[Raytrace] Dall Null

[Robbin Palmer]

Regarding 22” f/4.5 Dall Null: I made a math error in calculating the
angle the null lens must be offset from the axis to clear the return
beam.  Depending on the mirror f number and lens used, the angle is
typically between 0.5 and 0.2 degree.  This still greatly increases the
wavefront error relative to the on axis case.   A lens placed 0.24
degree off axis adds enough astigmatism to increase the wavefront error
by about a factor of 5 compared to the on axis case.  Larger f number
mirrors are required to give small offset angles.  For example, the 25”
f/6 mirror described by Kestner in Kriege and Berry would result in an
offset angle of about 0.24 degree for the f=10 inch null lens used,
assuming a lens diameter of 2 inch.  On axis, the wavefront error would
be about 0.07 wave, off axis 0.24 dgree it is about 0.37 wave (His
actual setup may do better than this as I don’t know the exact lens
diameter used).  This could be improved somewhat by bringing the lens
back even with the knife edge where the returning cone of light is of
smallest diameter so that the offset angle can be reduced.  This puts
the light source back past the knife edge and makes viewing more
difficult.  Perhaps a small flat mirror behind the knife edge could be
used to deflect the knife edge image out to the side.

I tried turning the lens around per John’s tutorial, and got the error
down to a little over 1/10th wave, but this requires a larger entrance
aperature and thus larger offset angle.  If it is assumed that the lens
is good across 90% of its diameter then this setup gives about 0.4 wave
error with the lens off axis.  Since the null lens placed this way has
larger spherical aberation and coma than when turned around, I tried a
concave convex lens since it has even larger spherical aberation, and
varied the two radii of curvature with a slider bar while optimizing.
This gave improvement, but an insignificant amount.

With regard to John’s suggestion of viewing a rectangular strip across
the mirror to reduce wavefront error: The center point of the wavefront
I get with the pinhole and lens off axis is a saddlepoint.  Moving in
+/- x the slope decreases, +/-y the slope increases (depending on the
direction you tilt).  The max in y is on the same order as the min in
x.  So instead of placing the rectangle along x or y, it must be placed
at an angle for the least wavefront error.  If the off axis error is on
the order of 2 waves, then it can be brought down to a useful level
using a rectangular strip of about 1” or less height. The strip reduces
the error by a factor of ten or so – somewhat more of course for smaller
heights. I feel like I have tried about everything.  Anything I have
missed? Thanks for your help John.  OSLO is a wonderful tool to have.
Tom W. (Robbin P. in earlier posting due to using my wife’s email)