Some Unusual Telescope Designs

Dave Shafer

David Shafer Optical Design

Topics

• Gregorian designs

• Cassegrain designs

• All-spherical designs

• Uses of off-the-shelf Schmidt-Cassegrain components

• Tilted component telescopes

• Telescope sent to Saturn, Vesta, and a comet

Gregorian Designs

A classical Gregorian telescope has a parabolic primary and an elliptical secondary mirror. For a 1.0 meter diameter f/2 primary and a f/15 system with a 20% diameter obscuration it is perfect on-axis and has .37 waves r.m.s. at .55u at the edge of a +/- .25 degree field on a curved image.

• There is about equal amounts of coma and astigmatism at the edge of a +/- .25 degree field, on a curved image surface. Both mirrors are perfect on-axis.

• By using both of the mirrors’ conic surfaces as variables it is possible to correct for both spherical aberration and coma. The primary mirror is then just very slightly different from a parabola, while the secondary is close to the same ellipses as before.

• Then the design is perfect on-axis and has about .32 waves r.m.s. of astigmatism on a curved image surface. Not much better than before (.37 waves r.m.s.) but now it is pure astigmatism and it is quadratic with field, so it is a little better at smaller field angles than the classical Gregorian.

Field lens at image

Now suppose we add a tiny thin field lens right at the intermediate image. It will have no spherical aberration, coma, or astigmatism if it is right at the image

The power of this field lens gives independent control of where the pupil is for the two mirrors. That extra variable, plus the two conics as variables, allow us to correct for spherical aberration, coma, and astigmatism.

• The required field lens power for this solution is very weak and the mirror conics hardly change at all. The primary mirror conic is still very close to a parabola.

• Using a field lens at an intermediate image to give independent control of the pupil position before and after the intermediate image is a very powerful design tool and it affects all the system aberrations even though it has very little of its own aberrations.

• If the field lens is moved a little away from the intermediate image there is still an anastigmatic solution possible and it changes a little the primary mirror conic that is needed.

• There is then a solution where the primary becomes an exact parabola. Then this solution can be used with existing observatory parabolas, like at Mt. Wilson and Mt. Palomar.

Two weak meniscus shell lenses

When the field lens is moved away a little from the intermediate image, to give the exact parabola solution, the lens acquires a small amount of axial and lateral color

That color is corrected by splitting it into two lenses on either side of the intermediate image and making them weak meniscus lenses curved about the image.

Two weak meniscus lenses on either side of image

Secondary mirror

By curving the lenses about the image they can correct for both of their axial and lateral color with the same glass type. Here I used BK7 glass. The lenses do not add any to the axial obscuration.

The result is an f/15 design with a 1.0 meter diameter f/2 parabola, an elliptical secondary mirror and two weak BK7 lenses 30 mm in diameter.

On a curved image (radius 470 mm) the polychromatic (.486u- .656u) wavefront at the edge of +/- .25 degree field is .019 waves r.m.s. If it is reoptimized for a flat image the polychromatic value is .043 waves r.m.s. at the edge of the field.

• This is really very good performance over a sizable field of view by a simple addition to an observatory’s large parabolic primary mirror.

• The results here are for an f/2.0 parabola. The design works well for other values too.

• If we add some more lenses near the intermediate image we can get still better performance.

• Next I show a set of 4 BK7 glass lenses for a 2.0 meter diameter f/2.0 parabola and with a flat image.

Secondary mirror

Design has a 2.0 meter diameter f/2 primary parabola, elliptical secondary, 4 BK7 lenses and a polychromatic (.365u - .656u) wavefront of .030 waves r.m.s. at the edge of a +/- .25 degree field on a flat image.

image

To primary mirror

Very weak lenses

A purely reflective solution to the field lens region has two solutions, with two small aspheric mirrors.

Primary mirror

Primary mirror

With this in place we have an all-reflective design that works well for all wavelengths. For a 10 meter diameter f/1.0 parabolic primary and a conic secondary mirror and these two small aspheric field mirrors we get a design that is diffraction-limited in the visible over a ¼ degree diameter field on a flat image.

10 meter diameter f/1.0 parabolic primary, elliptical secondary, two small aspheric field mirrors.

Corrected for spherical aberration, coma, astigmatism, and Petzval.

F/1.0spherical primary,20 meters in diameter

f/5.0 image

The same type of system can work with a spherical primary mirror but with a much smaller field size.

Aspheric secondary

f/1.0 primary mirror

Caustic region near focus

The best focus on-axis spot size from a 20 meter diameter f/1.0 spherical mirror is 180 mm in diameter!

