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# Artificial Star Q

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### #1 Joe1950

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Posted 16 February 2020 - 08:57 PM

Seeing here is usually so bad, I often resort to using an artificial star for collimation and sometimes for a star test; though I know the latter is a slippery slope.

This is the formula, as I understand it, to determine how far an artificial star should be from the scope for star testing...

Determining SA for Near Focus Artificial Star:

N (ft) = 28 ( D/F )²

N is the distance where 1/4λ spherical aberration in the form of under-correction is added due to proximity.
D  is the Objective diameter in inches
F  is the focal ratio

So, as an example, lets say you have a 16" Newtonian, f/4.

By the formula, if the artificial star is 448 ft from the scope, you will get 1/4λ spherical aberration of under-correction added to whatever the mirror already has. To reduce that to 1/16 λ spherical aberration of added under-correction, so it wouldn't affect a star test as much, the artificial star must be a whopping 1792 ft distant. That's a third of a mile, or nearly 6 football fields!

This approach supposedly works for a Newtonian reflector. For some reason, the distance for a refractor is much more forgiving, and the artificial star can be closer without adding nearly as much proximity under-correction. I don't know if there is a different formula for a refractor, however.

My question is for an SCT, specifically my vintage C-8.

If, and this is what I don't know, the formula applies to an SCT the same way it would for a reflector, the result will give you a distance of about 18 ft with the added 1/4λ spherical aberration. And further, if you wanted to reduce that added error to 1/16λ, The artificial star would need to be a scant 72 ft distant!

In fact, if you can get the artificial star 144 ft away from the C-8, the added under-correction would only be 1/32λ. And that distance is doable in my back yard!

I'll add that I know the light source must be small enough as to be seen as a point source, not an extended object. I use a small (1/8") ball bearing with the sun, or a small but bright, single bulb LED flashlight several feet away at night.

So, after all this rambling, my question is... will this arrangement work as a star test for the C-8 if said light source is 144ft or more distant?

Believe it or not, the image is affected by seeing even at that distance on the ground over grass. But not nearly as much as it would be through my NJ atmosphere.

Thanks very much!

joe

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### #2 JohnBear

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Posted 16 February 2020 - 09:50 PM

I'd like to ask where you found the formula.

I have been doing artificial star rough collimations for some time, but never found formulas related to the process. I just experimented placing the point source as far away as I could within my house (about 35 feet), and seemed to get pretty decent results with my F/5-10 newts which makes sense using your formula.

I'd also like to know if the same formula applies to SCTs since I recently acquired two C8s.

Thanks.

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### #3 Joe1950

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Posted 16 February 2020 - 09:57 PM

I know where I got it... let me look it up. Ill be back.

It's talked about here, about 1/4 to 1/3 down the page. But, now that I'm thinking of it, I believe the formula I quote is from Suiter's book, which I no longer have. He or someone derived a simpler formula that works.

Sorry, not very scientific, but I believe the formula I quote is valid, since I copied it rather than manipulate it.

Also, in the yellow page site, It says...

"Catadioptric Newtonians with full-aperture Maksutov or Schmidt corrector are significantly less sensitive to reduced object distance than paraboloidal Newtonians, due to their spherical mirrors. Catadioptric two-mirror systems are not uniform enough in their production types to fall under some type of generalization.

For all-reflecting two-mirror systems, close object error of spherical aberration is given by Eq. 92 (also plots for the three most common systems), and for typical commercial SCT by Eq. 120.3.

Ordinary doublet achromat is very tolerant to the reduction in object distance in focal ratios ~ƒ/10 and slower. It is in part due to its relatively small apertures, but even a 200mm achromat will likely generate less than 1/20 wave P-V of under-correction with the object (artificial star) as close as 10 focal lengths away (given relative aperture, the error level is nearly in proportion to the aperture size)."

(My emphasis added)

--  Telescopeoptics.net

Now I'm really confused.

Edited by Joe1950, 16 February 2020 - 10:16 PM.

### #4 Joe1950

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Posted 16 February 2020 - 10:35 PM

On this page it talks more about commercial SCTs with mirror focusing.

They say:

"For the typical commercial ƒ/10 SCT, spherical mirrors and F1~2, the P-V error of spherical aberration induced by mirror focusing at close objects is approximated by W~D/72o', with o' being the object distance in units of system's focal length (as before, aperture diameter D is in mm).

(again, my emphasis)

--   --  Telescopeoptics.net

So,

For our C-8 SCTs, at f10, the formula is:

W ≈ D/72o'

W is the P=V SA error induced by proximity focusing

D is the aperture in mm

o' is the object distance in units of system's focal length

o' cant be in mm. That wouldn't work. I'm missing something.

