The document discusses how early lens design progress was hindered by slow hand calculations and lack of modern materials. It provides examples of simple lens designs that were possible even pre-computer but had limited applications without modern technologies. The document emphasizes that while computers have advanced design capabilities, fundamental design ideas and theories are more important. It provides several examples of innovative lens designs the author developed through conceptual thinking alone. The document cautions against overuse of new technologies like freeform surfaces and metasurfaces without consideration of conventional design alternatives.

1. What have we learned so far?
Dave Shafer
shaferlens@att.net

2. In the early days of lens
design, pre-computer,
progress was hindered by
1) the extremely tedious
and slow speed of hand ray
tracing calculations. A slide
rule is good for 3 place
accuracy but lens design
needs 6 place accuracy.
2) the absence of the
materials and means of
making optics that we take
for granted today.

3. One example of technology slowing
design progress is the very simple
monocentric ball lens from over 150 years
ago. It has good image quality at a pretty
fast speed over a very wide field of view.
Two different glass types allow such a
design to be corrected for spherical
aberration and color and there are no
field aberrations because the aperture
stop is at the common center of curvature
of the surfaces.
But the image is strongly curved and
there were no curved detector arrays or
fiber optics field flatteners back then so
nobody looked at more complicated
versions of this monocentric design
Such a design could be done by tracing just
2 non-paraxial real rays – one marginal ray
for spherical aberration and one ray for
color and then iterating by hand on the
very few design variables.

4. Thanks to modern technology, like fiber
optics field flatteners, the image from this
fast speed f/1.2 night vision objective can
be transferred from the strongly curved
image surface to a flat detector array. A
wide range of modern glass types
including anomalous dispersion ones as
well as using one or more small
monocentric airgaps allow for a very high
quality design like this to be developed.
A lot of what we have learned about
design is not due to software advances
but rather technology advances that made
there to be a point to developing further
some types of designs, like this one here.
Night Vision Objective

5. Curved image design
f/1.0 diffraction-limited
at .55u over 20 degree
field. 150 mm focal
length, corrected for
axial and lateral color, all
spherical surfaces. 2 mm
back focus distance.
Limited by secondary
color.
Here is a more complicated example of a curved image design. There would have been
no point in developing such a design before fiber optics field flatteners or curved detector
arrays existed, but both now exist. Yet such a design was well within the capability of very
experienced pre-computer lens designers, but what would be the point back then?
Large 150 mm aperture size

6. As new technologies developed – the laser, anomalous dispersion glass types,
diffractive optical elements, freeform surfaces, highly aspheric surface fabrication
techniques, metasurfaces, etc. the computational methods – software and advanced
computers also advanced a lot. That combination led to an explosion in the types and
sophistication of designs being developed. And that great diversity of designs led to us
learning a lot about design theory and optimization methods.
During this time some attempts
were made at semi-automatic
design and optimization, and over
the years so much progress has been
made that it is possible now for a
near-novice at optics and design to
use such programs to generate a
passable design in some situations.
That is pretty amazing!

7. Of course the design novice is
helped by the handy user-friendly
design program manuals.

8. Thanks to automatic design programs we human lens designers have
nothing left to do and can just relax all day. Right? But we can think in a
way the design programs can’t and that can lead to new design types.

9. Achromatic Schupmann design with virtual focus
Axial color is linear with lens power, quadratic with beam diameter, so axial color here
cancels between the lenses, one small with strong power and one large with weak power.
This simple achromatic design
here is not useful by itself, since
it does not form a real image,
but a virtual one. But it is a
good building block in more
complex designs.
Both lenses are same glass type
Here is an example of a new type
of design I invented by just thinking
and then developed further with
computer optimization.

10. The field lens images the other two lenses onto each other. That corrects the design for
lateral color. Why? (there will be a test later). It also corrects for secondary axial color.
field lens
Abe Offner
showed in
1969 the
effects of
field lenses at
intermediate
images on
secondary
color and
higher-order
spherical
aberration.
I worked with
Abe for a few
years at Perkin-
Elmer
Offner improvement = a field lens at the intermediate focus

11. Virtual image from Schupmann design
is made into a real image by adding
two mirror surface reflections here.
Virtual image design
Concave mirror reflection speeds
up real image f# by about 2X to give
a faster speed design, yet adds no
color. New design has small
obscuration near final image due to
hole in flat reflecting surface coating.
Flat
surface
Weak power surface
Can be bent to give
spherical aberration
correction

12. Simplest possible CMO type
design, with only 4 elements
All same glass type
10 mm f.l. and f/1.0
with small field size
Power of the two
lenses corrects
Petzval of concave
mirror. Bending
of front lens and
thickness of the
Mangin
lens/mirror
element corrects
spherical
aberration and
coma. Bending
and position of
tiny field lens
affects
astigmatism.

