PAGE 12
Copyright
– P. J. Smith
But permission is
given to distribute this material in unaltered form as long as it is not sold
for profit.
Various
Schemes for
Correcting
a One Metre Folded Cassegrain
Based
on an F:3.5 Primary giving a System of F:10
by
Peter John Smith.
A variety of sub diameter correcting lens options.
Aspheric deviation is used as sparingly as possible.
In some cases, schemes are included for the testing of Convex surfaces.
Rationale
Designs containing aspheric surfaces, particularly reflecting convex ones, will fall short of their potential unless rigorously tested.
In a well equipped optical facility aspherics are difficult but for the amateur the hurdle may be impossible.
Hopefully, some of these proposed schemes may be useful. They should be a good starting point for anyone interested in ray tracing.
Depending on experience and access to various test items, different schemes will appeal.
Optical glass is ubiquitous BK7 and F2. Exotic types are needed for much improvement.
It may be interesting to compare these designs with another elsewhere on this web site if you have not already read it.
Two designs use parabolic primaries.
These may be of special interest to some. Performance can be improved by removing this restraint.
These 'Classical Cassegrain types' have correcting lens structures of either a doublet (CC2) or two single lens elements (CC11)
Some designs use both Hyperboloidal Primaries and
Secondaries
These give the best performance as the basic Ritchey Chretien is the easiest to correct. This comes at the expense of more figuring and testing problems.
These 'Ritchey Chretien types' have correcting lens structures of either a single meniscus (RC1) or doublet (RC2).
This design can be extended to much wider fields although secondary size increases.
Some designs use a spherical secondary.
These are analogous to a Dall Kirkham and their Primary requires less figuring correction. Since they use two single meniscus correcting lenses, they are designated as DK11 types.
I must credit Kevin McCarthy with drawing the possibilities of this design to my attention. At the time I was concentrating heavily on the exquisite correction possible from the Ritchey Chretien and a doublet corrector.
Unfortunately, four air to glass surfaces seem necessary for a DK type to be successful but the design has much to offer.
When spacing restraints imposed by folding the light path and reducing the secondary diameter are relaxed, distinctly better correction is possible from this type.
Layout.
The general layout of each design is shown. They are not strictly to scale although corrector drawings are indicative of relative size.
Light enters the correctors from the left.
In some cases the fold is a considerable distance above the mirror. This reduces secondary and corrector diameters.
The eyepiece position should not be too high above ground if care is taken with the telescope mounting system.
Target
criteria.
1. Maximum field of 0.6 degree. This corresponds to a linear diameter of approximately 100 mm.
2. Image quality must closely approach or better the limits set by diffraction over a 25 X 25 mm field.
3. Spot sizes must better the commonly accepted 25 micron film criterion across a 55 X 55 mm field.
4. Field curvature must be small enough to use unbent film over a 55 X 55 mm area.
5. Secondary obscuration must be no more than 30 % (Unbaffled)
6. Minimum of glass air surfaces.
Some of the correctors in these telescopes may be too large to cement although the smaller ones (RC2) should be satisfactory. If neither cemented nor oiled a doublet represents kittle advantage two separate singlets.
7. The highly corrected field must be achieved with sub diameter correctors.
8. The design must deliver a comfortable and safe observing position. Thus the field correcting lens must be in a position which allows folding.
9. At least 250 mm back focus must be provided behind the last lens to allow placement of attachments such as a Binocular Viewer.
10. Aspheric deviations must be as small as possible.
Aspheric
Deviation.
These are given both in terms of Schwarzschild constant AND a figure in microns. (See Prescriptions)
Unfortunately, the Schwarzschild constant is very misleading where it comes to amount of glass removal when moving from best fit sphere to aspheric.
It allows reasonable comparison between similar surfaces unless diameter and radius of curvature are very different ?
What may seem an insignificant conic constant, when applied to a lens of short radius of curvature, may demand overwhelming glass removal.
Another matter should be considered.
