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# how to defocus 10 wavelengths?

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### #1 Doliometer

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Posted 24 August 2018 - 02:26 PM

It's a little embarrassing to ask but I think my focuser should travel .58 inch per revolution of coarse knob.

The fine knob is geared down 8-to-1, so 1.84 mm per revolution.

If 10 wavelengths is 5 micrometers, then 10 wavelengths would be accomplished with less than 1 degree of knob turn.

That can't be right, can it?

### #2 sharkmelley

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Posted 24 August 2018 - 02:46 PM

Your maths looks correct to me.  But why do you want to defocus 10 wavelengths?

Mark

### #3 sg6

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Posted 24 August 2018 - 02:52 PM

Wavelength is just a length, usually talked of in nm or nano-meters, which is 1/1000 smaller then a micrometer.

So the terms do not make an answer easy.

It it is 0.58" that is 14.732mm, 8:1 would be 1.8415mm for the fine.

As therefore 1.815 = 360 degrees of rotation you get 1.815*1000 micrometers movement per 360 degrees.

1815 micrometers = 360, so 5 = (360/1815)*5 = 0.99 degrees of rotation.

Figures appear correct.

But that is for a movement of 5x10-6 meters, not 10 "wavelengths".

### #4 bobzeq25

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Posted 24 August 2018 - 03:54 PM

A number of things affect focus on a practical level, optics are not perfect.  There's the "depth of focus".  Roughly (it depends on the scope) you need to be able to focus to 20-200 micrometers.  That's about 4-40 degrees of rotation.

The camera is more sensitive to focus than your eyes, which can compensate a bit.

Here's one way to do it.

http://rigel.datacor...ocus faq 3.html

http://rigel.datacor...s/rigelsys.html

More here.   Note that the numbers are somewhat different, exactly how good focus needs to be can be debated.  Note also that the field curvature of most scopes is more than enough to affect things off center.

https://starizona.co...ial/focusing-2/

Edited by bobzeq25, 24 August 2018 - 04:05 PM.

### #5 Joe1950

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Posted 24 August 2018 - 04:18 PM

If you're speaking about defocusing a star image for a star test 10Î» inside and outside of focus, I use Aberrator to calculate the distance.

For example, if you have a 102mm refractor, F/8. The 'Focus (Waves)' box is set to -10.00Î» and the 'Focus (mm)' box shows -2.82 mm.

This means to defocus 'Inside' focus (you use a negative number) you would move the focuser a total of 2.82 mm in or down. Outside focus, or +10.00Î», would be 2.82 mm out or up.

This gives you the most sensitive setting, 10Î», to evaluate correction or spherical aberration. Larger defocused positions would be more sensitive to higher order aberrations such as zones or turned edges.

Give me the numbers on the scope, Aperture, Focal Ratio and include Central Obstruction and I'll run them in Aberrator and post the results, if you don't have it.

Edited by Joe1950, 24 August 2018 - 04:19 PM.

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### #6 sharkmelley

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Posted 24 August 2018 - 05:27 PM

For example, if you have a 102mm refractor, F/8. The 'Focus (Waves)' box is set to -10.00Î» and the 'Focus (mm)' box shows -2.82 mm.

This means to defocus 'Inside' focus (you use a negative number) you would move the focuser a total of 2.82 mm in or down. Outside focus, or +10.00Î», would be 2.82 mm out or up.

Interesting ...

I admit that I know nothing about star testing but what is the exact formula for converting 10 wavelengths into 2.82mm?

Is it the wavelength of light being used or is this microwaves?

There's clearly something I'm missing!

Mark

Edited by sharkmelley, 24 August 2018 - 05:28 PM.

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### #7 Joe1950

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Posted 24 August 2018 - 05:37 PM

There is a formula, Mark, but I don't know what it is. It is using the wavelength of light. Green, I believe.

All I do know is the longer the focal ratio the longer the offset distance is, so there must be an additional factor along with the actual wavelength involved

There is also a chart is Suiter's Star Testing book and an explanation. As I said, I use Aberrator to find the distance and it is accurate for the offsets.

Hopefully one of the optics folks will stop by and explain.

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### #8 sharkmelley

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Posted 24 August 2018 - 06:11 PM

There is a formula, Mark, but I don't know what it is. It is using the wavelength of light. Green, I believe.

Thanks.  I've done a bit of Googling and it all becomes clear.

