My method for designing zoom lenses, explained step by step

1. A Zoom Lens Design Method
Dave Shafer
1) Start with the simplest possible monochromatic design, using
low-order aspherics and appropriate vignetting
2) Optimize until pretty good performance is reached
3) Replace aspheric lenses, one at a time, with spherical doublets
4) Achromatize moving groups, then achromatize fixed lenses
5) Complete optimization

2. Focal length
range)
8 mm – 30 mm (minimum
Sensor
2/3“ HD
F-number 2.8, constant over the zoom range
Mechanical constraints
overall length < 160 mm
back focal distance > 20 mm
number of zoom movements: 2
Wavelength
Zoom design
example specs
VIS
Distortion
<3%
Polychromatic MTF at 40 LP/mm >75% on-axis
Relative illumination @ 5.5 mm >35%
Focus Range
group
Infinity to 250 mm with separate focusing
Let’s look at
some relevant
designs

3. Compact Zoom
Example 3: n p n p
Designed
by Zeiss
•
•
•
Dodoc, ‘Toward the global optimum in zoom lens design’, SPIE 8488
Disadvantage: Very large variator group (green), 3 movements

4. 4mm
„Retrofocus“
Designed by Zeiss
10mm
20mm
40mm
Alexander Epple SPIE contestwinning design for shortest 20X
zoom with 4 aspheric lenses.
This is a PNNP design. But it is
f/10 and might not work well for
our f/2.8 design requirements.
60mm
80mm
Carl Zeiss SMT AG, Alexander Epple, LIT-TSD
„Telephoto“
Page 4

5. New designs for this talk
PNNP
30 mm f.l.
PNNP was tried, with 4
aspherics. Very short –
only 80 mm long. But
performance was not too
good and it has some
strong aspheres.
8 mm f.l.

6. NNPP was also tried but it has bad
vignetting problems. OSLO’s ASA
program was used to find
PNNP, NNPP, and PNPP paraxial zoom
solutions. PNPP has the best vignetting
situation, Petzval sum, and zoom
motions.
Other system specs might give different
preferred zoom type, like NPNP.

7. PNPP design
30 mm f.l. – 21 degree field
Design with 4 aspheric lenses
meets the monochromatic
performance goals over field
and zoom range. Length =
105 mm. Spec is <160 mm.
8 mm f.l. - 68 degree field

8. • We will replace all of these aspheric singlets with equivalent spherical
doublets
• The order in which we do the replacements has some effect on the outcome
• The first-order and other aspherics will change some during the
replacement process
• If there is enough design time available, try changing the order of the
aspheric replacements to see what gives the best final non-aspheric design
• There are usually several possible quite different spherical doublet
equivalents to an aspheric singlet. Try several choices to see what works
best
• I started here with the non-moving lens after the fixed stop. The pupil does
not move with respect to this lens. I found that three lenses were needed
instead of two to get a good performance replacement for this aspheric.

9. Aspheric lenses
Replaces
aspheric
singlet
30 mm F.L.
zoom position
Monochromatic
Zoom Design
with Aspherics
two zooming
motions
8 mm F.L.
zoom position

10. Aspheric lenses
Fixed aperture stop.
Fixed lenses after
stop have zero net
Petzval, are used to
speed up convergence
angle.
Front lens does not
move but its pupil
position changes during
zoom. Use aspherics
on moving lenses and
on front lens with
moving pupil.

11. or
or
Aspheric lens
Possible
equivalents
to aspheric
singlet
Spherical lens doublets with same 3rd order
spherical
aberration, coma, astigmatism, Petzval and
distortion as the aspheric lens
or
or
11

12. Aspheric lenses
Aspheric singlet here
is replaced with a
monochromatic
aberration equivalent
doublet.
Aspheric lenses
Alternate solution –
not as good
performance

13. aspheric
Aspheric negative
singlet here is replaced
by an aberration
equivalent doublet
30 mm F.L.
Now two of the
three aspherics have
been removed. The
last one is harder
8 mm F.L.

14. Aspheric lens
Doublet
equivalent
to aspheric
singlet
Chief ray at edge of field for 30 mm
F.L. (top) and 8 mm F.L. (bottom)
Get TIR at
edge of
field due
to convex
radius
+/- = Bad solution (top)
-/+ = Good solution (bottom)
Aspheric lens
Doublet equivalent
to aspheric singlet
Steep angle
No TIR problem

15. All aspherics are
removed. Design has
pretty good
monochromatic
performance
Very short length (102
mm) = good
Zooming group diameter
is too big = bad
Front lens is too big

16. Zoom motions

17. • New constraint added – front lens is
too big, first moving group is too big
• Considerable size reduction is needed
• When size is slowly reduced, good
performance is lost
• What to do?

