Wednesday, August 5, 2015

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