Here's a useful link that describes what is going on and gives the formula:

https://www.telescop...et/defocus1.htm

When they talk about "10wave defocus" it does not mean that the focal plane is moved by 10 wavelengths.  Instead it means that the focal plane is moved by an amount that causes a maximum 10 wavelength error in the resulting P-V wavefront (P-V means peak-valley)

Rearranging formula 24.1 in the link I provided:

Defocus (mm) = 8 * lambda * f_ratio^2 * number_waves

So for 10wave defocus at f/8 at wavelength 0.55microns (green light) we have

defocus(mm) = 8 * 0.00055 * 8*8 * 10 = 2.82mm which is the result you gave from Aberrator.

So, returning to the OP's question, we need to know the focal ratio and the wavelength of interest before the defocus in millimetres can be calculated.

Mark

Edited by sharkmelley, 24 August 2018 - 06:18 PM.

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### #9 Joe1950

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Posted 24 August 2018 - 06:36 PM

Excellent Mark!!!!  I'm glad you did that.  I'm not surprised you found the answer in the 'Yellow Pages.'  But to tell the truth, I sometimes have trouble understanding the table of contents!   Great resource but very math heavy.

F-ratio2.  That explains why the distance gets larger out of proportion with the f/ratio.

Thanks Mark.

joe

### #10 MitchAlsup

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Posted 24 August 2018 - 07:52 PM

It's a little embarrassing to ask but I think my focuser should travel .58 inch per revolution of coarse knob.

The fine knob is geared down 8-to-1, so 1.84 mm per revolution.

If 10 wavelengths is 5 micrometers, then 10 wavelengths would be accomplished with less than 1 degree of knob turn.

That can't be right, can it?

You are forgetting about the Focal Ratio. What you have written is correct only for an F/1 scope.

The 10 waves criterion is to get enough out of focus that the diffraction pattern is easy to see but not too dim. The distance out at F/3 is 3.3X smaller than at F/10.

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### #11 MKV

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Posted 24 August 2018 - 07:54 PM

This is very simple. One wavelength defocus  = 8Î»F2/n, where Î» = wavelength used, F is the focal ratio (F-number) of the optical system, and n is the refractive index of the medium (air is 1.0 for all practical purposes).

To get 10 waves simply multiply that expression by 10, i.e 80Î»F2/2.

Thus for the green light of 0.00055 mm wavelength, medium refr. index of 1 (air), and focal ratio F = 5, 10 waves defocus = 80*0.00055*25/1 = 1.1 mm

Edited by MKV, 24 August 2018 - 07:54 PM.

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### #12 Joe1950

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Posted 24 August 2018 - 08:06 PM

Mark got a handle on it. I used Aberrator as an easy way to find the distance. I was good in math, but never got to the higher levels. I got up to Gizinta mathematics. Four gizinta twelve three times, five gizinta twenty four times and so on.

Nice to see you, bud!

Edited by Joe1950, 24 August 2018 - 08:06 PM.

### #13 sharkmelley

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Posted 24 August 2018 - 08:13 PM

This is very simple.

No doubt it's simple for you ATM, Optics and DIY folk.  But the question was originally posted on the General Astronomy Beginners Forum!

Mark

Edited by sharkmelley, 24 August 2018 - 08:14 PM.

### #14 MKV

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Posted 24 August 2018 - 09:54 PM

Mark got a handle on it. I used Aberrator as an easy way to find the distance. I was good in math, but never got to the higher levels. I got up to Gizinta mathematics. Four gizinta twelve three times, five gizinta twenty four times and so on.

Nice to see you, bud!

Hi Joe, I'm my "usual wonderful self."  :o)

I just noticed that Mark got the right equation from Vla's trusted site.

Somewhre in my tolerances equations from Warren Smith's Modern Optical Engineering. The equations have been worked out for 1/4 wave (Reyleigh limit) of all sorts of parameters, and one of them is "out of focus" tolerance. It's only a matter of algebraic rearrangement of parameters to get 1 wave defocus distance = 8Î»F2/n from the Rayleigh limit = Î»/2nsin2u  -- where sinu is simply 0.5/f-ratio.

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### #15 Joe1950

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Posted 24 August 2018 - 10:02 PM

It's only a matter of algebraic rearrangement of parameters to get 1 wave defocus distance = 8Î»F2/n from the Rayleigh limit = Î»/2nsin2u  -- where sinu is simply 0.5/f-ratio.

You know, I was just going to mention that!

Edited by Joe1950, 24 August 2018 - 10:04 PM.

