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C11 Light Path and Light Cone

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#1 MarMax

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Posted 03 March 2021 - 09:39 PM

So I started by searching up a bunch of info regarding the C11 and light cone drawings. Did not find exactly what I was looking for so I tried to draw it up based on measurements of my CPC 1100. The measurements are not perfect but close enough to a first try, maybe +- 5 mm. And I did not draw the complete outside of the OTA for simplicity. The shape of the mirrors is just a guess and only serves to get a rough idea on light path length.

 

gallery_332504_14303_53403.jpg

 

Adding up the physical light path I get 43.4 + 44.56 + 74.1 = 162.06 (1621mm). And I added 20cm (200mm) after the edge of the baffle tube lock ring for backfocus. In this C11 Light Path thread it's explained the that the primary mirror has a 2x magnification and the secondary has 5x magnification. So basically 2x5x280 = 2800. But there has to be a way to use a drawing to show the magnified light path dimensions.

 

Can someone explain how the magnification factors adjust the physical dimensions? 



#2 photoracer18

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Posted 03 March 2021 - 09:53 PM

 In all catadioptric systems with primary mirror focusing the focal length varies by the distance between the primary and secondary mirrors. I think it gets longer the closer they get.



#3 jimhoward999

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Posted 03 March 2021 - 11:14 PM

The Primary is F/2.5.  Its aperture is 280mm and its focal length is 700mm.  I think those figures are known,

 

The secondary is indeed 5X converting the F/2.5 primary to the F/10 final F/#.   The distance from the secondary to the final image is 741mm per your diagram.    Since the secondary is nominally operating at 5X, the focus of the primary mirror must lie 741/5X= 148mm behind the secondary.   That means the vertex separation between the primary and secondary must be about 700mm - 148mm = 552mm.     But per your diagram it isn't.  So something is a little wrong in the diagram.

 

(Primary focal length (700mm) - Primary-to-secondary separation ) x 5 = secondary to final image distance

 

So either the secondary-to-image distance is a little longer than you measured, or the primary-to-secondary distance is a little more than you measured.  



#4 jimhoward999

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Posted 04 March 2021 - 12:48 AM

Oops.   My math is wrong....sorry.

 

the primary is f/2 not f/2.5.   So it’s focal length is 560mm.   The vertex separation from primary to secondary must be about 560-148 = 412mm.



#5 MarMax

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Posted 04 March 2021 - 02:22 AM

Oops.   My math is wrong....sorry.

 

the primary is f/2 not f/2.5.   So it’s focal length is 560mm.   The vertex separation from primary to secondary must be about 560-148 = 412mm.

If the 741 (secondary to focal point distance) seems about right and the primary to secondary separation calculates out to 412, which makes sense, the corrector to primary distance would be about 401. 

 

Edited to say I played with the numbers and I still do not see how you get to 2800.

 

Without knowing any better it sounds like the overall focal length is just the total physical light path multiplied by two (2), the primary magnification factor. For this example it's (2)(741+412+401) = 3108.

 

The published 2800 number is probably at a point where the primary is near the center of travel. You can probably back things in from there if the above 2x assumption is correct.


Edited by MarMax, 04 March 2021 - 02:57 AM.


#6 davidc135

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Posted 04 March 2021 - 03:30 AM

The corrector to mirror distance isn't relevant to the total path length other than being a convenient position to attach the secondary. Just as the corrector position in a Schmidt Newtonian has no bearing on the focal length.

 

F = f1.f2/(f1-f2-s)   where s= separation of mirrors and f1 is the primary and f2 is the secondary. f1,f2 and s are negative 

 

and

 

mag m = f2/(f1-f2-s)

 

You need mirror separation s measured along the axis between vertices but those formulae don't help you without making assumptions. Hmm, it's a tricky one just working on separation measurements.

 

David



#7 davidc135

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Posted 04 March 2021 - 03:58 AM

There is an online Cassegrain calculator which tells me that it is not possible to work out the scope's f.l with only mirror and focal point separations even if you know the primary focal length.  David



#8 luxo II

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Posted 04 March 2021 - 05:10 AM

2800 = b x D/d

where d = secondary diameter, D = scope aperture at the corrector and b is the backfocus from the vertex of the secondary to the focal plane.
 

The aperture stop for SCTs is the corrector aperture not the primary mirror diameter - the latter is slightly oversized in SCTs to reduce the effects of vignetting off-axis across the field of view. Likewise the secondary mirror is usually oversized by 1-2 mm than simple geometry would suggest.

 

Mirror spacing is closer to 410 than 445 mm.

 

The complete solution requires accurate measurements of the maradi of both mirrors.

 

By the way your figures are so rough the 2 decimal places are a bit meaningless...


