A variety of optical designs are developed and discussed, inspired by Gabor's very simple and largely unknown design. Some are extremely high NA (0.999!!!) with a wide field of view and diffraction-limited correction.

1. Dennis Gabor’s Catadioptric Design
and Some New Variations
David Shafer
David Shafer Optical Design
Fairfield, Connecticut
#203-259-1431
shaferlens@sbcglobal.net

2. Gabor telescope
This is sometimes confused with the Maksutov
telescope and is only correctly described in a 1941
British patent (#544,694) by Dennis Gabor. It is not
clear if Gabor himself understood the aberration
characteristics of this design – probably not based on
the very short patent text. It is extremely simple with
an interesting theoretical basis.

3. The Gabor design will be our jumping
off point for some more complicated
designs. Let’s see where that leads us.

5. Center of curvature
of lens front surface
Center of curvature
of the mirror
Aplanatic back surface
bends the chief ray a little Gabor design

6. 5th order adds for
each surface
5th order nearly
cancels
Bouwers
Gabor

7. For small field sizes
the stop can be
moved up to the first
element without
much performance
change. For large
field sizes the stop
should be out in front
some, ideally at the
center of curvature of
the first surface. But
that makes the design
a lot longer

8. Paraxial axial mirror
diameter is 1.32 X front
aperture size

10. Surface order = concentric, concentric, concentric – all around chief ray, then
aplanatic – about axial ray , concentric about new chief ray
Bouwers
lens
Gabor
lens
Can be corrected
for 3rd and 5th
order spherical
aberration but
not 7th order.
Not as good as
when Bouwers
lens is in double-
pass.
Stop position

11. By using two Bouwers meniscus lenses better
higher-order correction is possible. Total lens
thickness directly correlates with performance.
To avoid unreasonably thick lenses and still get
good high-order correction Charles Wynn split
the meniscus lenses in two to get this 4 lens
design. Then glass choice can also correct for
color.
Wynne was a
great designer, in
pre-computer
days. He was
active up till his
death at 89.

12. James Baker designed some very fast speed
wide angle satellite tracking cameras based on
the Bouwers type of system. They were color
corrected, had a curved image and the paraxial
axial beam diameter at the mirror is close to the
size of the entrance pupil diameter. These
designs had aspherics and that let the meniscus
lenses be thinner.

13. Although the Baker-Nunn design has great performance it has 4 aspherics.

14. 100 mm F.L. .70 NA, diffraction-limited
(monochromatic) over 5 degree total
field on a curved image.
100 mm F.L. .80 NA, diffraction-limited
(monochromatic) over 5 degree total
field on a curved image.
Extra meniscus lens helps higher-order performance, giving a higher NA.
Gabor +
Bouwers

15. Two weak meniscus lenses improve the higher-order correction of the Gabor lens design.
Gabor lens

16. 100 mm F.L. .80 NA 10 degrees total field. Diffraction-limited
(monochromatic) on a curved image
Additional weak power lens further improves performance

17. 100 mm F.L. .95 NA, 5 degrees total field, diffraction-limited
(monochromatic) on a curved image
All spherical surfaces

18. 100 mm F.L., .95 NA, 5 degrees total field, .55u monochromatic, curved image

19. Modified Gabor has additional weak
power elements
Terrific correction with no aspheres
But curved image
And not corrected for color
Summary so far

20. Some new solution regions will now be found

21. Since the correction is so good at very high NA values and modest field sizes it should also
be good at lower NA values and wide fields, with a similar etendue. So I took the .95 NA
design with a 5 degree field and reoptimized it for .75 NA and 30 degree total field.
That moved the design into a different solution region, shown here, that is closer to
having all the surfaces concentric about the stop. The Gabor lens became weaker and
played less of a role in the correction.
On axis rays Edge of field rays

22. That reminded me of a completely monocentric design that I discovered many years ago. It
can be corrected for 3rd, 5th and 7th order spherical aberration with just these two monocentric
elements. It has phenomenal correction – this 100 mm F.L. design is diffraction-limited
(monochromatic) at 0.999 NA!! over any field angle, on a curved image. There is no need for
an aperture stop. The .999 NA rays leave the first element at grazing angle and internal
reflection losses make for the equivalent of a rotating aperture stop for any field angle.

23. The two main problems with this design
are the very thick glass path and the mirror
size . For a 100 mm F.L. the first element is
161 mm thick and the 2nd is 189 mm thick
and is seen in double pass. The paraxial
diameter of the mirror is 2.28X the
entrance pupil diameter.
By going down from .999 NA to .70 NA it is possible to
greatly reduce the element thicknesses and still get
diffraction-limited correction. Here both elements are
50 mm thick for a 100 mm F.L. design. The second
element has had its concentric lens part split off from
the mirror. It is still a monocentric design.
.70 NA

24. The paraxial axial mirror diameter is 1.56 X
the entrance pupil size, which is smaller
than the 2.28X ratio of the previous design
on the last slide.
This looks just like Wynne’s design but there is a key
difference. In Wynne’s design the second lens is only
gone through once while in the design above it is seen
in double-pass. That turns out to make a big
difference in the correction level.

