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# DK derivative (thinking outside of the square)

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### #1 clivemilne

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Posted 12 August 2017 - 10:28 PM

I am inclined to put up for discussion my thoughts on a type of catadioptric based on the basic DK configuration.

The goal: Create an instrument optimized for visual (deep sky) which delivers the best experience using the available
degrees of freedom to that end.

Constraints:
Feet on the ground.
Maximum (sensible) aperture; probably 32" or there abouts.

Let's up the ante and make it a binocular instrument.

In my experience (using a pair of 20" binoculars) I found that 95% of my time was spent with a 3mm exit pupil.
If one is prepared to release the constraint of achieving larger exit pupils, the system f/d can be relaxed to f10.

If we assume that we will be using a sub aperture corrector to tidy up field aberrations, why not release the
constraint of achieving a specific aspheric on the primary. The optician is then free to concentrate on producing
a smooth figure of revolution with the residual SA being corrected by the lens assembly after measuring the Z
of the primary upon its completion... in this case, who cares if we miss the target Z by a couple of percent?

Incidentally, one aspect of the DK design which few people are aware of is that the coma penalty is pretty much
all in the choice of the primary f/d, and not significantly influenced by the overall system f/d. Ergo, if we slow
the primary down to f/5, the aberrations become much better behaved. Whilst there is no such thing as an easy 32"
optic, an f5 Z=-0.6 would be a doddle compared to f3 Z=-1, especially if you didn't have to nail the exact Z directly

Now, let's try and visualize the layout...
Separation between primary and secondary would be a little over 110" using an 8" (spherical) secondary, with the
focal plane 30" above the primary. If we chew up 24" of bfd folding the lightpath out the side of the tube assembly,
the eyepieces will be located something like 60" up the ota (away from the primary) So it would be a similar
observing position as you might expect to deal with as a 32" f2-ish Newtonian... give or take.

Choice of eyepiece(s):
Why not use something simple like a 5 element Masuyama, 32mm 84 degree?
Use the degrees of freedom in the field corrector to compensate for its field curvature and astigmatism.

Sure, it would be a bit of a one trick pony, but I think could live with that.

fwiw) Magnification would be 254x with a field of 20 arc minutes @ f/10 and 3.2mm exit pupil.

Anyway it would be one heck of a visual instrument.

best
~c

Edited by clivemilne, 12 August 2017 - 10:33 PM.

### #2 Mike I. Jones

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Posted 12 August 2017 - 11:55 PM

First-order Cass calculations (no corrector):

32" f/5 = 160" focal length "f"

Proposed separation = 110"

Secondary distance inside focus = 160 - 110 = 50"

Amplification A = 2

b = distance from primary vertex to Cass focus

p = (f+b) / (A+1), b = p(A+1) - f = 50(2+1) - 160 = -10"

So DK focus is 10" above primary vertex.

p' = pA = 50 x 2 = 100"

Rs = 2pp' / (p'-p) = 200"

Assume field width d = 1.5"

Sec diam = (D-d)p'/fA + d = (32-1.5)100/(160Ã—2) + 1.5 = 11.03", meaning you'll need an 11" diameter secondary.

Placing focus 24" from axis puts the foldout diagonal center 76" from secondary, 34" above primary vertex.

Mike

### #3 Mike I. Jones

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Posted 13 August 2017 - 02:39 PM

Here's a configuration to consider.  32" f/5 primary, f/10 overall.  The corrector lenses would need to be custom-made, COTS lenses don't work here.  Zemax and OSLO files attached.

### #4 Mike I. Jones

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Posted 13 August 2017 - 02:40 PM

Layout drawing for 32" f/10 CDK.  25" from the optical axis to the focal plane.  The corrector lenses and diagonal would presumably all be mounted in a common cell, with the diagonal being adjustable in tilt.  It would take 2 sets of spiders for this, one to hold the secondary and baffle, and the other to hold the primary baffle and corrector/mirror assembly.  The vanes would need to be aligned to each other to minimize additional diffraction.

### #5 Mike I. Jones

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Posted 13 August 2017 - 02:42 PM

Spot diagrams and shaded drawing for 32" f/10 CDK.  Note the UV to NIR spectral correction over a full-frame 35mm, right to the corners.

I put in baffle tubes and black spots on the primary and secondary to help cut down on stray light.  You can see the primary spot in the plot.

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### #6 Arjan

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Posted 13 August 2017 - 07:29 PM

So where is the catch?
If you relax tolerance on the primary, doesn't it mean you need to make the corrector to high precision?

