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Tolerance on DK Cass secondary radius

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#1 Mike I. Jones

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Posted 03 February 2013 - 12:35 AM

There are several good current ongoing discussions about Cassegrains, and about Dall-Kirkhams in particular. A recurring theme is the looser tolerances for a DK than for Cassegrains with non-spherical secondaries. Rather than these posts getting lost far down in long threads, I chose to start a new thread, showing how much more forgiving a DK secondary is to being a little off in radius from nominal design, if the spacing between mirrors is allowed to vary.

A 12.5" DK with an f/4 primary, f/15 overall, 10" BWD and 1.5" unvignetted field was chosen as the nominal system for study. The nominal system prescription is shown in this first figure.

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#2 Mike I. Jones

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Posted 03 February 2013 - 12:38 AM

Next, I created a nine-position multi-configuration version of the 12.5" DK that varied the secondary radius of curvature from the nominal value over a ± 2 inch range, in 1/2" increments. The mirror separation was allowed to individually vary across the nine configurations. The BWD was held to 10" for all configurations, and the primary conic was constant for all, that being the value for the nominal design. I optimized the multi-configuration system, then wrote a simple macro in Zemax to list the secondary radius, the delta Rs, system EFL and f/#, mirror spacing, P-V and RMS wavefront errors, and finally Strehl ratio for each configuration. This created a tolerance table, shown in the figure, with the nominal system highlighted in pale yellow.

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#3 Mike I. Jones

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Posted 03 February 2013 - 12:39 AM

Plots of the variation in system EFL and mirror separation are shown in this figure. As the secondary radius is made longer (flatter) than nominal, the system EFL and optimum mirror spacing are seen to decrease.

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#4 Mike I. Jones

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Posted 03 February 2013 - 12:41 AM

Variation in wavefront error (WFE) peak-to-valley and RMS values versus delta secondary radius are shown here. The Strehl ratio is also plotted on the secondary axis.

The immediate thing to notice is how much the DK secondary mirror radius can vary while producing very little impact on system P-V and RMS wavefront error. And this is even with the back working distance (BWD) being held constant and only the mirror spacing changing.

Also notice that the Strehl ratio remains very high over this large range in secondary radius, never dropping below 0.99 over the range.

Bottom line is: one could build this DK and be off on the secondary radius by as much as 2" either way. As long as the secondary mirror is truly a smooth, zone-free sphere, and the mirrors were spaced properly, absolutely no change in system performance would be visible under any kind of operational environment.

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#5 Mike I. Jones

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Posted 03 February 2013 - 12:58 AM

and finally, here's the OSLO-EDU file for this particular DK Cassegrain.

I tire of reading baseless, subjective posts here saying "I think that...etc. ... something happens this or that blah blah" about the behavior of complicated optical systems in general. Rather than qualitative, useless pontification, I encourage all to directly do the same kind of hands-on tolerance analysis similar to what I have shown here. Vary system parameters in question, re-optimize things that can be sensibly changed in a real design, tabulate the results, and plot them up! This is real science, directly applicable to an ongoing optical project, and not unresearched guesswork or inexperienced intuition.

Mike

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#6 siriusandthepup

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Posted 03 February 2013 - 01:35 AM

Wow Mike,

That tolerance analysis is a beautiful beautiful thing.

I do not currently have the skills to do such work. I haven't been very effective with conveying just how insensitive my 25" wsDK project is to secondary radius.

Any chance you might have the time to show what the Strehl variance looks like with a secondary radius variance of +- 10" on my project scope?

Thanks and again those charts are beautiful!

#7 Mike I. Jones

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Posted 03 February 2013 - 01:50 AM

Sure, glad to help. But it looked to me like you're beginning to get the hang of OSLO-EDU, and with that and Excel, you already have the tools to do tolerancing, you just need the practice. Change your secondary radius a little, use OSLO sliders to tweak the mirror spacing and re-establish on-axis wavefront error, write down what you see, and plot the results. I guarantee you'll get better at OSLO, and fast! But I'll still be glad to help, and give you what I get to compare to. Post up your prescription or the OSLO file so I have something to work with.
Mike

#8 siriusandthepup

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Posted 03 February 2013 - 02:06 AM

Thanks Mike,

I downloaded OSLO two days ago, but as yet, I have not opened it. I did down load your file so I will have something good to initially try out. Maybe I can plug my parameters into your file in OSLO and then see what happens. I'll see how it goes and report back tomorrow.

thanks,

#9 MKV

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Posted 03 February 2013 - 11:01 AM

Ed, I just used sliders to radically altered your design in OSLO to read as follows (your original values are in parentheses):

Primary rad. of curv. = -240.93695 (-246)
Secondary rad. of. curv. = -173.876894 (-183.446)

mirror separation = -84.07 (-87.07)

primary conic = -0.694020 (-0.70402)
secondary conic = -0.300 (0)

Unless I made another silly mistake :), even as radical as this alteration is, the system is still fully corrected and diffraction limited over an FOV of 0.06 degrees (about 0.214 inches) in diameter. So, even assuming large production deviations from your theoretical prescription, the system can still be optimized by refiguring or respacing.