Reflective field elements

The field mirrors obscuration can be 25% of the pupil diameter with this f/1.0 spherical mirror focus.

F/1.0spherical primary,20 meters in diameter

f/5.0 image

By letting the field mirrors both be curved and aspheric we can get a design that is diffraction-limited at .5u over a 1/20 degree field diameter, or a 100 mm flat image diameter at the final f/5.4 focus.

Aspheric secondary

Primary mirror and 25% diameter obscured pupil

Rays from secondary mirror towards final focus, off page to the right

This shows the region around the two aspheric field mirrors. The 25% diameter obscuration due to the field mirrors matches the 25% obscuration due to the secondary mirror.

Secondary mirror

Cassegrain Designs

What can be done with a classical Cassegrain telescope to improve its image quality? Here a 1.0 meter diameter f/2 parabola and a hyperbolic secondary mirror are perfect on-axis but have .48 waves r.m.s. at the edge of a +/- .25 degree field, on a curved image.

The conventional way to improve a classical Cassegrain is to add some field lenses. The result is a design corrected for spherical aberration, coma, astigmatism and Petzval curvature, as well as axial and lateral color

BK7 lenses

• What else could be done, instead of this?

• At the edge of a +/- .25 degree field the classical Cassegrain design has about equal amounts of coma and astigmatism.

• The coma from the primary mirror is 4% larger than the coma from the secondary mirror and they are of opposite signs, so they almost cancel.

• Can something be done to make them cancel exactly, without changing the mirror surfaces?

• Yes – we add a nearly zero power lens next to the secondary mirror. It puts in a tiny amount of coma.

A very weak, nearly zero power lens right in front of the secondary mirror makes the coma cancellation be perfect. But it introduces very small amounts of spherical aberration and color.

Nearly zero power BK7 lens

Secondary mirror

By bending the lens into a very weak power meniscus lens the spherical aberration and axial color that it has can be eliminated

• The resulting design has the same amount of astigmatism as a classical Ritchey-Chretien design.

• So just by adding this nearly zero power element to a classical Cassegrain we give it the same performance as a Ritchey-Chretien, without changing the mirror surfaces.

• The remaining astigmatism, Petzval, and a very small amount of lateral color can be fixed by adding a single thick field lens to the design, as is shown next here.

Thick BK7 glass field lens corrects design for astigmatism, Petzval, and lateral color

Splitting the thick field lens in two gives more design variables and avoids the glass thickness of the simpler design.

BK7 lenses

2.0 meter f/2 parabolic primary mirror, 3 BK7 lenses, evaluated for polychromatic (.365u to 1.0u) wavefront on a flat image for a +/- .25 degree field. Conventional design with field lenses = .089 waves polychromatic r.m.s. at edge of field.

New design = .049 waves polychromatic r.m.s. at edge of field. New design has better chromatic performance.

lens

All-spherical Designs

• What about a design with spherical primary and secondary mirrors and a subaperture corrector?

• In the late 1980’s I published a very simple design for amateur telescope makers that was later made and sold by Vixen Optics. It has two spherical mirrors and a single thick meniscus lens with nearly zero power.

Around 1990 I designed a 500 mm aperture version with a split corrector lens (to avoid a very thick single lens) for the Swansea Astronomical Society in Wales. It was made and has been in use ever since.

With a ½ meter diameter f/2.5 spherical primary mirror this all spherical design is diffraction-limited through the visible region over a small field

Swansea, Wales observatory telescope

By adding two BK7 field lenses near the image the correction can be greatly improved and this is now diffraction-limited through the visible spectrum over a ½ degree diameter field on a flat image, with all spherical surfaces.

500 mm diameter f/2.5 spherical primary

Klevtsov design

Mangin lens/mirror element

A different type of design is by Klevtsov and it has a little better performance than the other design that I did.

The Klevtsov design, at left, is a little better over a small field than the design at the bottom. But this is not a fair comparison. The top design has only two corrector elements while the design at the bottom has three – two lenses and a mirror. Let us split the Klevtsov Mangin element into a separate lens and a mirror.Then the performance gets a little better and is then about 25% better polychromatic wavefront than the bottom design.

Mangin element separated into a mirror and a lens

Two element Klevtsov design is slightly improved by going to this three element design

By having three BK7 lenses next to the secondary mirror the performance can be improved a lot and then a 1.0 meter diameter f/2.5 spherical primary design can be diffraction-limited through the visible spectrum over a ½ degree diameter field on a flat image.

