1) The document describes a proposed design for an unobscured astronomical camera with a 22 degree field of view and f/2 speed, to be used for a new large telescope in Hawaii. 2) It explores starting with an existing 5-mirror spherical design that was used on space missions, but determines a 3-mirror freeform aspheric design may be better. 3) The document presents an example 3-mirror freeform aspheric design that meets the requirements, with all mirrors tilted and shaped as aspheres to produce an unobscured 22 degree field of view at f/2.

1. Freeform Aspheric Telescope with an External Pupil
Dave Shafer
David Shafer Optical Design
Fairfield, Connecticut
Shaferlens@att.net

2. A 30 meter diameter telescope is being built for a new observatory in Hawaii

3. Its mosaic mirror with 492 segments will be 6 times larger than the single mirror
Mt. Palomar 5 meter Hale telescope in California. The tertiary mirror directs light
to very large size instruments, such as a spectrograph.

4. After the star light has been
dispersed by some very large
prisms the dispersed rays are
collected and focused by a camera.
There are two cameras, one for the
blue light and one for the red light.
Each needs to be 300 mm aperture
f/2.0 with a 22 degree full field.
The pupil must be 600 mm in front
of the first element. The spectral
range is very broad, from the near
UV to the near IR.
The dispersed light seems to be
coming from a pupil in front of the
focusing camera.

5. Because of the large size of the camera a refractive design is almost impossible to
make, and would require some calcium fluoride lenses about 500 mm in diameter
for secondary color correction. The distant front external pupil makes a lot of
problems, and so does the color correction in such large size lenses.

6. The project wants a camera design with no obscuration, because of diffraction
effects. A catadioptric design would still require some very large lenses. The
best design would be an unobscured all-reflective design, with a front pupil.
Freeform aspherics help a lot in getting to a 22 degree f/2.0 unobscured design.
Here is a 15 degree f/2.0
unobscured freeform aspheric
design with very good performance
but with an internal pupil.

7. Front
pupil
Image
plane
A catadioptric design
was considered but
the lens sizes would
still be impractical and
this freeform aspheric
design shown here
would still need color
correction and even
more large size
lenses.
External
pupil

8. This 4 mirror freeform
aspheric design has an
external pupil but is too
slow speed and narrow
angle.
Two convex field
mirrors correct for
Petzval
The big appeal of a reflective design is not having to
deal with the enormous spectral range of the project.

9. There is an interesting 5 mirror unobscured design with an external pupil in my
1978 patent (US 4,226,501). All the mirrors have spherical surfaces.

10. The basis of this design is the well-known two
concentric spheres, with spherical aberration
correction and no coma or astigmatism
A concentric design stays well corrected if it is
used backwards – a very useful fact to know.
Here it then gives a virtual image.

11. Both versions of the
concentric spheres can
be made unobscured by
decentering the pupil.
We are interested in the
virtual image version.

13. A combination of decentered pupil and off-axis
field makes for the best unobscured configuration

14. Convex grating surface
Spectrum
By making the convex
mirror in the Offner 1X
relay become a grating, you
get a high performance
spectrograph.

15. This design, as a telescope/spectrograph, was made and
sent on the Cassini spacecraft to Saturn. It is unobscured,
5 spherical mirrors, and has loose tolerances.

16. Another one of this telescope/spectrograph designs was sent on the Dawn
spacecraft to the asteroid Vesta and is now orbiting the dwarf planet Ceres.
In case you have not been following this,
there are several bright lights coming from
the surface of Ceres!!

17. NASA’s theory that these bright
spots are reflections of the sun
from ice is clearly false since the
brightness does not change as
the “reflection” angle changes a
lot. The spots are also too bright
to be defuse reflections, like from
snow.

18. Fortunately the internet
has the answer to this
mystery. The bright lights
are clearly city lights of the
aliens who live on Ceres.
The answers to many of
life’s mysteries can be
found on the internet.
Citizen of Ceres

19. A third example of
my design was sent on
the Rosetta spacecraft
to orbit a comet.

20. The success of this design on several space missions makes it an interesting
candidate to consider for the start of a freeform aspheric design for astronomy
that is unobscured, f/2.0, 22 degree field and with an external pupil.
But there is a very similar design that is a better starting point.

21. The design already discussed
starts out as two independently
corrected systems, with just
Petzval at the 3rd-order level.
Then the combined design is
optimized and both Petzval and
distortion can be corrected, with
just spheres. But if the eventual
design will have aspheres then
there is better starting point,
with one asphere. It looks very
similar but has some important
differences.

22. First design front part = concentric
mirrors, corrected for spherical
aberration, coma, and astigmatism
but not Petzval.
Exit pupil located at entrance
pupil.
Second design front = convex mirror M2
at focus with same radius as M1 mirror.
Stop at center of curvature of M1 mirror.
Corrected for coma, astigmatism and
Petzval but not spherical aberration.
Telecentric exit pupil
Center of curvature
of M1
Center of curvature
of M1 M2 at focus of M1

23. New design, with one aspheric
Decentered pupil is
imaged onto 4th mirror,
which is made aspheric
Telecentric rays
Telecentric rays
This 2nd type of front end gives better
correction results than the 1st type .