We all know that exactly targeting glass removal of precise amounts in specified places is an impossible dream. This means figuring from the best fit sphere is often unlikely to work. It may be more useful to plan on a less efficient approach which better fits our experience or the known quirks of some polishing machine. Or is safer in terms of the dreaded TDE.
Thus, in practice, far more glass may be needed than a simplistic calculation indicates.
In most cases, micron deviations are given in terms of a good fitting spherical envelope but not the very best case.
It should be noted that if some vignetting is allowed, the diameter of correcting lenses may be reduced. This is especially true for correctors far from the final image. Any aspheric correction on such a lens is subsequently reduced.
Obscuration,
Baffling and Vignetting.
These designs were guided, but not driven obsessively by minimum obscuration.
No baffling solutions are provided. In any case, there are no hard and fast solutions as individual use will dictate maximum allowable vignetting.
To facilitate comparisons, secondary and corrector sizes are given for different vignetting cases.
Remember, the secondary and correcting lens sizes given in the prescription is for full illumination.
If acceptable, these sizes may be reduced somewhat.
These are for a total unvignetted image and a 25 X 25 mm central unvignetted area.
|
CC11 |
CC2 |
RC1 |
RC2 |
DK11 |
|
314 |
268 |
300 |
300 |
295 |
|
295 |
250 |
282 |
286 |
290 |
Of course, baffling will always increase this somewhat - possibly by about 5 %.
Reducing the diameter of correcting lenses increases Vignetting at the edge but has little effect on the central area.
Designs such as the RC types where the corrector is close to the image require a smaller correcting lens.
To aid assessment, the diameter of the front correcting lens for full illumination and a suggestion of what reduction may be possible is listed.
This is based on no worse than 50 % vignetting at the edge of the image or no incursion into the middle half of the image, whichever occurs first.
|
CC11 |
CC2 |
RC1 |
RC2 |
DK11 |
|
220 |
220 |
118 |
114 |
178 |
|
150 |
150 |
110 |
108 |
126 |
Surface
Testing.
Concave Spheres of medium curvature are straightforward to test at their centre of curvature. Foucault, Ronchi, and Wire tests all come to mind. As the curvature increases, refinements may need to be added.
Convex spheres are more difficult and require a less direct test.
Concave test plates may be used but the method soon gets out of hand as more and more are needed.
Bonded surfaces within doublets are unique in that, as one is always concave, the pair provide their own test plate. As a bonus, shape tolerances are relaxed when bonded or oiled. Some of the correctors in these telescopes may be too large to cement although the smaller ones should be satisfactory.
If neither cemented nor oiled a doublet represents little advantage over two separate singlets.
If at all possible, common radii are introduced so that a concave surface in the design becomes a test plate for a common convex surface elsewhere.
Convex Null Test
A useful null test for convex spheres is to test from the rear through the glass.
For a perfectly spherical surface to produce a true null the surfaces must be concentric.
If the surfaces are not truly concentric, the resulting test surface is aspheric.
Since many of the correcting lenses are meniscus in shape, some are sufficiently close to concentric for this test to produce a close enough approximation to a sphere to be useful.
Some designs assume this test AND ANY SUBSEQUENT DEPARTURE FROM A SPHERE IS ALLOWED FOR IN THE TOTAL DESIGN.
Light passes through the first surface and reflects back from the rear. Thus it exactly retraces its path.
It is possible to modify this test by longitudinally spacing object and image to produce a larger range of better nulls.
Since this requires accurate measurement no use has been made of this in these tests and the simplest possible test adopted.
Various practical problems arise, mainly associated with shorter radius of curvatures when wider angle beam occur.
Various modifications to standard tests may be needed. In this context, a single wire test may be especially useful.
When some vignetting is acceptable the consequent reduction in correcting lens diameter makes this test easier and more accurate.
Special Test Plates
In some of these designs, one concave surface of a correcting lens matches and becomes a common test plate for the secondary mirror.
In the DK designs, after the concave spherical surface of the correcting lens is figured, this can then be used to figure the
convex spherical secondary. Since the secondary is larger in diameter this is far from a perfect scheme.
