A survey of some unusual telescope designs. One has a 20 meter diameter f/1.0 spherical primary mirror while others are suitable for amateur astronomers to make.

1. Some Unusual Telescope Designs
Dave Shafer
David Shafer Optical Design

2. Topics
• Gregorian designs
• Cassegrain designs
• All-spherical designs
• Uses of off-the-shelf Schmidt-Cassegrain components
• Tilted component telescopes
• Telescope sent to Saturn, Vesta, and a comet

3. Gregorian Designs

4. A classical Gregorian telescope has a parabolic primary and an elliptical
secondary mirror. For a 1.0 meter diameter f/2 primary and a f/15 system
with a 20% diameter obscuration it is perfect on-axis and has .37 waves
r.m.s. at .55u at the edge of a +/- .25 degree field on a curved image.

5. • There is about equal amounts of coma and astigmatism at
the edge of a +/- .25 degree field, on a curved image
surface. Both mirrors are perfect on-axis.
• By using both of the mirrors’ conic surfaces as variables it
is possible to correct for both spherical aberration and
coma. The primary mirror is then just very slightly
different from a parabola, while the secondary is close to
the same ellipses as before.
• Then the design is perfect on-axis and has about .32 waves
r.m.s. of astigmatism on a curved image surface. Not much
better than before (.37 waves r.m.s.) but now it is pure
astigmatism and it is quadratic with field, so it is a little
better at smaller field angles than the classical Gregorian.

6. Field lens at image
Now suppose we add a tiny thin field lens right at the intermediate image. It
will have no spherical aberration, coma, or astigmatism if it is right at the image
The power of this field lens gives independent control of where the pupil is
for the two mirrors. That extra variable, plus the two conics as variables,
allow us to correct for spherical aberration, coma, and astigmatism.

7. • The required field lens power for this solution is very weak and the
mirror conics hardly change at all. The primary mirror conic is
still very close to a parabola.
• Using a field lens at an intermediate image to give independent
control of the pupil position before and after the intermediate
image is a very powerful design tool and it affects all the system
aberrations even though it has very little of its own aberrations.
• If the field lens is moved a little away from the intermediate image
there is still an anastigmatic solution possible and it changes a little
the primary mirror conic that is needed.
• There is then a solution where the primary becomes an exact
parabola. Then this solution can be used with existing observatory
parabolas, like at Mt. Wilson and Mt. Palomar.

8. Two weak meniscus shell lenses
When the field lens is moved away a little from the intermediate image, to give the
exact parabola solution, the lens acquires a small amount of axial and lateral color
That color is corrected by splitting it into two lenses on either side of
the intermediate image and making them weak meniscus lenses curved
about the image.

9. Two weak meniscus lenses on either side of image
Secondary
mirror
By curving the lenses about the image they can
correct for both of their axial and lateral color with
the same glass type. Here I used BK7 glass. The
lenses do not add any to the axial obscuration.

10. The result is an f/15 design with a 1.0 meter diameter f/2 parabola, an
elliptical secondary mirror and two weak BK7 lenses 30 mm in diameter.
On a curved image (radius 470 mm) the polychromatic (.486u- .656u)
wavefront at the edge of +/- .25 degree field is .019 waves r.m.s. If it is
reoptimized for a flat image the polychromatic value is .043 waves r.m.s. at
the edge of the field.

11. • This is really very good performance over a sizable field
of view by a simple addition to an observatory’s large
parabolic primary mirror.
• The results here are for an f/2.0 parabola. The design
works well for other values too.
• If we add some more lenses near the intermediate image
we can get still better performance.
• Next I show a set of 4 BK7 glass lenses for a 2.0 meter
diameter f/2.0 parabola and with a flat image.

12. Secondary
mirror
Design has a 2.0 meter diameter f/2 primary parabola, elliptical
secondary, 4 BK7 lenses and a polychromatic (.365u - .656u) wavefront
of .030 waves r.m.s. at the edge of a +/- .25 degree field on a flat image.
image
To primary mirror
Very weak lenses

13. A purely reflective solution to the field lens region
has two solutions, with two small aspheric mirrors.
Primary
mirror
Primary
mirror
With this in place we have an all-
reflective design that works well
for all wavelengths. For a 10
meter diameter f/1.0 parabolic
primary and a conic secondary
mirror and these two small
aspheric field mirrors we get a
design that is diffraction-limited in
the visible over a ¼ degree
diameter field on a flat image.

14. 10 meter diameter f/1.0 parabolic primary, elliptical
secondary, two small aspheric field mirrors.
Corrected for spherical
aberration, coma, astigmatism,
and Petzval.

15. F/1.0
spherical
primary,
20 meters
in diameter
f/5.0
image
The same type of system can work with a spherical primary mirror
but with a much smaller field size.
Aspheric
secondary

16. f/1.0 primary mirror
Caustic region near focus
The best focus on-axis spot size from a 20 meter
diameter f/1.0 spherical mirror is 180 mm in diameter!

