A tour through some optical design ideas where the important role of negative lenses is explored

1. The Power of Negative Thinking
Dave Shafer
David Shafer Optical Design

2. Plan for talk, in 2 parts
• Part I - review of material that I have given before.
Required background for Part II
• Part II - new ideas and designs

3. The final $1,000,000 question is in two parts – an easy
part and a hard part. Which part do you want first?

4. “and when was he born?”

5. • Limiting aberrations for highly corrected
designs =
higher-order Petzval and sagittal oblique
spherical aberration
• Mostly induced aberrations, not intrinsic

6. Mirror has Spherochromatism
Incoming ray angle and conjugate
change with wavelength

7. • Chief ray aberrations inside design cause
induced higher-order Petzval curvature
• Rays have different angles and surface
intersection heights than 3rd-order assumes
• 3rd-order assumes paraxial quantities

8. Chief rays aimed at paraxial pupil

9. Inverse triplet – small chief ray aberration

10. Reason for very small chief ray aberration
Paraxial pupil
Nearly concentric, nearly aplanatic
Nearly aplanatic, nearly concentric

11. 3rd-order triplet field curves
All 3rd-order = 0 for both
designs, not ray optimized
3rd-order inverse triplet field
curves, 20X smaller scale

12. All to same scale, same F.L.
Triplet has smallest lens volume,
longest back focus, worse chief ray
aberrations, worst field aberrations
•Double-Gauss has shortest back
focus, best aperture aberrations,
about same field aberrations as
triplet.
•Inverse triplet has largest lens
volume, best chief ray aberrations,
best field aberrations

13. Induced oblique spherical aberration has a
different cause =
astigmatism and Petzval between surfaces
results in beam footprint on each surface that
changes shape and conjugates with field angle

14. Triplet with all 3rd-order = 0
Field curves
Front surface footprint
Middle surface footprint
Last surface footprint

15. Front lens by itself
Next
surface
• This is an induced aberration effect,
not an intrinsic one
• 3rd-order assumes round beams on
each surface and no change in size
with field angle
• Result is bad oblique aberrations
Petzval and astigmatism of front
lens makes beam footprint elliptical
on next lens. Effect increases with
lens separations. Off-axis tangential
rays see less overcorrected spherical
aberration from negative middle lens
because Y beam width is smaller
than X beam width. Rear lens is
affected same way.
Middle lens beam footprint at edge of field

16. All 3rd-order = 0
Middle lens footprints
On-axis
footprint
Edge of
field
footprint

17. Ray optimized triplet
10X smaller scale than
3rd-order triplet plot
Petzval radius = 2.7 X f.l.
Front surface footprint
Middle surface footprint
Last surface footprint

18. • Ray-optimized triplet has about
20X better performance than 3rdorder triplet, for this field and
aperture example
•Ray optimized design has beam
footprints nearly circular, not
elliptical
•Much closer to 3rd-order
assumptions = smaller induced
aberrations = better
performance
Beam footprints at edge of field
3rd-order triplet
ray-optimized triplet
Front
Middle
•But chief ray aberrations only
slightly improved.
•Diameter of circular footprint
changes with field, due to
Petzval, so still gives induced
aberrations
Back

19. In complicated optical systems both the intrinsic and the
induced aberrations can all cancel out, at the 5 th-order level.
This looks sort of like the
triplet but
• the beam compression
is much more at the
middle negative lens
• the lens powers are
much stronger, especially
the strong negative lens
All 3rd = all 5th = 0.0
No ray optimization
• rays fail at larger field
angles
With right glasses can also correct for axial and lateral color

20. • At least 6 lenses are necessary to correct all the 3rd and
5th order aberrations to 0.0, if no aspherics are used
• Need that many design variables
• Many 6 element solutions exist but most have strong
curves and limited potential – bad 7th order
• More elements helps, gives weaker curves
• First order configuration helps the most.
• No solutions seem to exist with long back focus,
regardless of number of lenses

21. Double Gauss cannot be corrected for all the 3rd and
5th, regardless of number of lenses, because back
focus is too big and wrong first-order configuration

22. 22

23. This lens form is very versatile and can cover both fast speeds
and wide angles with good performance, with no vignetting
f/2, 60 degrees, no vignetting
f/1.25, 35 degrees, no vignetting
High performance design where index difference is important
23

24. TV projection lens.
Aberration corrector - focusing lens - field lens

25. • In an ideal world every element has power,
astigmatism, and Petzval independent of each
other
• Gives great control over induced aberrations
inside design
• Diffractive and aspheric surfaces can provide
this

26. 100 mm EFL, diffractive and aspheric surfaces

27. Diffraction-limited monochromatically

28. Part II - new ideas

29. Cooke triplet again
Consider effect of splitting lenses

30. A typical lithographic 4X stepper lens design, from 2004. It is .80
NA, 1000mm long, has 27 lenses and 3 aspherics. The 27 mm
field diameter on the fast speed end has distortion of about 1.0
nanometer, telecentricity of about 2 milliradians, and better than
.005 waves r.m.s. over the field at .248u. More modern designs
have more aspherics and fewer lenses.
30

31. No aspherics or diffractive surfaces. Large index differences
Lens powers = alternating - + - + - +

32. Diffraction limited, 100 mm EFL, f.2.0, 30 degree
field, no vignetting. Long back focus.

33. Axial and lateral color corrected

34. Achromatic with no extra lens

35. .35
NA, no aspheres or diffractive surfaces

36. 100 mm EFL, .35 NA, 30 degree field, no vignetting

37. No diffractive surface but strong aspherics
50 mm EFL, f/2, 45 degrees field, no vignetting

38. 50 mm EFL, f/2, 60 degrees field, no vignetting

39. 50 mm f.l. , f/ 60 degree field, no vignetting
2,

40. . Color corrected design
Alternate color corrected design

41. Achromatic performance, 50 mm f.l. , f/2, 45 degrees, no vignetting