### #5 JohnBear

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Posted 16 February 2020 - 10:41 PM

Thanks Joe.  You have given me a good start lead. I appreciate the reference very much.

One of the things I like about astronomy is that there is So Much to Learn (and try) (and helpful bright people to get to know). It keeps cobwebs from forming between the ears.

Thanks!

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### #6 Joe1950

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Posted 16 February 2020 - 10:50 PM

The graph puts the CLOSE FOCUS LIMIT FOR 8-INCH SCT (Appx) at an OBJECT DISTANCE of about 20  f1

Telescopeoptics.net

But, 20 units of what, I don't get.   Plus, that's a moving secondary.

I hope someone can translate all this for me.  I'm totally lost now!  Right now I don't think I even have cobwebs!

Edited by Joe1950, 16 February 2020 - 10:55 PM.

### #7 Joe1950

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Posted 16 February 2020 - 10:54 PM

John, you'll figure it out!  Thank you!

### #8 BGRE

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Posted 16 February 2020 - 11:57 PM

Seeing here is usually so bad, I often resort to using an artificial star for collimation and sometimes for a star test; though I know the latter is a slippery slope.

This is the formula, as I understand it, to determine how far an artificial star should be from the scope for star testing...

Determining SA for Near Focus Artificial Star:

N (ft) = 28 ( D/F )²

N is the distance where 1/4λ spherical aberration in the form of under-correction is added due to proximity.
D  is the Objective diameter in inches
F  is the focal ratio

So, as an example, lets say you have a 16" Newtonian, f/4.

By the formula, if the artificial star is 448 ft from the scope, you will get 1/4λ spherical aberration of under-correction added to whatever the mirror already has. To reduce that to 1/16 λ spherical aberration of added under-correction, so it wouldn't affect a star test as much, the artificial star must be a whopping 1792 ft distant. That's a third of a mile, or nearly 6 football fields!

This approach supposedly works for a Newtonian reflector. For some reason, the distance for a refractor is much more forgiving, and the artificial star can be closer without adding nearly as much proximity under-correction. I don't know if there is a different formula for a refractor, however.

My question is for an SCT, specifically my vintage C-8.

If, and this is what I don't know, the formula applies to an SCT the same way it would for a reflector, the result will give you a distance of about 18 ft with the added 1/4λ spherical aberration. And further, if you wanted to reduce that added error to 1/16λ, The artificial star would need to be a scant 72 ft distant!

In fact, if you can get the artificial star 144 ft away from the C-8, the added under-correction would only be 1/32λ. And that distance is doable in my back yard!

I'll add that I know the light source must be small enough as to be seen as a point source, not an extended object. I use a small (1/8") ball bearing with the sun, or a small but bright, single bulb LED flashlight several feet away at night.

So, after all this rambling, my question is... will this arrangement work as a star test for the C-8 if said light source is 144ft or more distant?

Believe it or not, the image is affected by seeing even at that distance on the ground over grass. But not nearly as much as it would be through my NJ atmosphere.

Thanks very much!

joe

The formula is unadulterated nonsense.

It fails a very simple test:

Assume that its correct for a particular telescope then double the dimensions the wavefront error is also doubled but the distance satisfies the formula.

The distance cannot simply be a multiple of some power of F/D.

The correct formula is likely to have an extra power of D in it.

Raytracing is the answer.

Exact analytic solutions are possible for simple optical systems such as a Newtonian.

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### #9 MKV

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Posted 17 February 2020 - 12:12 AM

The formula is unadulterated nonsense.

It fails a very simple test:

Assume that its correct for a particular telescope then double the dimensions the wavefront error is also doubled but the distance satisfies the formula.

The distance cannot simply be a multiple of some power of F/D.

The correct formula is likely to have an extra power of D in it.

Raytracing is the answer.

Exact analytic solutions are possible for simple optical systems such as a Newtonian.

Bruce, it's not F/D (as in focal length/aperture = focal ratio); the F in D/F, as Joe says = focal ratio. Ouch! IOW -- F is the "f-number" or F#. Unorthodox definitions tend to confuse...I agree. If you work out the equation, then you do have a power of D: D/F#  = D/(f/D) = D2/f, where   is the focal length

The equation is calculated for minimum RMS OPD of 0.25 waves at the focus. Raytracing confirms it.

Edited by MKV, 17 February 2020 - 12:13 AM.