17. Reflective field
elements
The field mirrors obscuration can be 25% of the pupil diameter with
this f/1.0 spherical mirror focus.

18. F/1.0
spherical
primary,
20 meters
in diameter
f/5.0
image
By letting the field mirrors both be curved and aspheric we can get
a design that is diffraction-limited at .5u over a 1/20 degree field
diameter, or a 100 mm flat image diameter at the final f/5.4 focus.
Aspheric
secondary

19. Primary mirror
and 25%
diameter
obscured pupil
Rays from secondary mirror towards final focus, off page to the right
This shows the region around the two aspheric field mirrors. The 25%
diameter obscuration due to the field mirrors matches the 25%
obscuration due to the secondary mirror.
Secondary
mirror

20. Cassegrain Designs

21. What can be done with a classical Cassegrain telescope to improve its
image quality? Here a 1.0 meter diameter f/2 parabola and a hyperbolic
secondary mirror are perfect on-axis but have .48 waves r.m.s. at the
edge of a +/- .25 degree field, on a curved image.

22. The conventional way to improve a classical Cassegrain is to add some
field lenses. The result is a design corrected for spherical aberration, coma,
astigmatism and Petzval curvature, as well as axial and lateral color
BK7
lenses

23. • What else could be done, instead of this?
• At the edge of a +/- .25 degree field the classical
Cassegrain design has about equal amounts of coma and
astigmatism.
• The coma from the primary mirror is 4% larger than the
coma from the secondary mirror and they are of opposite
signs, so they almost cancel.
• Can something be done to make them cancel exactly,
without changing the mirror surfaces?
• Yes – we add a nearly zero power lens next to the
secondary mirror. It puts in a tiny amount of coma.

24. A very weak, nearly zero power lens right in front of the secondary
mirror makes the coma cancellation be perfect. But it introduces very
small amounts of spherical aberration and color.
Nearly zero power
BK7 lens
Secondary
mirror

25. By bending the lens into a very weak power meniscus lens the
spherical aberration and axial color that it has can be eliminated

26. • The resulting design has the same amount of
astigmatism as a classical Ritchey-Chretien design.
• So just by adding this nearly zero power element to a
classical Cassegrain we give it the same performance
as a Ritchey-Chretien, without changing the mirror
surfaces.
• The remaining astigmatism, Petzval, and a very small
amount of lateral color can be fixed by adding a single
thick field lens to the design, as is shown next here.

27. Thick BK7 glass field lens corrects design for
astigmatism, Petzval, and lateral color

28. Splitting the thick field lens in two gives more design variables
and avoids the glass thickness of the simpler design.
BK7
lenses

29. 2.0 meter f/2 parabolic
primary mirror, 3 BK7
lenses, evaluated for
polychromatic (.365u to
1.0u) wavefront on a flat
image for a +/- .25 degree
field. Conventional design
with field lenses = .089
waves polychromatic r.m.s.
at edge of field.
New design = .049
waves polychromatic r.m.s.
at edge of field.
New design has better
chromatic performance.
lens

30. All-spherical Designs

31. • What about a design with spherical primary and
secondary mirrors and a subaperture corrector?
• In the late 1980’s I published a very simple
design for amateur telescope makers that was
later made and sold by Vixen Optics. It has two
spherical mirrors and a single thick meniscus
lens with nearly zero power.

32. Around 1990 I designed a 500 mm aperture version with a split corrector
lens (to avoid a very thick single lens) for the Swansea Astronomical
Society in Wales. It was made and has been in use ever since.

33. With a ½ meter diameter f/2.5 spherical primary mirror this all spherical
design is diffraction-limited through the visible region over a small field
Swansea, Wales observatory telescope

34. By adding two BK7 field lenses near the image the correction can be
greatly improved and this is now diffraction-limited through the visible
spectrum over a ½ degree diameter field on a flat image, with all spherical
500 mm diameter
f/2.5 spherical primary

35. Klevtsov design
Mangin lens/mirror element
A different type of design is by Klevtsov and it has a little better
performance than the other design that I did.

36. The Klevtsov design, at
left, is a little better over a
small field than the design
at the bottom. But this is
not a fair comparison. The
top design has only two
corrector elements while
the design at the bottom
has three – two lenses and
a mirror.
Let us split the Klevtsov
Mangin element into a
separate lens and a mirror.
Then the performance gets
a little better and is then
about 25% better
polychromatic wavefront
than the bottom design.

37. Mangin element separated into a mirror and a lens
Two element Klevtsov design is slightly improved by going to
this three element design

38. By having three BK7 lenses next to the secondary mirror the performance can
be improved a lot and then a 1.0 meter diameter f/2.5 spherical primary design
can be diffraction-limited through the visible spectrum over a ½ degree
diameter field on a flat image.

