Appeal No. 2002-1788 Page 9
Application No. 09/217,667
function F(c). But, from relation (5), e3(Xs3)-e2(Xs2)=Xs3+c. Therefore, for the point
Xs2 =X*s2; F(c)=Xs3+c=e3(Xs3)-e2(Xs2) and (5) yields
Xs3+c=F(c) (6)
This expresses the relation between the correction c and the sensor
measurement Xs3. Now as mentioned above, for proper registration we would like
Xs3=0. It can be shown that the value of c that achieves this result may be
determined using the iteration
ci+1=ci+Xs3i (7)
where the subscript i indicates that the parameter is associated with the i-th
sheet of paper. The convergence conditions for this iteration are well known; in
the current application convergence will not be an issue.
In the absence of noise the iteration (7) will yield the desired correction. In
the presence of noise however, it should be modified to
Ci+1=ci+b*Xs3i0<b<1 (8)
It can be shown that the factor b has the effect of providing averaging
which regulates the stability of the iteration. Smaller values of b increases both
stability and the time required to calibrate the sensor.
The method for calibrating the sensor requires feeding sheets of paper to
different lateral positions of sensors 132 and 134. The gamut of which must
encompass the sensor range. This is difficult to do when feeding out of a paper
feeder. A better method moves a single sheet of paper back and forth in the nips
many times. On the return move, the nips position the sheet to different lateral
positions and orientations at datum 2. This provides the initial conditions for the
forward calibration move. The return move can be either deterministic or random.
In the results below a random return move was chosen.
The above procedure can also be ganged to adjust the position of a sheet
at a third location. The position of the sheet at a third location can be measured
and the desired position at the second position can be adjusted accordingly so
that the sheet is properly registered at the third location.
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