OPTICAL TRIANGULATION ON INSTATIONARY WATER SURFACES

Abstract

The measurement of water surfaces is a key task in the field of experimental hydromechanics. Established techniques are usually gauge-based and often come with a large instrumental effort and a limited spatial resolution. The paper shows a photogrammetric alternative based on the well-known laser light sheet projection technique. While the original approach is limited to surfaces with diffuse reflection properties, the developed technique is capable of measuring dynamically on reflecting instationary surfaces. Contrary to the traditional way, the laser line is not observed on the object. Instead, using the properties of water, the laser light is reflected on to a set of staggered vertical planes. The resulting laser line is observed by a camera and measured by subpixel operators. A calibration based on known still water levels provides the parameters for the translation of image space measurements into water level and gradient determination in dynamic experiments. As a side-effect of the principle of measuring the reflected laser line rather than the projected one, the accuracy can be improved by almost a factor two. In experiments a standard deviation of 0.03 mm for water level changes could be achieved. The measuring rate corresponds to the frame rate of the camera. A complete measuring system is currently under development for the Federal Waterways Engineering and Research Institute (BAW).

This article shows the basic principle, potential and limitations of the method. Furthermore, several system variants optimised for different requirements are presented. Besides the geometrical models of different levels of complexity, system calibration procedures are described too. The applicability of the techniques and their accuracy potential are shown in several practical tests.

Full text

OPTICAL TRIANGULATION ON INSTATIONARY WATER SURFACES
,C. Mulsow
a,
*, H.-G. Maas
a
, B. Hentschel
b
a
Institute of Photogrammetry and Remote Sensing, Technische Universität Dresden
01062 Dresden, Germany, (christian.mulsow, hans-gerd.maas)@tu-dresden.de
b
BAW, Kussmaulstrasse 17, D-76187 Karlsruhe, Germany
bernd.hentschel@baw.de
Commission V/1
KEY WORDS: Optical Triangulation, Water Surfaces, Laser Light Sheet
ABSTRACT:
The measurement of water surfaces is a key task in the field of experimental hydromechanics. Established techniques are usually
gauge-based and often come with a large instrumental effort and a limited spatial resolution. The paper shows a photogrammetric
alternative based on the well-known laser light sheet projection technique. While the original approach is limited to surfaces with
diffuse reflection properties, the developed technique is capable of measuring dynamically on reflecting instationary surfaces. Contrary
to the traditional way, the laser line is not observed on the object. Instead, using the properties of water, the laser light is reflected on
to a set of staggered vertical planes. The resulting laser line is observed by a camera and measured by subpixel operators. A calibration
based on known still water levels provides the parameters for the translation of image space measurements into water level and gradient
determination in dynamic experiments. As a side-effect of the principle of measuring the reflected laser line rather than the projected
one, the accuracy can be improved by almost a factor two. In experiments a standard deviation of 0.03 mm for water level changes
could be achieved. The measuring rate corresponds to the frame rate of the camera. A complete measuring system is currently under
development for the Federal Waterways Engineering and Research Institute (BAW).
This article shows the basic principle, potential and limitations of the method. Furthermore, several system variants optimised for
different requirements are presented. Besides the geometrical models of different levels of complexity, system calibration procedures
are described too. The applicability of the techniques and their accuracy potential are shown in several practical tests.
1. MOTIVATION
Despite improved analytical simulation techniques, the
application of scaled physical models remains an essential
method to solve complex problems in connection with project
planning in river engineering (ATV-DVWK, 2004). For the
verification of theoretical modelling approaches practical
experiments on modelled systems like water channels (see Figure
1) are still necessary (Godding et al., 2003). One of the most
important parameter for the description of hydromechanical
phenomena is the water level height. Water surface models are
often determined by point-wise water gauge measurements,
monitoring the vertical motion of a floater or by ultrasonic height
measurements in cylinders, which are connected with the channel
bed via conduits.
Figure 1. Test bed of a river model, pointwise gauge
measurement (source BAW)
These methods are limited in their temporal and spatial
resolution, and they may affect the behaviour of the water
surface. To overcome these limitations, a non-contact profile-
wise photogrammetric water surface measurement technique has
been developed in a cooperation of the Institute of
Photogrammetry and Remote Sensing at TU Dresden and the
Federal Waterways Engineering and Research Institute (BAW)
in Karlsruhe. Due to the surface properties of water (reflection
and transparency) it is impossible to apply common structured
light based optical surface measurement techniques. In the
literature several attempts to overcome the problems by adapting
established methods can be found. Basically, four different
methods based on the characteristics of water can be identified:
 Water as a diffuse reflective surface (eg. rough sea in a
coastal zone, (De Vries et.al., 2009), (Santel et.al., 2004))
 Artificial targeting of water surface or body (eg. markers on
the water surface (Henning et.al., 2007) or fluorescent
particles in the water body (Große et.al., 2016))
 Use of specular reflection properties (e.g. processing of
mirrored images of known objects, (Rupnik et.al., 2015))
 Use of transparency of water (eg. observation of a
homogeneous light field through water, (Jähne et al. 2005))
The method presented in the following chapters uses the specular
reflection properties of water. Depend on the intended use and
grade of complexity, variations of the measuring principle will
be described. Chapter 2 will explain the basic principle. Further,
a simple system is described which is capable to measure water
level changes of still water surfaces. Chapter 3 shows the
expansion of the basic principle in order to enable the system to
measure moving water surfaces. A system capable of measuring
multiple profiles sequentially will be presented in chapter 4.
____________________________
* Corresponding author
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLI-B5, 2016
XXIII ISPRS Congress, 12–19 July 2016, Prague, Czech Republic
This contribution has been peer-reviewed.
doi:10.5194/isprsarchives-XLI-B5-85-2016
85