### #7 clivemilne

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Posted 13 August 2017 - 08:14 PM

That's very impressive Mike, I greatly appreciate the time you put in there.

Spherical primary anywhere from f/3 to f/6... I guess that would make it a Pressman-Carmichael derivative.

System f/d must be f12 or faster

Diameter 32"

bfd can float freely but focal plane must be accessible.

focal plane does not need to be flat (within reason)

some field aberrations are tolerable (within reason)

Secondary can be a two element mangin using common glass.

bonus points if complimentary radii can be found such that concave surfaces can be used as test plates for convex surfaces in the design (as per Houghton)

sub aperture components can employ concave surfaces with a mild aspheric (within reason)

additional lens elements can be used as field correctors near the focal plane.

I'd be curious to see if a practicable design is in there somewhere...

best
~c

### #8 Mike I. Jones

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Posted 13 August 2017 - 08:14 PM

As this is a single telescope build and not a production system, the design would be re-optimized as components are finished, using as-fabbed values.  The order to do these four elements are:

1. Finish the secondary as closely as possible to the spec radius, while achieving a very smooth sphere.  Measure and record the finished radius value.

2. Re-optimize the system using this exact secondary radius.

3. Finish the primary to the re-optimized vertex radius plus a small additional value to account for deepening to the conic.  Figure to the new conic constant value while monitoring the vertex radius.  The value of the primary conic constant is a function of the vertex radius, which is why to make the spherical secondary first, and tailor the primary to it.  The goal is to hit the primary vertex radius and re-optimized conic at the same time.  Measure and record the final vertex and conic constant.

4. Re-optimize the system using the finished secondary and primary values.

5. At this point the lens radii and thicknesses have been re-optimized and are ready for manufacturing by an optical shop (unless Clive makes them).  The radius, thickness, wedge and diameter tolerances for the nominal system lenses will not have changed appreciably, but the optical shop (or Clive) will make them to the final optimized values, not the nominal values.

6.  When all four elements are finished and real values are known for all parameters, one last optimization is performed on all the airspaces (the only remaining possible variables).

Mike

PS: Where in West Oz are you?  Perth or thereabouts?  Oz is on our bucket list for sure.

### #9 clivemilne

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Posted 13 August 2017 - 08:25 PM

So where is the catch?
If you relax tolerance on the primary, doesn't it mean you need to make the corrector to high precision?

Just to be clear, the tolerance pertains to the value of the aspheric not the accuracy of the aspheric.

Think of the Hubble telescope when it was first put up. It was figured fantastically accurately, but just
to the wrong strength of correction. It has been brought back to the diffraction limit using a corrector
at the focal plane.... Point being; if you accept that you will be employing a corrector as a priori,
the degree of spherical aberration it needs to correct can be dialed in AFTER the primary has been finished.
This is what makes it a catadioptric... realeasing the constraint that the mirrors have a native focal plane
that must correct for all the SA in the system.

### #10 clivemilne

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Posted 13 August 2017 - 08:39 PM

As this is a single telescope build and not a production system, the design would be re-optimized as components are finished, using as-fabbed values.  The order to do these four elements are:
1. Finish the secondary as closely as possible to the spec radius, while achieving a very smooth sphere.  Measure and record the finished radius value.
2. Re-optimize the system using this exact secondary radius.
3. Finish the primary to the re-optimized vertex radius plus a small additional value to account for deepening to the conic.  Figure to the new conic constant value while monitoring the vertex radius.  The value of the primary conic constant is a function of the vertex radius, which is why to make the spherical secondary first, and tailor the primary to it.  The goal is to hit the primary vertex radius and re-optimized conic at the same time.  Measure and record the final vertex and conic constant.
4. Re-optimize the system using the finished secondary and primary values.
5. At this point the lens radii and thicknesses have been re-optimized and are ready for manufacturing by an optical shop (unless Clive makes them).  The radius, thickness, wedge and diameter tolerances for the nominal system lenses will not have changed appreciably, but the optical shop (or Clive) will make them to the final optimized values, not the nominal values.
6.  When all four elements are finished and real values are known for all parameters, one last optimization is performed on all the airspaces (the only remaining possible variables).

Mike
PS: Where in West Oz are you?  Perth or thereabouts?  Oz is on our bucket list for sure.

Hi Mike,

Yes,
Perth.... we are probably going to be moving at the end of the year, however.