13. f/1.0 BK7 glass design. 10 mm f.l. and 1.2
degree diameter field
We know that this
very simple 4
element catadioptric
design will work well
because of the
aberration theory
behind it. Then we
use the computer to
optimize it and find
out just how good it
is. Then we may
make it more
complicated to get
higher performance.
But it starts with
ideas, before
computer use.

14. A very great design idea is
that of developing certain
features of designs that have
one or more intermediate
images. Brian Caldwell
showed some examples like
this one here where both
very wide fields of view and
very fast speeds can be
delivered by a design with
one intermediate image. In
such a system aberrations of
field and aberrations of
aperture can then be
independently corrected in
different parts of the design,
which is impossible without
an intermediate image.
Designs like this are very long compared to their focal
length. Amazing correction is possible and it takes the
computer to make that happen. But the idea behind it
only requires thinking and no computations.

15. A recent 1.35 NA Chinese catadioptric immersion design for lithography
This catadioptric design has two intermediate images and that opens up even more
aberration correction possibilities. By using a lot of aspherics the number of lens
elements can be greatly reduced compared to this design here. Incredible performance
is possible. I invented this type of catadioptric configuration in 2003 for DUV lithography
and a similar design to this has been used to make many billions of state of the art
computer chips. The key design feature is the two mirrors in the middle correcting the
Petzval aberration of the lenses, and a lens relay system on both sides of that mirror pair.
Some very high zoom ratio purely refractive zoom lenses also use the idea of an
intermediate image.

16. There is a special type of aspheric – freeform ones
with no rotational symmetry - that has gotten a lot of
development recently with respect to its use in
designs as well as ways to make them. They are not
new and 50 years ago I was doing some space-based
mirror system designs with some freeform aspherics.
But since nobody could make them back then it was
just for design studies and nothing much happened
with such designs until recently. They can be an ideal
and very powerful design tool when one or more of
these system conditions are met – 1) aperture size too
large to be practical for lenses or 2) a spectral
requirement (too long, too short, too wide) unsuitable
for lenses or 3) a strange system geometry. All three
conditions are met in EUV lithography, the most
advanced type of lithography today, which uses an
xray wavelength of 13 nm (.013u). I have done a lot of
EUV designs with 6 freeform aspheric mirrors.
I have also done design studies for
the spectrograph camera, above here,
for the 30 meter telescope project,
with 5 freeform mirrors. It had the
difficult requirement of a distant front
exterior pupil. The 3 large mirrors are
¾ meter in diameter.
This design is based on an idea that
combines two separate designs.

17. Here Rube Goldberg devises an elaborate system for
cooling his hot soup, instead of simply blowing on it.
In a like manner the novelty
of new technologies, like the
ability to make freeform
aspheric surfaces, has led
them to be featured in many
recent published freeform
design articles where a
conventional refractive design
can do the same job in a very
much smaller space and
weight. There are many
special situations where
freeform designs are
definitely the best way to go –
like EUV lithography designs,
but that is not what we are
often seeing in many
publications these days.

18. 3 freeform aspheric mirrors
Both systems
are for 8u-12u
Wide angle retrofocus
form, from recent
Journal article
In this situation
using a freeform
aspheric mirror
design when a
very much smaller
conventional
aspheric lens
design will do just
as well is like
bringing Godzilla
to do a task that
Bambi can handle.

19. In all the very many recently published journal articles about freeform mirror designs
they are usually 3 mirrors (sometimes just 2) in a retrofocus configuration and I have
never seen a size comparison with a conventional refractive optics design meeting the
same specs. The equivalent conventional refractive designs are always very much
smaller.
A hybrid refractive/diffractive design with
the same 25 mm aperture, f/3.7 and 15 X 20
degree field with similar performance
(nearly diffraction-limited over .4u to .7u
range) is dramatically smaller and lighter.
Same
Scale
Two freeform mirrors

20. A recent journal
article – 3 freeform
mirrors, 40 mm
aperture f/4, with 4 X
4 degree field. Almost
diffraction-limited
from .40u - .70u
Single optical
axis, 3 pure
conic mirrors,
same specs as
freeform
design, similar
image quality
3 aspheric lenses, anomalous
dispersion glasses, same specs as
freeform, similar image quality
Design size comparison
All to same scale