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### #10 Joe1950

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Posted 17 February 2020 - 12:54 AM

Okay, Bruce! Thanks. I think I knew it was too easy to be true. That’s why I threw it out there.

I have no idea how to Raytrace, Bruce.  I’m not even close to you folks in knowledge of optics. In fact, the more I read the more I realize I don’t know!

Hello Mladen!  Thanks for your info.  I can’t say I understand it   but I always appreciate your take. As well as everyone else’s!

Telescopeoptics.net (the yellow pages as I call them), presented a formula specifically for a commercial f/10 SCT with a moving mirror for focusing. It’s a ballpark formula, but how valid it would be I have no idea. It gives the P-V proximity SA error W, as an approximation of D, the scope aperture in mm, over 72 (o’)

W ~ D/72o’

From Telescopeoptics.net, page  almost at the end of the page, just before the SCT baffle system and extended focus section.

once again it states:

“For the typical commercial ƒ/10 SCT, spherical mirrors and F1~2, the P-V error of spherical aberration induced by mirror focusing at close objects is approximated by W~D/72o', with o' being the object distance in units of system's focal length (as before, aperture diameter D is in mm).”

— Telescopeoptics.net

DAVIDG was kind enough to tell me o’ is a ratio of the distance from the scope to the object (artificial star) to the focal length of the scope (both in the same units).

So for my C-8, lets say the distance to the artificial star is 100 ft.

And, lets say the focal length is in feet. 2000mm = 6.56 ft

Therefore o’ would be 100/6.56 = 15.24

So,

W ~ 200/ (72 x 15.24)

W ~ 200/ 1097

W ~ 0.18 λ  P-V

again as a rough estimate of SA overcorrection due to proximity of the scope to the object (artificial star)

Edited by Joe1950, 17 February 2020 - 02:01 AM.

### #11 Joe1950

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Posted 17 February 2020 - 01:09 AM

For the longest distance I can work with, about 170’ in my backyard, I would get o’ of 25.9.

So in that case W ~ 0.11 λ

A little better than 1/8 λ

Anyway, I’ll just wait for some decent seeing when it gets warmer and check it on Polaris again.

The last time I did that, the 10 λ defocused images, inside and outside, looked very similar.  Better than I’ve seen in many other scopes.  But imaging the disks was impossible due to seeing conditions. Maybe the eye smooths out things where imaging does not.

Thanks to all!  Appreciate the info on a topic very challenging to me.

joe

### #12 MKV

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Posted 17 February 2020 - 01:45 AM

Joe, that's correct. Raytracing shows that placing an art. star at 30,480 mm (100') in front of a C8 and refocusing (optimizing) with the primary mirror moving, the resulting OPD residual will be 0.182 (about 1/5.5) waves. However, the RMS OPD error will be much smaller, at 0.0267 (or 1/37) waves.

Normally, C8 has a focal length of roughly 2,000 mm (and a back focal length of 526.414 mm). Placing the art. star at 100 feet pushes the back focal length to 620.763, and for the best focus at 620.844 mm. his will cause the OPD to be 0.19 vs 0.18, Insignificant. Even if you don't focus for minimum RMS (best focus), you should be able to use this method for alignment and optical quality testing.

Mladen

Edited by MKV, 17 February 2020 - 01:45 AM.

### #13 Joe1950

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Posted 17 February 2020 - 02:07 AM

Great! Thanks Mladen!  I’ll give it a try and stretch it out to about 170’.  I have to mow it all the time, might as well use it for something productive  .

I appreciate the information very much!  Always good to hear from you, bud.

Again, thanks to all for the help!

joe

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### #14 BGRE

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Posted 17 February 2020 - 02:36 AM

Bruce, it's not F/D (as in focal length/aperture = focal ratio); the F in D/F, as Joe says = focal ratio. Ouch! IOW -- F is the "f-number" or F#. Unorthodox definitions tend to confuse...I agree. If you work out the equation, then you do have a power of D: D/F#  = D/(f/D) = D2/f, where   is the focal length

The equation is calculated for minimum RMS OPD of 0.25 waves at the focus. Raytracing confirms it.

Mea Culpa (usually F# or anything other than F is used for F/D), I actually have a derivation of a more general formula (for a paraboloid plus extensions to achromats etc) somewhere (probably on the failed laptop). Not sure that I ever posted it.

Actually the formula can be rewritten as

constant*D^4/f^2

IIRC the general form is

constant*(D^4)/(epsilon*lamda*f^2)

where epsilon is the SA measure in waves, lambda is the wavelength.

