curacies can be expected when employing the more precise
standards. Relative measurements have been carried out for
lateral positions ([Mazza et al. 1995]). The results — also
verified by measurements using other sensor types — have
demonstrated that super resolution down to 50nm can be
achieved with the proposed approach.
Two other tests investigating numerical weaknesses in the
Bundle Adjustment are shown in table 2 and 3. The self-
consistency of four numerically weak parameters, which are
the parallactic angle ®°, the magnification M'** and the
CMO term E, is tested in table 2 . In the self consistency
test check points and control points of the very same data set
are exchanged. None of the normalized differences |A|/oa
are statistically significant. Notice that oa is computed from
the Bundle Adjustment's normal equations. Therefore one
can state a satisfactory self-consistency of the parameters.
The same procedure is carried out in table 3. This time
two data sets acquired with a time difference of 2 month
are compared. lt is obvious that the parallactic angle ® suf-
fers from relatively weak repeatability. Of course, not only
numerical oscillations but also mechanical instabilities of the
system hardware and inhomogeneities of the calibration stan-
dard (the target points used for calibration are not the same
in both runs) lead to differences. A part of the differences
Ag can be explained by the correlation between ® and E
(worst case: 85%). High correlations occur also between var-
ious other parameters. Thus, the whole parameter set must
be considered as a unity. Repeatability tests can not concern
one single term of the whole imaging model but must be an-
alyzed through the accuracy performed in the object space.
The latter is adequate also for the long term repeatability.
6 CONCLUSION
A new imaging model for Stereo Light Microscopes has been
theoretically derived in [Danuser and Kiibler 1995] and is
now successfully implemented on a fully operating micro vi-
sion system. On a medium zoom level (optical resolution
4 pm) empirical accuracies of laterally 3.8 um and vertically
6.5 pm are obtained. This corresponds to a relative accuracy
of 1: 1000 (lateral) and 2 : 100 (vertical), respectively. In
the image space the relative accuracy is 2 : 10000. The dis-
crepancy between object space and image space accuracy is
caused by the limited precision of the underlying calibration
standard currently available. Better standards will be used
in the future, hopefully allowing me to measure with a preci-
sion of some tens of nanometers on the highest magnification
level. Good results for lateral position measurements support
this expectation.
One of the outstanding features of the imaging model is
the computation of distortions originating from non paraxial
optics. The application of this model is not limited to mi-
croscopy but may as well improve the performance of macro-
scopic systems relying on non paraxial optics.
REFERENCES
[Codourey et al. 1995] A. Codourey, W. Zesch, R. Büchi,
and R. Siegwart. A Robot System for Automated Han-
dling in Micro-World. In /ROS 95 Conference on Intel-
ligent Robots and Systems, volume 3, pages 185 — 190.
IEEE/RSI, Aug. 1995.
5% = right = gf
[Danuser and Kübler 1995] G. Danuser and O. Kübler. Cal-
ibration of CMO-stereo-microscopes in a micro robot sys-
tem. /APRS - International Archives of Photogrammetry
and Remote Sensing, 30/5W1:345 — 353, 1995.
[Danuser 1995] G. Danuser. A photogrammetric model for
CMO Stereo Light Microscopes. Technical Report 167,
Image Science, ETH Zurich, 1995.
[Faugeras 1993] O. Faugeras. Three-Dimensional Computer
Vision. The MIT Press, 1993.
[Forstner and Giilch 1987] W. Forstner and E. Gülch. A Fast
Operator for Detection and Precise Location of Distinct
Points, Corners and Centres of Circular Features. In Fast
Processing of Photogrammetric Data. ISPRS, 1987.
[Ghosh 1989] S.K. Ghosh. Electron Microscopy: Sys-
tems and Applications. In H.M. Karara, editor, Non-
Topographic Photogrammetry, chapter 13, pages 187 —
201. American Society for Photogrammetry and Remote
Sensing, 1989.
[Gleichmann et al. 1994] A. Gleichmann, M. J. Kohler,
M. Hemmleb, and J. Albertz. Photogrammetric determi-
nation of topography of microstructures by scanning elec-
tron microscope. In C.J. Cogswell and K. Carlsson, ed-
itors, Three-Dimensional Microscopy: Image Acquisition
and Processing, volume 2184, pages 254 — 265. SPIE,
1994.
[Kim et al. 1990] N. H. Kim, A. C. Bovik, and S. J. Aggar-
wal. Shape Description of Biological Objects via Stereo
Light Microscopy. IEEE Transactions on Systems, Man
and Cybernetics, 20:475 — 489, 1990.
[Maune 1973] D.F. Maune. Photogrammetric Self-
Calibration of a Scanning Electron Microscope. PhD
thesis, The Ohio State University, 1973.
[Mazza et al. 1995] E. Mazza, G. Danuser, and J. Dual.
Lightoptical deformation measurements in microbars with
nanometer resolution. Microsystem Technologies - Sensors
- Actuators - System Integration, to appear, 1995.
[Richardson 1991] J. H. Richardson. Handbook for the Light
Microscope. Noyes Publications, 1991.
[Taylor et al. 1992] D. L. Taylor, M. Nederlof, F. Lanni, and
Waggoner A. S. The New Vision of Light Microscopy.
American Scientist, 80:322 — 335, July 1992.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
KEYWORL
ABSTRAC
This paper :
in particulai
pictures eigl
used. The n
geometric :
distortions 1
KURZFAS:
Dieser Beitr
(im kontrete
Für die Pr
angeordnet
(was sowoh
Bildverarbe
Mitte des Z
The planet
ZEISS star
and with e
projectors
lectures in
planetarium
planetary s
projectors
panoramas
positions ne
were rathe
brightness d
quite obviou
the projectc
P20
P1C
F
jec
The given |
the project
between th
