>> This a stupid (maybe) idea (long way out of my field)
>>
>No Idea is stupid Steve, thanks for the suggestion

So here is my suggestion. Assuming the paper can be run over a rounded
surface (it could be an existing guide roller) so that you know it is flat
against the surface (i.e. under some tension), then my thought was to use
ultrasonic sensors to measure the thickness difference between the paper
height and the roller. You could have a number of sensors across the width
of the paper if necessary.

>> Light permeability
>> For a lamp of given intensity the translucence of the sheet
>> could be used as a thickness measurement
>> This could work if the light source is self calibrating,
>> allowing for the gradual degradation of the lamp.
>
>Anyone know how well this could be used to measure a change
>of fractions of a micron?

Yes. The way I would do it, taking the roller arrangement I suggested above,
is to shine the light so it is shining along the tangent of roller onto a
linear CCD. The roller will cause a shadow, which you use as reference, and
the paper will increase the shadow height. Readout speed will probably be
limited to the clockout rate of the CCD.

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