Laser scanning is the use of opto-mechanical assembly to scan a certain area on the ground with laser beam (photons ) as the sensing carrier (Wehr & Lohr, 1999). It is an active system in that the assembly emits the sensing photons and collects the reflected photons through a sensor. The intensity of the reflected light depends on the reflecting surface and can therefore be used in sensing the type of topography. Since the laser consists of a narrow beam of light (narrow instantaneous field of view), laser scanning involves deflecting the beam in a pre-defined pattern to cover the region of interest in the lateral direction. The forward motion of the assembly completes the full sampling coverage of the region with high point density (see lower part of Figure 3.1).
A laser scanning assembly not only detects the properties of the illuminated region on the ground but also measures the distance between that region on the ground and the assembly, a process called ranging. This is determined by time of flight measurements, that is, by measuring the time the photons are emitted to the time they arrive in the sensor. If is the distance, called the range, from the ranging unit to the object’s surface, and is the speed of light, the traveling time of the photon can be determined as,
A laser scanner works in the same way as a RADAR (RAdio Detection And Ranging) except that the ranging signal is a laser beam in the near infrared to visible wavelengths. For this reason, laser scanner is also known as LADAR (LAser Detection And Ranging) or LiDAR (Light Detection And Ranging). LiDAR data can be used in conjunction with an onboard GPS and Inertial Navigation System (INS) for precise determination of locations (Lang, McCarty, Wilen, & Awl, 2010).
When the laser was invented, it was called a solution seeking for a problem. Nowadays, lasers are ubiquitous in our technology dependent society. The advantage of using laser in ranging is its susceptibility to be produced in high energy pulses at short time intervals (see Section 3.1) and its highly collimated (narrow) beam (due to spatial coherence) requires a narrow aperture. Soon after the invention of the laser, its precise ranging potential was immediately realized. When pulsed lasers with high repetition rates became available, scanning laser systems were soon contemplated. The use of lasers for remote sensing was conceptualized in the 1960s (Ritchie, 1996) but rapid growth of the use of commercial airborne LiDAR with fine spatial resolution was realized only in the latter half of the 1990s (Lang, McCarty, Wilen, & Awl, 2010).
The primary components of a laser scanning assembly are shown in Figure 3.1. They can be subdivided into the following:
1. laser ranging unit – consists of the emitting laser and the electro-optical receiver
2. opto-mechanical scanner – component responsible for the scanning action of the laser
3. control and processing unit
The two popular types of lasers, namely the pulsed laser and continuous-wave laser, provide two ways of laser ranging: pulsed ranging and continuous-wave ranging, respectively.
Pulsed Laser Ranging
The basic principle of pulsed laser ranging is shown in Figure 3.2. Laser pulses are incident to the ground and the reflected pulses are collected by a detector (receiver in the figure). The range can be determined by measuring the time of flight according to Eq. (3.1.1), which in this case takes the form
while the properties of the reflecting surface are determined by analyzing the reflected intensity. The time of flight is equal to the delay time of the arrival of the reflected pulse as shown in Figure 3.2. It is measured as the time difference of the leading edges of the transmitted and reflected pulses using the time counter of the laser. The emitted and the reflected pulses are shown in the figure. The range resolution depends on the resolution of the photon time of flight, that is, from Eq. (3.1.1)
An important parameter in LiDAR operation is the maximum unambiguous (measurable) range . This is determined by the maximum time of flight that the instrument can handle:
To achieve higher , should be large. However, larger means that the pulses stay longer in flight, which makes them more susceptible to attenuation. This energy loss limits the achievable maximum unambiguous range.
Accuracy is another important parameter of a LiDAR system. It is given by
for pulse ranging where is the rise time of the pulse and is the signal-to-noise ratio, which depends on several factors like the power of received signal, background radiation, sensitivity of the detector, etc. Figure 4 of Ref. (Wehr & Lohr, 1999) outlines the relation of several parameters and their influence on the signal-to-noise ratio and the accuracy.
If the received signal power is low that only thermal noise is important, the square root of is proportional to the received (reflected) optical and the ranging accuracy can be written as
where Bpulse is the noise input bandwidth, which is inversely proportional to the rise time and is the peak reflected optical power. Since it is hard to measure the reflected optical power, for practical purposes one can replace it with the transmitted power ,
One can also define an average transmitted power using the formula,
where tp is the duration of the pulse while is the pulse repetition rate.
Continuous Wave Laser Ranging
In continuous wave (CW) laser ranging, the laser intensity should be modulated by a time-varying signal, e.g. a sinusoidal signal. For sinusoidally modulated laser intensity, ranging is accomplished by measuring the phase difference between the returning signal and the emitted signal as shown in Figure 3.3. The time delay is extracted from the phase difference according to:
Since the sine wave gives the same magnitude for angles that differ by a multiple of , the phase difference can be written as
where is the period. The integer can be interpreted as the number of full wavelengths included in the distance from the laser to the receiver. From Eq. Error! Reference source not found., the range can be written as
Since the second term is not much useful in ranging, we can just drop it from Eq. (3.2.4),
The range resolution can then be written as,
It is to be noted that the range resolution is determined not only by the resolution of the phase difference but also by the frequency (or wavelength) of the modulating signal. The higher the frequency (shorter wavelength) of the modulating sine wave, the finer (smaller ) is the range resolution for a given phase resolution. Since the maximum value of is , the maximum unambiguous range is given by
In order to achieve both higher resolution (smaller ) and higher maximum unambiguous range, multifrequency modulating signals are used with the signal having the longest wavelength (lowest frequency) determining while the signal with the highest frequency determining the range resolution.The accuracy of continuous-wave laser ranging is given by
If the only important noise is thermal noise (for low reflected power), the square root of the signal-to-noise ratio is proportional to the reflected power and the accuracy becomes where Bcw is the bandwidth of the input noise.
