Re: [ATM] Off-Axis Paraboloid

[Anthony Stillman <atmer@flash.net>]

One of the great things about the amateur newtonian is the near irrelevance
of the final focal length.  The amateur off axis paroboloid does this one
better.  The focal length and the angle of deflection are both somewhat
irrelevant.

The largest difference between a sphere and a best fit off axis
paraboloidal segment, tested as if it were a sphere, is astigmatism. After
that, coma.  Way after that, power.  And way after that, trifoil.  In a
slow system only the stig matters.

If the mirror is tilted just enough to place the focal plane outside the
incident light cone, the angle of deflection (theta) is small.  With theta
small and assuming f/long, there exist a "simple" relationship(1) between
theta and the difference in the astigmatic radii.  This relationship shows
that that difference goes as theta^2.  Doubling the tilt angle, increases
the difference in the two ROCs by a factor of four.  Hence, a small
deviation from the desired amount of astigmatism can be ignored in
preference to a just plain dumb luck smooth figure.

Using OSLO LT, I found that for a 6 inch, with a focal plane one diameter
away from the incident optical axis, an f/24 sphere is passable.  At f/20,
fixing the stig is a should, at f/18 a must.  That must amounts to 5 mm of
difference between the tangential and sagittal radii(2).  Five millimeters
in five thousand(3).  At f/12 coma comes into play.  This can be removed by
further figuring using a null test.

With a corrector a perfect off axis paraboloidal segment would function
well down to f/10ish.  Off axis means f/slow.


Anthony


AMABO CENSE
PLEASE VOTE




1) Cs - Ct = (cos(theta) * sin(theta)^2) / (2 * F)
     where:
        Cs          1 / ROCsagittal
        Ct          1 / ROCtangential
        theta       deflection angle
        F           focal length

2) The tangential plane is the paper the drawing's on.  The sagittal plane
comes straight up out of the paper and is perpendicular to it. (4)

3) For an f/18 150mm diameter off axis segment with a theta of 3.2 degrees
(one diameter off axis) the two radii differ by 4.8mm.  The physical sag
across the mirror along the tangential and sagittal diameters, differs by a
little less than 1 wave.

4) Yea I know, that description leaves a lot to be desired.  How about I
add that theta lies in the plane of the paper and, never a sentence a
preposition end with.


_______________________________________________
ATM mailing list http://www.atmlist.net/