Dennis Gabor’s Catadioptric Design and Some New Variations

David ShaferDavid Shafer Optical DesignFairfield, Connecticut#203-259-1431shaferlens@sbcglobal.net

Gabor telescope

This is sometimes confused with the Maksutov telescope and is only correctly described in a 1941 British patent (#544,694) by Dennis Gabor. It is not clear if Gabor himself understood the aberration characteristics of this design – probably not based on the very short patent text. It is extremely simple with an interesting theoretical basis.

The Gabor design will be our jumping off point for some more complicated designs. Let’s see where that leads us.

Center of curvature of lens front surface

Center of curvature of the mirror

Aplanatic back surface bends the chief ray a little Gabor design

5th order adds for each surface

5th order nearly cancels

Bouwers

Gabor

For small field sizes the stop can be moved up to the first element without much performance change. For large field sizes the stop should be out in front some, ideally at the center of curvature of the first surface. But that makes the design a lot longer

Paraxial axial mirror diameter is 1.32 X front aperture size

Surface order = concentric, concentric, concentric – all around chief ray, then aplanatic – about axial ray , concentric about new chief ray

Bouwers lens

Gabor lens

Can be corrected for 3rd and 5th order spherical aberration but not 7th order. Not as good as when Bouwers lens is in double-pass.

Stop position

By using two Bouwers meniscus lenses better higher-order correction is possible. Total lens thickness directly correlates with performance. To avoid unreasonably thick lenses and still get good high-order correction Charles Wynn split the meniscus lenses in two to get this 4 lens design. Then glass choice can also correct for color.

Wynne was a great designer, in pre-computer days. He was active up till his death at 89.

James Baker designed some very fast speed wide angle satellite tracking cameras based on the Bouwers type of system. They were color corrected, had a curved image and the paraxial axial beam diameter at the mirror is close to the size of the entrance pupil diameter. These designs had aspherics and that let the meniscus lenses be thinner.

Although the Baker-Nunn design has great performance it has 4 aspherics.

100 mm F.L. .70 NA, diffraction-limited (monochromatic) over 5 degree total field on a curved image.

100 mm F.L. .80 NA, diffraction-limited (monochromatic) over 5 degree total field on a curved image.

Extra meniscus lens helps higher-order performance, giving a higher NA.

Gabor + Bouwers

Two weak meniscus lenses improve the higher-order correction of the Gabor lens design.

Gabor lens

100 mm F.L. .80 NA 10 degrees total field. Diffraction-limited (monochromatic) on a curved image

Additional weak power lens further improves performance

100 mm F.L. .95 NA, 5 degrees total field, diffraction-limited (monochromatic) on a curved image

All spherical surfaces

100 mm F.L., .95 NA, 5 degrees total field, .55u monochromatic, curved image

Modified Gabor has additional weak power elements

Terrific correction with no aspheres

But curved image

And not corrected for color

Summary so far

Some new solution regions will now be found

Since the correction is so good at very high NA values and modest field sizes it should also be good at lower NA values and wide fields, with a similar etendue. So I took the .95 NA design with a 5 degree field and reoptimized it for .75 NA and 30 degree total field. That moved the design into a different solution region, shown here, that is closer to having all the surfaces concentric about the stop. The Gabor lens became weaker and played less of a role in the correction.

On axis rays Edge of field rays

That reminded me of a completely monocentric design that I discovered many years ago. It can be corrected for 3rd, 5th and 7th order spherical aberration with just these two monocentric elements. It has phenomenal correction – this 100 mm F.L. design is diffraction-limited (monochromatic) at 0.999 NA!! over any field angle, on a curved image. There is no need for an aperture stop. The .999 NA rays leave the first element at grazing angle and internal reflection losses make for the equivalent of a rotating aperture stop for any field angle.

The two main problems with this design are the very thick glass path and the mirror size . For a 100 mm F.L. the first element is 161 mm thick and the 2nd is 189 mm thick and is seen in double pass. The paraxial diameter of the mirror is 2.28X the entrance pupil diameter.

By going down from .999 NA to .70 NA it is possible to greatly reduce the element thicknesses and still get diffraction-limited correction. Here both elements are 50 mm thick for a 100 mm F.L. design. The second element has had its concentric lens part split off from the mirror. It is still a monocentric design.