39. Uses of off-the-shelf
Schmidt-Cassegrain
components

40. Celestron and Meade sell 200 mm
aperture and 275 mm aperture f/10
Schmidt-Cassegrain telescopes. There is
a front aspheric plate/window, a
spherical primary mirror and a spherical
secondary mirror.

41. The aspheric plate/window is made by a very clever method that
allows for mass production at a very low cost. The design has quite
a lot of coma off-axis and it would take another aspheric surface to
fix that.
How can we use these optical elements to make other designs?
Commercial Schmidt-Cassegrain telescope

42. Aspheric plate moved out in front to
correct for coma.
Coma is corrected and astigmatism is very small if the aspheric plate is
moved out in front further, giving a bigger well-corrected field size.
The optical elements have not been changed at all, just the positions.
Secondary mirror needs a new way to be supported

43. These mass produced 200 mm or 275 mm aperture aspherics are very much
less expensive than a custom made aspheric. Buy two Schmidt-Cassegrain
telescopes and take the two aspheric plates and put them together. Then make
a new spherical primary mirror to get an inexpensive f/1.75 Schmidt telescope
with a wide field of view on a curved image, with no coma or astigmatism.
Using only one aspheric plate (and a different mirror) gives a f/2.25 design.
Two identical aspheric plates
Spherical mirror

44. Prime focus corrector, after
removing secondary mirror
About 15 - 20 years ago I designed a prime focus corrector for Celestron, but they
never did anything with it. It was f/2.3 and used the standard aspheric plate and
primary mirror, with the secondary mirror removed. Back then image sensors were
much smaller than today. Now they have revived this idea and there is a new product
like this for their 275 mm aperture telescope. I did not do the new design, shown next.

45. The new design looks like this, for a much larger image sensor size
than was available when I did my design a long time ago.
Not to scale

46. Camera body or special image
sensor attaches here.
Celestron 275 mm
aperture f/2.2
astrocamera

47. The point of showing these designs is to emphasize
the use of existing optical elements, especially aspheric
surfaces, to make new aspheric designs without the
expense of a custom made aspheric.

48. Unobscured Tilted Component telescopes

49. Unused and
absent portion
of aspheric
plate
Spherical
mirror
Unobscured decentered pupil Schmidt telescope
Aperture
stop

50. A decentered pupil on a Schmidt aspheric plate sees just one side of
the spherically aberrated wavefront coming from the aspheric.
Suppose we decompose this off-center section of the wavefront using
an off-center coordinate origin. Then the off-center piece of spherical
aberration looks mainly like astigmatism and some coma, when
expanded about this new coordinate origin.
Absent
part of
wavefront

51. Tilted lenses vertex lie on this line
Schmidt telescope axis that includes the mirror’s
center of curvature
Three tilted lenses can have their powers, bendings and tilts chosen so that
they simulate an off-axis piece of spherical aberration and also that is constant
with field angle. No off-axis pieces of lenses are used. They are centered (but
tilted) on a different axis from the mirror.

52. f/4.0 design has a polychromatic spot size in the visible region of 6
arc seconds that is constant over a 3 X 10 degree field curved image.
Completely symmetrical lens group
The design can be made half as long, by moving the lens group up near the
image, and there is still a well corrected image possible – as shown next.

53. This shorter design has a good solution with just two lenses, but with a
smaller field than the long design. F/4.0 with 6 arc seconds polychromatic
spot size over a 2.0 degree diameter field on a curved image.
For slower speeds, like f/6, the two lenses can each be made flat on one
side and have a common radius, as is shown next.

54. Plano-convex and plano-concave BK7 glass lenses, same radius
Spherical mirror
150 mm aperture f/6.0 unobscured design. Diffraction-limited in
visible spectrum over a 1.5 degree flat image, which is tilted. The
fold mirror is flat.

55. Telescope sent to Saturn,
Vesta, and a comet

56. One of my first
patents, in 1977,
was for an
unusual kind of
unobscured
telescope that
only has spherical
mirrors.
Many years later one of these unusual telescopes was sent on the Cassini
space craft to Saturn, where it took many closeup pictures. Later another
one went to the asteroid Vesta, and it was there a few years ago, taking
photographs. Now a third spacecraft with one of my telescopes on-board
is approaching a comet and it will try to land on it.

57. This is the Cassini space craft
before being launched, on its mission
to Saturn.
Close up of asteroid
Vesta, taken recently from
space with my telescope.

58. The Cassini mission to Saturn wanted a telescope on-board that was
1) all-reflective, 2) easy to make and align with no aspherics, 3)
unobscured, 4) well-corrected over a large field size, and 5) able to
become a spectrograph with no extra elements
This drawing from my patent, not to scale, shows the design. What
is very unusual is that all the mirrors have their centers of curvature on
a single optical axis, unlike other tilted mirrors designs. Also the
convex mirror “25” in the drawing is the aperture stop. If this is made
a grating surface then the final image is a sharp in-focus spectrum.

59. Any questions?