This document outlines a general design method for optical lenses using photographic lens examples: 1. Always start with a monochromatic design using a single glass type to achieve the required performance. Use aspherics temporarily but remove them later. 2. Add color correcting surfaces in a way that minimizes changes to the monochromatic design. Use no more than 3 glass types and minimize color inside the design. 3. The example lens design is walked through step-by-step, starting with a monochromatic BK7 design and improving it using aspherics, then removing aspherics by replacing them with doublet lenses while maintaining performance. Color correction is then addressed.

1. A General Design Method, With Photographic Lens Examples
Dave Shafer
David Shafer Optical Design
shaferlens@sbcglobal.net
203-259-1431

2. Where do we get our ideas about how to do optical design?

3. Without a good design method our chances for success
are similar to those of this hitchhiker – quite limited.

4. With my general design method producing a high
performance camera lens design can be a piece of cake

5. SESSION 1. . . . . . . . . . . . . . . . . . . . . . . . WED 8:30 AM TO 10:00 AM
Lens Design Methodology I
Session Chair: R. Barry Johnson, Alabama A&M Univ. (USA)
A zoom lens from scratch: the case for number
crunching (Invited Paper),
Donald C. Dilworth, Optical Systems Design, Inc. (USA) . . . . . . . . . . . . . . .
[9947-1]
I strongly urge you to go to
Don Dilworth’s talk tomorrow
morning at 8:30. He has the
complete opposite approach to
design from me and I am quite
unhappy that it works so well.

6. This evening we will look at a
detailed plan for building up a high
performance camera lens design
from scratch, using a general design
method applicable to many diverse
situations.

7. A General Design Method
1) Always do a monochromatic design first, even if starting from an existing color-
corrected design. See if color-correcting surfaces can be removed with no loss in
monochromatic correction. Goal is simple starting design with single glass type.
Find the simplest design that meets the required monochromatic performance
2) Use aspherics during the monochromatic design evolution but remove them later
3) Find locations to add color correcting surfaces that require the least change in the
monochromatic design and the least change in the monochromatic performance
4) Minimize amount of color inside the design. Use no more than 3 glass types.
5) If run into problems, always go back to an earlier monochromatic design to solve
them.

8. This whole slideshow is on the
internet at
www.slideshare.net/operacrazy/
camera-lens-talk
There is no need to take notes
I will give this link again on the last slide

9. Design method is shown with a photographic lens design example
• Design a 50 mm focal length f/1.7 camera lens for a digital sensor
with a +/- 15.7 mm diagonal field
• Length to image < 170 mm, long back focus for flip mirror
• Spectral weights quite small below .4861u, about equal from .
4861u to .6563u
• Distortion < 1%, vignetting 50% at edge of field
• Focus down to 500 mm object to image, with no performance loss
• Very high MTF performance required

10. A General Design Method
1) Always do a monochromatic design first, even if starting from an existing color-
corrected design. See if color-correcting surfaces can be removed with no loss in
monochromatic correction. Goal is simple starting design with single glass type.
Find the simplest design that meets the required monochromatic performance
2) Use aspherics during the monochromatic design evolution but remove them later
3) Find locations to add color correcting surfaces that require the least change in the
monochromatic design and the least change in the monochromatic performance
4) Minimize amount of color inside the design. Use no more than 3 glass types.
5) If run into problems, always go back to an earlier monochromatic design to solve
them.
First step

11. You don’t want to weigh down the design effort
by attempting too many tasks at once.

12. • Estimate, by means of some experiments with a perfect
system , what wavefront error will give the required
MTF values on axis and at the edge of the field
• Further estimate how that wavefront error might be
divided into a monochromatic part and a chromatic
part.
• This takes some time and experience but it then gives
correction goals for the beginning stages of the design.
• We now look at that for our camera lens example.

