A broad spectral band high NA catadioptric design is developed that has a long working distance. The design is developed from first principles and the evolution of the design shows what the process of lens design is like.

1. Ultra-broad spectral band catadioptric design
Dave Shafer
David Shafer Optical Design

2. Goals –
• Excellent aberration correction across a very broad
spectral range, including the UV region
• Very small obscuration
• Few elements
• Long working distance
• Good tolerances

3. Design Method
• Separate the different design tasks from each
other and try to work on them independently
• Fix low-order problems first
• Consider alternate solutions
• Be willing to go back and start over again

4. Low-order requirements
(Does not include image quality)
• Small obscuration
• External aperture stop
• Telecentric image
• Long working distance with .60 NA
• 6 mm focal length, .5 mm image diameter
• Flat image (Petzval correction)
• First-order color correction

5. This meets all of the low-order requirements except flat
image and first-order color correction
Aperture stop
Field lens
Silica lenses

6. Color correction problem
• For deep UV spectral range only two glasses are practical
– silica and calcium fluoride
• For a very large spectral range, secondary color is too large
in an all-refractive color-corrected lens group
• So use catadioptric type of design where low-order color
can be corrected with just silica
• Then higher-order color can be fixed with a small use of
calcium fluoride
• Try to maximize use of mirror power and minimize use of
lens power = minimizes amount of color to be corrected

7. Opposite color from silica lenses
(But not nearly enough to cancel)
All silica

8. Color from strong power is enough to cancel color from lens
group but is too strong – get TIR (total internal reflection) from
outer rays and terrible aberrations. We need to split this into two
weaker power elements.
TIR (total internal reflection)

9. Low-order axial color cancels, small lens gives low-
order lateral color cancellation. More mirror power and
less lens power than before.
Design has less power in positive lens group
than before = less color to be corrected

10. Design evolution for color correction

11. If these + and – power silica lenses were thin and in contact then
higher-order color would also cancel when low-order color cancels. But
the + and – lenses have a considerable airspace between them and that
causes a small amount of higher-order color that does not cancel.

12. Primary color is corrected,
and secondary color is 7.5u
focus shift over the .365u to
1.0u spectral band. Much
too large! Axial depth of
focus at .60 NA is +/- .5u at
.365u and +/- 1.5u at 1.0u
What we need is both the
+ lens group and the – lens
group to have slightly
different dispersion
characteristics than just
having all silica lenses. We
can get that by using a mix
of silica and calcium
fluoride in both groups.

13. Calcium fluoride
All silica lenses
Two lenses switched from silica to
calcium fluoride
Top focus shift is about 7.5u
over .365u to 1.0u band, while
bottom is about 1.5u focus shift
Different scale

14. The Petzval radius of this design is 5.8 mm and it is almost entirely
due to the small convex mirror. If all the image aberrations were
perfectly corrected the image would still have a radius of 5.8 mm
and that is much too curved to be acceptable.
The image size is +/- .25 mm and the sag of a 5.8 mm image
curvature over that image diameter is 5.4u. If we choose the focus
correctly we can split this to be an out of focus error of +/- 5.4u
divided by 2, or +/- 2.7u. But the depth of focus of a .60 NA system
(see previous slide) is +/- .5u at .365u and so the +/- 2.7u number is
more than 5X too large. We need a Petzval image radius that is at
least 5X longer than the 5.8 mm of this design, or at least 30 mm.
And that does not leave anything for residual color focus error.
So we have to correct for Petzval aberration very well.

15. Notice that we are working our way through these low-order design
tasks with no attempt yet to optimize image quality. If low-order
problems cannot be fixed then there is no point in worrying about
higher-order image quality.
There are two ways to correct the Petzval curvature of the design. One
way is to replace the small convex mirror, which is the source of almost
all of the Petzval curvature, with a lens/mirror element that has the
same power but no Petzval curvature. The negative lens part of this
element has opposite Petzval to the convex mirror part and they can
cancel out.
Mirror
surface
Mangin mirror replacement for
tiny spherical convex mirror

16. The other way to correct the system for Petzval is to add some strong
negative lens power to the small diameter part of the design. We will try
this first and then look later at the other idea from the last slide.
In a 1.0X afocal magnification situation like this the negative lens is
stronger than the sum of the positive lenses and so the combined Petzval
curvature is that of the negative lens – and is what we need for our
design. But we need a lot of this and it makes for strong power lenses
and aberration problems. It makes for lateral color problems so we need
to use calcium fluoride and silica together to fix that in this Petzval
curvature corrected design. It also causes chief ray correction problems.
Strong powers can cause
spherical aberration of the chief
ray and that makes for
telecentricity errors over the
image diameter. This has to be
corrected and can be quite large if
not fixed.

