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Copyright
– P. J. Smith
But permission is
given to distribute this material in unaltered form as long as it is not sold
for profit.
An
F:10 One metre Photo Visual Cassegrain.
by
Peter John Smith.
A description of a 'no holds barred' very large Cassegrain
Rationale
This telescope will be a very real challenge. To deliver its potential performance, fabrication will push the ATM fraternity to its limit.
No apology is given for its very difficult optics.
Looking at the amateur revolution in very large telescopes evident today, the author has concluded there is now a core of ATM,s who have skills equal to yesteryear's celebrated opticians.
If very advanced amateurs are tackling 60 inch Newtonians, I feel they should at least know the optical performance available from the very best field corrected Ritchey Chretien Cassegrain.
It uses a field correcting achromat and two hyperboloid mirrors which have frightened amateurs away in the past. One is very deep. The achromat was chosen because it allowed good correction but eliminates extra air/glass surfaces arising from the use of a more complex corrector.
The basic Ritchey Chretien Cassegrain has good performance. But, coupled with a purpose designed field correcting lens, its performance becomes outstanding. The field corrector is almost trivial as a construction task compared to the main mirrors but is the key to sparking performance.
I suspect few ATM's would consider this form of telescope as they are not aware of its potential performance. Their latent talent has usually targeted the traditional Newtonian telescope in very large sizes.
If, after rational examination of the design and an honest self assessment of fabrication skills, builders opt for a Newtonian, I must certainly respect their judgement. In fact, I would insist that no one tackle such a difficult project without a realistic appreciation of the pitfalls.
But it would be sad to see very advanced ATM,s make their choice lacking knowledge of the potential of a design such as this.
Target
criteria
1. Visual quality must be superb over the full field covered by an eyepiece.
2. Spots must be under the accepted 25 micron film criterion across the entire field.
3. Image must be flat across a 5 X 4 film holder.
4. Secondary obscuration must be no more than 25 % for very good visual performance. (Unbaffled)
5. Minimum of glass air surfaces.
6. The highly corrected field must be achieved without a full diameter corrector.
7. The design must deliver a comfortable and safe observing position. Thus the field correcting lens must be in a position which allows it to fold out of the primary light path
No restrictions were placed on the primary and secondary mirror shapes. It was accepted the much harder to fabricate hyperboloids found in a Ritchey Chretien would not be ruled out. In the past, amateurs have distanced themselves from this family of telescopes. This is understandable. But the primary is not too far removed from a paraboloid and a large Cessegrain secondary is a difficult task in any case.
Basic
Description
Focal length = 10 m. Diameter = 1 m.
System F:NO = 10 Primary F:NO = 2.5
NOTE - The top of the drawing simply represents the end of the telescope tube and is not a corrector plate.
The sheer size of this telescope precludes a Newtonian viewing position. The observer would be at least 30 feet high balancing precariously on a dew covered slippery ladder.
Obviously, the fold mirror is well placed to divert rays through the altitude axis of a large Alt-Azimuth mount. Undoubtedly, it will be of driven Dobsonian form.
The field corrector is a large achromat of the ubiquitous glass types BK7 and F2. It is positioned about two inches in front of the image plane.
If necessary, additional correction can be obtained by making the first concave surface aspheric. This would not be too difficult to fabricate. Fortunately, very high performance can be achieved without this complication. If difficulty is encountered when final figuring on star tests, this surface can be aspherised with advantage.
The design delivers an absolutely flat 140 mm. (5.5 inch) field about 2 inches behind the field correcting lens. This should be sufficient distance to throw out of focus any dust on the correcting lens. To maintain this distance at the design length, a simple 'prefocus' adjustment will be necessary in conjunction with a distance setting piece.
The delivered image size will fully cover a 5 X 4 filmholder with the exception of a very small 5 mm triangle in each corner.
Since a Barlow lens is unlikely to be used with this telescope, no extra space should be needed between image and correcting achromat.
Optical Prescription
The correcting lens is an achromat made of very common optical glasses. While most ATM's do not make lenses there is nothing particularly difficult about their construction. Surface accuracy can be relaxed to 1/4 of that required of the mirrors. In common ATM language, a 1/4 wave accuracy is sufficient.
The two mirrors are aspheric. Both are hyperboloids. The conic constants are given as Schwarzschild Constants as is usual in most optical work. The primary mirror is quite close to a paraboloid and will not be too far removed from the experience of an advanced ATM.
Primary
mirror deviations from spherical are given for figuring.
The Y coordinate is measured outwards from the optical axis towards the mirror edge.
The secondary will tax the ingenuity of any optician. Since the performance on axis could reach 1/40 wave RMS, both mirrors should be of exceptional accuracy.