13. Need very high monochromatic performance in order to be able to
reach desired polychromatic MTF, and then need very good color
correction for this 50 mm f/1.7 lens.
Monochromatic performance - Need about .14 waves r.m.s. or
better at .55u on axis and .22 waves r.m.s. or better at .55u at edge of
field, with 50% vignetting
Typical monochromatic MTF that is needed Required polychromatic MTF
Axis spec
Edge of field spec
Polychromatic MTF specs
Monochromatic MTF

14. Design starting point – monochromatic, no aspheres, all BK7.
Double-Gauss plus negative front lens, gives long BFL
On-axis = .26 waves r.m.s., Edge of 50% vignetted field = .46 waves r.m.s.
Goal = .14 waves r.m.s. .22 waves
r.m.s.
Design needs 2X improvement in monochromatic correction

15. Low index glass designs
• In the beginning stages of a design it might not be clear how
important secondary color will be.
• I always start out with a low index monochromatic design.
If secondary color is important, then reducing it is easiest in
low-index designs – shown here later.
• If it is not important then you can always raise the glass
index later, which will almost always improve performance.

16. Splitting front or back meniscus lens does little to help performance.
Use aspheres to find out where design needs new correction means.
On-axis = .24 waves r.m.s., Edge of 50% vignetted field = .42 waves r.m.s.
goal = .12 waves r.m.s. = .22 waves r.m.s.
.
Split lens

17. A General Design Method
1) Always do a monochromatic design first, even if starting from an existing color-
corrected design. See if color-correcting surfaces can be removed with no loss in
monochromatic correction. Goal is simple starting design with single glass type.
Find the simplest design that meets the required monochromatic performance
2) Use aspherics during the monochromatic design evolution but remove them later
3) Find locations to add color correcting surfaces that require the least change in the
monochromatic design and the least change in the monochromatic performance
4) Minimize amount of color inside the design. Use no more than 3 glass types.
5) If run into problems, always go back to an earlier monochromatic design to solve
them.
Next step

18. Use “temporary” aspherics to
1) Ease transition between one solution region and
another nearby one.
2) Identify where in the design you need to split lenses or
add elements to improve performance.
3) Predict what performance will be of design once
lenses have been added and the aspherics have been
removed

19. 1) Add an aspheric at front of design, at back of design,
and one or two in the middle of the design
2) Use only 4th
and 6th
order terms
3) Optimize design for better performance
4) Remove aspherics, one at a time.
5) Some can be removed with little effect, others require
replacing an aspheric lens with a doublet lens

20. On-axis = .11 waves r.m.s., Edge of 50% vignetted field = .16 waves r.m.s.
goal = .14 waves r.m.s. .22 waves
r.m.s.
Four Aspheres
Design
This exceeds the monochromatic MTF goals
Lens added so can have
an aspheric near the stop
Aspherics shown in red color

21. • Usually only one of the 3 or 4 aspheres has a big effect on
performance
• We will try removing them one by one until we find which is
the “good” one
• Why not just try adding one aspheric to different places in the
design, instead of adding several and then removing all but
one?
• Glad you asked – because what if the aspheres do not give
enough performance improvement, even with 3 or 4 of them?
• Then you will know immediately that you need a different
first-order configuration. So this is a quick way to find out.

22. On-axis = .08 waves r.m.s., edge of 50% vignetted field = .23 waves r.m.s.
Two of the four aspherics were removed without much effect,
since they were found to do very little to help the correction
Has acceptable monochromatic correction
2 aspherics remain

23. Strong lens with aspheric was
split in two, with no aspheric
Only one
aspheric left
On axis = .13 waves r.m.s., edge of 50% vignetted field = .25 waves
r.m.s.
Almost meets monochromatic wavefront, MTF goals
New shape

24. Sometimes an extra lens, here used to help replace an
aspheric single lens, can also help the design move into
a different solution region – just as aspherics can do that
Once the design is in the new solution region, the extra lens might not be needed
anymore, although it was needed to make the transition . Here this lens will be gone in
the final design, just as we removed aspherics that were only temporarily in the design.