The availability of powerful pulsed lasers makes pulsed-laser ranging the standard commercially available LiDAR system. LiDAR sensors can be mounted on satellites and aircrafts or carried by terrestrial means. These sensors are designed for high speed and highly accurate measurements and therefore facilitate the description of the geometric structure of the given target. The ability to very quickly (thousands of points per second) measure the distance between the sensor and the target allows the generation of 3D cloud points which, by applying appropriate algorithms, makes it possible to digitally reconstruct and describe the structure of the target for examples trees with high precision (Pfeifer, Gorte, & Winterhalder, 2004; Rossel, et al., 2009a; Rosell, et al., 2009b). For these reasons, in spite of their limitation for dusty environments, LiDAR systems have turned out to be one of the most used sensors for the geometric characterization of vegetation and infrastructure.
LiDAR can generate both geometric and radiometric data. LiDAR sensors can measure multiple reflections or returns, which occur when an object partially blocks the path of a laser pulse and the remaining portion of the pulse continues to the next object (Reutebuch, Andersen, & McGaughey, 2005). These small number of returns, otherwise known as discrete returns, are used to down-sample the dominant reflections, usually the first and last returns. Multiple returns therefore allow ranging of different layers of topography, forest canopy, and vegetation. The majority of commercial LiDAR instruments is generally mounted on fixed-wing or helicopter platforms and utilizes this discrete-return logic. Discrete-return LiDAR sensors extract 1-4 returns per pulse, 3D points, and intensity values that correspond to backscatter amplitude. This is in contrast to full-waveform instruments where the LiDAR return is sampled at high frequency, providing much greater information on the vertical profile of the returned signal. Full-waveform LiDAR samples, at GHz rate, the entire reflected waveform for computer-intensive post processing and extraction of points and elaborate waveform features (Wagner, Ullrich, Ducic, Melzer, & Studnicka, 2006). While full-waveform capability LiDAR systems have increased in number and are an important development, recent progress has typically been aimed at producing finer point spacing and increased temporal sampling of discrete-return signal, rather than full-waveform capability.
Most discrete-return LiDAR studies of vegetation have tended to use empirical, semi-empirical or statistical relationships between LiDAR returns and tree-level or forest stand-level parameters (Lefsky et al.,1999; Holmgren et al., 2003; McCombs et al., 2003; Riaño et al., 2003). Often in these studies, LiDAR system characteristics such as scan angle, footprint size (i.e. the illuminated area on the ground), signal triggering threshold, variations in canopy structure etc., are not accounted for and are ignored (Brandtberg et al., 2003; Riaño et al., 2003; Zimble et al., 2003; Koetz et al., 2007), or included implicitly through the expression of LiDAR canopy height as percentile values. Even where the impact of 3D canopy structural information is considered explicitly in examining the LiDAR signal, this tends to take the form of statistical distributions in a 3D ‘voxel’ space of parameters such as leaf area index (LAI) and leaf angle distribution (LAD) (Houldcroft et al., 2005), or via the use of simple geometric primitives representing individual tree crowns, with some statistical description of extinction within and between tree crowns (Sun and Ranson, 2000; Goodwin et al., 2007). Other studies have used region growing methods to explore the impact of canopy structure on LiDAR returns at the individual tree-level (Hyyppä et al., 2001). The problem in all these cases lies in deciding what the appropriate ‘equivalent’ structural parameters (LAI, LAD, extinction coefficient etc.) should be for a given canopy. Hopkinson and Chasmer (2009) showed the impacts of canopy structure and system characteristics on estimates of canopy cover from discrete-return LiDAR. Lefsky et al. (2002) review issues of canopy structure (in particular the vertical and horizontal amount and distribution of vegetation) on the LiDAR signal, particularly for ecosystem applications.
Various studies have been carried out to assess the impact of LiDAR system and survey characteristics. Næsset (2009) provides perhaps the most comprehensive attempt to quantify the impact of such effects practically, through a comparison of LiDAR returns from two different instruments at different flying altitudes and pulse repetition frequencies (PRFs). Yu et al. (2004a, b) studied the effect of flight altitude on the number of detected trees and on the estimation of tree height. The results suggest that increasing the flight altitude increases underestimation of tree height, and that pulse density is a crucial factor for tree height measurements (although this effect was not separated from the impact of using different pulse densities at different altitudes). In a similar study, Hirata (2004) examined footprint diameter (via changing altitude) in mountainous terrain and found that retrieved height increased with increasing footprint size. Hirata (2004) also studied different sampling density by subsampling existing data and showed the rate of extraction of treetops increased with sampling density. Maltamo et al. (2004) examined bias in estimating timber volume caused by footprint size.