.70 NA

The paraxial axial mirror diameter is 1.56 X the entrance pupil size, which is smaller than the 2.28X ratio of the previous design on the last slide.

This looks just like Wynne’s design but there is a key difference. In Wynne’s design the second lens is only gone through once while in the design above it is seen in double-pass. That turns out to make a big difference in the correction level.

Designs shown to same scale. Both are 100 mm F.L. and .70 NA. The Gabor + Bouwers at the bottom is diffraction-limited over a 5 degree total field on a curved image. The Bouwers with two lenses at the top is also diffraction-limited at .70 NA on a curved image but over any field size since it is monocentric. The Gabor + Bouwers is much shorter and has much less glass path.

Does this now cover all that can be done with just a few lenses and a mirror? Of course not!

We usually have more choices in the design process than we think, at first.Even with extremely simple problems.

The Rosch design is very interesting. The lens has a flat front surface and the back surface and the mirror have the same center of curvature, where the stop is. As shown above it is corrected for 3rd order spherical aberration but not for 5th order.

By adding a Bouwers type lens in double pass, as shown here, both 5th and 7th order spherical aberration can be corrected while keeping a monocentric design. Then it is diffraction-limited (monochromatically) at .999 NA for a 100 mm F.L. over any field size on a curved image. With no vignetting!

100 mm F.L., .999 NA, monocentric design, same MTF for any field angle

Because of the flat front surface there is distortion for large field angles. There is a limit, for no vignetting, for the NA and field angle combination before the rim rays almost intersect the second surface twice.

For the 100 degree field shown here the NA cannot be higher than .95 or the rim rays will hit the second surface again and cause vignetting. But it is always diffraction-limited.

Shown to same scale, for .95 NA and a 100 degree field. The Rosch + Bouwers design on the left is much larger than the monocentric design on the right. But the refraction at the flat front surface of the design on the left reduces the field angle inside the design by a factor of the glass index n and that makes the obscuration due to the image for large field angles much better for that design than it is for the design on the right.

Surface order = concentric about chief ray, aplanatic about axial ray, aplanatic abut axial ray, concentric about chief ray, concentric, concentric, concentric.

By inserting a thick aplanatic/aplanatic airspace inside the first thick lens we can remove a lot of glass.

By dropping the concentric and aplanatic curvature solves and varying all the parameters we get this simple design which is 100 mm F.L. .95 NA and diffraction-limited (monochromatically) over a 5 degree field on a curved image.

By adding another lens it is possible to reduce the mirror size by quite a lot.

100 mm F.L. .90 NA diffraction-limited (monochromatically)over a 5 degree field on a curved image.

We have met our goal of small glass path and relatively small mirror size while keeping very high NA correction.

By reducing the NA of the .90 NA, 5 degrees field design it is possible to get much larger field sizes while staying diffraction-limited. .80 NA gives a 20 degree field, shown here, while .70 NA gives a 30 degree field.

100 MM F.L., .80 NA, 20 degree field, diffraction-limited (monochromatic) on a curved image

Adding an aspheric surface

By adding an aspheric element at the aperture stop much higher performance is possible, such as this .90 NA, 30 degree field design, diffraction-limited (monochromatic) over the whole field – on a curved image.

Aspheric element

100 mm F.L., .90 NA, 30 degree field, monochromatic on a curved image. One aspheric surface

By taking the .90 NA, 30 degree field design and reducing the NA to .80 it is possible to remove two lenses and get this .80 NA, 30 degrees field that is also diffraction-limited, on a curved image.

It now looks like a version of the Baker Super-Schmidt, above, but without the color correction provided by the two glass doublet here.

Aspheric

Color Correction

It is hard to get good color correction with only spherical surfaces. Here there are 8 lenses for a .80 NA, 20 degree field and the polychromatic MTF is not as good as I would like. More work is needed to find a better design.

Color corrected design, no aspheric

100 mm F.L., .80 NA, 20 degrees field, curved image, .45u-.65u color correction, all spherical surfaces

100 mm F.L., .80 NA, 20 degrees total field, curved image, one aspheric

aspheric

Good color-corrected design

100 mm F.L., .80 NA, 20 degrees field, curved image, one aspheric

.45u -.65u color corrected design

In summary, the Gabor catadioptric design was a very productive jumping off point for generating a series of very high performance designs with very high NA and large field sizes.