From: Kevin and Danielle McCarthy 
To:  atm{at}shore.net
Reply-To: Kevin and Danielle McCarthy 


        I have a technical question regarding the fringe testing of
convex surfaces, and would appreciate guidance from knowledgeable folks on
this list.  I am part way into a Lurie Houghton project, as well as a Dall
Kirkham, bith of which require the production of convex spherical surfaces.
 In the case of the L-H, the fact that there is a concave surface (that can
be null tested via the Focault test) to match each of the two convex
surfaces is handy, and suggests that fringe testing would provide
relatively easy method of monitoring of the convex figures.  Now comes the
potential snag:
        I have a copy of Malacara's "Optical Shop Testing", and Chapter
one covers Newton (fringe) interferometers.  He notes, however, that it is
important that the rays passing through the concave element reflect
perpendicularly off the convex surface under test.  To do so, the opposite
face of the concave element (the one facing the light source and viewpoint)
needs to have a fairly steep convex radius on it.  He provides a formula: r
= ((n-1)*(R+T)*L) / ((n*L) + R + T), where R is the radius of the convex
surface under test, L is the distance to the light source, n is the
refractive index of the concave test plate, and T is the center thickness
of said plate.  This leads to a fairly steep convex curve on the other side
of the concave test plate.  For example, if the convex radius is 1.0
meters, and the test plate is 35 mm thick and made from BK7 (n=1.5168), and
the light source / viewing distance is 1 meter, then the convex radius of
the test plate is 0.210 meters!  For a corrector diameter of 250 mm, this
is an f/0.42 curve, with a sag of 37 mm!  Moreover, the 35 mm. center
thickness is not chosen lightly - it must be at least 29 mm thick to have a
non-zero edge thickness for a 250 mm diameter.  This is all a little
disturbing, and threatens what was otherwise the only convenient way to
figure the convex surfaces.  What, if anything, do I have wrong??  I could
suggest two items - one might be a confusion between light source distance
and viewing location.  I worked this up in OSLO and it looked as though it
is more the light source location (a point source) that matters; while the
returning rays are not perfectly parallel, they diverge gently and, more
importantly, strike the convex surface under test at 90 degrees.  The other
thing that I may have gotten wrong is the difference between a strictly
rigorous test set-up in which you can count the number of rings to
determine not only the figure but actual radius difference between the two
surfaces.  I don't really care about exact radius, so much as I do the
sphericity of the surface.  Could it be that any old test plate rear
surface (eg, my other L-H corrector plate) will do fine for sphericity
checks, just not exact radius?  Here's hoping I can find some help here.
 Thanks in advance.

Kevin McCarthy

--- BBBS/NT v4.00 MP