The constant depends on the details of the optical design as well as the method of focusing (for compound systems - eg Cassegrains etc)

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### #15 BGRE

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Posted 17 February 2020 - 08:06 AM

Found the result I derived for a paraboloid (e.g. Newtonian primary).

C8= -(1/384)*(D^4/R^3)*(1-2*(s/R))/(s/R)^2

where s is the source conjugate

R is the paraxial RoC of the paraboloid.

D is the diameter of the paraboloid

C8 is the amplitude of the Z8(Wyatt enumeration/ordering) Zernike polynomial

C8 is zero for s= R/2 or infinity.

For large s (i,e. s/R>>1) this can be simplified to

C8= (1/192)*(D^4/R^2)/s

or s =  (1/192)*(D^4/R^2)/C8

or s =   (1/768)*(D^4/f^2)/C8

or s =   (1/768)*(D^2/(F#)^2)/C8

for a 1/4 ptv of wavefront error

s = (1/64)*(D^2/(F#)^2)/lambda

N.B. this is only true for a paraboloid.

Ray tracing indicates that refractors etc have a similar dependence on D, F# etc

s = k*(D^2/(F#)^2)/lambda but k differs for each type of telescope and in general the method of focussing.

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### #16 MKV

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Posted 17 February 2020 - 10:12 AM

I have to mow it all the time, might as well use it for something productive  .

Finally, now I know why we need all those endless areas of overgrown unused grassy surfaces! But if you get an optical flat, you don't have to mow or deal with air currents, and you can test it in the living room when She Who Must be Obeyed is not around. :o)

Edited by MKV, 17 February 2020 - 10:12 AM.

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### #17 Joe1950

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Posted 17 February 2020 - 10:14 AM

Bruce, you really know the subject!  Thanks for that information.

### #18 Joe1950

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Posted 17 February 2020 - 10:20 AM

You’re absolutely right Mlaven!

I’d love to have a 9-10” optical flat, but those boys are expensive!  I look on eBay now and then and even a 6”er is \$1k.

But that is the way to go!

I may try oil again, keep the thickness down to 1mm, if possible and see how that works out!

Thanks M.

### #19 RaulTheRat

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Posted 17 February 2020 - 10:27 AM

What about purely for collimation and not optical testing. Any guidelines on how close it can be if all you need is a small enough image for collimation?
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### #20 MKV

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Posted 17 February 2020 - 10:37 AM

Found the result I derived for a paraboloid (e.g. Newtonian primary)...

You can generalize this by including the conic constant (K). The relationship changes somewhat when the source is at ROC.

All these can be derived based on simple equations

, and min rms

where LA or LAm sometimes stands for long. aberration (i.e. SA), D is the mirror aperture diameter, K is the conic constant, sin u is the sine of incidence angle (i.e. 0.5/F#) and f is the mirror's focal length (1/2 rad. of curv.), etc. Basic stuff.

NB this is for testing at ROC

Edited by MKV, 17 February 2020 - 11:01 AM.

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### #21 MKV

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Posted 17 February 2020 - 10:46 AM

What about purely for collimation and not optical testing. Any guidelines on how close it can be if all you need is a small enough image for collimation?

Your best indicator of good alignment in most telescopes is absence of coma. You adjust alignment until there's no perceptible coma in the FOV center using the highest power eyepiece (without a Barlow lens!). Thus, the rules should be the same, but if coma is not an indicator then optical quality is irrelevant. Anything too close, however, will result in a larger alignment error due to parallax.

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### #22 MKV

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Posted 17 February 2020 - 10:55 AM

I’d love to have a 9-10” optical flat, but those boys are expensive!  I look on eBay now and then and even a 6”er is \$1k.

For AC you don't need an expensive absolute flat, but but its residual long curvature must be spherical (i.e. the figure must be a sphere, also termed "regular"). A few waves of "power" as they say (i.e. concavity or convexity) will do just fine for 99.9% of ATM mirrors. Even for an f/2 up to 7 waves (14 fringes) is theoretically okay -- but I wouldn't push  it  For an f/4 it will be more than adequate.

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### #23 Joe1950

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Posted 17 February 2020 - 01:50 PM

I always keep an eye out for a usable flat. One of these days I hope to catch a good deal. It’s a great thing to have on hand!

### #24 luxo II

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Posted 17 February 2020 - 03:08 PM

And maksutovs behave differently again - Mak Newtonians, Gregory Maks and Rumaks.

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### #25 Joe1950

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Posted 17 February 2020 - 04:13 PM

I read that as well!

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