tion 3). Finally, in section 5, | discuss results from various
calibration runs.
2 SYSTEM HARDWARE AND OVERVIEW
Ocular Ocular
beam splitter
CCD Sensor
À
common main
objective
chief ray
of left image
Figure 1: Cross section of the common main objective lens
(CMO) type stereo microscope.
In our project, the SLM to be calibrated is integrated into a
nano robot system [Codourey et al. 1995]. The stereo effect
of the microscope is generated by refraction in a common
main objective (CMO) lens. A scheme of the fundamental
optical subsystems of this microscope type is shown in figure
1. The specific advantages of the CMO stereo image forma-
tion for our robot system with respect to two separate ob-
jective lenses (Greenough system) are discussed in [Danuser
and Kiibler 1995]. For detailed information the reader can
refer to [Richardson 1991]. The relatively low N.A. of 0.136
results in enough space (D = 6.3cm) for the robot manip-
ulation tools. The serious disadvantage of the low N.A. lens
is its poor resolution of 2.4 um. Fortunately, for the 2D case
we have demonstrated in [Mazza et a/. 1995] that as long as
the target object itself is larger than the optical resolution,
motion and deformation of micro-structures can be analyzed
down to a measurement limit of at least 50nm.
The digital imagery is collected by two monochrome CCD
cameras with 756x582 elements. The crucial point in mi-
croscopy is the illumination. The optimum setup for our ap-
plications consists of a ring light source enclosing the CMO
lens with a supplementary diffuser. Before entering the op-
tical system, the light waves are polarized. This strongly re-
duces the appearance of glancing spots in the imagery. The
latter problem also requires to keep the illumination power as
low as possible. Thus, to get images of sufficient brightness,
cameras with optional frame integration are used.
For the geometric calibration with Bundle Adjustment we em-
ploy planar gratings. The required 3D point distribution is
then generated by lifting the grating within the depth of fo-
cus. The gratings used for simulations in [Danuser and Kübler
1995] turned out to be inappropriate for the real system. A
pattern of squares is now employed (see figures 3-B and 3-
F). The image contrast results from the different reflectivity
of Silicon (dark) and Siliconoxyd (bright). Such gratings are
manufactured with photo lithography. The accuracy of pat-
terns produced by this process is limited by the mechanical
tolerance of the mask as well as by the quality of the lithog-
raphy itself. The original photo lithographic mask has been
produced with an optical pattern generator which yields an
accuracy of about 3 pm. It will be demonstrated in section 5
that this accuracy is the limiting factor of my calibration.
Calibration runs with simulated data proved that for sufficient
determinability of all the parameters, images of four views of
the grating rotated 90? between each view have to be ac-
quired. In our setup the lifting and rotation of the grating
are carried out by the robot system. However, for my calibra-
tion procedure it is sufficient to have approximate rotations.
In particular, the mathematical model of the Bundle Adjust-
ment takes into account that the rotation is not concentric
with respect to the optical axis. Thus, all the needed motions
of the grating could be achieved with off the shelf micrometer
tables.
ee A
yes => reference position
T ye
|| Automatic detection of |
Target Points in all images E
- False matches?
— Accept uncertain matches?
Images with 3 point categories
good — uncertain — invalid
no
yes => Final image
coordinate set
Stop Data Snooping?
3 mE |
TS yes => Final image coordinate set for calibration
Parameter set ok?
Final Result
Figure 2: Scheme of processes, data flow and user interaction
in the calibration procedure.
Figure 2 schematically shows the various processes, the data
flow and the user interaction of the calibration procedure.
The left column contains the computation steps that run
completely automatically. The kernel of the algorithm con-
sists of two blocks outlined in light gray boxes. The first block
is responsible for the detection and for measuring the precise
location of target points in all the images. The processes
of the second block compute the parameters of the imag-
ing model. Both blocks are based on the properties of SLM
imagery and therefore require a completely new photogram-
metric implementation. The image coordinate acquisition is
described in section 4. The mathematical model of the Bun-
dle Adjustment is briefly outlined in section 3.
User interaction, symbolized by question marks in figure 2,
is reduced to four stages. The dark boxes in the center of
the flow chart represent the data interfaced to the user. The
only required user interaction is to accept or reject the im-
ages, i.e., the user has to decide whether the illumination and
102
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
the sharpness
teractions (acc
snooping and |
able to improv
omitted in situ
more importan
3-1
To provide the
framework is «
this discussion
and for the de:
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equations. Th
servations and
calibration stai
(8
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Se
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calibration pro
approximately
vector. Îts inde
in the left or
$, Is defined v
together with t
mulation of (S|
calibration grid
is introduced.
system and the
Equation (1) i
microscopy. T
fore disappears
is introduced, |
and vertical po:
spective distort
are given by £j
stopped when 1
in most cases 1
inaccuracy of 1
than the accur:
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images, respect
ing the orienta
spect to the o
primary, secon
the microscopi
view view v
qe UN.
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frames. The C!
to particularly
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! Qee is the cof