One possible solution is to produce an oversize correcting lens and finally cut it down to size. A separate special test plate is another obvious solution. Using an under size test plate off centre is another possibility
One possible mitigating factor in favour of using an under size test plate is that, in a cassegrain, an appreciable amount of the centre of the secondary is not used.
I believe an undersized test plate made of the correcting lens is a viable option.
The CC2 design represents a design compromise requiring the production of ONE test plate for the entire system.
It needs to be aspheric (slightly hyperboloid) to produce the secondary. The same test plate is then used to test the two outer surfaces of the correcting lens. Since these lenses are considerably smaller the amount of asphericity transferred to the corrector surfaces is only about 1.5 microns. If some vignetting is allowed this is even smaller as the lens diameters reduce.
The inner surfaces of the correcting doublet are of course tested against each other.
Despite a little field curvature the spot sizes are remarkably small considering the small amounts of asphericity used.
The use of multiple conics usually introduces alignment problems. Although I have not yet done tolerancing, the small amounts of some of these aspheric deviations should not make this too much of a problem.
It might be wondered why no method of back testing the secondary mirror using optical glass has been considered. This is because, considering the sheer size of the secondary, it has to be thick to resist bending and at the same time have low thermal inertia or expansion. Optical glass, except for quartz, is thus ruled out. To be satisfactory as a reflective surface, any back test needs extremely homogenous glass.
Optical
Performance
The General capability of these designs is probably best summed up by considering the Strehl Ratio at different field positions.
Strehl Ratio.
CC represents the performance of an uncorrected F:10 cassegrain. A Strehl of 0.8 is often considered to represent the diffraction limit. This is open to interpretation but is a useful guide. Certainly, performance much in excess of this will not often be possible with a 1 m. telescope because of limits set by atmospheric turbulence.
Spot Diagrams.
Great care should be taken when interpreting performance based on this presentation. Spot diagrams poorly represent the energy distribution over the spot and their appearance can be easily changed by varying plot density. These are for 0, 0.1, 0.2 and 0.3 degrees half field and are superimposed on the Airy Disk.
It may be useful to relate these diagrams to the RMS spot size from the following graph.
Wherever possible, an attempt has been made to optimise the designs so performance is better on axis.
Remember that an RMS spot size of 10 u as delivered at the edge of the field by CC2 will probably be acceptable photographically. This assumes that perfect film placement occurs which is only possible with a flat field or a correspondingly bent film. Visually, at the magnification provided by an eyepiece covering a 100 mm diameter field, 20 u is excellent at the edge of the field of vision.
Focal Plane Curvature.
This is critical when assessing performance on flat film or CCD's.
Visually, some field curvature is allowable over a 100 mm field. In fact, most eyepieces will perform better with a slight to moderate backward curving field.
An attempt has been made to cover a 2.25 X 2.25 inch film holder with an essentially flat field.
Since the image forms at F:10, there is more latitude in focal plane tolerance than one would expect.
Although the DK11 field curvature plots indicate the presence of some astigmatism, there is certainly no problem over a 2.25 X 2.25 film. Even over the 100 mm field little deterioration will be apparent on film.
One thing a perfectly flat field delivers is greater film or CCD placement tolerance.
This represents the 'depth of focus' available for different criteria.
The largest tolerance is for a 2.25 X 2.25 square film assuming spots of 25 u. This is the light hatching.
The next tolerance is for a 1 X 1 square image assuming spots of 10 u. Medium Hatch.
The smallest tolerance is for film covering the entire 100 mm diameter field at 25 u. Darkest hatch.
Note that for CC2, 100 mm field coverage is impossible unless the film is slightly curved.
Special Comments
RC2 obviously gives best performance and only uses 2 air glass surfaces. No easy way exists to make the secondary. It is possible with the right equipment but its difficulty should not be underestimated.
Although the conic of the secondary mirror seems huge, its large radius of curvature makes it much less than expected in microns. See prescription.
A null back test is intended to assess the only non common convex surface in the corrector.
Anyone considering this design should assess their requirements very carefully to see if images of this quality are really required.