Edited by luxo II, 04 March 2021 - 05:21 AM.


#9 MarMax

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Posted 04 March 2021 - 12:25 PM

2800 = b x D/d

where d = secondary diameter, D = scope aperture at the corrector and b is the backfocus from the vertex of the secondary to the focal plane.
 

The aperture stop for SCTs is the corrector aperture not the primary mirror diameter - the latter is slightly oversized in SCTs to reduce the effects of vignetting off-axis across the field of view. Likewise the secondary mirror is usually oversized by 1-2 mm than simple geometry would suggest.

 

Mirror spacing is closer to 410 than 445 mm.

 

The complete solution requires accurate measurements of the maradi of both mirrors.

 

By the way your figures are so rough the 2 decimal places are a bit meaningless...

Excellent information jim, david and luxo. I feel like the fog is clearing a bit.

 

Yes, wrong precision for sure. That's just Autocad since I had not adjusted the precision from the previous drawing. It's good for mocking things up though. And it's easy to modify.

 

Corrector aperture "D" is 276mm and the secondary "d" is 78mm. But I have no idea what the "miradi" of a mirror is . . lol.

 

2800 = b x D/d    or  2800 = b x 276/78  and b = 791

 

So we've got the "b" based on the actual measurement of "D" and "d". I know that the mirror travel is 37 turns lock-to-lock which corresponds to about 28mm. And I can more accurately measure the distance between the primary and secondary with the focuser all the way forward or back.

 

Also, I've done the primary mirror focus spring shift modification so my lock-to-lock travel is limited rearward about 4-5mm. If I measure this distance it should be with the primary all the way forward.

 

So here is a 2nd draft of the schematic drawing. And one of things I had hoped to figure out with this exercise was the placement of the UAGII telecompressor so that its 35mm aperture matches up with the C11 light cone.

 

gallery_332504_14303_130565.jpg

 

 

The two formulas that seem to be applicable are:

 

b = (560 - x*)(5)      and    2800 = b(D/d)

 

Where x* is the distance between the primary and secondary.

 

Using both we end up with an x* = 402mm

 

Using an online Cassegrain calculator (I have no idea what I'm doing):

 

Input Parameters

Primary mirror diameter: 279.4
Enter field: 1(deg)
Primary mirror focal length: 560
System focal length: 2800
Back focal length: 390

 

Output Parameters

Primary mirror diameter 279.4000 mm
Primary mirror focal length 560.0000 mm
System focal length 2800.0000 mm
Back focal length 390.0000 mm
Distance secondary from system focus 791.6666 mm
Distance secondary from prime focus 158.3333 mm
Distance secondary from primary 401.6666 mm
Radius of curvature of secondary mirror 395.8333 mm
Primary mirror conic constant -1.0000
Secondary mirror conic constant -2.2500
Extension factor 5.0000

 

The bold numbers seem to be pretty darn close.


Edited by MarMax, 04 March 2021 - 06:25 PM.


#10 speedster

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Posted 04 March 2021 - 11:47 PM

Per Celestron, back focus is 139mm.  That assumes you are operating at the designed f/10.  Because the secondary is 5x, changing the primary location by focusing also changes the f/#.  There is enough focus travel to go from about f/8.5 to over f/13 so the back focus distance changes by inches through the possible range.  The farther you go from f/10, the worse things get. 



#11 MarMax

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Posted 05 March 2021 - 02:03 AM



Per Celestron, back focus is 139mm.  That assumes you are operating at the designed f/10.  Because the secondary is 5x, changing the primary location by focusing also changes the f/#.  There is enough focus travel to go from about f/8.5 to over f/13 so the back focus distance changes by inches through the possible range.  The farther you go from f/10, the worse things get. 

Also, Celestron says the backfocus is 152mm from the 3 inch (actually 3.28") baffle tube lock ring which I've shown in the drawing. The previously discussed formulas don't really work with the 152mm number so something is still fishy. I can see that 250mm is a bit much. Perhaps the focal lengths of the primary and secondary are not exactly f/2 and f/5.

 

I do need to re-measure the secondary to baffle tube lock ring distance. This is a fixed distance which should be equal to [b - 152].



#12 MarMax

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Posted 05 March 2021 - 12:53 PM

All right, possibly more stupidity from the newb, but since night viewing is a premium and it's dark, can I do a focal point test during the day with the Sun and solar filter?

 

It's so much easier and more comfortable to do daytime testing. I can use my NexStar+ controller and do a solar alignment on the Sun. Then just remove the visual back and use an index card. I can mount the card on a microphone stand or some other fixed object so I can move it to obtain focus. And I can do this with the primary in different positions and then measure the distance from the baffle tube lock ring to the card.

