Understanding Spot Size in Laser Scanning

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3DSCANNING
Understanding Spot Size
for Laser Scanning
Geoff Jacobs
S
everal features of a laser scanner contribute to the level of definition it is
capable of achieving in a high-definition survey. This article provides insight into spot size, as I have found
that many professionals do not fully understand or appreciate the important subtleties of
this feature.
As reported in an earlier article (Professional
Surveyor Magazine, February 2005), several features of a scanner contribute to the level of definition or resolution that can be achieved via the
data it collects. Since the greatest differentiating
technical feature of a laser scanner, compared
to traditional survey tools, is the detail it can
collect, it helps to clearly understand these key
contributing features:
■
■
■
■
Scan density
Scan noise
Accuracy of each measurement
Spot size
Generally, the higher the scan density, the less
noisy the data, the higher the accuracy of each
measurement, and the smaller the spot size, then
the higher the definition of the survey.
High-definition scans, such as this one of a landslide, benefit from a small
diameter laser beam. Image courtesy: Silicon Valley Land Surveying, Inc.
in surface reflectivity, and oblique angle effects. Another advantage
of small spot size, especially for topographic surveys with vegetation
and for complex piping surveys, is that a smaller beam has a better
chance of “sneaking through” tight clearances to get to the desired
surface, such as terrain or a pipe or structure located behind other
pipes in a rack.
Consider the two images in Figures 1 and Figures 2. These are scans
from a rock face from two different models of scanners at a range of
25 meters from the scanner. Both scans represent the same scan density (i.e., vertical and horizontal spacing between scan points). The
scan in Fig. 1 is higher definition than that in Fig. 2, as evidenced by
the extra detail visible for the subject rock surface. The spot size of
the scanner that captured the data in Fig. 1 was smaller than the spot
size of the scan in Fig. 2. For scientists wanting to assess geologic formations, fractures, etc., this higher level of definition can offer significant value. (Note that spot size is also an important feature of a
standard reflectorless total station, so some of the discussion in this
article will also apply to better understanding and appreciating this
feature for reflectorless total stations).
What is the Definition?
Profile view of landslide a reveals how a narrow scan beam
can penetrate vegetation to reach ground surfaces.
Image courtesy: Silicon Valley Land Surveying, Inc.
Smaller spot size, especially combined with
higher density, provides advantages because
captured points will be less susceptible to edge
effects, surface curvature effects, abrupt changes
Today, it is rare for a laser scanner vendor to provide information in their specs about how they define their “spot size” or “beam
diameter”. What exactly does a spot size of “6mm” or “15mm” or
“50mm” mean? Is it the maximum diameter - fuzzy edge and all - or just
the main, center part of the beam? How can you tell from a
vendor’s spec?
There are currently two popular, yet different, definitions of spot
size in industry. The first is based upon on a model of a Gaussian
DISPLAYED WITH PERMISSION • PROFESSIONAL SURVEYOR MAGAZINE • October 2006 •
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3DSCANNING
which its intensity equals 1/e2 x Imax
where:
e = mathematical constant
(approx. 2.7183)
Imax = maximum intensity of
laser beam
It turns out that 1/e2 approximately
equals 0.135 or 13.5 percent. So based
on a Gaussian diameter definition, a
“6mm diameter beam” means that at a
beam diameter of six millimeters, the
intensity of the beam is 13.5 percent of
the maximum intensity at its center. The
full beam actually extends beyond this
diameter, but the vast majority of the
Figure 2: Rock face scan with
Figure 1: Rock face scan with smaller
beam’s energy is within this diameter. In
larger spot and more noise.
spot and less noise
a sense, using a scientific, Gaussian diameter definition of beam diameter for
Images courtesy: UCLA Department of Earth and Space Sciences
laser scanner specification purposes is
distribution of the beam’s intensity, or irradivery conservative.
ance, across its diameter. Surveyors, engineers,
The second type of definition of beam diameter is the full-width
physical scientists, and statisticians should all
half-height or FWHH-based definition. This definition asks the quesbe generally familiar with the concept of Gaustion, “At what diameter of the beam is the intensity of the beam equal
sian distribution as a type of statistical distributo 50 percent of its maximum, center intensity, Imax?” Clearly, this
tion with the familiar bell-shaped graphical repdefinition results in a smaller beam diameter value than that based
resentation. Basically, the Gaussian model of a
on the Gaussian diameter.
laser beam characterizes the beam’s maximum
intensity as being at the center of the beam, with
Either the Gaussian or FWHH definition is relevant as long as you
intensity falling off in a Gaussian profile as you
compare apples to apples for different scanners. However, for those
go outward (See Fig. 3). Many laser beams conwho like to pore over manufacturers’ specs, be careful. Unless a venform to this profile. The best laser beams, ones
dor is clear about how they define their spot size, there is no way to
that give the minimum spot size over range, are
know if the spot sizes being compared are based on the same defialways Gaussian in profile, what physicists call
nition. There are currently no standards in the survey industry that
diffraction limited.
cover this aspect, so vendors are free to define spot size however they
The second popular definition is the width
like, using Gaussian diameter, FWHH diameter, or some other basis
of the beam at the half-intensity points. This
that they prefer. (Note that these kind of issues, such as how scan resis a more general definition that can be apolution relates to beam size, will be considered in the standards initiplied to any beam intensity profile, not just
ative on 3D Imaging Systems under the auspices of ASTM. Until such
Gaussian profiles.
standards are in place, however, users are advised to do additional
homework to properly understand vendor specifications).
