditions are computationally traceable. Airborne Laser Scanning Applications Case 1: Tree Height Estimation Forest parameter extraction using lidar techniques is common practice nowadays. Here we present some preliminary results achieved by simulating a TopEye Mk II laser scanner over a model forest 150 m 150 m in size and applied to an individual-tree-based inventory. The total number of trees within the stand was 100, with a mean height of m and a standard deviation of 0.58 m. The tree crowns were characterized by a m mean crown diameter with 1.40 m deviation, and modeled by means of a sinusoidal surface with 5.0 cm grid spacing. The simulated data presented in Plate 1 was acquired using three flight directions at an altitude of 200 m and a flight speed of 25 m/s. The pulse repetition frequency was set at 30 KHz, and the scanning angle at 20 degrees. The 1.0 mrad laser beam sub-sampling was set according to the model grid spacing at the flight altitude used, giving 53 sub-beams within the 20 cm footprint area at ground level. Furthermore, a constant detector energy threshold was used to extract the first echo 3D-points from the simulated 1.0 GHz Plate 1. Simulated laser point cloud and tree tops from the tree model exposed (red dot). Some deviated treetops extracted from the data can be seen as blue dots. PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING October

8 scanner output waveform data. The treetops were extracted from the simulated data using an approach depicted in Hyyppä et al. (2001), which consists of Gaussian prefiltering and local maxima finding. The approach is also used for operative tree locating tasks from laser scanner data. As a result, simulated treetops indicated a 0.33 m underestimation of the tree heights compared with the known ground level in the model. However, when the ground surface was modeled by the simulated points, and tree heights were computed, the underestimation in tree height extraction decreased to 0.02 m. Tree location was extracted to 0.15 m accuracy by considering the selected maximum height point as the trunk location. This was rather a good estimation, thanks to the relatively dense point spacing and the smooth shape of the tree canopy model. According to the international Tree Extraction comparison (Kaartinen and Hyyppä, 2007), the best models, using a point density of 2 to 8 pt/m 2, resulted in a median error of 0.5 m in location. However, in this international comparison, the segmentation errors of individual trees were the main source of errors, and the variability of tree heights and locations was relatively higher than in this example. Tree trunks are also not always vertical in the real environment. Case 2: Scanning Geometry Effect The developed simulation method was also tested for the simulation of three different existing laser systems: TopoSys II, TopEye Mk II, and Optech ALTM In this test, the reference environmental model of the Espoonlahti test area was used. The environment model was computed from the first echo point data of 18 overlapping scanning strips acquired with TopoSys II in May 2003 at an altitude of 400 m. This is partly the same area featured in the EUROSDR/ISPRS project Tree Extraction, coordinated by the Finnish Geodetic Institute. The simulated data were acquired using typical systemcharacteristic parameter values of the three scanners, determining the spatial distribution of the laser beams, pulse transmission, and waveform detection. The resulting data are summarized in Table 2. The trajectory at an altitude of 400 m and 80 m/s flight speed of the sensor were kept the same for each simulation. The resulting simulated point clouds for the three discussed scanners are presented by image captures from TerraScan software in Plate 2. Points were colored by elevation, and they express the same location of the model. The data characteristics for each scanner type are clearly observable in the images, and the capability of each system to capture objects in along- and cross-track directions is illustrated. The level of detail in the original TopoSys II first pulse data and the environment model was reproduced by the simulation. Some erroneous points could be detected on the walls, as the environment model computation from the laser survey data could lead to TABLE 2. SIMULATION PARAMETERS FOR THE SCANNING GEOMETRY SIMULATION (f p PULSE REPETITION FREQUENCY, f s SCAN FREQUENCY, u max MAXIMUM SCAN ANGLE, D p PULSE DURATION, N wf NUMBER OF WAVE SAMPLES, f wf SAMPLING FREQUENCY) Parameter ALTM3100 TopoSys II TopEye Mk II f p 50,000 Hz 83,500 Hz 50,000 Hz f s 70 Hz 653 Hz 35 Hz u max D p 8.0 ns 5.0 ns 4.0 ns N wf f wf 1 GHz 1 GHz 2 GHz Plate 2. Simulated point clouds for three scanner types. From the top: TopoSys II, Optech ALTM 3100 and TopEye Mk II. false artifacts, the effect of which depends on the grid cell size that has been used. The data validation was carried out by comparing the simulated first echo data to the environment model, and, separately, to the first echo data from an independent TopoSys II flight strip (later referred to as reference data) that was not used for the environment model computation 1184 October 2009 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING

