You don't need the ['fiche viewer] screen to
form the image, you
only need the (virtual) image from the viewer's lens system to be
focussed in the same plane as the scanner's optics.
Pointing the scanner at
the plane in space that happens to be the
viewing plane of the fiche viewer isn't going to result in an image.
It
doesn't make any difference to the focussing of the scanner optics
whether it's seeing an image produced by light reflected from a
plane, or light from some other source producing an image in that
same plane.
Ah, but it does.
The image formed by the viewer optics is formed by light radiating
from a central point (to a first approximation - the
source is not
perfectly pointlike or there would be no need for optics).
The image required by the scanner is light converging on the scanner's
sensors.
Light reflected from a paper document is reflected in all directions
(again, to a first approximation) and enough of it lands on the sensor
for everything to work. But light radiating from 'fiche viewer optics
towards a focal plane where there normally is a viewing screen will not
behave that way; it will continue to radiate outwards rather than being
nice and cooperative and focusing on the scanner sensor. It is no more
readable to the scanner optics than to your eyes, and for very much the
same reason.
If you leave the viewing screen in place, everything will work - not
because it changes either of the optical focus planes, but because it
acts to take the light radiated more or less in one direction (away
from the projector optics) and scatter it more or less
evenly in all
directions - in particular, with a suitable fraction heading towards
the sensor. Again, this is very much like the reason the screen is
needed for human viewing.
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