RC1 is very similar to RC2 except for a simpler correcting lens. Its convex surface is meant to be back tested. The same problem of testing the secondary exists as in RC2. If this can be overcome the design becomes attractive.
CC11 is an attempt to correct an existing parabola. Although it uses four air to glass surfaces only one test plate is needed. The shape of this lens does not lend itself well to back testing. The other convex surface in the corrector is tested using a common curve elsewhere in the design.
The correcting lens design is a little more 'critical' than the others so needs care.
Of course, the secondary requires special equipment although it is not extreme.
CC2 is an attempt to produce fair to good correction from an existing parabola. Unlike CC11 a scheme for figuring the secondary is possible by first making a concave hyperbolic test plate. Since this has quite small asphericity, using it to test the secondary is more feasible. The corrector is large but may be reduced considerably if vignetting is allowable. When this is done, it is not overly difficult.
DK11 uses a spherical convex secondary. All of the variants here use a corrector lens surface that can test the secondary. Unfortunately, four glass to air surfaces are needed in the corrector.
Designs are given which incorporate back testing of the convex surfaces in the corrector. Unfortunately, the back null test uses wide beams in this design and in one case produces considerable asphericity.
If the design without any back testing is selected, two test plates are needed.
A reasonable compromise is the design needing only one test plate as the one remaining back test produces a very small aspheric deviation.
Another advantage of the DK type is reduced figuring on the primary. Although unfamiliar to most ATM's it should be easier than a paraboloid.
Optical Prescriptions.
CC2
(TRIPLE H) - THREE LIGHT IDENTICAL ASPHERIC SURFACES
SECONDARY
AND TWO COMMON SURFACES ALL FIGURED FROM ONE TEST PLATE
|
Surf |
Radius |
Thicknes |
Glass |
Diameter |
Conic |
Remove |
|
STO |
-7000 |
-2662.1 |
MIRROR |
1000.18 |
-1 |
9 u |
|
2 |
-2096.5 |
2329.42 |
MIRROR |
267.616 |
-2.0920 |
3.5u |
|
3 |
2096.59 |
15 |
F2 |
220.117 |
-2.0920 |
2 u |
|
4 |
760.655 |
20 |
BK7 |
219.065 |
0 |
0 |
|
5 |
-2096.5 |
1039.08 |
|
218.727 |
-2.0920 |
2 u |
|
IMA |
Infinit |
|
|
104.8365 |
|
|
...................................................................
DK11B
- ALL SPHERICAL CORRECTOR - COMMON SECONDARY
|
Surf |
Radius |
Thicknes |
Glass |
Diameter |
Conic |
Remove |
|
STO |
-7000 |
-2561.4 |
MIRROR |
1000.18 |
-0.7753 |
7 u |
|
2 |
-2915.3 |
1793.02 |
MIRROR |
295.189 |
0 |
0 |
|
3 |
-2915.3 |
15 |
BK7 |
165.3617 |
0 |
0 |
|
4 |
-724.15 |
0.93248 |
|
165.044 |
0 |
0 |
|
5 |
425.619 |
15 |
BK7 |
162.846 |
0 |
0 |
|
6 |
283.4081 |
822.382 |
|
158.4457 |
0 |
0 |
|
IMA |
Infinity |
|
|
105.061 |
|
|
....................................................................
DK11
- TWO ASPHERIC CORRECTOR SURFACES - BACK FIGURED - COMMON SECONDARY
|
Surf |
Radius |
Thicknes |
Glass |
Diameter |
Conic |
Remove |
|
STO |
-7000 |
-2556.5 |
MIRROR |
1000.18 |
-0.7762 |
7 u |
|
2 |
-2928.3 |
1789.55 |
MIRROR |
296.554 |
0 |
0 |
|
3 |
-2928.3 |
15 |
BK7 |
167.0307 |
0 |
0 |
|
4 |
-712.09 |
0.93248 |
|
166.718 |
-0.639 |
4 u |
|
5 |
475.827 |
15 |
BK7 |
164.572 |
-0.0292 |
0.5u |
|
6 |
303.972 |
843.3977 |
|
160.3432 |
0 |
0 |
|
IMA |
Infinity |
|
|
105.0538 |
|
|
.....................................................................