2. MEASURING PRINCIPLE
The method presented here uses the specular reflection properties
of water surfaces in combination with optical triangulation (see
figure 2). Basically, the measuring principle works as follows: a
laser line is projected onto the water surface with an appropriate
angle (~45°). The reflected laser line is then projected on to a
vertical plane. Then the resulting line pattern is observed by a
camera. Variations of the water surface will cause a change in the
laser line pattern on the projection plane.
Figure 2: Basic measurement principle
In first instance the water surface will be dealt as a horizontal
plane. By measurement of laser line change the water level
change can be calculated by:
LaserW
HH 

(1)
where ∆H
w
= water level change
λ = conversion factor
∆H
Laser
= change of laser line height
For calibration the conversion factor λ must be determined. This
can be done simply by measurement of at least two known water
level heights (see figure 3).
Figure 3: Optical triangulation using a vertical projection plane
The conversion factor can be calculated by following equation:
12
12
PWW
PP
HH HH




(2)
In case of an incident angle of laser light sheet of 45° and a
vertical projection plane, the conversion factor λ=2. That means
a sensitivity of the system for water level change of factor 2. The
water level can be determined with high temporal resolution,
which is only limited by frame rate of the camera used. The
method was presented first by (Maas et.al., 2003). In experiments
an accuracy of 0.03 mm for water level changes could be
achieved (0.7m wide profile, 1000x768 pixel video camera). But
it was also shown, that the accuracy and reliability is prone to
waves.
As figure 4 shows, the main problem of this projection-plane
method is the ambiguity of effects causing a change of the laser
line projection, which can either be caused by water level change
or by slope variation. A compensation method for small regular
waves based on image sequences was presented in (Maas et.al.,
2003).
Figure 4: Effect of water movement on height measurement
3. TWO PLANE SYSTEM
A general solution of the wave problem can be achieved by the
integration of a second vertical projection plane into the system
(see figure 5). Now a complete reconstruction of reflected laser
light sheet is possible. In addition to the water level height, also
the surface normal direction can be obtained. Essential is here the
knowledge about the relative orientation of system components,
like the orientation of the projected laser light sheet as well as the
projection planes. Furthermore a reference water level must be
known.
Figure 5: Setup with two projection planes
Figure 6: System layout with vertical grid as first projection
plane and principle of profile point determination.
Projection Plane
Camera
HW1
HW2
HP2
HP1
α
α α
α
Laser
Water surface
HW
HP1*
HP1
α α
Laser
Camera
Water surface
HW
HP2‘
HP2
α α
Laser
Camera
Water surface
HP1‘
HP1
laser sheet
camera
first projection plane
rear projection plane
vector
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLI-B5, 2016
XXIII ISPRS Congress, 12–19 July 2016, Prague, Czech Republic
This contribution has been peer-reviewed.
doi:10.5194/isprsarchives-XLI-B5-85-2016
86

