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sensors to our robot system, e.g. a force sensor directly mounted on the robot’s working tool. Stereo images 
further provide very nice visualization for interfacing the macro- and micro-world. We intend to generate a 3D 
view of the micro-space on a standard stereo device with the option to overlay some simple graphics (e.g. 6D 
cursor or even a virtual robot). With this tool the user has access to the actual robot motion and manipulations. 
We employ a Zeiss Stemi 11 microscope with a common main objective lens (CMO). A schematic of the most 
important optical subsystems of this microscope is showed in Figure 1. The advantages and disadvantages of 
the CMO type when compared to the Greenough type are explained in detail in [Richardson 1991]. The main 
advantage of the CMO type is that the intermediate planes for the two microscope systems are parallel to the 
sample plane. Therefore, both images are sharply focused over the entire FoV. Non-paraxial optics is the most 
striking disadvantage of this imaging technique. This leads to image distortions that have to be compensated. 
T'wo sensitive video cameras are mounted directly behind the zoom lens optics. The cameras are provided with 
an option for frame integration by hardware. Thus, good images of scenes with limited illumination can still be 
acquired. 
Figure 1: Cross section of a common main ob- 
jective lens (CMO) type stereo microscope. Note 
that the image formation for the stereo pair is 
   
    
       
D 7 Zoom lens system s . 
1 /2b\ | produced by the one main objective lens. In con- 
7 : : - 
qb, common main trast to this type, Greenough microscopes pro- 
m objective vide a separate objective lens for each optical 
chief ray —\| |; path. 
of left image M2 I D 
  
  
The high requirements for accuracy and reliability in this project demand a thorough calibration of the mi- 
croscopes. We intend to achieve a relative lateral accuracy of 1073 (1um in a FoV of Imm?). Unfortunately, 
the narrow convergence angle of only 20 degrees between the two chief rays causes a poor vertical to lateral 
accuracy ratio of about 8 : 1. This calls for improving the relative accuracy in the image down to 107%. A 
relative accuracy of 107* requires to measure the distance between the robot tool and the target object with 
sub-pizel precision. 
The rest of the paper addresses the calibration procedure for CMO light microscopy. In Section 2 we give a brief 
review of related work. We discuss some important differences between macroscopic and microscopic imaging. 
Then we introduce our calibration approach which takes these differences into account. Section 3 addresses the 
problem of finding adequate 3D calibration standards. In Section 4 the mathematical framework for parameter 
and precision estimation is established. In Section 5 numerical results based on simulated data are discussed. 
2 RELATED WORK AND INTRODUCTION TO THE NEW 
APPROACH 
A. Calibration of Stereo Microscopes 
Photogrammetric techniques in 3D light microscopy are very rare. The lack of quantitative techniques for the 
stereo microscope may be due to the small depth of field. In addition, the limited illumination available in light 
microscopes often causes difficulties in obtaining sufficient contrast and good image quality which is required 
for reliably solving the stereo correspondence problem. Nevertheless, a paper by [Kim et al. 1990] describes a 
photogrammetric reconstruction of biological specimens under a Stereo Light Microscope. This work is based 
on orthographic projection without any initial calibration. It simply uses the technical specifications of the 
manufacturer. The authors stress the limitation in accuracy originating from the incomplete imaging function. 
They propose that a refined model as well as powerful statistical tools may improve the quality of the results. 
It is exactly the purpose of our work to focus on such refinements and the statistical analysis of microscopic 
mapping functions. 
B. The new approach for microscopic calibration - an overview 
Our approach is based on the well-known non-linear bundle adjustment using self-calibration. However, some 
differences between macroscopic and microscopic imaging have to be considered: 
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences”, Zurich, March 22-24 1995