Secondary
mirror deviations from spherical are given for figuring.
Optical
Performance
The performance capable from this design is probably best summed up by considering the Strehl Ratio at different field positions.
On axis, the Strehl value is about 0.98. This represents an exceptional performance.
At no point does it fall below 0.9 so performance can very comfortably be called diffraction limited.
The Strehl ratio is calculated based on a weighted average wavefront error at different wavelengths. These have been chosen to reflect the sensitivity of the eye to brighter objects as indicated in the table.
Through focus wavefront errors at
various field angles.
The solid lines represent angular fields of 0 and 0.4 degrees off axis.
Dotted lines are intermediate fields at 0.1, 0.2 and 0.3 degrees off axis.
The performance is obviously well below the diffraction limit across the entire field.
RMS spot sizes through focus at various field angles.
The field is obviously very flat.
Film placement will not be too critical at the system F:NO of 10.
Taking 25 microns as a reasonable spot diameter for film, it is evident that depth of focus should range over about 0.8 mm. before any degradation occurs in the recorded film image.
Field curvature and distortion with corresponding spot diagrams
While the previous information defines performance in a far more meaningful way, these spot diagrams certainly give one a warm feeling.
Field curvature and distortion plots again emphasise the flat field covering about 5.5 inches.
This makes it suitable for standard 5 X 4 inch film holders.
Aperture obscuration and
Modulation Transfer Function.
An MTF plot is probably the best indicator of performance on extended objects such as the moon and planets.
This shows the loss of contrast at different spatial frequencies relating directly to film resolution.
It is immediately evident that :-
(a) Performance is extremely close to the best theoretical limit for a telescope with 25%obscuration.
(b) The larger obscuration has some effect on performance.
Two things should be considered very carefully with respect to these figures. Firstly, large Cassegrains often have 30% or more obscuration. 15% is only just detectable by experienced observers.
Newtonians seldom have less than 15% and often more than 20% obscuration.
Radius
Tolerances
Obviously, form tolerances on all the surfaces must be tight.
Final figuring will most likely be done on star test data on the secondary surface.
But, for this final figuring to realise design performance, the curvature of each other surface must be within acceptable tolerance. Slight variations will then simply be taken care of by figuring and slightly varying the secondary to corrector distance.
It is suggested these tolerances not be an excuse for poor workmanship. They will, however, help an ATM realistically assess the difficulty of construction.
Primary - Ideally within 5 mm of design radius. Absolute maximum is 10 mm deviation.
Secondary - Ideally within 5 mm of design radius. Absolute maximum is 15 mm deviation.
The tolerances given below assume the corrector to film distance is maintained and final figuring occurs on the secondary mirror. In conjunction with figuring, the distance from secondary to primary will vary for optimum performance.
It may be difficult to hold the primary to radius tolerance. If this is impossible the most sensible strategy is to make the primary as close to tolerance as possible and recalculate the secondary curvature and figure.
If only the secondary is recalculated the primary may vary by 20 mm.
If both secondary and correcting lens are redesigned it is not impossible to compensate for a 50 mm error in the primary radius of curvature.
Baffling
I have absolutely no experience in baffling a Cassegrain and am a little surprised at what a balancing act it is.
While different people will no doubt have different priorities, the dimensions given should be a good starting point. The front baffle represents an attempt at keeping obscuration to no more than 26 %.
If the centre baffle is made so R = 70 mm, vignetting begins at about 0.1 degrees. This does not shade all skylight as the diagram shows. Only the very centre of the field is completely baffled. Whether the result is acceptable will probably depend on the application.
On the other hand, if R = 65 mm, baffling is almost complete. The only portion accepting skylight is the very edge of the film.
Both vignetting plots are given.
The plots never reach more than about 92 %. This is the result of the obscuration by the secondary mirror and can not be avoided.
Before passing judgment on the amount of vignetting, it may be worth comparing with other designs. Many are far worse.
It may be possible to make the telescope with interchangeable baffle disks so the user can select the most appropriate compromise for the work at hand.
Eyepieces
It is intended to design a Magnum eyepiece specifically for this telescope. But with a system F:NO of 10 good quality commercial ones should work very well.
Caveat
I believe the original design criteria have been met.
No real originality is claimed for this telescope as all principles are well known. The specific design, however, has not been copied from anywhere. I claim no patent etc for it (I would think this is impossible anyway) and would be willing to help anyone who is serious finetune the design to the vagrancies of construction constraints if needed.
Finally, I cannot guarantee the design to be totally error free but would appreciate confirmation of possible errors or lack of by anyone willing to do some design checking.
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