Uses of off-the-shelf Schmidt-Cassegrain components

Celestron and Meade sell 200 mm aperture and 275 mm aperture f/10 Schmidt-Cassegrain telescopes. There is a front aspheric plate/window, a spherical primary mirror and a spherical secondary mirror.

The aspheric plate/window is made by a very clever method that allows for mass production at a very low cost. The design has quite a lot of coma off-axis and it would take another aspheric surface to fix that. How can we use these optical elements to make other designs?

Commercial Schmidt-Cassegrain telescope

Aspheric plate moved out in front to correct for coma.

Coma is corrected and astigmatism is very small if the aspheric plate is moved out in front further, giving a bigger well-corrected field size. The optical elements have not been changed at all, just the positions.

Secondary mirror needs a new way to be supported

These mass produced 200 mm or 275 mm aperture aspherics are very much less expensive than a custom made aspheric. Buy two Schmidt-Cassegrain telescopes and take the two aspheric plates and put them together. Then make a new spherical primary mirror to get an inexpensive f/1.75 Schmidt telescope with a wide field of view on a curved image, with no coma or astigmatism. Using only one aspheric plate (and a different mirror) gives a f/2.25 design.

Two identical aspheric plates

Spherical mirror

Prime focus corrector, after removing secondary mirror

About 15 - 20 years ago I designed a prime focus corrector for Celestron, but they never did anything with it. It was f/2.3 and used the standard aspheric plate and primary mirror, with the secondary mirror removed. Back then image sensors were much smaller than today. Now they have revived this idea and there is a new product like this for their 275 mm aperture telescope. I did not do the new design, shown next.

The new design looks like this, for a much larger image sensor size than was available when I did my design a long time ago.

Not to scale

Camera body or special image sensor attaches here.

Celestron 275 mm aperture f/2.2 astrocamera

The point of showing these designs is to emphasize the use of existing optical elements, especially aspheric surfaces, to make new aspheric designs without the expense of a custom made aspheric.

Unobscured Tilted Component telescopes

Unused and absent portion of aspheric plate

Spherical mirror

Unobscured decentered pupil Schmidt telescope

Aperture stop

A decentered pupil on a Schmidt aspheric plate sees just one side of the spherically aberrated wavefront coming from the aspheric. Suppose we decompose this off-center section of the wavefront using an off-center coordinate origin. Then the off-center piece of spherical aberration looks mainly like astigmatism and some coma, when expanded about this new coordinate origin.

Absent part of wavefront

Tilted lenses vertex lie on this line

Schmidt telescope axis that includes the mirror’s center of curvature

Three tilted lenses can have their powers, bendings and tilts chosen so that they simulate an off-axis piece of spherical aberration and also that is constant with field angle. No off-axis pieces of lenses are used. They are centered (but tilted) on a different axis from the mirror.

f/4.0 design has a polychromatic spot size in the visible region of 6 arc seconds that is constant over a 3 X 10 degree field curved image.

Completely symmetrical lens group

The design can be made half as long, by moving the lens group up near the image, and there is still a well corrected image possible – as shown next.

This shorter design has a good solution with just two lenses, but with a smaller field than the long design. F/4.0 with 6 arc seconds polychromatic spot size over a 2.0 degree diameter field on a curved image.

For slower speeds, like f/6, the two lenses can each be made flat on one side and have a common radius, as is shown next.

Plano-convex and plano-concave BK7 glass lenses, same radius

Spherical mirror

150 mm aperture f/6.0 unobscured design. Diffraction-limited in visible spectrum over a 1.5 degree flat image, which is tilted. The fold mirror is flat.

Telescope sent to Saturn, Vesta, and a comet

One of my first patents, in 1977, was for an unusual kind of unobscured telescope that only has spherical mirrors.

Many years later one of these unusual telescopes was sent on the Cassini space craft to Saturn, where it took many closeup pictures. Later another one went to the asteroid Vesta, and it was there a few years ago, taking photographs. Now a third spacecraft with one of my telescopes on-board is approaching a comet and it will try to land on it.

This is the Cassini space craft before being launched, on its mission to Saturn.

Close up of asteroid Vesta, taken recently from space with my telescope.

The Cassini mission to Saturn wanted a telescope on-board that was 1) all-reflective, 2) easy to make and align with no aspherics, 3) unobscured, 4) well-corrected over a large field size, and 5) able to become a spectrograph with no extra elements

This drawing from my patent, not to scale, shows the design. What is very unusual is that all the mirrors have their centers of curvature on a single optical axis, unlike other tilted mirrors designs. Also the convex mirror “25” in the drawing is the aperture stop. If this is made a grating surface then the final image is a sharp in-focus spectrum.

Any questions?