The Power of Negative Thinking
Dave Shafer
David Shafer Optical Design
Plan for talk, in 2 parts

• Part I - review of material that I have given before.
Required background for Part II
• Part ...
The final $1,000,000 question is in two parts – an easy
part and a hard part. Which part do you want first?
“and when was he born?”
• Limiting aberrations for highly corrected
designs =
higher-order Petzval and sagittal oblique
spherical aberration
• Mos...
Mirror has Spherochromatism

Incoming ray angle and conjugate
change with wavelength
• Chief ray aberrations inside design cause
induced higher-order Petzval curvature
• Rays have different angles and surfac...
Chief rays aimed at paraxial pupil
Inverse triplet – small chief ray aberration
Reason for very small chief ray aberration

Paraxial pupil

Nearly concentric, nearly aplanatic

Nearly aplanatic, nearly ...
3rd-order triplet field curves

All 3rd-order = 0 for both
designs, not ray optimized

3rd-order inverse triplet field
cur...
All to same scale, same F.L.
Triplet has smallest lens volume,
longest back focus, worse chief ray
aberrations, worst fiel...
Induced oblique spherical aberration has a
different cause =
astigmatism and Petzval between surfaces
results in beam foot...
Triplet with all 3rd-order = 0

Field curves
Front surface footprint

Middle surface footprint

Last surface footprint
Front lens by itself

Next
surface

• This is an induced aberration effect,
not an intrinsic one
• 3rd-order assumes round...
All 3rd-order = 0

Middle lens footprints
On-axis
footprint

Edge of
field
footprint
Ray optimized triplet

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

...
• Ray-optimized triplet has about
20X better performance than 3rdorder triplet, for this field and
aperture example
•Ray o...
In complicated optical systems both the intrinsic and the
induced aberrations can all cancel out, at the 5 th-order level....
• At least 6 lenses are necessary to correct all the 3rd and
5th order aberrations to 0.0, if no aspherics are used
• Need...
Double Gauss cannot be corrected for all the 3rd and
5th, regardless of number of lenses, because back
focus is too big an...
22
This lens form is very versatile and can cover both fast speeds
and wide angles with good performance, with no vignetting
...
TV projection lens.

Aberration corrector - focusing lens - field lens
• In an ideal world every element has power,
astigmatism, and Petzval independent of each
other
• Gives great control over...
100 mm EFL, diffractive and aspheric surfaces
Diffraction-limited monochromatically
Part II - new ideas
Cooke triplet again
Consider effect of splitting lenses
A typical lithographic 4X stepper lens design, from 2004. It is .80
NA, 1000mm long, has 27 lenses and 3 aspherics. The 27...
No aspherics or diffractive surfaces. Large index differences
Lens powers = alternating - + - + - +
Diffraction limited, 100 mm EFL, f.2.0, 30 degree
field, no vignetting. Long back focus.
Axial and lateral color corrected
Achromatic with no extra lens
.35

NA, no aspheres or diffractive surfaces
100 mm EFL, .35 NA, 30 degree field, no vignetting
No diffractive surface but strong aspherics

50 mm EFL, f/2, 45 degrees field, no vignetting
50 mm EFL, f/2, 60 degrees field, no vignetting
50 mm f.l. , f/ 60 degree field, no vignetting
2,
. Color corrected design

Alternate color corrected design
Achromatic performance, 50 mm f.l. , f/2, 45 degrees, no vignetting
The power of negative thinking in optical design
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The power of negative thinking in optical design

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

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The power of negative thinking in optical design

  1. 1. The Power of Negative Thinking Dave Shafer David Shafer Optical Design
  2. 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. 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. 4. “and when was he born?”
  5. 5. • Limiting aberrations for highly corrected designs = higher-order Petzval and sagittal oblique spherical aberration • Mostly induced aberrations, not intrinsic
  6. 6. Mirror has Spherochromatism Incoming ray angle and conjugate change with wavelength
  7. 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. 8. Chief rays aimed at paraxial pupil
  9. 9. Inverse triplet – small chief ray aberration
  10. 10. Reason for very small chief ray aberration Paraxial pupil Nearly concentric, nearly aplanatic Nearly aplanatic, nearly concentric
  11. 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. 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. 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. 14. Triplet with all 3rd-order = 0 Field curves Front surface footprint Middle surface footprint Last surface footprint
  15. 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. 16. All 3rd-order = 0 Middle lens footprints On-axis footprint Edge of field footprint
  17. 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. 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. 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. 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. 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. 22
  23. 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. 24. TV projection lens. Aberration corrector - focusing lens - field lens
  25. 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. 26. 100 mm EFL, diffractive and aspheric surfaces
  27. 27. Diffraction-limited monochromatically
  28. 28. Part II - new ideas
  29. 29. Cooke triplet again Consider effect of splitting lenses
  30. 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. 31. No aspherics or diffractive surfaces. Large index differences Lens powers = alternating - + - + - +
  32. 32. Diffraction limited, 100 mm EFL, f.2.0, 30 degree field, no vignetting. Long back focus.
  33. 33. Axial and lateral color corrected
  34. 34. Achromatic with no extra lens
  35. 35. .35 NA, no aspheres or diffractive surfaces
  36. 36. 100 mm EFL, .35 NA, 30 degree field, no vignetting
  37. 37. No diffractive surface but strong aspherics 50 mm EFL, f/2, 45 degrees field, no vignetting
  38. 38. 50 mm EFL, f/2, 60 degrees field, no vignetting
  39. 39. 50 mm f.l. , f/ 60 degree field, no vignetting 2,
  40. 40. . Color corrected design Alternate color corrected design
  41. 41. Achromatic performance, 50 mm f.l. , f/2, 45 degrees, no vignetting
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