18. When size of front lens and
first zooming group is
reduced, the performance
suffers quite a lot
So add back in aspherics
= aspheric
Then get back the good
performance of the larger size
design
Aspheric after the stop has
little effect so not used.
Then replace aspherics with
extra lenses
Design meets smaller size
Is still a monochromatic
design

19. Use same process as
before. Aspherics are
replaced by equivalent
doublets, one at a time.
This takes quite a lot of
experimentation and
time and some luck
I will only show the
final result here

20. New lens to help replace aspheric
Targets for smaller size are reached here.
No aspherics, good monochromatic performance.

21. Color correction is next.
Monochromatic design is all same glass type – SK2
SK2 crown glass has same index as F5 flint glass, so
we can put in “buried surfaces” without changing
monochromatic correction – always good for doing
preliminary color correction by hand
Once paraxial axial and lateral color are corrected
then we can try other glass types

22. A
C
B
Real ray
stop
30 mm f.l.
Entrance pupil position
Entrance pupil position
stop
Real ray
8 mm f.l.
Group A has changing
lateral color due to large
amount of pupil shift
during zoom, and also
changing axial color due
to changing entrance
pupil size during zoom.
Group B has changing
axial and lateral color
during zoom due to
changing
conjugates, changing
pupil position, and
changing beam diameter
on lenses.
Group C has axial and
lateral color that do not
change during zoom.

23. B
B
Group B has two parts
– a front moving negative
group and a rear moving
positive group. If both
groups are separately
achromatized then Group
B will be corrected for
axial and lateral color
during zoom, in spite of
changing
congugates, changing
pupil position,
and changing beam size.
But then Group A
would still have changing
axial and lateral
color, due to changing
pupil position and
changing beam size

24. Strategy #1
B
C
A
B
- Don’t separately achromatize
the two moving parts of the B
group. Instead add color
correcting lenses to Group B so
that its changing axial and lateral
color during zoom is equal and
opposite to the changing color
during zoom of Group A. This
does not require adding any lenses
to Group A. Horray!!
The catch – you can cancel the
change in axial and the change in
lateral color during zoom between
Groups A and B this way but you
are still left then with a large
constant amount of axial and
lateral color, during zoom. Too
large to be easily fixed by adding
lenses to Group C. Boo!!

25. Strategy #2
B
C
A
B
Separately achromatize the
two moving parts of the B
group. Also achromatize
Group A, so that its axial
and lateral color do not
change due to shifting pupil
position during zoom and
changing entrance pupil
diameter during zoom.
Finally, achromatize Group
C. So Groups A, B , and C
are all separately
achromatized, including
separate achromatizing of
the two moving parts of
Group B.

26. Lucky break – the lenses
already in the two moving
parts of Group B are
enough, with the right glass
choices, to separately
achromatize the two parts of
B. No extra lenses are
needed in Group B.
Achromatizing Group C is
easy but requires two new
lenses.
Achromatizing Group A
can be done in more than
one way, but requires strong
new lenses, so two new ones
are needed - to reduce the
powers.

27. Fully color corrected
design. After Groups A, B
and C are each separately
achromatized then complete
system optimization will
make each group depart
some from this condition.
As a result it may be
possible to remove a
lens, and have just a singlet
right after the aperture stop.
Optimum glasses were
selected for best MTF
results

28. 30 mm F.L.
15 mm F.L.
8 mm F.L.

29. But now we have a big
problem! The design
needs to be able to focus
down to 250 mm
away, with good
performance.
This is very difficult!
It may be necessary to
go back to an earlier
stage in the design
evolution (probably
monochromatic), solve
the focusing
problem, and then do
the design
achromatization all over
again.

30. •
Always be willing to drop back to earlier versions of the
design and solve new problems with the simplest possible
design.
• Time lost by back-tracking is usually quickly recovered
once a simpler design is found that solves the new
problem.
• A monochromatic focusing solution should be
found, maybe even using an aspheric - to be then replaced
by a doublet.
• In general, it is best in zoom designs to consider focusing
early in the design evolution

31. My time is finished
- any questions?