25. How to replace an aspheric surface with a doublet lens
1) Add zero-thickness flat
lens next to aspheric
2) Write down
system 3rd
-order
values
3) Remove aspheric terms
Remove all system
variables. Remove merit
function
4) Vary only flat plate radii
and aspheric surface radius
5) Correct spherical aberration, coma, and Petzval to values from step 2)
(A systematic method)

26. Aspheric
Zero power, zero
thickness lens
Simplest case, where there is no
other lens right next to aspheric
surface
Case where there is already another
lens surface next to aspheric
Flat plate
added
between
lenses

27. • 2 new surfaces plus aspheric surface radius = 3 radii variables
• Correct 3rd
-order spherical aberration, coma, and Petzval = 3 aberrations
• Petzval correction makes power of these 3 surfaces be the same as original
power of aspheric surface. Can be done by other means too.
• Solutions are found the easiest, due to non-linearities, if aperture stop is
temporarily shifted to be at the aspheric surface, unless it is very far from
the stop
• With stop at aspheric, aspheric has astigmatism and Petzval linked together,
• So only need to correct for spherical aberration, coma, and Petzval
• Then insert the new doublet without an aspheric in the original system in
place of the aspheric lens, and reoptimize with all the system variables

28. 1) When a lens is right next to
an aspheric lens, we can use the
radius of that lens that is closest
to the aspheric as another
variable, in addition to the two
new radii added in of the flat
plate. You just have to keep the
sum of the curvatures fixed. If
aspheric element is thin than can
use both of its radii as variables.
But best results happen if all radii
variables are in direct contact.
2) Multiple solutions are best
found by starting out with radii
made to have right net power and
be +/- doublet, -/+ doublet, or
with one lens being a negative
meniscus. Try all of these.
New solution region Aspheric
replacement
No aspherics
Last aspheric
Is now weaker

29. Design with no
aspherics meets
monochromatic
wavefront and
MTF goals
Removing last aspheric
was quite difficult. Several
doublets were tried before
this one was found with good
higher-order match to
aspheric it replaced
Monochromatic MTF

30. Summary
Starting point = very optimized
monochromatic design with no
aspherics
3 or 4 aspherics added to get best
performance
One at a time, aspherics are removed or
replaced with doublet. This can be
tricky and take a lot of work. Result
usually has same performance as
aspheric design

31. A General Design Method
1) Always do a monochromatic design first, even if starting from an existing color-
corrected design. See if color-correcting surfaces can be removed with no loss in
monochromatic correction. Goal is simple starting design with single glass type.
Find the simplest design that meets the required monochromatic performance
2) Use aspherics during the monochromatic design evolution but remove them later
3) Find locations to add color correcting surfaces that require the least change in the
monochromatic design and the least change in the monochromatic performance
4) Minimize amount of color inside the design. Use no more than 3 glass types.
5) If run into problems, always go back to an earlier monochromatic design to solve
them.
Next steps

32. Color correction plan
1) Minimize the amount of color inside the design.
Use low dispersion crown glass like FK51 for positive lenses.
2) Use glasses with good partial dispersion match.
This requires strong curves, so have to compromise
some in glass choice or design complexity.
4) Try to correct color with the smallest changes to the
monochromatic design’s first-order values and lens shapes.

33. Correction of primary axial and lateral color
• Achromatize with buried surfaces of glasses of about
the same index, to minimize changes in the
monochromatic design performance.
• Minimize number of new lenses needed to
achromatize the design.
• Use stop shift theory to do this.
• Use temporary stop shift to help in lateral color
correction.