9 described above. Each simulated point data was converted to a 20 cm grid so that the elevation value corresponds to the highest hit in each cell. The meaningful (i.e., not empty) cell values were subtracted from the corresponding model grid cell values for elevation difference evaluation. The means and standard deviations for the elevation differences are presented in Table 3. The mean differences reveal that the simulator slightly overestimates the object elevations. For the TopEye Mk II scanner, the overestimation is somewhat larger in comparison to the two other simulations. This could be explained by the differences in scanning operation, and especially by the scanning angle, as the data contains many more echoes from the vertical objects, such as the walls, than the corresponding TopoSys II and Optech ALTM 3100 data. When the wall hits were neglected, the mean elevation difference decreased to m, with a m standard deviation. The results were comparable to other simulated data sets. The elevation differences between the environment model and the TopoSys II reference point cloud showed an approximate 16.0 centimeter drop for the point elevation in the reference data. Deviation between the real TopoSys point cloud and the environmental model was 2 to 3 times larger than for the simulated Optech and TopoSys data sets. The systematic discrepancy in mean elevation differences for the simulated and reference data sets could be explained by the navigation errors in the reference data, or by the vendordriven systematic strip adjustment. In Table 4, the results for cross-comparisons between the simulated and reference 3D point data (TopoSys II) are given. For each point data set, the highest and lowest hit grids were computed and pairwise comparison between common occupied cells in corresponding reference and simulated data grids was performed. The comparison shows approximately 0.20 m systematic overestimation in point elevations for both the highest and the lowest point comparison, as the simulated points were a bit higher than the points in the reference data. When the grid cells with a deviation larger than 0.5 meter in point elevations (e.g. wall points) were neglected from the computation, the mean elevation difference, e.g., for the simulated TopEye Mk II data was reduced to 0.08 m with 0.10 m standard deviation in comparison to the reference point cloud. It is also noted that the reference data strip was systematically 16.0 cm below the environment model (see Table 3), which increases the elevation differences between simulated and reference point data. By eliminating this factor, the mean elevation differences in the point data comparisons closely corresponded to the 0.08 m of the wall elimination case (see also Table 4). Plate 3 shows a data cross-section of the reference and simulated data, each presented as a distinct color. Reference TopoSys II data is presented in purple, simulated TopoSys II in green, Optech ALTM 3100 in red, and TopEye Mk II in yellow. Some minor differences are found, due to the different spatial distribution of points in each data within the cross-section area. The point spacing and elevation information are comparable to the reference TopoSys II data, noting the observed elevation difference between the reference point data and the environment model used in the simulation, which is also perceptible in Plate 3. In this case, the oscillating scanners produced denser point spacing in the cross-track direction and sparser point spacing in the along-track direction (see Plate 2). The latter could be improved by changing the flight speed, or by increasing the scan frequency, which leads to a decrease in cross-track point density. For the fiber-based line scanner, the point density is better in the along-track direction, as the scanning frequency is superior to the others, but the acrosstrack point pattern is more fixed, unless hardware or flightmode modifications are added. The conic scanners had the advantage of relooking at the object once measured by the front part of the scan circle. The resulting point pattern is denser in the side areas of the pattern than in the center. Plate 3. Cross-section of the reference and simulated point data. Reference