Quasi-simple constructive suggestion: Use the method of images.
In more detail:
I reckon the students are overdue for a lesson in "real
images" and "virtual images". Information about this is
easy to obtain.
Here are some possibly edificational experiments:
For a source, the collimator lens is usually set up to be one
focal-length (f) away from the source chip or filament.
1) Instead, move it twice that far away, so that it forms
a real image 2f on the other side of the lens. You can
easily verify this by holding a card in the beam and
looking for the waist.
Play with the geometry to verify that the real image
upholds the equation 1/a + 1/b = 1/f.
Apply the same idea to the collimator on the detector.
This is harder to verify, but you should be able to
measure the lens focal length, and then trust the
formula: 1/a + 1/b = 1/f.
Now measure the signal as a function of the image-to-image
i.e. focus-to-focus distance x. I haven't done the experiment,
but I would expect it to uphold the inverse square law pretty
closely.
It may be possible to fry the detector at small x
with such a setup, so you may want to establish
procedures to avoid that.
2) Move the source filament much closer to its condenser
lens, closer than it should be, only 0.9 f away. This
should create virtual image on the same side, 9 f away,
which is a lot. Virtual images are not easy to verify,
and the leverage is unfavorable, so there will be quite
a bit of uncertainty, but you may be able to check the
size of the beam as a function of distance and ask how
far back you would have to go to extrapolate to zero size.
Again measure the signal as a function of image-to-image
distance. Again it should follow the inverse square law,
but the distances are dramatically larger than they were
in part (1), and data is unavailable over most of the
range. That is, data is only available for x = 9 f and
above.
If you don't look too closely the data might look linear,
but really it is just a far-out piece of an inverse
square law.
3) At this point it should be possible to understand some
of the many things that went wrong in the experiments
that provoked this thread. The perfectly collimated beam
has a virtual image (virtual focal point) at minus infinity.
So there is no hope of observing an inverse square law.
Any dependence you do observe will result from nonidealities,
and figuring it out will require a laborious detailed analysis.