21. I have explored freeform
telescope designs with
three mirrors and four
reflections, which give
some rather interesting
package configurations.
The two top designs have a
double reflection on the
first mirror. The two
bottom designs have a
double reflection on the
second mirror.
My favorite one

22. Freeform Version of the Offner1.0X Relay
David R. Shafer and Luc Gilles
David Shafer Optical Design,56 Drake Lane, Fairfield, CT. 06824 USA
Thirty Meter Telescope Observatory Corp., 100 W. Walnut St, Suite 300, Pasadena, CA 91124, USA
shaferlens@sbcglobal.net , lgilles@caltech.edu
OSA Freeform Optics Conference, Washington DC, June 10-12 2019
22
A very useful application of freeform mirrors is modifications of the Offner 1.0X relay design.
Exactly 4 years ago in June 2019 I reported on how that can very greatly extend the field size of a
long strip field. In one version the Offner mirrors are made freeform aspherics. In another version
the Offner mirrors are spheres but two 45 degree fold flats are both made freeform aspherics. This
is the kind of use of freeform surfaces where there are big advantages over convention refractive
designs, unlike the situation with most 3 freeform mirror telescopes.

23. A metasurface has an
inherent problem with the
default conditions of very large
color due to very high
dispersion and low energy
efficiency. Ways must be found
to deal with that and progress
to date has been slow.
The exciting new field of metasurfaces and specifically flat metalenses has been
done a great disservice by an enormous amount of hype over the last few years.
There are many potentially useful applications of metasurfaces but a single flat
metasurface cannot replace your compact SLR camera lens, now or ever. A picture
like the one above from some journal neglects to mention that extremely large
amounts of coma of this .99 NA flat surface would reduce the useful field size with
good correction to about one atom in diameter!!! OK, two atoms maybe.

24. Here is a flat metasurface corrected for spherical
aberration with .90 NA and there is an enormous
amount of unavoidable off-axis coma. Assume that
the single flat metasurface is diffraction-limited at
.55u on-axis. The diffraction-limited image size is
then less than 1.0 micron in diameter, due to
enormous coma!! And this good image size is
independent of the diameter of the metasurface.
The .99 NA metasurface from the previous slide
would have a much smaller diffraction–limited field
size. Probably a few atoms!
It is a disservice to the exciting new field of
metasurfaces and their potential applications not to
point out basic Optics 101 level problems with a
super high NA metasurface like this one here.

25. Just as with freeform designs there is also a complete lack of design comparisons with
metasurfaces. In a recent journal article an achromatic metasurface is described. It is f/2.5 and is
diffraction-limited on-axis from .49u to .55u This flat metasurface is, however, only 200u in
diameter! That very tiny metalens would be just barely visible to the naked eye.
A simple comparison would show that a single f/2.5 plano-convex glass lens, also 200u in
diameter, that has no color correction at all, is diffraction-limited on-axis from .44u to .70u – a
much broader spectral range - because the very small size makes the uncorrected color fall within
the depth of focus of the lens.
Another recent journal article describes an unusually large single surface metalens – 80 mm in
diameter – with no color correction - that is f/3 to f/4 depending on its 1.2u to 1.6u IR wavelength
range. The measured on-axis Strehl is above 80% over that wavelength range, after refocusing for
the large amount of axial color, but the energy efficiency drops off substantially away from 1.45u
where it is 81%.
A single 80 mm diameter f/3 plano-convex glass lens with a conic surface, by contrast, has nearly
100% energy efficiency from .40u to 2.0u and is diffraction-limited from .40u to 2.0u after
refocusing, with much less color focus shift than the metalens.
All published metalens articles should be required to include comparisons like this!

26. Dispersion engineered metasurface
Instead of trying to eliminate the large amount of color in a metalens a
much easier and more useful achievement would be a slightly altered
chromatic dispersion function, altered to better match the partial
dispersion function of optical glasses. There is some recent promising
progress on that front. Then a metasurface would be a very useful addition
to a conventional glass lens design and help a lot with color correction.
But instead there seems to be efforts to have metasurfaces do far too much
work

27. Recently much time has been spent by some on designs for cell phone cameras. They are very
difficult to do and require a wide field, fast speed and a short length. The short length is most difficult.
Most designs are 5 or 6 lenses with highly deformed aspherics for many of the surfaces. A typical
design on the left here has inflexion regions on the surfaces which are difficult to make. A special
purpose camera lens is on the right with a 120 degree field and f/2.2 with low distortion. Unlike the
design on the left it is long compared to its focal length These designs usually have one or two nearly
zero power “wiggly” aspheric lenses near the image. They are a very important key part of the designs.
FOV 120 degrees, f/2.2,
length = 7.0 mm