34. • If primary axial color is uncorrected (non-zero) then
there is always an aperture stop position that corrects
for primary lateral color (i.e. makes it zero)
• If we achromatize at that stop position, the design is
then corrected for both axial and lateral color
• It stays that way then, regardless of stop position
• In an ideal world we could then correct both axial and
lateral color with a single cemented surface between
two glasses, at the right position in the design.
Temporary stop shift

35. 10X smaller scale
Lateral color in
all BK7 design
Move aperture stop to find out what position corrects for lateral color,
then achromatize at that location, then move stop back to original position.
Original stop location
Temporary stop location

36. = lateral color corrected stop position
All same glass type
Actual stop position
More dispersive positive power to left of stop moves lateral color
corrected stop position to the left. So does more dispersive negative
power to right of stop.

37. 1) Achromatize at stop
position that corrects for
lateral color
2) May require thickening
up a lens there to give
enough room for a strong
cemented surface
Thicker lens
Too thin for strong cemented surface
3) There might be a small
monochromatic correction penalty

38. Another example – a more
inverse front end shape. We
will stay with this new other
example for a few slides
All same glass type – SK16
= stop position for no lateral color
To achromatize at this stop
location requires much too
strong a cemented surface of
F2 glass – not practical

39. F2 flint glass here
Shifts lateral color corrected stop position to here
Then achromatize here
Stronger flint here
All SK16 except
Shifts achromatizing
position further to left
Then achromatize here
+/- doublet
-/+ doublet

40. In this design we could have corrected both axial and lateral color
by making cemented lenses here and here. But that would require
much stronger lens powers. My method gives weaker powers and
has a systematic rational to it.

41. Chromatic variation in
aberrations is mostly
induced by color coming
into certain surfaces, and
is not mainly an intrinsic
aberration.
All lenses are FK51 glass
Largest amount of spherical aberration in design
Proof –
1) set index of that lens to be same for all wavelengths. Result is almost no change in
chromatic variation of spherical aberration. It is not intrinsic to that surface
2)) set index of lenses before that surface to be same for all wavelengths, so no color coming
into that surface. Result = almost zero chromatic variation in spherical aberration
3) This shows why we want to minimize the amount of color inside the design

42. • Now we are returning to our original design
example and trying some glass choices for color
correction.
• First we see what happens if we don’t try to correct
secondary color. How bad is the polychromatic
MTF?

43. Design is not good enough –
too much secondary color. Need
different glasses. But keep the
very good monochromatic
correction
All BK7 except F5
BK7 and F5 design,
no aspherics
Extra lenses for color correction have
allowed this to revert to a single lens

44. 1) Minimize the amount of color inside the design. Use
very low dispersion glass like FK51 for positive lenses.
2) Use glasses with good partial dispersion match.
Demonstration of the color correction design principles
Ultra low
dispersion
glass
Relative
partial
dispersion

45. Herzberger secondary color correction method
Connect 3 glasses to give a triangle with largest possible area, to minimize lens powers
Extreme example = FK51, SF57, and KZFS1 - all three are anomalous dispersion glasses
Relative
partial
dispersion

46. Three anomalous
glasses gives very
small residual
color. Very dense
flint in front has
very little power.
Herzberger method gives
good results but requires 3
glasses. If you avoid
extreme crowns and flints
then result is very high
lens powers.
SF57-FK51-KZFS1
100 mm focal length

47. Herzberger secondary color correction method
Connect 3 glasses to give a triangle with largest possible area, to minimize lens powers
As base of triangle becomes more horizontal , the power of the 3rd
glass gets weaker
and weaker. That 3rd
glass, at top right, disappears when triangle base is horizontal.

48. Want two glasses to be on horizontal line for super-achromat.
FK51 and BK7 are a good pair. Glass pairs on “normal” glass line
give
BK7 and F2 fall on “normal’ glass line

49. Glass pairs with the same partial dispersion have relatively small
dispersion difference, so strong lens powers are needed for a given
focal length, or multiple doublets stacked up in a row.
BK7-F2 achromat FK51-BK7 superachromat
10X smaller scale than
other graph on left
Quadratic color Cubic color
Crown/flint glass pair Crown/crown glass pair

50. • When partial dispersions match, want largest possible
dispersion difference to reduce required lens powers
for achromatism. FK51 and the BK glasses are
therefore the optimum glass pair by this criterion.
• SSKN8 and KZFSN4, for example, have good match
for partial dispersion but very small dispersion
difference - so requires very strong lens curves in a
doublet.
• There are significant differences within the BK
glasses, when matched to FK51. BK1 is better than
BK7 for residual secondary color.