25. Designs shown to same scale. Both are 100 mm
F.L. and .70 NA. The Gabor + Bouwers at the
bottom is diffraction-limited over a 5 degree total
field on a curved image. The Bouwers with two
lenses at the top is also diffraction-limited at .70
NA on a curved image but over any field size since
it is monocentric. The Gabor + Bouwers is much
shorter and has much less glass path.
Does this now cover all that can be done with
just a few lenses and a mirror? Of course not!

26. We usually have
more choices in the
design process than
we think, at first.
Even with extremely
simple problems.

27. The Rosch design is very interesting. The
lens has a flat front surface and the back
surface and the mirror have the same
center of curvature, where the stop is. As
shown above it is corrected for 3rd order
spherical aberration but not for 5th order.
By adding a Bouwers type lens in double pass, as
shown here, both 5th and 7th order spherical
aberration can be corrected while keeping a
monocentric design. Then it is diffraction-limited
(monochromatically) at .999 NA for a 100 mm
F.L. over any field size on a curved image. With
no vignetting!

28. 100 mm F.L., .999 NA, monocentric design, same MTF for any field angle

29. Because of the flat
front surface there is
distortion for large
field angles. There is
a limit, for no
vignetting, for the NA
and field angle
combination before
the rim rays almost
intersect the second
surface twice.
For the 100 degree
field shown here
the NA cannot be
higher than .95 or
the rim rays will hit
the second surface
again and cause
vignetting. But it is
always diffraction-
limited.

30. Shown to same scale, for .95 NA and a 100 degree field. The Rosch + Bouwers
design on the left is much larger than the monocentric design on the right. But
the refraction at the flat front surface of the design on the left reduces the field
angle inside the design by a factor of the glass index n and that makes the
obscuration due to the image for large field angles much better for that design
than it is for the design on the right.

31. Surface order = concentric about chief ray, aplanatic
about axial ray, aplanatic abut axial ray, concentric
about chief ray, concentric, concentric, concentric.
By inserting a thick
aplanatic/aplanatic airspace inside
the first thick lens we can remove a
lot of glass.

32. By dropping the concentric
and aplanatic curvature
solves and varying all the
parameters we get this
simple design which is 100
mm F.L. .95 NA and
diffraction-limited
(monochromatically) over a
5 degree field on a curved
image.

33. By adding another lens it is possible to reduce the mirror size by quite a lot.
100 mm F.L. .90 NA
diffraction-limited
(monochromatically)
over a 5 degree field
on a curved image.
We have met our
goal of small glass
path and relatively
small mirror size
while keeping very
high NA correction.

34. By reducing the NA of
the .90 NA, 5 degrees
field design it is
possible to get much
larger field sizes while
staying diffraction-
limited. .80 NA gives a
20 degree field, shown
here, while .70 NA
gives a 30 degree field.
100 MM F.L., .80 NA, 20 degree field, diffraction-limited (monochromatic) on a curved image

35. Adding an aspheric surface

36. By adding an aspheric
element at the aperture
stop much higher
performance is
possible, such as this
.90 NA, 30 degree field
design, diffraction-
limited
(monochromatic) over
the whole field – on a
curved image.
Aspheric
element

37. 100 mm F.L., .90 NA,
30 degree field,
monochromatic on a
curved image. One
aspheric surface

38. By taking the .90 NA, 30 degree field design and reducing
the NA to .80 it is possible to remove two lenses and get
this .80 NA, 30 degrees field that is also diffraction-
limited, on a curved image.
It now looks like a version of the Baker
Super-Schmidt, above, but without the
color correction provided by the two glass
doublet here.
Aspheric

39. Color Correction

40. It is hard to get
good color
correction with only
spherical surfaces.
Here there are 8
lenses for a .80 NA,
20 degree field and
the polychromatic
MTF is not as good
as I would like.
More work is
needed to find a
better design.
Color corrected design, no aspheric

41. 100 mm F.L., .80 NA,
20 degrees field,
curved image, .45u-
.65u color correction,
all spherical surfaces

42. 100 mm F.L., .80 NA,
20 degrees total
field, curved image,
one aspheric
aspheric
Good color-corrected design

43. 100 mm F.L., .80 NA,
20 degrees field,
curved image, one
aspheric
.45u -.65u color
corrected design

44. In summary, the Gabor catadioptric design was a very
productive jumping off point for generating a series of very high
performance designs with very high NA and large field sizes.