17. Design fixed for Petzval image curvature, lateral color, and
telecentricity variation over the image diameter.
Petzval correction part
Calcium fluoride
Calcium fluoride

18. Top picture shows design
rays at edge of the field at
.55u and bottom picture
shows rays at .365u. This
shows quite dramatically the
importance of getting lens
drawings that show rays at
both of the upper and lower
wavelength boundaries in any
broad spectral band design.
This design is corrected for
spherical aberration of the
chief ray (monochromatic
variation in telecentricity
over the image diameter) but
there is still a lot of chromatic
aberration of the chief ray –
way too much!!
.55u rays
.365u rays

19. If we trace just the chief ray we can see that most of the axial color of
the chief ray must be coming from here, where the ray height is the
largest. So that part of the design must be changed some to fix this
problem.

20. Unfortunately changing that part of the design, to fix chromatic
aberration of the chief ray (telecentricity variation with wavelength),
makes lateral color problems and the design starts to get quite
complicated. The conclusion is that the method used to correct
Petzval (some strong negative lenses) makes for a lot of other
problems. We will work on this a little more and then we will go
back and look at the alternate Petval correcting solution (a Mangin
lens/mirror element) from many slides ago.
Lesson – always be prepared to start over again when you run into
problems.
Notice that we are still working with low-order aberrations,
like color of the chief ray. Until all the low-order aberrations
are fixed there is no point in doing image quality optimization

21. After a lot of design work a solution was found that fixed the
chromatic variation of telecentricity without hurting the lateral color
correction. This required several new lenses of calcium fluoride.
All the positive
lenses here are
calcium fluoride
Calcium
fluoride
New –
negative/positive
doublet instead of
positive/positive

22. This design was polychromatic Strehl optimized and is diffraction-
limited over the image diameter from .365u to 1.0u. The chromatic
telecentricity variation over the spectrum is about one degree. The
next step is to try to simplify the design.

23. It was found that the big calcium fluoride element can be replaced
with silica if this smaller lens is made to be calcium fluoride. The
result has the same good performance and looks like this picture.
A focus near a lens surface
needs to be looked at but
is just a small detail now,
for later work.

24. The very weak power silica
lens/mirror element was
replaced with a simple
mirror and with about the
same performance. The
resulting design meets all of
the initial requirements.
There is no need to go
back and look at the other
alternate method of
correcting Petzval (replacing
the small convex mirror with
a Mangin lens/mirror
element), since this design
ended up quite good.
Simple mirror
Mangin lens/mirror element

25. Final design – no large calcium fluoride lenses (shown in red here).
20% diameter obscuration. 12 mm working distance. 0.50 mm field
size and .60 NA.
.365u through 1.0u

26. Notice that we ended up with almost all of the .60 NA being due
to the mirror power. There is very little lens power and that helps
the color correction a lot.

27. Next step – slowly lower the short wavelength, from.365u towards
.254u and this will be very difficult to do. Extra lenses will be
needed. But first let us look at the alternate Petzval correction design
approach, to see if this has better short wavelength potential.

28. Simpler design – fewer lenses and weaker lenses. But one large
calcium fluoride lens. About the same shorter wavelength potential
.365u through 1.0u
Mangin lens/mirror element

29. • The Mangin mirror replacement for the convex secondary mirror
results in a simpler design, so why would we not choose it?
• The shape of that Mangin lens/mirror element and the need for some
glass edge run-off when the piece is made will result is somewhat
higher obscuration than that of the design with the convex secondary
mirror. That could be a reason to choose the other design.
• This whole presentation assumes no prior knowledge of patents on
similar designs. With some prior knowledge you would start right out
with a configuration that has almost no lens power – the opposite of
the Slide #5 starting point here.
• So this is mostly intended to show what the process of design is like,
for teaching purposes.