51. Calcium Fluoride and Silica FK51 and BK1
Has small reverse secondary color Very flat over most of spectrum

52. High index of LAK8 makes
for weaker curves, better
aberrations and chromatic
variation of aberrations, but
it also increases the Petzval
of the doublet.
FK51- LAK8 doublet

53. • Result of all this is good secondary color
correction with just two glasses
• These two glasses, FK51 and a BK glass have
very high transmission in the blue region
• The resulting design is a very low index
design.
• If the blue wavelengths are not too important
than can use a more dispersive flint than BK
glasses. Result is reduced (but not corrected)
secondary color and weaker lens curves.

54. A glass pair of FK51 and a BK glass like BK7 requires only one anomalous dispersion glass
type – FK51, which is quite expensive. A different choice, with two anomalous glass types,
both expensive, is FK51 and KZFS2. Their partial dispersions are not quite on a horizontal
line and their dispersion difference is considerably larger than that of FK51 and BK7. That
gives much weaker powers of the lenses for color correction.
Not quite horizontal line

55. FK51 and BK7 FK51 and KZFS2
Weaker powers = better
aberrations
But very expensive and
more residual color
2.5X larger scale
Different scales

56. • All of these results are for thin lenses in contact.
In a real design with substantial lens separations,
like a Double-Gauss or Distagon, the optimum
glass pairs may shift some on the glass chart.
• But this is a relatively small effect. Try some
glasses near the thin-lens optimum choice to see
what gives the best result.
• The importance of all this depends on the spectral
weighting. If deep blue wavelengths are
important then secondary color can be very
important.

57. In this design example we will only use one anomalous
dispersion glass, FK51, in order to keep the lens cost
down. An interesting exercise would be to use KZFSN2
instead of BK7, giving greater cost and not as good
secondary color, but weaker powers and see how the
performance is affected. Chromatic variations of
aberrations would be less due to the weaker powers.

58. Paraxial focus shift from .4000u to .7000u
For a 100 mm focal length lens
Glasses focus shift strongest lens
BK7, F2 +/- 100u 45 mm focal length
FK51, BK7 +/- 7.5u 23.5 mm focal length
FK51, KZFSN2 +/- 15u 35.7 mm focal length
FK51, F2, KZFSN4 +/- 5u 32.4 mm focal length
FK51, SF6, KZFSN4 +/- 2u 35.9 mm focal length
FK51, LAK8, SF6 +/-1u 31.1 mm focal length
FK51, LAK8, KZFSN4, SF6 +/- 0.3u 27.0 mm focal length
FK51, BAFN11, SF1, SF6 +/.03u 16.4 mm focal length
these are not the absolute optimum combinations but are close to it
This goes outside the scope of this talk, where our design will only use
one anomalous dispersion glass, but if several different anomalous glasses
are used then amazing broad spectral band color correction is possible.
3000 X better

59. Color Correction Summary
• Goal is to correct color with smallest change to the good
monochromatic correction
• Temporary stop shift shows where to add color correcting
surfaces
• Glass choice can minimize color inside the design, giving
good chromatic variation in aberrations and low
secondary color
• Result has few flint lenses and very few glass types

60. Almost meets
polychromatic MTF
spec, but is slightly low
All FK51 except LF5 50 mm f/1.7,
no aspheres,
just two glass
types

61. Doesn’t quite meet the
on-axis MTF goal. Very
constant over the whole
field
50 mm, f/1.7 design
with no aspherics and
just two glasses
All FK51 except LLF6
Extra lens added
A low index design – highest
index is n = 1.53!

