# The accuracy the calibration method not lim-ited the sensor noise

364 *17 Reverse Engineering Using Optical Range Sensors*

choice. Surfaces of 3-D objects usually consist of segments with low
bandwidth and transients with high frequency between them. They have no
“reasonable” shape, as it is preconditioned for linear filters.“Optimal”
filters like *Wiener* or *matched filters* usually
minimize the *root mean square* (RMS) error. Oscillations of the
signal are allowed if they are small. For visualization or milling of
surfaces curvature vari-ations are much more disturbing than small
deviation from the ideal shape. A smoothing filter for geometric data
should therefore mini-mize curvature variations and try to reinduce an
error that is smaller than the original distortion of the data. These
are the requirements we considered when we designed our new smoothing
method.

We present a new method for calibration of optical 3-D sensors [1].
An arbitrary polynomial is used as a *calibration function*. Its
coefficients are determined by a series of measurements of a
*calibration standard* with exactly known geometry. A set of flat
surface patches is placed upon it. These intersect virtually at exactly
known positions *xi*. After measuring the standard, an
interpolating polynomial *p* with *xi = p(x′*can be found.
Due to aberrations, the digitized surface patches are not
*i)*

flat. Therefore polynomial surfaces are approximated to find the
virtual intersection points *x′i*. In order to fill the whole
measuring volume with such calibration points, the standard is moved on
a translation stage and measured in many positions.

*Figure 17.2: a Calibration standard with three tilted planes; and
b eight range images of these planes.*

17.4.1 Example

Calibration of a range image with 512*×*540 points takes about
3 s on an Intel P166 CPU. Calibration error is less than 50 % of the
measurement uncertainty of the sensor. It is sufficient to use a
calibration polynomial of order 4, as coefficients of higher order are
usually very close to zero.

17.5 Registration