Proc. of the EOS Topical Meeting on Optoelectronics Distance Measurements and Applications, Nantes, July, 8-10, (1997)
New Range Sensors at the Physical Limit of Measuring Uncertainty
G. Häusler, S. Kreipl, R. Lampalzer, A. Schielzeth, B. Spellenberg
Chair for Optics, University of Erlangen, Staudtstraße 7/B2, D-91058 Erlangen
tel: +49 9131 858382, fax: +49 9131 13508
email: [email protected]
ABSTRACT
Coherent noise is the major source of the measuring uncertainty of triangulation at rough surfaces. This is well
known for laser based systems. We will discuss coherent noise in phase measuring triangulation systems that work
with white, large incandescent lamps. Surprisingly, the remaining small amount of coherence still limits the distance
uncertainty of all triangulation sensors. We will demonstrate two new sensors that utilize this knowledge, and
display extremely small distance uncertainty.
One sensor is completely incoherent and can be applied to on-line measurement during laser material processing,
the other sensor is a “real time“ 3D-video camera.
1. Introduction
Active triangulation is essentially based on the projection of some pattern onto the object, via a certain
direction, and on the localisation of this pattern by observation from a different direction. The angle
between these direction is called the triangulation angle θ. The uncertainty of triangulation methods is
essentially limited by the uncertainty of the pattern localization. An illustrative example is the ubquitous
laser triangulation with a small spot that is projected onto the optically rough surface (we assume here
technical surfaces such as ground, milled, turned... surfaces). In the spot image on the camera chip we
will observe a speckle pattern [3]. As a consequence, the locus of the spot image be determined with
only a statistical uncertainty δx [2] of
δx = C ⋅
λ
2π ⋅ sin uobs
(1)
where sin u obs is the aperture of the observation, and λ is the wavelength. C is the speckle contrast.
Taking into account the triangulation angle θ, we get the uncertainty of distance measurement δz
δz = C ⋅
λ
2π ⋅ sin uobs ⋅ sinθ
(2)
Figure 1 illustrates the influence of the coherence on the measuring uncertainty: In Figure 1 we see the
(laser-triangulation-) profile across a milled surface that displays considerable noise originating from the
coherent illumination. in Figure 2 we covered the surface by a thin fluorescent layer, and utilized the
fluorescent light for measurement, instead of the laser light. Since fluorescence is completely (spatially)
incoherent, there is no speckle noise at all and the measurement uncertainty is reduced dramatically. We
learn from this experiment that − at least for triangulation − laser illumination is not the best choice. In
the following sections we will use this knowlegde.
Fig. 1: The influence of coherent noise in laser triangulation illustrated by the profile across a milled surface which is
measured by laser light.
Fig. 2: The object surface is covered by a thin
fluorescent layer and the measurement is done by the fluorescent light which shows no spatial coherence. The
measuring uncertainty is reduced dramatically.
2. A “noise free“ sensor for laser material processing
It is not always possible to prepare the object surface by fluorescent layers. In laser material processing
however we can make use of the thermal radiation of the heated material. This radiation is again
completely spatial incoherent.
The sensor is sketched in Figure 3 [4]. It is a so-called “focus sensor“, based on nothing but
triangulation. The plasma spot on the object surface is imaged through a double slit aperture. The
unsharp projection of the aperture displays two peaks. The distance of these peaks is connected to the
depth location of the plasma spot. Now the important trick is: Since there is no coherent noise on the
image signal we can apply a hundredfold subpixel interpolation that allows a measuring uncertainty δz
less than 10 µm, despite a lot of turbulence and spot instability, as displayed in Figure 4.
Fig. 3: Principle of the focus sensor working with an
unsharp projection of a double slit aperture. The distance information about the plasma spot is given by the mutual
distance of the two image peaks.
Fig. 4: Because there is no coherent noise at all, a
hundredfold subpixel interpolation of the camera signal results in a measuring uncertainty of less than 10 µm.
3. Is there coherent noise in phase measuring triangulation?
Competing to laser triangulation, phase measuring triangulation (pmt) is well established. Here we do
not project a single laser spot but a fringe pattern. The illumination is usually done by some
incandescent (spatially incoherent) source. In the context of our noise considerations the question
arises if we still have to take coherent noise into account. To keep it short: Yes, we have to, and the
contribution is significant. This might be surprising for two reasons:
Even though the source is incoherent, coherence theory tells us that we have some spatial coherence
on the object that can easily be calculated by the van Cittert-Zernike theorem [1]. As a consequence we
will see low contrast speckles in the image plane of our sensor. As the speckle contrast is usually low,
one might not be aware of the speckle noise, but it can be measured. A beautiful experiment to convince
people of the ubiquitous speckle is to look at your fingernail in sunlight. Since the sun is a small source
(30 arcminutes in diameter), we can see wonderful speckles, if the observation aperture sin u obs is larger
than the illumination aperture sin u ill .