TopoSys II data is presented in purple, simulated TopoSys II in green, Optech ALTM 3100 in red, and TopEye Mk II in yellow. TABLE 3. ELEVATION DIFFERENCES BETWEEN THE ENVIRONMENT MODEL E mdl AND SIMULATED AND REFERENCE POINT CLOUDS E mdl -ALTM3100 E mdl -TopoSys II E mdl -Mk II E mdl -Reference MEAN m m m m STD m m 7.38 m 1.85 m TABLE 4. ELEVATION DIFFERENCES BETWEEN THE REFERENCE AND SIMULATED DATA FOR THREE SIMULATION CASES. DIFFERENCES WERE COMPUTED FOR HIGHEST AND LOWEST HIT GRID PAIRS (HIGH, LOW) Reference-ALTM3100 Reference-TopoSys II Reference-Mk II High Low High Low High Low MEAN 0.24 m 0.24 m 0.21 m 0.29 m 0.23 m 0.23 m STD 1.41 m 1.58 m 1.60 m 1.78 m 1.47 m 1.55 m PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING October

10 Mobile Mapping There is a special group of applications for lidars attached to ground-based mobile platforms (e.g., Talaya et al., 2004; Kukko et al., 2007). The field of autonomous vehicles with lidar-aided navigation is also of great interest (e.g., Montemerlo et al., 2006). In these areas of interest, more optimal constructs and arrangements could be tested using simulation. Performance analysis and comparison between desired layouts and scanner properties could also be carried out. Case: SICK LMS in Mobile Platform Use Plate 4 shows a cloud of points simulated for a SICK LSM profile scanner in mobile use. The scanner was set up approximately 2 m above the ground, the ground speed was set at 11 m/s, the scanning plane was 30 degrees off-nadir, and the maximum lidar range was assumed to be 30 meters. The angular resolution of the sensor was set at 0.5 degrees. A surface model with 20 cm ground resolution was used in the simulation. The mean elevation difference for the highest hit grid was 0.02 m, and 0.05 m for the lowest hit grid, in comparison to the environment model used in the simulation. Standard deviation in both cases was 0.39 m. From the simulation data illustrated in Plate 4, we can see how the spatial data distribution changes over the measurement angle: at close range, the number of ground hits is far greater than at distances further from the scanner, where the measurement angle is more than 50 degrees off-nadir cross-track. Details, such as cars on a parking lot and the trees around it, are clearly visible. Shadowing of different obstacles in the scene can be detected, and such information is valuable when determining the effect of sensor altitude and measurement geometry on the data acquisition and coverage, especially for street mapping purposes. Discussion More advanced point discrimination schemes than the detector threshold utilized in the derivation of point data for this paper are based on finite differences of numerical derivatives (e.g., the detection of local maxima or the zero crossings of the second derivative), or, more generally, the zero crossings of a linear combination of time-shifted versions of the signal (Wagner et al., 2004). Such an approach, for example, is the constant fraction discriminator, which determines the zero crossings of the difference between an attenuated and a time-delayed version of the signal (Gedcke and McDonald, 1968). Some of the methods, like maximum, zero crossing, and constant fraction are invariant with respect to amplitude variations, and therefore, to a certain extent, changes in pulse width (Wagner et al., 2004). These methods are usually applied in waveform data processing to take advantage of better performance over the amplitude-dependent discrimination methods. The application and analysis of these more advanced methods in the processing of simulated waveform data were excluded from this issue, to be further explored in future work. It is also expected that the applicability of the simulation in this kind of research will vary considerably, as the simulation case for mobile mapping indicates. The data acquired with a hypothetical construct of a mobile mapping platform, or an airborne system, gives us an impression of the data properties and thus helps in determining the final construct of the sensor platform. It also provides data for system performance analysis and algorithm development for street mapping purposes. Since simulation makes it possible to acquire data from an unchanged object with different scanning geometries, it is possible to perform a thorough analysis of the effect of scanning geometry on the quality of laser products. This is usually not possible using real data. Different laser scanners have, in addition to the geometric characteristics, unique properties for pulse transmission Plate 4. SICK LSM D laser scanner simulated to determine its applicability for mobile mapping October 2009 PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING