Glass and Abbe' offset error
Posted by
Elliot Burke
on 2000-03-20 08:50:47 UTC
It is true that optical flats are made from fused silica , ULE, Zerodur and
the like. There is a very good reason for this: Low CTE. This doesn't
matter much when using the stuff, but when polishing, heat is generated,
causing a temperature gradient in the flat. This is unavoidable, even with
a cooling bath. This tends to warp the surface convex. So a low expansion
part has a big advantage. With higher expansion glass the part is polished
to a convex figure, then when cooling it goes back to a flat profile, maybe.
Rather tricky to do to the precisions required for a large lambda/20 flat.
You can really bear down on the silica while polishing without fear of the
heat generated warping the part much. For lower precision work in thinner
material it is much cheaper to use the higher expansion glass, which
polishes far more rapidly than fused silica does.
Also fused silica scratches less easily than BK7, which matters for flats,
not for windows and gratings.
Cast borosilicate is used by the group out at Steward Observatory to make
their lightweight mirrors in a rotary mold. The rotation of the mold gives
the top of the liquid glass a parabolic shape, which means less glass needs
to be removed when grinding.
Would I be rehashing old stuff if I brought up Abbe' offset error into the
discussion of accurate measurement?
On a mill the scales are usually a considerable distance from the axis of
motion though the cutter. Thus any angular motions of the stage cause a
measurement error of the distance between the axis of measurement and the
scale times the sine of angle. If the ways are slightly loose the stage can
have a shift in angle when the direction of motion is reversed.
It is possible to relax the requirement for good measurement stages if the
effects of abbe' offset error are prevented by alignment of measurement
axes.
The book, Foundations of Ultraprecision Mechanism Design, by Smith and
Chetwynd has lots of interesting info on these and other subjects.
I agree with what everyone says about expansion of metal when cutting
causing machining errors. Also mounting stresses that are relieved when
unmounting can cause dimensional changes.
Elliot Burke
the like. There is a very good reason for this: Low CTE. This doesn't
matter much when using the stuff, but when polishing, heat is generated,
causing a temperature gradient in the flat. This is unavoidable, even with
a cooling bath. This tends to warp the surface convex. So a low expansion
part has a big advantage. With higher expansion glass the part is polished
to a convex figure, then when cooling it goes back to a flat profile, maybe.
Rather tricky to do to the precisions required for a large lambda/20 flat.
You can really bear down on the silica while polishing without fear of the
heat generated warping the part much. For lower precision work in thinner
material it is much cheaper to use the higher expansion glass, which
polishes far more rapidly than fused silica does.
Also fused silica scratches less easily than BK7, which matters for flats,
not for windows and gratings.
Cast borosilicate is used by the group out at Steward Observatory to make
their lightweight mirrors in a rotary mold. The rotation of the mold gives
the top of the liquid glass a parabolic shape, which means less glass needs
to be removed when grinding.
Would I be rehashing old stuff if I brought up Abbe' offset error into the
discussion of accurate measurement?
On a mill the scales are usually a considerable distance from the axis of
motion though the cutter. Thus any angular motions of the stage cause a
measurement error of the distance between the axis of measurement and the
scale times the sine of angle. If the ways are slightly loose the stage can
have a shift in angle when the direction of motion is reversed.
It is possible to relax the requirement for good measurement stages if the
effects of abbe' offset error are prevented by alignment of measurement
axes.
The book, Foundations of Ultraprecision Mechanism Design, by Smith and
Chetwynd has lots of interesting info on these and other subjects.
I agree with what everyone says about expansion of metal when cutting
causing machining errors. Also mounting stresses that are relieved when
unmounting can cause dimensional changes.
Elliot Burke