The power of negative thinking in optical design

The Power of Negative Thinking

Dave ShaferDavid Shafer Optical Design

• Part I - review of material that I have given before. Required background for Part II

• Part II - new ideas and designs

Plan for talk, in 2 parts

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

• Mostly induced aberrations, not intrinsic

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 surface intersection heights than 3rd-order assumes

• 3rd-order assumes paraxial quantities

Chief rays aimed at paraxial pupil

Inverse triplet – small chief ray aberration

Nearly concentric, nearly aplanatic Nearly aplanatic, nearly concentric

Reason for very small chief ray aberration

Paraxial pupil

3rd-order triplet field curves

3rd-order inverse triplet field curves, 20X smaller scale

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

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

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

Front surface footprint Middle surface footprint Last surface footprint

Triplet with all 3rd-order = 0

Field curves

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.

Next surface

Front lens by itself

Middle lens beam footprint at edge of field

• 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

All 3rd-order = 0

On-axis footprint

Edge of field footprint

Middle lens footprints

Ray optimized triplet

Front surface footprint Middle surface footprint Last surface footprint

10X smaller scale than 3rd-order triplet plotPetzval radius = 2.7 X f.l.

• Ray-optimized triplet has about 20X better performance than 3rd-order 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

•But chief ray aberrations only slightly improved.

•Diameter of circular footprint changes with field, due to Petzval, so still gives induced aberrations

3rd-order triplet ray-optimized triplet

Front

Middle

Back

Beam footprints at edge of field

In complicated optical systems both the intrinsic and the induced aberrations can all cancel out, at the 5th-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

• rays fail at larger field angles

With right glasses can also correct for axial and lateral color

All 3rd = all 5th = 0.0No ray optimization

• 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

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

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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

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 induced aberrations inside design

• Diffractive and aspheric surfaces can provide this

100 mm EFL, diffractive and aspheric surfaces

Diffraction-limited monochromatically

Part II - new ideas

Cooke triplet again

Consider effect of splitting lenses

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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.

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

50 mm EFL, f/2, 45 degrees field, no vignetting

No diffractive surface but strong aspherics

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

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

. Color corrected design Alternate color corrected design

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