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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004
3.2 Spatial discrimination
3.2.1 Laser beam propagation & resolution
Optical laser scanners resolution is limited by the diffraction of
the laser light. Calculating the maximum possible spatial
resolution requires an arbitrary definition of what is meant by
resolving two distinct features. The Rayleigh Criterion assumes
that two points sources can be assumed as being separate
(resolved) when the centre of the Airy Disc (imaged) from one
overlaps the first dark ring in the diffraction pattern of the
second. Even in the best emitting conditions (single mode), the
laser light does not maintain collimation with distance (e.g.
check the beam divergence on scanner specifications sheets). In
fact, the smaller the laser beam, the larger is the divergence
produced by diffraction. For most laser scanning imaging
device, the 3D sampling properties can be estimated using the
Gaussian beam propagation formula and the Rayleigh criterion.
This is computed at a particular operating distance, wavelength
and desired spot size within the volume. Figure 4 illustrates that
constraint (A = 0.633 um). The solid line shows the relationship
batween the X and Y axes (direction perpendicular to the laser
projection) and the physical dimensions of the object to be
scanned. A detailed analysis of this propagation property as
applied to 3D scanners can be found in (Rioux et al., 1987;
Beraldin et al., 1994). A number of scanner manufacturers use
laser re-focusing techniques to achieve better resolutions at a
cost of slowing down the effective acquisition data rate.
10mm
imm
> pe
$m -—
X-Y Diffraction limited | ez eis
[venu
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di
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4
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e ; NM : / “i k
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lem 10 cm 1m om Figure 5. Wave (undulations) phenomenon created by the motion
Figure 4. Physical limits of 3D laser scanners as a function of
volume measured. Solid line: X-Y spatial resolution limited by
diffraction, Dashed line: Z uncertainty for triangulation-based
systems limited by speckle, from Rioux 1994.
For 2D cameras used in photogrammetry and texture mapping
applications (see Section 4.3), one must match the sensor pixel
size to how well an image can be resolved within an adequate
depth of field (DOF). In these imaging applications, spatial
resolution can be limited by diffraction. The smallest resolvable
feature, d, for a circular aperture is given by
d «1.22 A fn (6)
where d — smallest resolvable feature
À = light wavelength (e.g. 0.55 um)
Jn = lens f-number (e.g. f/22, f/4, etc.)
For example, at 0.55 um and for f/8, the smallest resolvable
feature is about 5.4 pm (close to typical pixel sizes). Another
example of interest (for display systems) shows that for the
human eye with a pupil diameter of about 2 mm (bright room)
977
can resolve | arc-min or for f=20 mm, 6.7 um (matches the eye
receptors). Finally, the DOF for an imaging system is
approximately given by
ry
DOF. = an Blur (7)
[o
where — Z- distance lens-object
Blur = blur spot (circle of least confusion)
® = aperture diameter
For example, at Z=2.5 m, f=25 mm, Blur spot = 5.5 um and
®=1 mm (f/22), than the depth of field is about 1.4 m. Some
camera systems use the Scheimpflug condition to extend the
system’s DOF (see Beraldin et al., 1994 for laser scanner case).
3.2.2 Measurement uncertainty
As described above, diffraction limits impose a constraint on
the resolving power along the X and Y-axes. For laser
triangulation systems, along the range axis (Z), one could
expect a continuous improvement as the amount of laser power
is increased. Unfortunately, this is not the case; indeed the
coherence of the laser light produces damaging interference
effects known as speckle noise which limits the resolving power
of the laser spot sensing (see Section 2.1.1). When the
uncertainty due to speckle (8p) is projected back into the scene
(8z — see eqn.(1)), it often means hundreds of micrometers in
triangulation-based system (doted line in Figure 4).
of the 3D camera wrt the scene.
We discussed uncertainty, which represents the random part of
the total system errors. The other part is the systematic error.
All 3D systems exhibit this type of error to different degrees
and for different reasons (e.g. poor calibration). Waves in the
raw 3D images are produced when the camera or the object
being scanned moves. This is shown in Figure 5. The waves can
be removed by proper sensor choice (faster scanner), reducing
motion or filtering the raw 3D images. Unfortunately, filtering
can altar the spatial resolution.
3.3 Objects material and surface texture effects
It is said that with structured light (active) approaches, minimal
operator assistance is required to generate a large quantity of
3D coordinates, and that the 3D information becomes relatively
insensitive to background illumination and surface texture. The
first comment is indeed true if you compare to methods based
on contact probes or photogrammetry. But one must be aware
that not all the 3D information is reliable (Soucy et al., 1990;
Paakkari, 1992; Hebert et al, 1992; El-Hakim 1994,1995:;
Boehler et al., 2003). The latter comment about surface texture