62. 50 mm, f/1.7 design
with no aspheric and
just two glasses
All FK51 except LLF6
As the flint glass choice is
changed from F5 to LF5 to
LLF6 the secondary color
keeps getting better.
The line connecting FK51
to the flint glass gets more
horizontal as partial
dispersions become more
equal. But the powers
become stronger as the
dispersion difference gets
smaller.
FK51 and F5 pair and
FK51 and LLF6 pair

63. Once get a good design, look for other
versions with same number of lenses
Very slightly short of
MTF specs
Meets MTF specs
-/+
+/-
+/-
-/+

64. This alternate solution has a stronger
negative lens, so making it a flint
glass shifts the lateral color corrected
stop position further to the left = a
good thing
This doublet replacement for the last
aspheric lens has very little negative
power, so making that lens a flint glass
has little effect on lateral color
Try to correct axial and lateral
color with the smallest change to a
good monochromatic design, and
adding the least number of new
lenses

65. This is very unusual – we now
have a very high performance
camera lens design with only two
glass types and with n<1.53!

66. That is as rare as catching Volkswagons going at it,
which they usually only do at night.

67. • If blue spectrum is more important than in this
example, then secondary color must be better
corrected
• Then flint glasses must be better partial dispersion
match to FK51 crowns, such as BK glasses
• This requires more lenses to keep the negative lens
powers from being too strong.
• Or can use both FK51 and KZFS2 to get good color
correction but at increased glass expense

68. Now we have a good
design. What’s next?
There are only two
glass types, both very
low index. Now we
can consider looking at
some higher index
glasses, maybe de-
cementing one or both
of the doublets to get
more design variables,
optimizing for
tolerances, etc.
My design method gives a good design
that can then be fed into optimizers like a
glass expert program to get even better
performance. The good design here can
be the end of the road or the start of a
new path to an even better one.

69. Moves as a pair
Focusing from infinity down to
500 mm object to image distance.
stop
stop
Correction should not
change, throughout focusing
range - very hard to do
I could not find a good
solution with this design.
What to do next?
Back end of design Focusing Requirement

70. And you thought that
you were all done!
Best plan is to go back to
monochromatic design and
temporary aspherics and
build in good focusing
correction at an early stage
of the design evolution.
Be willing to start over !
Difficult tasks should not
be left to the end of the
design process, but should
be solved much earlier.

71. When an almost
mature design gets
stuck on a difficult
requirement it is almost
always best to try to
solve that problem at
an early stage of the
design evolution. In
other words, start over
again!

72. A General Design Method
1) Always do a monochromatic design first, even if starting from an existing color-
corrected design. See if color-correcting surfaces can be removed with no loss in
monochromatic correction. Goal is simple starting design with single glass type.
Find the simplest design that meets the required monochromatic performance
2) Use aspherics during the monochromatic design evolution but remove them later
3) Find locations to add color correcting surfaces that require the least change in the
monochromatic design and the least change in the monochromatic performance
4) Minimize amount of color inside the design. Use no more than 3 glass types.
5) If run into problems, always go back to an earlier monochromatic design to solve
them. Be willing to start over!

73. A General Design Method - Review
1) Always do a monochromatic design first, even if starting from an existing color-
corrected design. See if color-correcting surfaces can be removed with no loss in
monochromatic correction. Goal is simple starting design with single glass type.
1) Find the simplest design that meets the required monochromatic performance
2) Use aspherics during the monochromatic design evolution but remove them later
3) Find locations to add color correcting surfaces that require the least change in the
monochromatic design and the least change in the monochromatic performance
4) Minimize amount of color inside the design. Use no more than 3 glass types.
5) If run into problems, always go back to an earlier monochromatic design to solve
them

74. In addition to being
intellectually stimulating
this design method is also
more fun than sitting
around waiting for some
global optimizer to slowly
grind away at the design
task.

75. This camera lens would be great for nude photography

76. My time is finished
- any questions?
This whole slideshow is on the internet at
www.slideshare.net/operacrazy/camera-lens-talk