PARABOLA
The Parabola was
named 300 B.C by Appalonia 600 years later 300 AC
Menachmus described the
dimentions X^2=Y AND Y^2= 2X. and
PaPaS (290-350) \
Qualfies
parabola-focus (on vertical line) & “Directrix” a (horizontal line below), the distance from focus to parabola is allways equal to the
distance from parabola vertical to the Directrix line. The focal point is vertical above the parabola center. If you roll a parabola along a straight line, its focus traces out a catenary according to :
Wells, D. The
Penguin Dictionary of Curious and Interesting Geometry
The shape
of a Catenary (hanging cable/chain) is based
only on gravety and distance it is not
The shape of the Parabola which is based upon the reflection angle
of paralel-light to produce a Focal point. The distance from the Parabola focal point to the
Parabola face is always equal to the"Directrix" line (a line below
the Parabola 90 degree from center-line) on every point on the Parabola,
therefore the vertex is closer to focus
than the rim, (shorter FL) but since we cannot add
material to the mirror, we move the focal point minutely closer during
Parabolizing-correction. While the mirror-rim stays un-corrected, the amount of
glass that has to be removed during correction at the vertex is between 1 and 2
ten-thousants inch (0.00015”) but since parabolizing is done with polishing, it
takes as much time as the rough-grinding. Short FL mirrors need more center-correction
than long FL.mirrors, but fortunally our mirrors are usually near flat, like F5
a section around the vertex. And we start usually by grinding a spherical concave which is close to a parabola See below.
The parabola rim and the sphere rim
are the same. While the centers have different F.L.
Long Foc.Length mirrors (F12 and
longer) do not need to be corrected. Are near spherical
PARABOLA
TESTING
The first testing
for parabolic shape is done on the Foucalt tester by calculating zones
(rings)of the mirror surface called Cauder zones of equal surface area, the
Focal length of each (different) zone is computer calculated with Figure X
program, the testing correctness is done on the Foucalt tester, thereby using
not the focal length but the Radius of Curvature distance of the sphere,which
is twice the Focal-length, this makes the mirror-zones Null-test distances having
much larger numbers as they are in reallity (each seprate zone needs to (NULL) on
the R.O.C ).when correct, even as the whole Sphere nulls when correct. While
the parabola whole mirror only Nulls at Focal-Length. The Parabola and the
Sphere can both be star-tested and Auto Collimated with Null and Rounche screen
for straight lines tested
OTHER TEST AVAILABLE
For mirror-surfaces and quality are Star-test,
Auto-Collimation,Interferometry
Parabolizing is done by
hand and also by machine, by Casting, Slumping or Flexing the mirror
On a 10” F5 mirror the center to rim zone diff. on ROC is
0.114 while the real FL diff.=0.00078”
PARABOLA-CORRECTION DIFFERENT WAYS
It
is posible (and has been done)to parabola-correct a mirror by hand and
spin-table, during pre-polish at the end of fine grinding when ready for
polishing, Mark the mirror-edge again with a pencil-line around. Continue fine
grinding with 5 or 9 micron, the Mirror on Top using the Circular Stroke with
40 % overhang and light weight (the Parabola-Correction-Stroke)continually
until reaching the pencil-line, than change from fine grinding to full-size
pitch-lap-polishing with the same P.C. stroke until complete polished and
parabolized
Alternate way is: at the
end of fine grinding the sphere, start polishing with P.C.stroke and create the
parabola during the polishing
