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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part BS. Istanbul 2004
laser scanner systems is analysed. Though the analyses focus
on terrestrial systems, the AMTF and EIFOV model can also be
applied to ALS
2. LASER SCANNER RESOLUTION
2.1 Sampling interval and beamwidth reporting
Sampling and beamwidth reporting in sales literature varies
substantially from one vendor to the next, which can cause
confusion about a system's capabilities. To demonstrate, some
of the salient properties of four TLS systems are listed in Table
|. The selected scanner vendors use two methods for reporting
their finest angular sampling interval: spatial interval as a
function of range (Optech and Leica) and angular increment
(Mensi and Riegl). Note that Leica only provides the interval at
one range (50 m), whereas Optech gives a linear function.
Make Model Angular Laser
Sampling Interval Beamwidth
Leica HDS2500 0.25 mm at 50 m < 6 mm from 0
- 50 m
Mensi GS100 0.0018° 3 mm at 50 m
Optech | TLRIS-3D | 0.026R mm, where | 0.17R+12 mm
R is the range to
target in m
Rieg] LMS- 0.0025* 0.25 mrad
ZA201 divergence
Table 1. Angular sampling interval and beamwidth reporting
styles for some commercial TLS systems.
The Optech specifications provide the most descriptive
beamwidth information in the form of initial diameter plus
linear divergence as a function of range. The Leica beam
diameter specification is given for the range O — 50 m, while
Mensi gives the diameter only at 50 m. Riegl provides the
beam divergence, in mrad, that corresponds to the increase in
beam diameter as a function of range. Divergence may also be
defined as the linear increase in radius (c.g., Weichel, 1990).
2.2 Positional uncertainty due to beamwidth
The inherent positional uncertainty due to beamwidth is
highlighted in Figure 1. which depicts a point cloud of a plumb
line (2 m long, = 0.1 mm diameter) scanned with a Cyra Cyrax
2500 (now known as the Leica HDS2500) from a range of 5.5
m. Also shown is the estimated plumb line determined by least-
squares 3D line fitting. The co-ordinate system is externally
defined (i.e. object space) and the X-axis scale has been greatly
exaggerated. Several sampling profile lines intersect the plumb
line, as indicated by the 2-4 mm long linear bands of points.
Angular measurement noise is apparent in the scatter of points
about the centreline of each band. The acute angle
(approximately 0.4°) between the plumb line and sampling
profiles is due to the scanner not being levelled. Levelling is
not possible with this instrument.
The band of points along each profile line is due to beamwidth-
induced uncertainty in angular position. Its cause is depicted
schematically in Figure 2. For each point in this cloud, the
range measurement to the backscattering surface (i.e. the plumb
line) is made to a point somewhere within the projected laser
beam footprint. Notwithstanding noise and quantisation effects,
the apparent angular position of the range measurement is
taken by convention to be the centre of the emitted beam.
Though a fine feature (such as a plumb line) can be resolved,
the actual angular position of the measured point may be biased
by up to one-half the beam diameter and cannot be predicted.
The position can only be estimated with analytical techniques
like redundant geometric form fitting. While a plumb line may
appear to represent an extreme case, it highlights very well the
inherent positional ambiguity due to beamwidth that can exist
in all point clouds but may be less obvious upon visual
inspection. Beamwidth uncertainty can also manifest itself at
edges and tangent to curved objects such as cylindrical pipes.
A model that quantifies the uncertainty is proposed in the next
section.
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217