The main problem in this system design is the first vertical
projection plane. This plane has to be semi-transparent. A
practical solution was presented in (Mulsow et.al., 2006). Here
the first vertical plane is constructed as a grid (see figure 6). This
allows parts of the laser light sheet to pass through to the rear
projection plane resulting a line pattern.
By connecting corresponding end-points of line segments on
both projection planes, a vector can be created (figure 7), which
can be intersected with the projected laser light sheet in order to
obtain the water level height together with the water surface
normal in the intersecting point (see figure 6).
Figure 7: Corresponding laser ends (left: still surface; right:
dynamic surface)
4. MODELLING AND CALIBRATION
The calibration of a two plane system is more complex due to
more components. Several methods were developed and
implemented. The degree of complexity depends on the intended
use, stability of the relative orientation of all relevant system
parts and additional components. In the following chapter several
approaches will be presented, starting from lower grade of
complexity.
4.1 System with wave detection
Here the rear projection plane acts as a simple wave detector. A
full reconstruction of the laser reflection is not necessary. The
height measurement itself is performed in the same manner as
with the single plane system. Image measurements of line
elements on front grid are the input for water level calculation.
Measurements on the rear projection planes provide information
about the orientation of the water surface normal in the piercing
point (see also figure 8). By calibration the system in the same
way like the single-plane system, the relative conditions between
laser measurements on both planes are known for the case of still
water surface (horizontal plane). In fact, the measurements on the
rear plane only provide the information if the water surface patch
measured in that specific moment is horizontal orientated or not,
Figure 8: Detection of horizontal water surface element based
on calibration on still water
This decision criterion can be described mathematical as follows:
1
1
12
12
RR
FF
RR
FF
HH HH
HH HH





(3)
where H
F1
/ H
F2
= laser height on front plane, calibration
water level H
W1
/ H
W2
H
R1
/ H
R2
= laser height on rear plane, calibration
water level H
W1
/ H
W2
H
F
/ H
R
= actual measurement on front- and rear
projection plane
Based on eq.3 now a separation between valid measurements on
horizontal water surface patches and non-valid measurements on
sloped surface patches is possible. If eq. 3 is fulfilled, the actual
water level can be calculated in the same way as for the single
plane system.
The approach only detects wave components for longitudinal
direction only. For the lateral component (see figure 9), the
principle presented above can be easily adapted.
Figure 9: shifts on rear plane induced by lateral waves
HW2
HR2
HR1
HF2
HF
HF1
HR
HW
HW1
front grid
Line se
g
ments on rear
p
lane
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLI-B5, 2016
XXIII ISPRS Congress, 12–19 July 2016, Prague, Czech Republic
This contribution has been peer-reviewed.
doi:10.5194/isprsarchives-XLI-B5-85-2016
87

Figure 10: Validation of measurements on rear plane
By defining “corridors” on the rear plane based on calibration,
valid measurements (without lateral slope) can be detected (see
figure 10). Obviously, a “perfect” valid measurement on a
temporal horizontal will never occur. By defining suitable
thresholds the problem can be solved.
Another way is the interpolation of virtual measurements in the
temporal domain. Each water surface patch is horizontal oriented
for specific moments (assuming a random moving water surface).
Based on eq. 1, reference laser positions on the rear plane can be
calculated from measurements on the front grid. By transferring
the discrete laser measurements into functions, a continuous
description of laser line movement on both planes can be
computed in the temporal domain (e.g. quadratic functions). The
point on the time axis, were the water surface patch was virtually
horizontal can now be estimated by intersecting the function of
reference with the function of line positions actually measured
(see figure 11). In tests the presented approach showed good
results and was therefore implemented in a system for use in
laboratory environment at BAW. The accuracy was evaluated in
first practical tests. From the results, a standard deviation of
~0.1 mm on a 20 cm wide profile can be estimated. Further tests
have to be carried out in future. The main problem is here the
provision of reference data for moving water surfaces.
Figure 11: Interpolation of valid measurements (example with
sinusoidal wave in longitudinal direction): The red circles mark
virtual measurements of horizontal water surface patches
Figure 12: Measured water profile line over a time period of 4 seconds, acquired with 25 fps. The surface was interpolated
between discrete profile points (blue dots).
Measured profile
HF2
HF1
valid measurement
invalid measurements
HF
Correspondence between
laser line segments
HR2
HR1
HR
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLI-B5, 2016
XXIII ISPRS Congress, 12–19 July 2016, Prague, Czech Republic
This contribution has been peer-reviewed.
doi:10.5194/isprsarchives-XLI-B5-85-2016
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4.2 System with strict reconstruction of laser reflection
A major limitation of the system with wave detection as
described in 4.1 is in the fact that it delivers measurements only
at (virtual) time instances with a horizontal surface. An essential
step forward can be achieved by the full geometric reconstruction
of the reflected laser light sheet and their intersection with the
projected laser light sheet as mentioned in chapter 2. An essential
requirement here is the determination of all relevant system
parameters, like:

orientation of projected laser light sheet

interior and exterior orientation of the camera

orientation of projection planes

orientation of reference still water level
As seen in figure 13, all system components are mounted on a
frame. The frame itself and on the projection planes are
signalised by markers. This allows the determination of
orientation of projection planes and provides a reference point
field for camera calibration and orientation. Furthermore, the
markers on the projection planes are used for transformation of
image measurements of laser line segments in to object space (see
also (Mulsow et.al., 2006)).
The construction of frame has to be rigid in order to ensure a
stable geometry. The coordinates of the reference points can be
measured with standard photogrammetric methods. In a next
step, the camera can be calibrated and orientated via spatial
resection. The projected laser light sheet can be determined for
example by an integrated calibration procedure (see chapter 4.3.).
The simplest way is to project the laser line onto a 3D-object and
to measure the laser projection in an oriented set of photographs
(spatial intersection). Of course, the mounting of the laser in the
system has to be stable. Before measuring the actual water
surface, a measurement on a still reference water level has to be
carried out. The determined point coordinates on the water
together with the surface normal define the plane parameters of
the reference water surface.
Figure 13: System layout with step motor.
4.3 System with rotating laser light sheet
A further extension of the design concept is the ability to measure
multiple profiles from one system position. For that task, a
stepper motor rotating the projection unit was integrated into the
system (see figure 13). This allows for variable settings of the
incidence angle of the laser light sheet and a sequential
measurement of multiple parallel profiles (see figure 14).
Figure 14: Variable setting of laser light sheet.
The angular rotation sensor of the stepper motor is able to provide
the motor position with an accuracy of 0.001°. The detected laser
line end points can be transformed into the 3D frame system with
a precision of 0.2 mm on the vertical grid and 0.3 mm on the rear
plane.
Figure 15: Data acquisition for calibration - direct and indirect
projection at different rotation angles.
For calibration, a set of images of different laser sheet incidence
angles is taken by the camera, both containing lightsheets directly
projected onto the planes as well as indirectly (i.e. mirrored at the
water surface), see figure 15. The laser segments are measured
and transferred into object space. Together with the angle
measurements from the angular rotation sensor, these coordinates
are the input for the calibration model. The model itself is the
mathematical description of the whole projection process
together with the rotating laser light sheet. All necessary
parameters can be determined in one integrated calibration
procedure. A detailed description can be found in (Mulsow et al.,
2006).
In experiments, an accuracy of 0.2 mm for water level changes
measured on a 30 cm wide profile could be achieved. This means
a decrease in precision comparing to the single plane system and
the system with wave detection.
Profiles
Step Motor
Laser
Camera
Water Surface
Step motor
Profile 1 Profile 2 Profile 3
Laser
Camera
Water Surface
Step motor
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLI-B5, 2016
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doi:10.5194/isprsarchives-XLI-B5-85-2016
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5. SYSTEM OPTIMISATION
The experimental setups as shown in section 3 and 4 showed the
potential of the method but also the limitations. One major
drawback for practical use in experimental hydromechanics is the
physical dimension the system. The size of the frame is defined
by the width of the profile to be measured as well as the accuracy
requirements. By increasing the distance between the projection
planes, the lever arm of the laser vector (between corresponding
end points) gets longer, which means a better accuracy of the
directional component of the vector. On the other hand, the
increased travelling path of the reflected laser can cause a
decrease in projection quality on the rear plane. Furthermore, the
image scale becomes larger, which means a decrease in
resolution of the laser projection in the camera image. Here an
optimum has to be found. The use of a standard laser line module
with an opening angle >0° means an increase of line width in
horizontal direction with growing projection distance. In the
experimental setups presented above, the fan angle of the line
laser was 45°. The measurement of a water profile of 20 cm needs
a distance of the laser from the water surface of ~25 cm. The
projection of the laser on the rear plane, for example 50 cm
further back, has a width of 60 cm.
In order to ensure a complete projection, the size of the rear plane
has to be quite large. To overcome this problem, a cylinder lens
has been placed in front of the laser module. The width of the
lens has to be at least as large as the intended profile width. A
telecentric projection can be achieved by placing the pupil of the
laser into the focal point of the lens. In the actual experimental
setup, a cylinder lens of 20 cm width together with a line laser
module with a fan angle of 45° is installed. This allows for
measurements over a 20 cm profile. Therefore, the system
dimension could be reduced significantly (see figure 17 and 18
left). A further improvement is the replacement of the grid with
a slit plate as front projection plane (fig. 18). This generates a
laser dot pattern rather than a line pattern on the rear plane. The
detection and measurement of dots in image is usually more
precise and faster compared to measuring line end points. On the
front plane the corresponding point to the dot on the rear is
represented by the intersection point of laser profile with the
appropriate slit. Thus, the error prone determination of the laser
line ends (especially the component along the line) can be
avoided (see figure 18, right).
All necessary steps, like camera control, calibration and the
measurement process itself can be controlled by the user in a
comfortable graphical user interface.
Figure 16: Setup of a laser line module together with a cylinder
lens (5cm), telecentric projection
Figure 17: Actual system with narrower frame and telecentric
laser line. The basin under the system is for test
purposes.
Figure 18: Left: Actual system with slit plate as front projection
plane, Right: laser projection with slit plate (moving
water)
Figure 19: Graphical user interface
line laser lense
500 mm
1000 mm
240 mm
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLI-B5, 2016
XXIII ISPRS Congress, 12–19 July 2016, Prague, Czech Republic
This contribution has been peer-reviewed.
doi:10.5194/isprsarchives-XLI-B5-85-2016
90