 

The secondary to baffle tube lock ring is a fixed distance so the "b" dimension is just the two added together.

 

What exactly will I see on the index card and will the focal point be easily identifiable?

 

And if the Sun is too big and bright for this type of test, can I use Mars or a bright star, or are they too dim?



#13 davidc135

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Posted 05 March 2021 - 02:42 PM

You'll need it bright. I taped a piece of paper to the back of a microscope slide which in turn was taped to the end of a drawtube. It's very obvious when the sun is in focus. I marked the diameter of the sun with a fine pencil and used that to work out the scopes focal length. The direct sun was used, unfiltered and full blast but I kept it brief. I think that a solar filter would make the image too dim but maybe some net curtain etc material would calm it down.

 

The sun's image should be close to an inch across in your scope.

 

David


Edited by davidc135, 05 March 2021 - 02:44 PM.


#14 charlesgeiger

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Posted 05 March 2021 - 06:18 PM

You could look at the moon and do the same evaluation.  I would not want the risk of burning your secondary baffle, overheating the secondary or loosening the adhesive holding the secondary by using the direct sunlight method.  You might also start a fire at focus if you have something combustible there. Additionally, you should easily be able to use a solar filter and project the image; after all, you use a eyepiece to magnify the image (after the solar filter) to see the sun.

Charlie



#15 MarMax

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Posted 18 March 2021 - 12:37 AM

I did a bit more testing on Polaris tonight based on the Celestron recommended 152mm (5.975") of backfocus for the C11 from the 3.28" baffle tube lock ring.

 

Using a bunch of 2" M48 extensions to a 2" by 1.25" Blue Fireball adapter I set up a TV 32mm plossl at 152mm from the baffle tube lock ring to the eyepiece field lens. I'm estimating my accuracy to be +- 1mm.

 

I then ran the primary all the way forward (counterclockwise) and then counted the clockwise focuser turns to reach focus on Polaris. The number of turns was 18.25. This is extremely close the middle position of the primary mirror which seems logical. The mid-point of primary mirror travel is 18.5 turns.

 

I will assume that 18.5 focuser turns (clockwise) from the full forward primary mirror position, i.e. placing the primary in the mid-point of its range of travel, is where the C11 is operating at f/10.

 

Assuming that the best performance is obtained when operating at f/10, the best way to create different gear configurations is to set the primary mirror at its mid-point and then adjust the backfocus of components until best focus is achieved.



#16 MarMax

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Posted 20 March 2021 - 02:41 AM

Here is a bit more based on the formulas in post #9. These are:

 

b = (560 - x*)(5)      and    2800 = b(D/d)

 

A cut and paste from an Excel spreadsheet and we have the following. The values FL, b and x are all in (mm).

 

 f/      FL       b      x     Turns

9.1    2548  720  416  37
9.2    2576  728  414  35.4
9.3    2604  736  413  33.3
9.4    2632  744  411  31.2
9.5    2660  752  410  29.1
9.6    2688  760  408  26.9
9.7    2716  768  406  24.8
9.8    2744  775  405  22.7
9.9    2772  783  403  20.6
10     2800  791  402  18.5
10.1  2828  799  400  16.4
10.2  2856  807  399  14.3
10.3  2884  815  397  12.2
10.4  2912  823  395  10.1
10.5  2940  831  394   7.9
10.6  2968  839  392   5.8
10.7  2996  847  391   3.7
10.8  3024  855  389   1.6
10.9  3052  863  387    0

 

If you accept these formulas and the 37 "Turns" of focuser travel (about 28mm) you can see that the focal ratio range is from 9.1 to 10.9. And the more the primary mirror is moved rearward from the mid-point position (the primary to secondary or "x" spacing is increased), the shorter the focal ratio.

 

Another way to look at it is each counterclockwise turn of the focuser, starting from a fully rearward primary mirror, is increasing the focal length by 13.6mm. With the focal length at the 18.5 turn mid-point being 2800mm. 

 

Edited to add that since the focuser shaft thread pitch is 0.75mm that for each 1mm of primary mirror movement the focal length changes about 18mm (13.6/0.75).


Edited by MarMax, 20 March 2021 - 02:47 AM.


#17 MarMax

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Posted 22 March 2021 - 11:54 AM

As I continue to go off the deep end on this I came across the Cassegrain Formulas and Tips by Mike Lockwood. I took the formulas and tips and further played with what I had previously. It all seems to work together which says that either both are a bunch of hooey or maybe they are correct.

 

Here is an image of the spreadsheet.

 

 

gallery_332504_14303_106137.jpg

 

An interesting note in the Lockwood tips is the statement that "when you decrease the spacing between the secondary and primary, the focal length of the system actually gets longer (!)".




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