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1995
347
1.) Microscopic imaging is characterized by nearly orthographic projection. Its treatment with full perspective
geometry can lead to numerical instabilities in the estimation of the still existing perspective center and
the principal point of autocollimation. We solve this problem by treating the imaging process as an affine
mapping. Higher order correction terms (perspective distortion terms) compensate for the difference
between perspective and orthographic projection.
2.) With the increasing magnification of the microscope the tolerances of the calibration standard may exceed
the accuracy level of image measurements. Therefore we have to establish a flexible calibration model
which is able to estimate deviations of the specified control point coordinates.
3.) Light microscopes have a very limited depth of focus compared to their large lateral FoV. 3D calibration
standards must take this into account. The unequal vertical and lateral dimensions can cause weak
determinabilities of some mapping parameters. Therefore, the calibration procedure has not only to
provide parameter values but also sensitive tools to detect unstable solutions and to exclude weakly
determinable parameters. We speak of a self diagnostic calibration.
4.) Microscopic imaging contains distortion types that vary from those involved in macroscopic imaging. In
this paper we establish a new function which describes non paraxial distortion in CMO microscopy.
3 CALIBRATION STANDARDS FOR MICROSCOPIC
STEREO IMAGING
The photogrammetric estimation of imaging sensors requires a 3D calibration standard with well defined target
points. Using the 3D coordinates of these control points and the 2D coordinates of their images as inputs, a
maximum likelihood estimation for the various mapping parameters can be derived by non-linear Least Squares
optimization. A short incomplete list of the requirements for such a calibration standard is given below:
(a) The control points of the calibration standard have to be regularly distributed across the field of view.
For estimating third order distortion terms, the distribution of the control points in the image must at
least contain three positions not related by radial symmetry.
(b) The images of the control points must be of high contrast and should have an extension of at least 10
pixels. In this case, very accurate image coordinates can be measured by Least Squares Template Matching
[Baltsavias 1991].
(c) Except for the control points, the calibration standard should have low contrast. This enables the extrac-
tion of unambiguous target point coordinates to initialize the non-linear matching procedure.
(d) Highly accurate 3D coordinate values and good knowledge about their errors must be available.
(e) The vertical range of the standard must fill the optical depth of field.
The design of macroscopic standards according to the above requirements is quite easy. In the microscopic case,
this becomes a very difficult, but however, essential task. The most troublesome requirements are given by (d)
and (e). We propose to use planar standards with any kind of regular grating pattern having a well defined
spatial frequency. For a precision level down to 500nm (which is accurate enough to calibrate light microscopes)
such gratings can be produced by photolithography. A 3D point distribution can then be generated by lifting
the grating with a motorized specimen table. The direction of the table motion defines the vertical z-axes of
the reference coordinate frame. We measure the amount of lifting with a laser interferometer.
z-axis of reference frame
(B ) ( C ) vertical motion
of the grating
gg silicon
siliconoxide
measuring the
amount of lifting %
with Laser
Interferometry
Figure 2: Calibration Standards for the light microscope: (A) Photolithographic grating (wavelength: 108 3: 11m) (Courtesy
of Institute of Mechanics ETH Zurich). The squares at the crossings demonstrate the result of an automatic detection of the
control points by an interest operator. These locations are then used as initial guesses for the fine positional measurements
with Least Squares Template Matching. Thus, image coordinates with a precision between 1/20pizel and 1/30pizel are
obtainable. In (B) a schematic illustration of the etchpit substrate is given. The same microstructure is used for the oriented
deposition of the diamond mono-crystals. Some edges of the octahedrally shaped dimples appear in the image (A) as lines of
IAPRS, Vol. 30, Part 5W1, ISPRS Intercommission Workshop “From Pixels to Sequences”, Zurich, March 22-24 1995
