A RESOLUTION MEASURE FOR TERRESTRIAL LASER SCANNERS
Derek D. Lichti
Department of Spatial Sciences, Curtin University of Technology, GPO Box U1987, Perth. WA, 6845, Australia —
d.lichti ? curtiu.edu.au
Commission V, WG V/1
KEY WORDS: LIDAR, Sampling. Resolution, Spatial, Quality, Terrestrial.
ABSTRACT:
Terrestrial laser scanners are increasingly being used for cultural heritage recording and engineering applications that demand high
spatial resolution. Knowledge of an instrument’s spatial resolution is necessary in order to prevent aliasing and estimate the level of
detail that can be resolved from a scanned point cloud. In the context of laser scanners. spatial resolution can be decoupled into
range and angular resolution. The latter is the focus of this paper and is governed primarily by angular sampling interval and laser
beamwidth. Both factors give rise to uncertainty in the angular position of a range measurement, though in terms of reporting
scanner resolution, it has become a common practise to emphasise one of these factors—typically sampling interval
as an indicator
of resolution. Since both affect the resolution of a scanned point cloud, consideration of only one can lead to a misunderstanding of
a system's capabilities. The ramification of this is that the actual resolution may be much lower than that perceived when visually
inspecting a scan cloud. It will be demonstrated that consideration of only one factor independent of the other is inappropriate
except under very specific conditions. A new, more appropriate resolution measure for terrestrial laser scanners is therefore
necessary and one is proposed in this paper. The effective instantaneous field of view (EIFOV) is derived by modelling the inherent
uncertainties in equal angular increment sampling and laser beamwidth with ensemble average modulation transfer functions
(AMTFs). The practical outcome of this approach is a scientifically sound method of quantifying laser scanner resolution for users
of the technology. Four commercially available terrestrial laser scanner systems are modelled with AMTFs and analysed in terms of
their angular resolution as measured by the EIFOV. It is demonstrated that point cloud resolution as indicated by the EIFOV is
much more coarse (by up to 21 times) than the sampling interval.
I. INTRODUCTION
Laser scanning instruments are increasingly being used for tasks
traditionally performed using photogrammetric and surveying
methods. They provide users with a three-dimensional sampled
representation—a point cloud—of an object or surface and are
used in a diverse range of applications including metrology, as-
built surveys, reverse engineering, airborne topographic
surveying, cultural heritage recording and volume estimation on
mine sites. Though the accuracy requirements for these
applications may differ considerably, spatial resolution is an
important aspect of any laser scanner survey.
Spatial resolution governs the level of identifiable detail within
a scanned point cloud and is particularly important for, say,
recording of cultural heritage features with fine details. For
laser scanners it can be decoupled into range and angular
resolution. Range resolution is the ability of a rangefinder to
resolve two objects on the same line of sight (Kamerman,
1993), which is directly proportional to timing resoluüon for
time-of-flight systems (Wehr and Lohr, 1999). Angular
resolution, the ability to resolve two objects on adjacent sight
lines, is a function of spatial sampling interval and the laser
beamwidth. For airborne laser scanner (ALS) systems, the
sampling interval is partially dependent upon aircraft motion,
whereas scanning mechanisms control it for terrestrial laser
scanners (TLSs).
Resolution is a term often abused and misunderstood: emphasis
in sales literature tends to be on the finest possible sampling
interval. which is often much smaller than the laser beamwidth.
Since both factors influence the resolution of a scanned point
cloud. consideration of only one can lead to a misunderstanding
of a system's capabilities. To illustrate, consider the article by
lavarone (2002), in which the author states that high scan
resolution can be achieved by correlated sampling (Le.
overlapping laser spots) and, therefore, laser beam spot size is
not a limiting factor. While this is partially true in the sense
that a fine sampling increment yields a high Nyquist frequency,
the benefit of correlated sampling is not fully realised because
sampling is not the only factor that influences resolution.
A scanned point cloud may appear to have very high spatial
resolution by virtue of a fine sampling interval and
corresponding high point density. The actual spatial resolution
may be much lower if the beamwidth is large relative to the
sampling interval because the fine details are effectively
blurred. It will be demonstrated in this paper that beamwidth
can be a significant factor in reducing the spatial resolution of a
scan cloud. even in the presence of correlated sampling.
Though perhaps not an issue for smooth surfaces, it certainly
could be for intricate surfaces with rapidly varying details that
might be encountered in cultural heritage recording or as-built
surveys of industrial plants.
A new angular resolution measure for laser scanners that
models the contributions of both sampling and beamwidth, the
effective instantaneous field of view (EIFOV), is proposed. Its
need is highlighted with a real dataset example that illustrates
positional uncertainty due to beamwidth. The EIFOV is
derived from an ensemble average modulation transfer function
(AMTF) that models the positional uncertainty due to both
factors. Following derivations of the AMTF and EIFOV, the
angular resolution of four commercially available terrestrial
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