It seems that no matter what kind of alterations you enter, or a number of them, the system can be brought back to correction, often simply by no more than respacing the mirrors.

There is also another parameter, refocusing, which is helpful for minor alterations, so not other parameter has to be changed.

Mladen

#10 siriusandthepup

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Posted 03 February 2013 - 11:13 AM

HahHahHah,

OSLO EDU has soundly and thoroughly kicked my backside. I have been unable to enter my data properly for my existing prescription - even with your file for a template - how sad is that?

My initial foray into OSLO was an utter failure. I really don't understand the "thickness" conventions well enough to accomplish anything useful at this time. The vast array of commands doesn't help either. The OSLO EDU internal help files reminds me of the Linux Man files. The thing is though - the OSLO help files make the Linux Man files look like kindergarten work. This is gonna take me a few years...

Mike here is my DK data. Mladen has pointed correctly that the sign is wrong on the radius/fl of the primary. That was my mistake way back when. I will eventually rework my spreadsheet to fix that.

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#11 siriusandthepup

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Posted 03 February 2013 - 11:46 AM

It seems that no matter what kind of alterations you enter, or a number of them, the system can be brought back to correction, often simply by no more than respacing the mirrors.

Mladen


Mladen, That is exactly the message I have been trying to convey (poorly)to everyone in the wsDK thread. Mike is wizard with the tolerancing analysis and if I had had his expertise with OSLO back in my early design days it would have saved me hundreds of hours of spreadsheet crunching and ATMOS spot diagrams to learn about the benefits of the wsDK variant. His tolerancing charts are exactly what you need to evaluate a design's sensitivties.

thanks,

#12 MKV

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Posted 03 February 2013 - 12:27 PM

Ed, the "thickness" category in OSLO is simply the distance to the next surface, including the focal surface.

below are the two configurations I mentioned ealrier. The upper one is your original and the one below is the vastly altered congfiguration (which could have easily been tweaked even further).

You can start by entering those numbers in your OSLO and compare the results you get. Just remember that almost every category on the screen has more sub-categories if your right click on them.

It's not a tolerance study like Mike did, but it simply shows that if, after grinding and figuring your optical components are not exactly as the designed on paper, the system can be adjusted fairly easily to optimize the performance. Which is exactly what you have been saying all along. This just illustrates that even a sloppily made DK can be made to work at optimum performance.

Good luck!

Mladen

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#13 siriusandthepup

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Posted 03 February 2013 - 01:06 PM

Mladen,

I have all the data entered into the surface data exactly as you do in "Ed's Original". Problems: I don't have the cc -.704 showing on mine and the draw doesn't show the beam coming from the secondary to the focal plane. It only shows the light lines from the primary to the secondary. What is my problem?
Oh - I don't have an "A" in the special block either. I right clicked the box and found the Polynomial Asphere (A) with a dozen subcategories but couldn't seem to get an "A" to fill the box??

Here's the file as i have it so far take a look for me please.

Thanks,
Ed

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#14 MKV

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Posted 03 February 2013 - 05:04 PM

Ok, Ed:
FIRST thing you ought to do is click on "Gen" in your "Surface data window" and change mm to inches. Otherwise your results will be off.

Now
1. click on "Lens" (in the upper left corner).
2. "Lens Drawing Conditions" (bottom)
3. "Final Dist"
4. "Imag srf"
5. Click on the "checkmark" to close.

You should see the rays coming to a focus. In that same lens Drawing Conditions, you cna change the number of rays (under "Rays") if you want more than three.

1. Now, click on "Special"
2. Polynomial Asphere (A) - hint "A"!
3. "Conic/Toric"
4. Enter -0.70402
5. click "checkmark" to close

By now, you should see the "A" in your special box

Look at your TW1 (text) window 1 (lower lewft)
1. Click on "Spe"
2. You should see "Conic and Polynomial aspheric data" reading 7.0402e-01

OSLO normally doesn't display special data. Perhaps there is a ccl that allows the program to show the special data but I am not aware of it. I always add it so that readers know what that A means.

Now click on your GW1 (graphics) window 1.
1. Clicko on the icon that looks like a starburst
2. You should see spot diagrams
3. Right click the window and pick "Re-calculate using new parameters"
4. Click on show airy disk

You should now see images with Airy disc showing as a circle

Click on "Filed Angle" in Surface date to 0.03 degrees then update the spot diagram by clicking the "starburst" icon again. You should see some coma off axis.

This should give you an idea how this works, but you will have to learn this yourself. There is an OSLO online manual you can download, there are instructional videos and articles. Experiment, try different fields, see what happens, or look for answers online. That's how I learned. Good luck.

Mladen

#15 siriusandthepup

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Posted 03 February 2013 - 06:58 PM

WooHoo!!

Thanks Mladen for your tutorial. I now have spots and Airy disks! Awesomeness...

#16 Mike I. Jones

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Posted 03 February 2013 - 07:23 PM

Ed - your numbers model fine, but do you really intend the fully illuminated field diameter to only be 0.75", or is it supposed to be a DIAMETER of 1.5"?