Figure 5 displays the measured speckle contrast versus the “incoherence ratio“ i = sin u ill / sin u obs for
quasi-monochromatic light. For i > 1, i.e. for u ill > u obs , the speckle contrast C is
1 sin uobs
C≅ =
i sinuill
(3)
This is an important result: Practically we cannot reduce the speckle contrast to extremely small values,
unless we use camera pixels much larger than the (diffraction-based) resolution of the observation
system.
Fig. 5: Measured speckle contrast C for partially spatial
incoherent illumination. The spatial incoherence is given by the ratio i = sin u ill / sin u obs .
Now, as we know about the presence of speckle noise we might hope that this is approximately
multiplicative for grating frequencies not too high and pmt is unsensitive against multiplicative noise.
So why worry? But nature never gives us any presents. Figure 6 displays the results of a depressing
experiment: We project a sinusoidal grating by spatially coherent illumination onto a rough planar
surface. The phase ϕ across the surface should display a perfect saw tooth (0 ≤ ϕ < 2π) if there is only
multiplicative noise. But figure 6 illustrates that there is much coherent noise in the phase.
Fig. 6: After projecting coherent sinusoidal fringes onto a
planar object the phase ϕ of the fringes is measured along one line across the surface. Instead of displaying a perfect saw
tooth graph, the phase is noisy and will cause significant uncertainty of distance measurement.
So, is speckle noise not multiplicative at all? To find out, we can make a different experiment: We
measure the phase at one certain object location (one certain camera pixel) while we shift the phase of
the illuminating grating. It turns out that the phase can be measured with at least ten times less noise
than in the experiment of figure 6 and the speckle noise can be considered approximately multiplicative.
The contradiction between these two experiments has a surprising solution: We measure the correct
phase, but we measure it at the wrong location. The objective speckle pattern in the observation pupil
introduces wedge shaped phase errors which cause a random lateral shift of image points with a
standard deviation of about the speckle size. So we do not exactly know where we look at by each
camera pixel. The consequence of this observation: Speckle noise limits the distance uncertainty of pmt
as well as of laser triangulation.
The limit δz of equation (2) that was derived for laser triangulation has to be modified just a little for pmt:
We have to put the speckle contrast C of equation (3) into equation (2) and we find:
δz =
λ
2π ⋅ sin uill ⋅ sin θ
(4)
(In our experiments which include some experimental unreliability, the pmt noise limit is even twice as
large.)
As a consequence of those considerations we should design pmt sensors with high illumination
aperture to reduce the physical noise limit.
4. The “real time“ 3D- video camera
Finally, we introduce a pmt sensor with a new technology, that displays 3D data presently after 320 ms,
and which has the potential to be at least hundred times faster [5]. The sensor is light weighed (400 g)
and small enough to be applied for intraoral measurements of teeth, or to be mounted on a small robot
(figure 9).
The fringe generation is based on astigmatic projection of a binary mask as shown in figure 7. The mask
is a ferroelectric pattern of electrodes as sketched in figure 8. Since there are only 2 × 4 electrodes (two
spatial frequencies, each with four electrodes for four phase shifts) the system is simple and not
expensive.
Fig. 7: Principle of astigmatic fringe projection
electrode A =
electrode B =
electrode C =
electrode D =
Seperately adressable
φ = 0°
φ = 90°
φ = 180°
φ = 270°
Fig. 8: Pattern of electrodes. The combination of
different electrodes displays the desired fringe pattern including the phase shifts.
Fig. 9: Sensor mounted on a small robot.
Fig. 10: Measured electronic circuit.
In figures 9 and 10 we display one embodiment of the sensor and one measuring result. We achieved a
measuring uncertainty of down to 6 µm within a volume of 15 mm × 15 mm × 15 mm, and this not far
from what is physically possible.
5. Conclusions
Coherent noise is limiting laser triangulation sensors as well as phase measuring triangulation. To avoid
coherence we can work with fluorescent light or with thermal excitation (this is possible in laser material
processing). To reduce coherence a good pmt sensor must have a large illumination aperture. With this
knowledge and FLC-technology we have built a “real time“ 3D-video camera working almost at the
physical limit of measuring uncertainty.
References
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[4] G. Häusler, J. M. Herrmann: Optischer Sensor
(1995)
[5] G. Häusler, R. Lampalzer, A. Schielzeth: Physirierter Beleuchtung - und wie man sie hinaustung, Techn. Akademie Esslingen (1996)
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