Szymon M. Rusinkiewicz
21 Nov 1996
Here are the basic arguments for the various tolerances:
For light fields:
Since we want to anti-alias the light field properly, we will use a large
aperture, and integrate over several aperture widths to get the final views
that will be combined into the light field. Therefore, it is necessary that we
know the position of the camera to within a fraction (e.g. 1/2) of the width
of the aperture. The maximum aperture we envision using is between 2 and
2.5mm, so around 1mm is the maximum error we can tolerate here. We know that
most of the error in this case will come from the bending of the arm, and the
big discussions we had a few weeks ago were about the tradeoffs involved in
increasing the arm diameter (for rigidity) or decreasing it (less shadowing).
For shape-from-light-fields:
Now we are assuming that we have several views of a point on the scene and we
wish to find the position of the point in space, by seeing where the "camera
rays" intersect. If the gantry were infinitely stiff and infinitely precise,
the limit on the accuracy of the reconstructed shape would be due to CCD
resolution. Therefore, one criterion for specifying the gantry tolerances is
that the error due to the gantry should be equal to the error from CCD
resolution.
What is actually seen by a CCD pixel depends on the field of view of the lens
and the CCD resolution. To take the worst case and allow for future
improvements in camera technology, we consider a 1000x1000 pixel CCD viewing
the entire 16" working volume. In this case, each pixel views 0.04 degrees, or
a little under 0.3mm at the near edge of the working volume. The
specifications of the gantry design in its current state suggest that of all
the sources of error in camera position and aiming, the biggest concern for
this application is the error in arm positioning. That is, if the arm moves
enough, the point we were interested in no longer corresponds to the pixel
where it "should" be, but rather some neighboring pixel. The worst case occurs
at the edge of the working volume, where a point in the scene will shift to a
neighboring pixel when the camera arm moves by (0.3mm)/(8in) radians, or 0.09
degrees. For 1/2-pixel accuracy, we get just under 0.05 degrees. Cyberware
says they can meet this using a slightly larger harmonic drive unit than they
had specified before.
For BRDFs:
These will be measured using the "thick" arm, and the accuracy given above is
more than enough.