om the calibration
the original image.
point search. The
-1). However, the
1 Tu A of (C1)
for the right point
age. (F) Result of
rejected points.
the [Forstner and
m has to partition
(6)
it correspond to a
target point distri-
duced. Each point
in target point set
= coordinates E; of
in O is given by an
T s
(7)
ane and when the
bal transformation
affinity A. There-
the parameters of
. A method based
>) has been imple-
th an approximate
L point set Po can
nly points mapped
ast affected by er-
the closest point in
pondence between
ter transformation
ins for the compu-
e analogous. The
996
(A)
(B)
Figure 4: Example of target point detection and location in the case of a rotated and widely damaged grating. (A) local
maxima of the interest operator. (B) result of LSM. Points labeled with A are fully rejected, points with a (C) are declared as
uncertain and may be manually accepted, points with a number and a filled O are automatically accepted.
better Ax, the more can Pr be extended towards the image
border. And vice versa, the more correct points are contained
in Pz, the more precise Az+1 can be estimated. A sample
for two iteration steps is given in figures 3-C1 and 3-C2. The
iteration is stopped if one of the two criteria (8) or (9) is
fulfilled.
Pr[55 96,4] > 95% (8)
Fr Pry =" Dr (9)
The criterion (8) means that false point correspondences be-
tween Py and Py have been established and thus A; become
worse than A&..,. In this case Ax_; is presumed to be the
best known transformation A. The criterion (9) means that
no new points in S can be identified as target points and
therefore A; is the optimal transformation À. Transforming
the whole set © with À results in a coordinate set Q which
can be used as initializations for LSM. Note that Q and P
may differ from each other. The poor contrast of the target
point pattern in the image does not guarantee a correspond-
ing local maximum in E for all target points. However, Q
contains the full grating independent of the successful detec-
tion of each target point by the interest operator.
A priori knowledge about the shape of the target points and
an analysis of the Point Spread Function (PSF) for each im-
age allows me to generate artificial templates (see figure 3-
D). This procedure is necessary because the sharpness dif-
fers for each of the 16 images due to the small depth of
field. The definitive image coordinates are computed apply-
ing LSM. A chain of statistical tests (global model test, joint
significance of all parameters and parameter subsets, exclu-
sion of non-determinable parameters, parameter testing in
the eigenspace) forms a powerful diagnostic tool. Its main
purpose is to detect false matches due to target point pat-
terns corrupted by manufacturing damages, scratches or dust
(see figures 3-E1 to 3-E4). The mean precision of the point
location turned out to be 0.03 pixel.
The high quality of this image coordinate acquisition scheme
can be verified in the data snooping procedure of the Bundle
Adjustment. My experience from many calibration runs is
that less than 0.0596 of image points still have to be excluded.
Another example in figure 4 demonstrates that the algorithm
works well even if the grating is rotated 7? out of the expected
orientation (figure 4-B) and if only a few target points result
in a well centered local maximum of the interest operator
response field (figure 4-A).
5 RESULTS
As in any calibration the suitability and the quality of the
underlying standard is the key for a successful procedure.
The currently available grating has a target point spacing
of 300 um (see figure 3-F). The estimation of the imaging
model requires at least seven by seven target points within
the field of view. Therefore, using this grating, the micro-
scope can only be calibrated on a medium zoom level where
the field of view exceeds 2.5 x 2.5 mm. For higher magnifi-
cation levels, a grating with 100 um spacing is necessary. A
new type of grating will be used in the future?. The most
important modifications of the new gratings are:
— Various zoom level dependent point features on one sin-
gle wafer.
— Improved contrast by etching Aluminium layers instead
of Siliconoxyd
— The mask is produced by a laser pattern generator which
is the very best currently available in micro electronic
manufacturing. Thus, a point precision all over the stan-
dard of 80nm is expected (compared to the 3 um of the
mask used for the tests below).
However, even the relatively inaccurate standard allows me
to demonstrate the great potential of the new algorithm.
The resolution of the microscope is 4 um on the zoom level
used for the presented tests. The depth of field measures
about 330 um. This must be compared with the 3.5 x 3.5 mm
field of view. Thus the relative depth of field can be defined
as about 1 : 10. Note that macroscopic close range pho-
togrammetry never is obliged to work with such asymmetric
point fields.
Table 1 contains results of calibration runs that investigate
various a priori stochastic models and six different imaging
models. The a priori model mainly consists of three param-
eters. The a priori standard deviation (Stdev) of the image
coordinates is described by oe, ?^. The Stdev of the lateral
and the vertical components of the control point position are
determined by a xy and oz, respectively. From these values
the cofactor matrices Qee and Qeze, are gained. The lateral
Stdev is obtained from the specifications of the grating while
?Due to some delivery problems of the manufacturer, they are not yet
available.
*When writing £ and 7) separately the components of an image coordinate
vector € are meant.
“For simplicity only one value for both components is shown. In the
software c; and c, can be defined, independently.
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
