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

Focal length 8 mm – 30 mm (minimum range)

Sensor 2/3“ HD

F-number 2.8, constant over the zoom range

Mechanical constraints overall length < 160 mmback focal distance > 20 mmnumber of zoom movements: 2

Wavelength VIS

Distortion <3%

Polychromatic MTF at 40 LP/mm >75% on-axis

Relative illumination @ 5.5 mm >35%

Focus Range Infinity to 250 mm with separate focusing group

Zoom design example specs

Let’s look at some relevant designs

Compact Zoom Example 3: n p n p

• Dodoc, ‘Toward the global optimum in zoom lens design’, SPIE 8488• Disadvantage: Very large variator group (green), 3 movements•

Designed by Zeiss

Carl Zeiss SMT AG, Alexander Epple, LIT-TSD Page 4

4mm

80mm

10mm

20mm

40mm

60mm

„Retrofocus“

„Telephoto“

Alexander Epple SPIE contest-winning 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.

Designed by Zeiss

30 mm f.l.

8 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.

New designs for this talkPNNP

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.

30 mm f.l. – 21 degree field

8 mm f.l. - 68 degree field

Design with 4 aspheric lenses meets the monochromatic performance goals over field and zoom range. Length = 105 mm. Spec is <160 mm.

PNPP design

• 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.

30 mm F.L. zoom position

8 mm F.L. zoom position

Monochromatic Zoom Design with Aspherics

Aspheric lenses

two zooming motions

Replaces aspheric singlet

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

Aspheric lens Spherical lens doublets with same 3rd order spherical aberration, coma, astigmatism, Petzval and distortion as the aspheric lens

or or

or orPossible equivalents to aspheric singlet

Aspheric singlet here is replaced with a monochromatic aberration equivalent doublet.

Aspheric lenses

Alternate solution – not as good performance

Aspheric lenses

Aspheric negative singlet here is replaced by an aberration equivalent doublet

Now two of the three aspherics have been removed. The last one is harder

aspheric

30 mm F.L.

8 mm F.L.

Chief ray at edge of field for 30 mm F.L. (top) and 8 mm F.L. (bottom)

Aspheric lens

Doublet equivalent to aspheric singlet

Get TIR at edge of field due to convex radius

Steep angle

Doublet equivalent to aspheric singlet

No TIR problem

+/- = Bad solution (top)-/+ = Good solution (bottom)

Aspheric lens

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

Zoom motions

• 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?

= aspheric

When size of front lens and first zooming group is reduced, the performance suffers quite a lot

So add back in aspherics

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

Is still a monochromatic design

Design meets smaller size

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

Targets for smaller size are reached here.No aspherics, good monochromatic performance.

New lens to help replace aspheric

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

AB C

30 mm f.l.

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.

Entrance pupil position

stopReal ray

stopEntrance pupil position

Real ray

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 during zoom.

B

B

Strategy #1

- 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!!

AC

B

B

Strategy #2

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.

AC

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.

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

30 mm F.L.

15 mm F.L.

8 mm F.L.

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.

• 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

My time is finished - any questions?