100
Spot Size as a Function of Range
PERCENT IRRADIANCE
80
60 FWHH-based
beam size
40
Gaussian-based
20 beam size
13.5
– 1.5W – W
0
W
1.5W
CONTOUR RADIUS
Figure 3: Gaussian Irradiance Profile
Scientific professionals in the field of optics universally refer to a beam’s diameter as its
Gaussian diameter, the diameter of the beam at
Another factor that complicates things for those doing their
homework is the fact that a beam’s diameter varies as a function of its
distance from
the
scanner.
Un m o d i f i e d ,
1
irradiance surface
W
e3
the diameter
e
W0
c con
ptoti
of a laser beam
asym
will
natural0
W0
ly tend to inZ
crease with disW0
tance (see Fig.
4). So all oth- Figure 4: If left unmodified, the beam waist radius, W0, tends
er factors be- to increase with range, Z
ing equal, the
definition of a scan will be less clear further away from the scanner
(decreasing scan density as a function of increasing distance compounds this effect). The beam diameter from such scanners can easily grow to 10X or even more over the specified range of the scanner!
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To calculate or estimate how large the beam
will grow, vendors of these types of scanners usually specify the diameter of the beam at the exit
of the scanner and then provide a divergence
value. Typically stated in milliradians, or mrad,
this reflects how fast the size of the beam grows
as a function of distance. For example, a beam
with a starting diameter of 10mm and a divergence value of 3 mrad will have a beam diameter
of 160mm at a range of 50m from the scanner.
For scanners that use this approach - and
many do - users may have to move the scanner
around the site frequently to achieve the spot
size and level of definition they want. Of course,
each setup and tear-down takes time, so this has
a direct impact on field productivity.
Collimated Beams
A second approach that some vendors use
is to collimate the laser beam. The idea here is
to insert a simple, non-moving beam expander
(i.e. lens) that acts like a reverse telescope such
that the beam stays relatively small over much of
the scanner’s useful range. In this case, a beam
may exit the scanner at 6mm, for example, narrow down to 3 or 4mm at 25m range, and then increase back to 6mm at 50m range. Past 50m, the
beam diameter will increase at a slightly higher rate than if the beam had not been collimated. The benefit is that the beam diameter will be
<6mm from its exit point all the way out to 50m
and it will still be smaller well beyond 50m than if
the beam had not been collimated. With this approach, all surfaces in the <50m range are captured with a spot size <6mm. Users don’t have
this, setup I want to achieve a spot size of Xmm at a distance of Ym”
and then dials it in. On the surface, this approach may seem attractive, but it has potential drawbacks. To achieve a focused, small
spot size further away, the beam will have to be larger closer to the
scanner. So objects in the near-field will be captured with a bigger
spot size, in some cases much larger depending on conditions. The
same holds true for objects much further away. A second potential
drawback is that variable beam expanders are moving, mechanical devices that can introduce additional error into each individual measurement and have to be calibrated over the full range of focus. So, while the visual definition of a particular object may appear
better to the eye, the actual measurement accuracy may suffer. Another drawback is cost and reliability, as these approaches add cost
and complexity to the optics system. Specifying the accuracy of such
systems is also a challenge, as accuracy specs have to state the extent to which a beam is being focused for a particular measurement
accuracy claim.
Try it Out
Regardless of how vendors specify their scanners with respect to
spot size (or any other feature), some vendors are more conservative
in their specs than others. So two scanners specified with the same
spot size, and all other factors being equal, can still show differences
in the level of definition achieved.
A scan beam that has a small diameter over a long, useful range
can provide users with significant benefits in both the level of definition achieved and field productivity. Those evaluating laser scanning should be careful to understand the basis of vendors’ specs for
this key feature and how a given scanner’s spot size changes with distance from any given scanner. Testing scanners and talking with peers
who have used different types of scanners can also help in assessing
this factor.
W0
beam expander
–
W(–ZR) = √2W0
–
GEOFF JACOBS is a senior vice president, strategic
marketing for Leica Geosystems, HDS, Inc. and also a
contributing writer for the magazine.
W(ZR) = √2W0
ZR
ZR
Figure 5: Focusing a beam expander to minimize beam
radius and spread over a specified distance
to worry about spot size being too big within
the 50m range. This type of approach can minimize the number of times the scanner has to
be moved around the site to achieve the desired
level of survey definition.
A third technical approach to optimizing spot
size is to apply a variable beam expander in the
path of the laser beam. The user can say, “From
DISPLAYED WITH PERMISSION • PROFESSIONAL SURVEYOR MAGAZINE • October 2006 •
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• ALL RIGHTS RESERVED
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