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Lidar systems operate on the same physical basis as that of Radio Detection And Ranging (radar) except that a laser (with a wavelength between 532nm and 1.5µm) is used instead of radio waves; we can therefore apply the measurement principle first introduced in radar remote sensing to describe the flow of radiant energy in lidar systems using the radar equation (Wagner et al., 2006):

where is the received power, the laser pulse energy at the transmitter, Dr the aperture diameter of the receiver optics, R the distance from the laser to the target, the beam divergence, and is the backscatter cross-section, computed as:

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where is the angle defining a backscattering cone in relation to surface roughness, the reflectivity of the scatterer and is the illuminated area of the scattering element. These equations were developed from Baltsavias (1999) but disregard atmospheric effects as these can have negligible effect on the measurements over the short ranges measured in a forest environment (Campbell, 2002; Wagner et al., 2006).

Assuming that all variables in the radar equation are constant except distance from the target, and that the target fills the entire beam footprint, the return power intensity can be simply expressed as:

There are two main types of lidar system, ‘time-of-flight’ and ‘continuous-wave’ (CW). The time-of-flight method, as the term suggests, measures the travel time of light from a laser transmitter to a target and back to a laser receiver. This method is based on the principle that light travels at known constant velocity and therefore the time for the pulse to return to the sensor translates directly to distance, that is - the range (Rees, 1990; Lefsky

et al., 2002; Jensen, 2006). CW lidar systems offer an alternative approach in which the phase shift between the transmitted and backscattered light of a continuous laser beam of known wavelength is used to measure delay and obtain the range (Campbell, 2002). Although CW systems are usually quicker to operate than those of time of flight, they only facilitate one range return measurement: deeming them unsuitable for structurally complex environments such as forests, and so this method will not be considered further here. The main features of the time-of-flight method can be described as follows. A pulse of strongly collimated light energy, the laser beam, is emitted in a systematic pattern from a transmitter within the lidar instrument (Pfeifer & Briese, 2007). Rotating mirrors inside the sensor head deflect the beam out of the instrument to travel through the atmosphere and interact with objects in its path. The beam footprint increases in size with the distance dictated by the laser beam divergence angle (Jiang et al., 2012). Typical beam divergence values are between 0.03 and 8 mrad (Lim et al., 2003; Mallet & Bretar, 2009). When the beam hits an object, the light energy is reflected, absorbed, or transmitted; the proportions of each depend on the nature of the surface, the wavelength of the energy, and the angle of

(4.2)

(4.3) 3

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illumination (Campbell, 2002). The reflected energy that travels the same path from the reflecting surface back to the sensor, the backscattered energy, is detected within the instrument (Pfeifer & Briese, 2007). Recorded return energy is sampled to a discrete ‘bin’ by range; the size of which is predetermined by the frequency with which the digitiser can sample the signal and governs the ‘range resolution’.

Different target materials have spectral reflectance curves of different shapes,their spectral signature, and this forms the basis for identifying the material type from lidar data (see Chapter 2.5: Remote sensing of vegetation). The reflectance of vegetation, for instance, is governed by the presence of absorbing pigments, water content, and other physical and chemical factors (Rees, 1990). The nature of the backscattered energy also depends on the sizes of surface irregularities (roughness or smoothness) in relation to the wavelength of the radiation (Campbell, 2002; Lichti et al., 2002). The range (R) is derived once the return pulse energy crosses an internally defined threshold, and is computed by the time (t) for a lidar pulse travelling at the speed of light (c) to travel to and return from a target, according to:

As a result, the accuracy of the range measurement is dependent on the time counting accuracy of the digitiser and the accuracy of detecting the backscattered energy above a noise level (Pfeifer & Briese, 2007). As lidar measurements work on a ‘line of sight’ principle, depending on the scene and the orientation of the laser scanning system, near- range objects in the path of the laser beam can obscure sampling of surfaces leading to occlusion (Kirchhof et al., 2008). This can be a significant limitation, particularly in TLS. The range and direction to reflecting surfaces is determined by the lidar scanner, which creates a 3D point cloud data set in relation to the scanners internally defined coordinate system; for instance the direction of the pulse is stored from the orientation of the internal mirror at the time of pulse emission. Therefore, the data is typically processed to transform the acquired measurements to a standard coordinate system, translating the output data from ‘scanner space’ to ‘object space’ (Heritage & Large, 2009).

In the case of pulsed lidars the energy returning to the sensor can be recorded according to several schemes; first return, where the first point at which the signal intensity rises above a defined threshold is recorded signalling the first ‘hit’; last return, where the furthest point

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is recorded; discrete return, where a number of ranges are recorded for each pulse full waveform, in which all the energy reflected from a target is recorded.

4.2.1 Intensity measurement

Along with the acquisition of range, some laser scanning systems also offer a quantitative measure of the return signal – the intensity: a measure of the strength of the backscatter recorded defined by the echo amplitude (Pfeifer & Briese, 2007; Vain et al., 2010). Intensity can be related to laser power, recorded as a sensor-specific digital number (DN), and can provide an insight into the material properties of the reflected surface (Lichti et al.,

2002; Lefsky et al., 2002; Mallet & Bretar, 2009). However, it is dependent on many factors (as defined in equation 4.1) including: target characteristics, such as the reflectance of the intercepted surface at the lasers wavelength or the ‘roughness’ of the surface;

atmospheric conditions, such as weather conditions during an airborne flight campaign;

lidar instrument characteristics, such as the total power of the transmitted pulse

conforming to eye-safety and; scan geometry, such as range from target or angle of scan. Due to these factors, calibration of intensity values is commonly performed to allow measurements to be compared.