### #11 Mike I. Jones

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Posted 13 August 2017 - 08:59 PM

A Pressman-Camichel scope has an oblate spheroidal secondary.  This means that the instantaneous radius of curvature shortens from center to edge, rather than lengthening like a prolate spheroid, paraboloid or hyperboloid.  I've not made one but estimate that it would be a booger to make to spec and be smooth and zone-free.  Maybe I'm being too pessimistic.  I'll give it a look sometime soon.

What do I get for "bonus points"?

### #12 clivemilne

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Posted 13 August 2017 - 09:21 PM

A Pressman-Camichel scope has an oblate spheroidal secondary. This means that the instantaneous radius of curvature shortens from center to edge, rather than lengthening like a prolate spheroid, paraboloid or hyperboloid. I've not made one but estimate that it would be a booger to make to spec and be smooth and zone-free. Maybe I'm being too pessimistic. I'll give it a look sometime soon.

Yeah, nah... I may consider a convex oblate spheroid if I ever get bored hitting my thumb with a hammer..

What do I get for "bonus points"?

As much time at the eyepiece as you could conceivably want..

Edited by clivemilne, 13 August 2017 - 09:48 PM.

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### #13 clivemilne

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Posted 13 August 2017 - 09:30 PM

Incidentally, when you plan the trip, be careful to understand that Oz is not a small country.

Most people seriously under estimate the distances between places.

A year or so ago a gentleman from Texas came over and had planned a sight seeing journey over the course of 14 days
in a hire car... until I pointed out to him that this would entail eight thousand miles of (mostly) driving through
desert.

Be sure to put the Flinder's ranges on the list of places to go (but not in summer)

Amongst the best skies in the world there...
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### #14 Arjan

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Posted 14 August 2017 - 08:22 AM

Just to be clear, the tolerance pertains to the value of the aspheric not the accuracy of the aspheric.

Clive,
Yes, that's what I meant to say. I am in the process of building a CDK myself, but chose to use off the shelf corrector lenses. The primary needs to be made to fairly tight tolerance (RoC and conic values) but this seemed to me easier than making a precise corrector.
Are you planning to actually start this project?

... Arjan

### #15 clivemilne

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Posted 14 August 2017 - 06:55 PM

Clive,
Yes, that's what I meant to say. I am in the process of building a CDK myself, but chose to use off the shelf corrector lenses. The primary needs to be made to fairly tight tolerance (RoC and conic values) but this seemed to me easier than making a precise corrector.

Arjan,
If you use off the shelf correctors, then you lose the freedom in prescription of the primary.

I guess the point of this exercise was to demonstrate the penalty imposed by stipulating a cassegrain
focus in the traditional position. It demands that the primary is fast (~f3) and the secondary baffle is large (~40%)
The mechanical tolerance on the correcting elements also becomes tight.

By allowing the focal plane to shift up the OTA, the performance increases and it becomes a lot easier to build.
The field lenses are simple enough and would add less cost (even if you had them custom made) than what you would
save by reducing the size of the secondary mirror.

Incidentally, if you look at Mike's f10 version, it should be obvious that if one was to allow the focal plane to
be placed further up the OTA, the final focal ratio could be reduced to around f7.5 or f8 without much of a penalty.
As I intimated earlier, with DK's, the poison is all in the speed of the primary.

One further point... the one penalty that you do have to wear by reducing the magnification ratio of the secondary
is that the aspheric on the primary increases proportionately.

As you approach 1:1, the system becomes a Newtonian so by definition, z=-1

best
~c

### #16 clivemilne

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Posted 15 August 2017 - 06:16 AM

Are you planning to actually start this project?

... Arjan

One day.

But I have a tube assembly for a 22" RC, a pair of 20" bino's to rebuild and a large aperture helioscope to finish before I take on anything else.

I did have a 32" blank sent over to Australia for this project quite some time ago but the optician turned out to be fraudulently dishonest and mentally ill, if you were to judge him by his actions..

This is going back 15 years with Dave Rowe & Peter John Smith doing the design work at the time. (both Dave and Peter are stand up guys, let's be clear)

Edited by clivemilne, 15 August 2017 - 07:16 AM.

### #17 Arjan

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Posted 15 August 2017 - 09:59 AM

Are you planning to actually start this project?

One day.

I see you have too much to do and too little time, sounds familiar...

Don't know about you, but I'm still in working life, cuts the available time even more.

Where are you moving in Australia? I just returned from Thailand, that's halfway to Oz, but this is still on the bucket list. Maybe I get there for work first...

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