24. M3, M4, and M5, the Offner 1X relay, can be made
any size. M2 always makes the rays leaving M2 be
telecentric and M4 is then always an aperture stop.
The center of curvature of M1 will always be
imaged onto M4, which is then made aspheric. The
two subsystems (M1-M2) and (M3,M4, and M5) are
independently corrected for coma, astigmatism and
Petzval but not for spherical aberration.
Aperture stop
aspheric
Aspheric at a stop
only affects spherical
aberration
Best starting point for a freeform aspheric design

25. 300 mm diameter
front pupil, >600 mm
in front of M2
Flat image, f/2.0
unobscured 22
degree field
All are freeform aspheric mirrors.
f/2.0 and 600
mm focal length
90% energy spot
diameter <40u
over whole 22
degree field.
Requirement is
<60u
M2 is moved away
from M1 focus

26. No attempt has been
made to see if some
mirrors can be normal
aspherics or even
spheres and still meet
the performance spec,
or if a different freeform
aspheric description
(like Zernike) might give
better performance.
The three concave
mirrors are each 750 mm
in diameter

27. The best starting point for a freeform aspheric design is one which already
works pretty well with mostly spheres or one or two conventional aspherics.
Here the requirement for a distant front pupil greatly restricted the design
options.

28. 1) If an external front pupil is not needed then the design task
is much simpler.
2) We will look now at a simple three mirror design with an
internal pupil, just to see what that might be like.
3) Just as is the case with camera lenses, a combination of wide
angle and fast speed is best served by the retrofocus
configuration, with a negative power first element and an
internal pupil.

29. Confocal parabolas – corrected for spherical
aberration, coma, and astigmatism
Afocal Mersenne system

30. The Baker-Paul design combines
the great aberration correction of
two confocal parabolic mirrors (M1
and M2) with the Schmidt principle
and a spherical third mirror M3 to
get an image with good correction.
The parabolic secondary mirror M2
can become a sphere when the
Schmidt aspheric at the center of
curvature of the M3 mirror has its
deformation superimposed on M2.
The result has a parabolic
primary and then two spheres and
can be used on existing large
observatory parabolas. The image
is curved.
This design is only good for small field
sizes and the image is not accessible.
Center of curvature of M3
M2
M3
M1

31. Good for small fields
Good for large fields
Reverse system to get better wide field starting point

32. Parabola
Hyperbola Sphere
Image
There is an inverse,
or retrofocus version
of the design, where
the first mirror is a
convex parabola and
the second mirror is a
concave parabola.
M2 is at the center of
curvature of the third
mirror M3, which is a
sphere. The Schmidt
aspheric to correct for
the sphere now adds
its deformation to the
second mirror and
turns the parabola
into a hyperbola.
This inverse or retrofocus configuration is much better suited to large
field sizes than the classical Baker-Paul design from the previous slide.
M1
M2
M3
This configuration is quite long and also has an inaccessible image

33. There is an alternate
solution which, at first,
looks very unpromising.
We start out with the first
two confocal parabolas
but now we add the
Schmidt aspheric to the
first mirror, the convex
one. That turns this
parabola into an oblate
spheroid. There is then a
virtual image formed of
this M1 mirror by the
second mirror and it lies
quite a bit to the left of
the second mirror. We
then make the third
mirror, the sphere,
concentric about this
virtual Schmidt aspheric
location.
This has terrible obscuration but the image is now in a better
location and the system length is much shorter.
Sphere
Parabola
Oblate
Spheroid
image

34. This design can then
be used far off-axis to
avoid most of the
obscuration and it
makes a good starting
point for a freeform
aspheric design. Here
it is frst optimized with
conventional aspherics

35. Three freeform aspheric
mirrors, f/2.0 and a 10 degree
diameter flat field. Spot size
is 10 arc seconds over field

36. Freeform aspherics allow this to
become an unobscured design
with a good image location
f/2.0, 10 degree
diameter flat field,
spot size = 20 arc
seconds over the
field.
M3 mirror is tilted to
make an unobscured
design

37. This design has a problem
with baffling, where light
hits the third mirror without
hitting the first mirror

38. By using different
signs of the tilts on
the second and third
mirrors this new
configuration of
mirrors results, which
is very much better
for baffling. The
flexibility of freeform
aspherics allows this
design to also have
good performance,
similar to that of the
previous design.
f/2.0, 10 degree diameter
flat field, spot size = 20 arc
seconds over the field.
Designs like
this were also
developed by
Optical
Research
Associates

39. 300 mm diameter
front pupil, >600 mm
in front of M2
Flat image, f/2.0
unobscured 22
degree field
All are freeform aspheric mirrors.
f/2.0 and 600
mm focal length
90% energy spot
diameter <40u
over whole 22
degree field.
Requirement is
<60u

40. Questions?