The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
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dependencies of the range measurements on the operating and 
the integration time are reported, and impacts of the external 
temperature have been published (Kahlmann, 2007). 
Only recently, Mure-Dubois and Hugh (2007) have reported on 
secondary reflections occurring between the lens or filter and 
the sensor of PMD cameras, which may yield heavy distortions 
of range observations hitherto disregarded by the PMD 
calibration community. This way calling extensive experiments 
and analyses into question again, one may become aware of the 
circumstance that the set of major PMD error sources has not 
been isolated yet. Aiming at comprehensive calibrations, it thus 
may be beneficial to investigate real-world data, possibly 
discovering important influences this way. Karel et al. (2007) 
capture scenes that feature planar faces, detect and reconstruct 
them based on the range observations, and investigate the 
ranging precision based on the deviations. Clear dependencies 
of the ranging precision on the true distance, the signal intensity 
and the position in the field of view are found. Lindner and 
Kolb (2007) use a PMD camera in combination with a 
conventional RGB camera, mounted on a common, solid rig. 
The authors observe interdependent influences on the range 
observations of the signal amplitude, the true distance, and the 
integration time. 
1.2 Objective 
PMD cameras feature sensor resolutions of a hundred by a 
hundred pixels only, but offer frame rates exceeding 20Hz. 
While other PMD calibration approaches base on the low- 
resolution still images, the presented work tries to capitalize the 
high temporal data resolution by evaluating image sequences. 
Following from the statements above, the employed data should 
furthermore be captured under conditions close to those of real- 
world applications, hence being affected by similar distortions 
and featuring some amount of randomness concerning the 
capture parameters. The quantification of individual error 
sources may be more complicated this way than it is under 
laboratory conditions. However, concerning the instrument's 
applicability, the enhancement of its overall performance is 
most interesting, not the quantification of specific phenomena. 
Moreover, a readily neglected point is the fact that even 
sophisticated experiments may not be able to isolate the 
influence of certain error factors either, e.g. varying the object 
distance while maintaining the amplitude level is hard to 
achieve. This makes the free choice of measurement conditions 
in the laboratory somewhat irrelevant. As stated above, the 
interior orientation has shown to be unstable, while the 
temporal stability of the factors distorting the range 
observations has not been proved yet. This again calls for self- 
instead of laboratory calibrations. In order to make it useful for 
a broader public, the strategy should furthermore avoid the 
requirement for auxiliary high-order reference devices. 
In this work, flat, circular targets stuck on a planar whiteboard 
at known positions are imaged by the range camera and 
detected in the amplitude images, allowing for the spatial 
resection of the camera pose. The object distance of each pixel 
footprint can thus be computed and compared to the actual 
range observation. The camera is guided by hand, this way 
introducing some amount of randomness. As the frame rate is 
rather high compared to the slow hand movements, the targets 
can be tracked automatically, allowing for the capture of huge 
data sets and the derivation of comprehensive statistics. 
With the approach being applied for the first time, the 
measurement conditions are slightly simplified for now and 
some potential error sources probably avoided. Thus, having 
activated the camera, the warm-up period is awaited, the device 
is operated under constant temperature conditions, and the 
target plane is chosen to reflect homogeneously. The different 
reflectivity on areas covered by the targets heavily affects the 
distance measurements, why these image regions are excluded 
from the evaluation of distance deviations. However, three 
concerns remain in conjunction with the approach. Although the 
influence of scattering is said to be rather low for surfaces of 
similar object distance, the affected area around the targets shall 
be investigated beforehand. Kahlmann (2007) reports on erratic 
fluctuations of the distance measurement system, possibly 
originating from the cooling system. At least the range of 
fluctuations shall be determined in advance. Finally, the 
camera’s movements during exposure certainly introduce some 
motion blur in the data. While this latter issue has not been 
investigated further so far, respective experiments concerning 
the first two are described in the following section. 
2. PRELIMINARY CHECKS 
2.1 Temporal Stability after Warm-Up 
This first preliminary check shall demonstrate that the camera 
features an acceptable level of measurement stability over time. 
For that purpose, both the camera’s orientation and the imaged 
object space keep unchanged during half an hour, while 
constantly gathering data. Figure 1 shows the arithmetic means 
of the amplitudes and distances captured in each frame of the 
sequence. With high peaks in the power spectrum around 22 
frames per cycle, the Fourier analyses of the two signals 
confirm the visually noticeable periodicity of both signals. Most 
important here, the distance varies within around 3mm, while 
the variation of the amplitude amounts to less than a thousandth 
of the encoding depth. Compared to the maximum range and 
the ranging precision, the temporal variation is considered being 
negligible concerning the purpose of this work. 
2.2 Scattering 
Considering the possibly wide-area impact of the scattering 
phenomenon reported in literature, a corresponding test seems 
to be vital that ensures the independence of range observations 
from the distance between the observing pixels and the targets’ 
images. As the effect needs merely be detected and not 
quantified, its reported slight anisotropy is neglected and a 
radial impact is investigated. Again, the camera is mounted on a 
tripod and directed towards a static, planar surface. Having 
captured dozens of images of the plane, one of the target 
markers later on used for the calibration test fields is brought 
into the field of view, dangling by a thread that is guided from 
above and outside the imaged area, closely in front of the plane. 
This way, the target is smoothly directed through the whole 
image. Having finished, further images of the static scene are 
gathered. The arithmetic mean of the images captured before 
and after the appearance of the target serves as background 
image. In the other images, the target is detected and the 
corresponding image areas together with those covered by the 
thread are excluded from further evaluation, making use of the 
knowledge of the approximate image scale. The background 
image is subtracted from the masked images, and the remaining 
range residuals are grouped and averaged by the distance 
between each observing pixel and the instantaneous position of 
the target in the image plane. Figure 2 presents the resulting