6. CONCLUSION
The paper shows, that the general principle of optical
triangulation can be adapted for measurement on water surfaces.
Several modifications in the system design and in the data
processing chain were implemented to adapt the system to
measurements on instable water surfaces. A strict solution to
measure height profiles on moving water surfaces has been
realised and validated in several prototype systems.
The installation of an operational system at BAW will not mark
the end of development. Experiences in practical use will led to
further needs and therefore to further improvements.
REFERENCES
ATV-DVWK, 2003. Feststofftransportmodelle für
Fließgewässer. In: ATV-DVWK-Arbeitsgruppe WW-2.4, March
2004
De Vries, S., Hill D., De Schipper, M.A., Stive M.J.F., 2009.
Using Stereo Photogrammetry to Measure Coastal Waves. In:
Journal of Coastal Research, Special Issue No. 56. Proceedings
of the 10th International Coastal Symposium ICS 2009, Vol. II
(2009), pp. 1484-1488
Große, M., Schaffer, M., Weinfurtner, S., 2016. Kontinuierliche
hochpräzise 3D-Oberflächenvermessung von Wasserwellen. In:
Proceedings of Oldenburger 3D-Tage 2016
Godding, R., Hentschel, B., Kauppert, K., 2003. Videometrie im
Wasserbaulichem Versuchswesen. In: Wasserwirtschaft WAWI
4/2003, pp. 36-40
Henning, M., Saharhage, V., Hentschel, B., 2007. 3D-PTV – Ein
System zur optischen Vermessung von Wasserspiegellagen und
Fließgeschwindigkeiten in physikalischen Modellen. In:
Mitteilungsblatt der Bundesanstalt für Wasserbau Nr. 90
Jähne, B., Schmidt, M., Rocholz, R., 2005. Combined optical
slope/height measurements of short wind waves: principle and
calibration, In: Measurement Science and Technology, Volume
16, Number 10
Maas, H.-G., Hentschel, B., Schreiber, F., 2003. An optical
triangulation method for height measurements on water surfaces.
In: Videometrics VIII (Electronic Imaging 2003), Ed. S. El
Hakim, SPIE Proceedings Series Vol. 5013
Mulsow, C., Schulze, M., Westfeld, P.,2006. An optical
triangulation method for height measurements on non-stationary
water surfaces. In: International Archives of the
Photogrammetry, Remote Sensing and Spatial Information
Sciences, pp. 213–217.
Rupnik, E., Jansa, J., Pfeifer, N., 2015. Sinusoidal Wave
Estimation Using Photogrammetry and Short Video Sequences
In: Sensors, 15,12.
Santel F., Linder, W, Heipke, C., 2004. Stereoscopic 3D-image
sequence analysis of sea surfaces. In: Proceedings of the ISPRS
Commission V Symposium, Istanbul, Turkey, Vol. 35, Part 5, pp.
708-712.
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLI-B5, 2016
XXIII ISPRS Congress, 12–19 July 2016, Prague, Czech Republic
This contribution has been peer-reviewed.
doi:10.5194/isprsarchives-XLI-B5-85-2016
91