Scanning can be considered a geodetic technique that does not enable any measurement redun-dancy at the level of individual points due to its fully automated measurement process. This some-what limits the use of its direct measurements (polar or cartesian coordinates) in the evaluation of displacements and deformations since their variance-covariance matrices are difficult to estimate (having only instrumental standard deviations at disposal). On the other hand, the measurement redundancy is significantly large if surfaces are considered indirect observables, making them a more convenient tool for possible change detection. Like in any measurement process, the quality of these observables is regulated by measurement errors, which have systematically been described by authors such as Reshetyuk (2009). In TOF (pulsed) TLS, the observables are particularly in-fluenced by distance related errors which are the outcome of physical limitations of reflectorless measurement process. To understand their effect, these limitations will be described in the next subsection. In addition, the quality of observables also depends on the scanning geometry, which will be discussed separately in the second subsection.
2.6.1 Physical limitations
The physical limitations of pulsed laser ranging are determined by a modified radar range equation that may be found in slightly different expressions in the literature with most of them derived from the work of Jelalian (1992). Wagner (2007) presented his version in the following form:
Pr = P0· d2a
(2D)2 · ρ · cos (α) · ηAT M · ηSY S (20) with P0 being the transmitted and Pr the detected (received) laser pulse power at distance D. da represents the receiver aperture diameter, ρ the reflectivity coefficient and α the incidence angle2. The atmospheric and system transmission factors, ηAT M and ηSY S account for the losses of the pulse propagation through the atmosphere and the transmitter-receiver optics. The 1/D2 decay of Pr can only be expected if the whole area of the laser spot is reflected from the object’s surface, otherwise higher orders of D have to be considered. Moreover, as demonstrated by, e.g., Riegl and Bernhard (1974), this power-distance dependency is further influenced by the configuration of laser emitter and receiver. Finally, in equation 20 it is assumed that the reflected laser light intensity (i.e., power density) decreases according to the Lambertian law, I (α) = I0cos (α), which only applies for an ideal diffuse reflection (scatterer) with the intensity being direction independent. Despite the fact that most anthropogenic surfaces can be considered rough for typical laser light wavelengths of commercial scanners (with λ in visible or near IR domain), this theoretical reflection model is more
2The incidence angle is the angle between the direction of the incoming laser beam and the surface normal.
likely to be replaced by more complex ones, e.g., Minnaert or Henyey-Greenstein found in Rees (2001).
If small scale displacements and deformations are to be estimated with sufficient precision it is important for the scanning to be performed with considerations based on equation 20 in the first place. The received optical power Pris processed (discretized in the case of fully digital systems) inside the receiver and the pulse travel time and amplitude estimated. A simple demonstration of this process is shown in Figure 5 where the latter two parameters were estimated on the basis of LSA using a Gaussian pulse model. Clearly, the object distance along with the receiver’s and
Figure 5: Time and amplitude estimation. In TOF systems a pulse is never a true Dirac delta function, that is why using a Gaussian model has proved to be more realistic and widely utilized (Wagner et al, 2006). The dots represent the discrete waveform with the interval [0,1]
corresponding to the dynamic range of the receiver.
signal processing unit’s characteristics become important factors that not only affect the quality of estimating the observables (surfaces) but also limit the use of this technology when the object’s reflectivity is too low or the loss of energy due to propagation through the atmosphere or device itself is large enough. Moreover, the incidence angle and the light scattering properties of materials (depending on the color, chemical composition, surface roughness, etc.) also determine the amount and direction of energy distribution on the object side resulting in further limitations in quality and reliability of distance estimation. Some of the systematic distance errors, such as atmospheric corrections, can be applied in a similar way as in the case of classical terrestrial measurements and must always be considered if their effects become significant. As for the errors which are regulated by surface material properties, their effects on the distance precision and the level of the instrument’s detectivity can be tested experimentally (see section 3.2).
All the interrelated functional parameters make the quality of surface estimation more influenced
by distance than angular systematic errors. Even if pulses are not transmitted at perfectly equal angular intervals, the irregularities in the resulting range image are only device dependent and do not alter the amount of detail being captured. Hence, the dense sampling pattern that nowadays systems are able to provide with small angular increments between consecutive laser pulses can be used for precise surface estimation despite the ever-present sampling irregularities. This means that apart from understanding the physical limitations of reflectorless laser ranging given by equation 20, it is also relevant to consider how the scanner is stationed with respect to the object in order to assure the sufficient object coverage, i.e., point density.
2.6.2 Scanning geometry
If point density is to be sufficient, not only the predefined scan parameters (angular resolution) but also the scanning geometry, i.e., the incidence angle and distance to the object should be examined (Figure 6). The selection of these parameters has a direct influence on the quality of the point clouds
Figure 6: Impacts on point density. Although D1 ≈ D3 the larger incidence angles at object 1 lead to wider spacing between individual points.
with the aim of assuring a comparatively homogeneous distribution of points on the whole object’s surface. The rate in which density is decreasing can be quite fast in the case of scanning larger objects from a close distance, for example roads, tunnels or long walls. Particularly in these short proximities, Soudarissanane et al (2008) have concluded that by simply moving the scanner for two meters the point cloud quality can be improved by around 25 %. The effects of the object surface orientation on the quality of the measurements have also been studied in, e.g., Soudarissanane et al (2007).
Moreover, the object coverage also depends on the selection of instrument (scanner) stations since it is usually not possible to capture the entire structure from one station only due to occlusions made by the surface features or other obstacles in the line of sight. The remaining gaps are to be filled by points coming from adjacent stations after the individual point clouds have been positioned in one common reference coordinate system. In the areas where the neighboring point clouds overlap, the higher point density can provide information on the quality of the absolute (relative) orientation of scan data which is closely connected with the proper configuration of scanner targets in the geodetic network. The size and complexity of the object determine the number of scanner stations needed to produce the final object image with small variations in range and incidence angle between individual points. Some of today’s high-end scanners are able to perform the acquisition process using angular increments lower than 1 arcsec, thus assuring millimeter point spacing in both directions through their full range of operation (Leica, 2011). Such high sampling capabilities lead to large local data redundancies and to a significant reduction of field work in general.