Distance needed to focus on an artificial star?

[Giles_B]

I'm considering buying an artificial star to further assist collimation of my f4,8 10" Dob - I find tracking a real star a bit tricky with a Dobsonian. However, although I travel to more open locations from time to time, a lot of my observing is done in my garden, and I am not sure if I have the necessary distance in my garden to focus on an artificial star - does anyone have any practical experience?

I realise not all artificial stars created equally, so really want a rough indication of the distance needed for a 20-50 micron unit.

 

[CraigT82]

You don’t need that much distance just for collimation, I’ve done it with about 30m I think, if you were planning on star testing with it it would need to be further to be viewed as a genuine point source. 
One problem I experienced (I used the Hubble optics star) was that I collimated nicely on the star with the scope pointing nearly horizontal, but when pointing the scope upwards to the sky the collimation shifts slightly. 

[vlaiv]

Distance for focus does not depend on size of artificial star.

You can focus at any distance, provided that you have enough out focus travel.

Here is simple formula to get you started:

1/focal_length = 1/star_distance + 1/new_focus_position

Focal length of your scope is ~1200mm, and say you want to focus at artificial star that is 10 meters away, so 10000mm. What is out focus (over normal focus at infinity) that is needed to focus?

1/1200 = 1/10000 + 1/new_focus_position

1/new_focus_position = 1/1200 - 1/10000

1/new_focus_position = (8.33333 - 1)/10000 = 7.33333/10000 

new_focus_position = 10000/7.333 = ~1363.6mm

So you need to move from 1200 to 1363 - focuser needs to be able to move additional 163mm from normal focus position at infinity. You would probably need 15cm extension to reach focus at 10 meters.

If you want to know the distance at which you won't resolve artificial star - that is another matter altogether.

You need to calculate airy disk size of your aperture, and see at what distance artificial star (here size does matter) subtends half of airy disk size.

 

 

 

[vlaiv]

Just to make answer complete, here is how you calculate distance at which you won't resolve artificial star.

Use this to get airy disk diameter:

https://www.wilmslowastro.com/software/formulae.htm#Airy

So diameter of airy disk is ~1". We can then take 1/2 or even 1/3 of that size and that is needed angular size of our artificial star.

Say you have 50um artificial star. At what distance does it need to be in order to present itself as 0.5" wide?

Here you use another calculator:

https://www.1728.org/angsize.htm

You solve for distance and use arc seconds as angular measure. Convert all distances in either meters or millimeters. 50um is 0.05mm

Answer is ~20626mm, or 20.6 meters away.

Smaller scopes have larger airy disks and that means that you can put artificial star closer (just mind out focus).

Btw, close focus introduces spherical aberration for optics corrected for infinity. If you want to star test telescope with artificial star, then things get much more complicated :D. You need to calculate distance at which added spherical is minimal, or if you do wavefront analysis - you can subtract spherical due to close focus from Zernike polynomials.

 

[Giles_B]

Thank-you both, for all of these answers. @vlaiv - I particularly appreciate your identifying and linking to the relevant calculators. Certainly the ball-park figures suggest I would have the room to use the artificial star, but I appreciate the help with the maths!

One thing both of your answers have made me realise is that there is a difference between using the artificial star for star testing and collimation. My understanding is that star testing is used as a final 'acid' test of collimation - that an out of focus star will show a pattern in the airy disk that indicates optical aberrations associated with miscollimation as well as other optical defects. What I don't fully understand in your answers is how I would use an artificial star to check collimation without doing a star test - could anyone explain?

[vlaiv]

1 minute ago, Giles_B said:

One thing both of your answers have made me realise is that there is a difference between using the artificial star for star testing and collimation. My understanding is that star testing is used as a final 'acid' test of collimation - that an out of focus star will show a pattern in the airy disk that indicates optical aberrations associated with miscollimation as well as other optical defects. What I don't fully understand in your answers is how I would use an artificial star to check collimation without doing a star test - could anyone explain?

Collimation check and star test are performed in the same way, but what you see is "read" for different things.

Say you have in/out focus images of a star looking like this:

For collimation - you want these rings to be concentric. Remember - you want to place star in dead center of high power eyepiece. When you adjust primary mirror - star image will shift and you need to move scope to bring it back in center.

If you have issues with collimation - image will look like this:

However, if you want to check for spherical aberration - you don't look at ring geometrical pattern at all. You look at something else entirely.

You look for this sort of pattern:

Inside and outside focus images being different in where brightness is concentrated. One will have brightness concentrated in center while other will in outer rings.

In fact - here is a "cheat sheet" for that:

Actual star image will be some combination of above - with different "terms" having different level of contribution (some will be there and some maybe won't - in perfect optics, well all are almost zero).

For collimation - you just want second set of images, or rather you want your star not to look like that - to have offset in rings, but you want rings to be concentric.

When you place artificial star far enough not to be resolved but still close to create spherical aberration - then brightness of in and out of focus images will be different even if you have perfect scope - because of artificial star being close and introducing spherical aberration to wavefront that has nothing to do with optics - but that won't mess concentricity of your rings and if they are concentric - you have good collimation.

[Giles_B]

Thank you for that really comprehensive answer!

[bluesilver]

Hi, Sorry to jump on in this post.

I was actually looking do do an artificial star test and came across this while i was doing a search.

For me i kind of got a bit lost in all the technical details there.

I have two scopes that i was planning on just trying this artificial star test out just for something different and see how things compare.

My scopes are a 16" f4.4 Dobsonian focal length of 1800mm  and a Celestron C14 XLT f11 focal length 3910mm

So i am trying to find the minimum distance to setup to collimate using an artificial star.

I got a tad lost in all the technical detail that you went through though.

I did read somewhere that they say for a general rule it is about 20 -25 times the focal length of the scope.

So for the Dobsonian , that would be around 36 - 45 meters

Ant the C14, it would be around 78 - 98 meters away,

Dose this sound about right?

I had a look at that site with the calculators,  but still can't figure out the distance needed,  I was only just going to use a the basic method of the artificial light which is a torch with aluminum foil and pin hole. 

So was hoping to get some basic advise on how to work out how far away i should be looking at.

Any advice would be appreciated.

 

 

Edited September 27, 2022 by bluesilver

[vlaiv]

2 hours ago, bluesilver said:

Any advice would be appreciated.

If you are going to use DIY pin hole, then don't bother with calculations as you don't know essential part - that is diameter of artificial star.

Put it as far as it is practical for you, but no less than say 30-40 meters for both scopes.

There is another way to make artificial star that you can try - it is even less involved than punching tiny hole in aluminum foil. Get very shiny and very small ball bearing. Take torch / flashlight to illuminate it. Make sure flashlight is one with narrow beam and place it few meters away from ball bearing. Setup should look something like this:

left is OTA and torch is shining at some angle at ball bearing. Distances are not to scale in above image. Place OTA at least 30-40 meters away and torch few meters away from ball bearing.

In this setup - specular highlight reflected of ball bearing is your artificial star, like this:

Size of it depends on size of light source causing it - that is why you want your flashlight to be far away enough so it causes only a tiny shiny dot.

[bluesilver]

Appreciated, I thought i might of been over thinking thigs a bit there.

Appreciate the advice and also the ball bearing method also.

I have plenty of room as i am on a rural property, so distance is no issue there.

I will give both a go and see how the results turn out like.

Appreciated.