#17 siriusandthepup

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Posted 03 February 2013 - 07:33 PM

Mike,

My experience is mainly visual. To me 0.75" fully illuminated field is fine for my low power viewing needs. I don't spend much time at lower mags anyway. My thinking was that 0.75" was ok if I decide to do a little rookie level ccd work too and stack short images.

I would acknowledge that a larger fully illuminated field is appropriate for more serious photo work. It would not require very much larger secondary and tertiary to accommodate that aspect. I would defer to your judgement on what would be appropriate for that.

#18 Mike I. Jones

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Posted 04 February 2013 - 01:13 AM

OK - secondary radius tolerancing done, with results you will like. First, the prescription and tolerance table.

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#19 Mike I. Jones

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Posted 04 February 2013 - 01:14 AM

Next, the peak-to-valley and RMS OPD plots, and Strehl ratio on the secondary axis. Notice that by re-spacing the mirrors, the telescope remains essentially perfect.

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#20 Mike I. Jones

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Posted 04 February 2013 - 01:16 AM

Here are the variations in mirror separation and system EFL as the secondary radius is varied from 10" too steep to 10" too flat, and mirror spacing re-optimized for each value.
Mike

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#21 siriusandthepup

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Posted 04 February 2013 - 04:20 AM

OK - secondary radius tolerancing done, with results you will like. First, the prescription and tolerance table.


I just love it!

Mike, stunningly beautiful work! That tells the story way better than my puny words can express. This insensitivity of primary to secondary matching is a key benefit of the wsDK. The targets are wide, and figuring primary and secondary together is not required for success; as it usually is in construction of a traditional DK optic set.

Care in figuring to smooth and zone free high tolerance is still needed of course so as not to impact the high system design Strehl capability. Actual Strehl will be determined by how well the optics are executed naturally.

I notice too that system Strehl remains above 0.999 from plus or minus 6" deviation on target secondary radius. That is plus or minus 3" on the secondary test plate focal length. That's not too hard a target to hit: from 88.7" to 94.7" on the test plate fl.

Thank you! Thank you :bow:

#22 Mike I. Jones

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Posted 04 February 2013 - 06:17 AM

You are most welcome! Now let's start wrangling them photons through the chute!

The low secondary amplification and resulting long ROC is indeed the reason for the loose radius tolerance. The limiting case is, of course, a flat secondary mirror!

Notice the asymmetry of the WFE curves going from too steep to too flat. They suggest that it is slightly better to err from nominal toward a longer rather than shorter radius, if you can stand the shorter system EFL.

Notice also that I pulled your foldout tertiary mirror away from your secondary by 3", reducing the path to focus from 28" to 25". I don't know if you were aware of it, but your tertiary was blocking a large lune of light headed from the lower side of the primary to the secondary.

Jus' sayin,
Mike

#23 siriusandthepup

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Posted 04 February 2013 - 10:44 AM

The low secondary amplification and resulting long ROC is indeed the reason for the loose radius tolerance. The limiting case is, of course, a flat secondary mirror!

Notice the asymmetry of the WFE curves going from too steep to too flat. They suggest that it is slightly better to err from nominal toward a longer rather than shorter radius, if you can stand the shorter system EFL.

Notice also that I pulled your foldout tertiary mirror away from your secondary by 3", reducing the path to focus from 28" to 25". I don't know if you were aware of it, but your tertiary was blocking a large lune of light headed from the lower side of the primary to the secondary.

Jus' sayin,
Mike


Mike,

In many ways the wsDK is more like a folded Newt than a traditional DK, without the drawback of the super sized secondary.

I did do a full size drawing of the optical layout and specifically made sure that the tertiary was completely hiding in the secondary shadow and that the light cone from the primary did not get vignetted. The full size drawing lets me see/design the largest/longest baffles I can get away with. The tertiary baffle will come very close to the primary light beam, but not intrude. On my spreadsheet I'm running a 3.5" tertiary and the distance from the flat to the focal plane is 17" - I am going to move the tertiary back to where I had it originally I think, which was 3" higher which will allow the focal plane to extend 6" from the side of the OTA. That is to accommodate binoviewing and an Ed Jones coma corrector. At this location the tertiary will be 20" from the focal plane. Again - 3.5" diagonal size. I am not sure where the 28" number came from, but it would require a 4" diagonal to intercept the light cone at that point, and in turn you are correct that the light from the primary would suffer vignetting.

Regarding the asymmetry - absolutely correct. I did run many scenarios and there is a mathematical non-linearity which kicks in on that side and causes things to begin to change quickly. I tried to give myself a little room from that side, while still giving me the the 8 to 8.3 F ratio I wanted. If this one was being designed for photo applications then you would want to go to that side for the faster F ratio and the flatter part of the curve. Any time you design a wsDK you should analyze where the "non-linearity" starts kicking in and move away from it some to the flatter part of the curve. This is the spot that gives you the most leeway on your as-built tolerances.

Thanks again for the wonderful charts and graphs,






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