Næsset (2004) found that first-pulse LiDAR returns did not vary much regardless of flight altitude/footprint diameter for footprints ranging between 16 and 26 cm, and that last-pulse returns were more sensitive to variations in footprint diameter. Goodwin et al. (2006) examined how canopy height profiles were affected when platform altitude was increased from 1000 to 3000 m (footprint size increased from 0.2 to 0.6 m) and found no significant differences. However, point spacing (i.e. PRF or sampling density) inferred from survey details was found to strongly affect retrieved attributes of individual trees, particularly height and canopy structure. Chasmer et al. (2006a,b) showed that PRF is associated with the ability of laser pulses to penetrate the canopy. Næsset (2009) confirmed a general tendency of retrieved canopy height distribution to be shifted upwards when reducing PRF from 100 kHz to 50 kHz. Hopkinson et al. (2006) attempted to reduce the effects of LiDAR survey configuration on empirical LIDAR-derived canopy height estimates.
Hopkinson (2007) used multiple surveys to examine the impact of altitude, beam divergence and PRF on pulse return intensity (and height distribution) for different vegetation canopies. Reducing peak laser pulse power (by increasing altitude, beam divergence or PRF) reduced penetration into short canopies, while increasing penetration slightly into tall canopies, where foliage tended to have slightly lower leaf area density. Hopkinson (2007) emphasizes the need to account for system and survey-specific variations in peak pulse power as far as possible in order to make different LiDAR surveys more directly comparable and proposes an empirical correction for systematic biases. Hopkinson (2007) also suggests that if such variations cannot be accounted for directly, their impact should be estimated via sensitivity analysis. The different technical specifications (and environmental impacts) among different surveys, and interdependencies between some of the parameters being investigated, make it difficult to generalize the impacts of system characteristics on the retrieval of canopy structural parameters, as noted by Hopkinson (2007). For example, platform altitude controls both LiDAR point spacing and footprint size (beam divergence), for fixed PRF; any alteration of altitude will change both point spacing (across track) and footprint size. Even for LiDAR points scanned from the same altitude, far-range (maximum off-nadir scan angle) points have larger footprints than those at nadir due to projection effects on the instantaneous field of view (IFOV). One method to separately investigate the effects of sampling density and footprint size is to apply thinning to the original LiDAR data in either a systematic (Yu et al., 2004a), random (Goodwin et al., 2006), or semirandom (Gobakken and Næsset, 2008) manner to keep a constant sampling density in order to make unbiased comparisons. Another method is to generate a reference survey, against which other surveys with varying properties can be normalized (Hopkinson, 2007).
In scanning LiDAR systems the scan angle can vary significantly across survey regions. Despite this, biases introduced by this angle variation are rarely considered as a source of information, or quantified (Hopkinson, 2007). Increasing scan angle tends to overestimate the mean, area-averaged canopy height in empirical estimators of height from LiDAR, due to seeing a larger proportion of higher points in the canopy (Næsset, 1997). However, the increased path length at greater scan angles will tend to cause greater attenuation of the signal, resulting in fewer ground returns, particularly in dense canopies (Lovell et al., 2005). Also, technical/electronic specifications (e.g. mono- or dual-receiver systems, scanning pattern, signal triggering method etc.) differ among airborne laser scanners (ALS), influencing the inter-comparability of LiDAR datasets acquired by various systems (Næsset, 2009). Even ambient temperature and the hours of operation can introduce variations in the power of the laser (Moffiet et al., 2005).
In addition to the use of controlled LiDAR surveys, there have been studies of the impact of LiDAR instrument characteristics using 3D simulation models. The main advantage of this approach is that the effect of various LiDAR parameters can be studied independently across a wide range of parameter values and canopy scenarios in such a way that would prove prohibitively expensive, or technically difficult for a real LiDAR survey. Simulation studies can also be a valuable tool to improve understanding of the limits of parameter retrieval from LiDAR data, particularly if combined with knowledge gained from empirical surveys. Using a geometrical forest model, Lovell et al. (2005) found that LiDAR height retrieval is less accurate at the edge of a swath due to uneven spacing of the sample points. Holmgren et al. (2003) used a geometric forest model to study the effects of LiDAR scanning angle on the proportion of canopy returns and height percentiles. The results showed that the two metrics varied with increased scanning angle, especially for long crown species. However, they used solid geometric objects (half-ellipsoids) to represent ‘trees’ and the LiDAR signal was modelled without divergence (i.e. using a parallel beam). These assumptions (particularly the first) will have potentially important impacts on model results due to overestimation of returns from the tree canopies (no probability of the signal penetrating a tree crown) which will in turn cause multiply scattered interactions to be misrepresented. Simulation studies clearly require a range of assumptions, not just at the stand-level, but also at the crown/within-crown level and the more simplified the model is, the more difficult it becomes to define useful ‘equivalent’ canopy structural parameters.