28. In any design that has 3 or more aspheric surfaces there will be very
many possible local minimum to the merit function. With these
designs with many aspherics the number of pretty good solution
regions is absolutely enormous. The chance of early on finding one of
the really good ones and then developing within it is very slim. Much
more likely is that some mediocre solution region will be found and
then you will be stuck in it going forward.
These designs have very high order aberrations inside them. My
theory is that most of the published designs you will see have surface
configurations and asphericity distributions within the design that
cannot be well corrected at the 5th order level and they are stuck in a
local minimum. Then 7th and much higher order aberrations are
introduced by those “wiggly” surfaces to partially balance out and
compensate for the uncorrectable (within the local minimum) 5th
order aberrations. To test this theory I did a design that was first
corrected to zero for all the 3rd and 5th order aberrations and then
dropped that and switched over to all rays. It is the bottom design on
the left here. Notice the smooth surfaces, no wiggles or inflexion
regions, none of which was I controlling, and the same correction with
4 lenses as the 5 lens design with the wiggly surfaces.

29. An aspheric surface has a surface that departs from a
base sphere by a sag difference that varies over the
surface aperture. By contrast a diffractive surface does
not use optical path length to add diffractive power and
diffractive asphericity to a wavefront, but instead uses
diffractive fringe spacing with widths that vary over the
surface aperture. When refractive asphericity and
diffractive asphericity are combined on the same surface
some very useful properties result.
As an aside, a nearly zero power strongly deformed
double aspheric element is very useful near a pupil or
near the image for aberration correction
Here we will look at this with the simple example of a
Schmidt telescope design that is .70 NA with a 20 degree
field diameter, a 100 mm focal length, a spherical mirror,
and a curved image. I show the monochromatic image
quality for several choices for the front element.

30. When a DOE (diffractive optical element)
surface is added on top of an aspheric
surface the two different sources of
wavefront asphericity gives extra
aberration control, especially higher-order
aberrations. For our design example it
makes a difference if the diffractive
surface is on the front or back of the lens
element, because of the double refractive
aspheric on the lens.
The best possible result happens when
there is both a refractive aspheric and a
diffractive aspheric on both sides of the
lens. That is shown next.

31. Classical Schmidt, one
aspheric
5.1 waves r.m.s.
Double aspheric lens
1.4 waves r.m.s.
Double aspheric, DOE on front
1.06 waves r.m.s.
Double aspheric, DOE on back
0.24 waves r.m.s.
Double aspheric, DOE on both
sides of lens
0.065 waves r.m.s.
.70 NA, 20 degree diameter field, 100 mm focal
length, spherical mirror, curved image,
monochromatic performance

32. You can see that the
rim rays are bent a lot
going into the lens by
the diffractive power
and diffractive
asphericity. That
would cause an
enormous amount of
color. But it is nearly
cancelled out by the
second surface and
the lens is nearly zero
net power.
With both refractive and diffractive asphericity together on a
surface the optical path length of a ray and its direction can be
independently controlled. That can be very useful.

33. A nearly zero power double aspheric lens can be a very powerful design element when used near a
pupil or an image. That is also true of a nearly zero power double diffractive lens element, with
diffractive asphericity. This shows here the effect of adding a double diffractive surface to a flat plate
and then to a meniscus lens. It is not clear why the base lens curvature of the double DOE lens matters
but that lens by itself with no DOEs does nothing to help the design’s correction.
Having aspherics
and DOEs on both
side of an element
in a design can give
amazing correction
possibilities. The
color of rhe two
DOEs nearly
cancels and it is a
nearly zero power
element.

34. As I look back on my 57 years in
lens design, since my first job at Itek
in 1966, it seems clear that what
will most change lens design in the
future is AI.
Today’s AI is sort of like the Wright
brothers first planes: no in-flight
movies, no snacks, and a bumpy
ride. But a 747 jetliner will be
arriving sooner than we think.

35. The future of AI in Optical
Design
Evolution may now jump over
from humans into AI computers

36. One thing is certain - in the future AI will substantially reduce the
employment options in many fields. Young people today are
becoming very concerned about that, as my last slide shows.
The recent explosion
in AI developments
will come to affect
almost every field of
human endeavor,
including lens design
Looking Ahead