Re: [ATM] convex secondary

[Richard <cnc@cncservo.co.uk>]

Jonathan,

As a follow up to the convex secondary testing thread, I had a
play around at the weekend with testing through the rear
surface, using optical glass BK7 for the mirror. It was
surprisingly easy to obtain an excellent Offner Null design
using two off the shelf lenses. In fact I started with the
offner design I had done for my primary, changed the mirror to
the secondary and it took only a few optimisations to get a good
result. I substituted the derived lenses for off the shelf
designs, re-optimised and got a 0.0008 wave null (for
theoretically perfect mirror and lenses of course).

What really pleased me was the sensitivity of the null to change
in conic constant, reducing from 21 waves at K=-4, through 10
waves at K=-5, 5 waves at K=-5.5, 0.9 waves at K=-5.9 and
finally to 0.0008 waves at the required -5.9852.

You have to set aside the extra cost of the optical glass for
the blank, and the cost of the (re-useable) lenses, but to have
a setup that turns a -5.985180 hyperbola into testing for a null
gives me a lot of confidence. Be interesting to see how the
theory translates to practice. I still feel it would be very
reassuring to have two means of testing. If your figured concave
test plate and the offner null agree you can be pretty certain
you have landed at the required end result.

As I mentioned before, there's an excellent worked example of
designing an offner null setup in Geary's book "Introduction to
Lens Design". The basis of the method uses Spherical wave
monochromatic light (laser plus GRIN lens eg) and two lenses. The
light goes through a plano-convex lens which has approx the same
amount of spherical aberration as the mirror (if concave) or
mirror-glass combination (if convex). That lens is called the
Generator. The light from the lens travels onto a Tuner lens
placed at or near the light path crossing point. The tuner
adds/subtracts any required remaining spherical aberration and
magnifies the beam to the required amount to fill the mirror.
After reflecting back along an identical path through the two
lens the light arrives back at the common image/object point.

The optimisation involves ensuring that each beam striking the
mirror radiused surface does so at as near to 90 degrees as
possible so that it is reflected back along the same path. Some
ray trace programs use the RAID = 90 optimisation (Real ray
angle of incidence in degrees) or similar at several points on
the mirror radius.

Before you start the design, you have to know the distance from
the mirror at which the object and image coincide. This is simply
the ROC for a concave mirror, but for a convex mirror looking
through the back, the glass modifies this, so you need to ray
trace the mirror first with a very small field, like 0.01
degrees and the PMAG = -1 (Paraxial magnification) optimisation
to achieve a magnification of -1. That gives you a good starting
point for the effective ROC as seen from the rear.

Here's my current prescription. I'd be very interested in comments
from anybody who has done this for real.

Surf     Type              Comment         Radius      Thickness                Glass      Diameter          Conic
 OBJ STANDARD                  IMG       Infinity       228.8853                                  0              0
   1 STANDARD     Edmunds NT45-716       Infinity             11                  BK7            50              0
   2 STANDARD       GENERATOR BACK         -38.76       103.3607                                 50              0
   3 STANDARD     Edmunds NT47-396       207.2123              5                  BK7            25              0
   4 STANDARD           TUNER BACK      -207.2123       11.72249                                 25              0
   5 STANDARD          POST BUFFER       Infinity            840                           3.037291              0
   6 STANDARD          MIRROR BACK       Infinity             25                  BK7           160              0
 STO STANDARD         MIRROR FRONT      -1309.942            -25               MIRROR           160       -5.98518
   8 STANDARD          MIRROR BACK       Infinity           -840                                160              0
   9 STANDARD               BUFFER       Infinity      -11.72249                           3.037119              0
  10 STANDARD           TUNER BACK      -207.2123             -5                  BK7            25              0
  11 STANDARD          TUNER FRONT       207.2123      -103.3607                                 25              0
  12 STANDARD       GENERATOR BACK         -38.76            -11                  BK7            50              0
  13 STANDARD      GENERATOR FRONT       Infinity      -228.8843                                 50              0
 IMA STANDARD                  OBJ       Infinity                                      0.0003275171              0

The 840mm is the effective ROC as seen through the back and the
11.7mm 'Buffer' is a spacing to allow for error in that ROC and
to ensure that the effective ROC plus its caustic happens in
front of the tuner lens. Surface 7, the stop, is the convex
mirror surface and surfaces 6 and 8 are the plano mirror back,
seen first on the way out and secondly on the lights way back
after reflection.

Here's the contribution of the W040 Seidel Spherical Aberration
Coefficients in waves of 632.8nm He-Ne from each surface to the
total.

Surf       W040
  1    0.080483 
  2   25.654061 
  3   -0.047889 
  4    0.030888 
  5    0.000000 
  6    6.930309 
STO  -65.281888 
  8    6.930314 
  9    0.000000 
 10    0.030890 
 11   -0.047891 
 12   25.654132 
 13    0.080484 
IMA    0.000000

TOT    0.013893 


-- 
Best regards,
 Richard



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