DK11
C - ONE ASPHERIC CORRECTOR SURFACE - BACK FIGURED - COMMON SECONDARY
|
Surf |
Radius |
Thicknes |
Glass |
Diameter |
Conic |
Remove |
|
STO |
-7000 |
-2519.8 |
MIRROR |
1000.18 |
-0.7819 |
7 u |
|
2 |
-3041.3 |
1763.91 |
MIRROR |
306.669 |
0 |
0 |
|
3 |
-3041.3 |
15 |
BK7 |
177.464 |
0 |
0 |
|
4 |
-820.24 |
0.93248 |
|
177.145 |
0 |
0 |
|
5 |
512.873 |
15 |
BK7 |
175.074 |
-0.0323 |
0.5u |
|
6 |
340.026 |
974.600 |
|
171.027 |
0 |
0 |
|
IMA |
Infinity |
|
|
104.951 |
|
|
......................................................................
RC1
- ONE ASPHERIC CORRECTOR SURFACE - BACK FIGURED
|
Surf |
Radius |
Thicknes |
Glass |
Diameter |
Conic |
Remove |
|
STO |
-7000 |
-2548.7 |
MIRROR |
1000.18 |
-1.1821 |
10 u |
|
2 |
-3017.7 |
2334.14 |
MIRROR |
299.466 |
-7.4862 |
6 u |
|
3 |
-150.83 |
25 |
BK7 |
118.372 |
0 |
0 |
|
4 |
-159.24 |
249.963 |
|
124.2077 |
-0.0092 |
2 u |
|
IMA |
Infinity |
|
|
104.712 |
|
|
.....................................................................
RC2
- ONE LIGHT ASPHERIC CORRECTOR SURFACE - BACK FIGURED
|
Surf |
Radius |
Thicknes |
Glass |
Diameter |
Conic |
Remove |
|
STO |
-7000 |
-2549.74 |
MIRROR |
1000.187 |
-1.18077 |
10 u |
|
2 |
-3112.00 |
2207.332 |
MIRROR |
299.2304 |
-8.18024 |
6 u |
|
3 |
-418.141 |
10 |
F4 |
113.7597 |
0 |
0 |
|
4 |
-313.027 |
10 |
BK7 |
114.2332 |
0 |
0 |
|
5 |
-681.475 |
250 |
|
114.6517 |
0.4591 |
0.5u |
|
IMA |
Infinity |
|
|
104.8347 |
|
|
.....................................................................
CC11
- ALL SPHERICAL CORRECTOR - ONE COMMON SURFACE
|
Surf |
Radius |
Thicknes |
Glass |
Diameter |
Conic |
Remove |
|
STO |
-7000 |
-2515.3 |
MIRROR |
1016.86 |
-1 |
9 u |
|
2 |
3115.75 |
-2361.0 |
MIRROR |
313.055 |
-4.5374 |
4 u |
|
3 |
-695.28 |
15 |
BK7 |
125.049 |
0 |
0 |
|
4 |
-215.49 |
39.4261 |
|
125.134 |
0 |
0 |
|
5 |
-175.95 |
20 |
BK7 |
112.933 |
0 |
0 |
|
6 |
-695.28 |
249.996 |
|
113.836 |
0 |
0 |
|
IMA |
Infinity |
|
|
105.366 |
|
|
Comment
All the designs may be pushed to F:8 and field expanded to 0.7 degrees over a 100 mm linear field. Some are more suitable but all are useful.
If the primary is left at F:3.5 the obscuration increases noticeably and secondary aspheric deviation increases slightly.
For a photographic instrument the F:3.5 primary may be quite acceptable.
If the primary is deepened somewhat, obscuration is reduced at the expense of noticeably harder to fabricate aspherics.
Caveat
There may be errors present. Take care.
GOTO TOP
GOTO INDEX