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### #16 MKV

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Posted 24 August 2018 - 10:06 PM

No doubt it's simple for you ATM, Optics and DIY folk.  But the question was originally posted on the General Astronomy Beginners Forum!

You did a great job rearranging Vla's formula. You can find these in any optical engineering book (such as online Warren Smith's Modern Optical Engineering) in the "aberration tolerances" section in much simpler form. But Vla does a great job showing how the equations are actually derived. What I meant by "easy" is that today the information is much easier to obtain than in the days when I was just starting as an ATM and you get to a physical library to get this stuff.

Cheers,

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### #17 Joe1950

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Posted 24 August 2018 - 10:23 PM

Oh!   Vladimir Sacek did the yellow pages?  Man that is some serious stuff, M. I thought I was pretty smart until I saw that stuff.

Mladen, did you see the movie Annihilation with Natalie Portman? Serious sci-fi written and directed by Alex Garland (Ex Machina). It's great and takes place around where you live!

If you get a chance, rent it. I had to watch it a couple times to understand it, but it is really a good film! Not to give out spoilers, but they run across a huge Alligator and it reminded me of the time you saw one on the beach walking your dog!

If that were me, I'd be the first human to run a 2 minute mile!

### #18 stargazer193857

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Posted 25 August 2018 - 08:06 AM

It's a little embarrassing to ask but I think my focuser should travel .58 inch per revolution of coarse knob.

The fine knob is geared down 8-to-1, so 1.84 mm per revolution.

If 10 wavelengths is 5 micrometers, then 10 wavelengths would be accomplished with less than 1 degree of knob turn.

That can't be right, can it?

Don't forget focuser slop and recoil and lag. How well machined is yours? How thick is the goo? Do the knobs stop where you let go? Attach a Ray and find out.

### #19 Doliometer

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Posted 25 August 2018 - 09:23 AM

Argh! I must confess I wanted to star test new scope and didn't know about the 8F^2, F = focal ratio, multiplier for focuser movement. <chagrin> "How can people be talking single digit wave length defocus?" I wondered. But with the f/5 I have, it now all seems possible.

Thanks for the resources. Much to learn.

But about that multiplier...seems like it depends on a Taylor expansion around 0 in the aperture diameter. I wonder how good it is for larger apertures. But maybe it's just a rule of thumb anyway...

Edited by Doliometer, 25 August 2018 - 09:29 AM.

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### #20 Pinbout

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Posted 25 August 2018 - 09:53 AM

Argh! I must confess I wanted to star test new scope and didn't know about the 8F^2, F = focal ratio, multiplier for focuser movement. <chagrin> "How can people be talking single digit wave length defocus?" I wondered. But with the f/5 I have, it now all seems possible.

Thanks for the resources. Much to learn.

But about that multiplier...seems like it depends on a Taylor expansion around 0 in the aperture diameter. I wonder how good it is for larger apertures. But maybe it's just a rule of thumb anyway...

what's more important is getting the same distance from focus, intra and exta focal images...

need shims for that and sometimes we don't have exactly the required shims for 10~ defocus...so ya make do...use two quarters...

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### #21 Asbytec

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Posted 26 August 2018 - 10:13 PM

"When they talk about "10wave defocus" it does not mean that the focal plane is moved by 10 wavelengths. Instead it means that the focal plane is moved by an amount that causes a maximum 10 wavelength error in the resulting P-V wavefront (P-V means peak-valley)"

Defocus error. That's interesting, never thought there was a difference between the focal plane distance and defocus error. Always treated them as the same and simple defocused to 10 waves PV.

As Danny said, you dont have to be exactly 10 waves pv defocus, just the same either side. Something close to 10 waves is nice to work with when comparing both sides (intra and extra) patterns. I cut shims to dimensions outlined in Suiters book or aberrator.

I usually test at 4, 8, and 10 waves. Even more and in focus, too, depending on what we're looking for. As for impromptu star testing, I just become familiar with the appearance of the diffraction artifact and kind of "feel" the defocus.

Danny does this, too, as he scrolls through focus in his videos. He kind of wags it on both sides. You can learn to see what's going on scrolling through focus and beyond a little each side.

Trick is to know what 10 waves defocus looks like, or is supposed to look like. If not, something is amiss. Then figure it out. You'll see this actively scrolling through focus.

Just stay within the realm where you see a few to several diffraction rings and not so far out you see the "donut" and an image of the secondary shadow. Google Mel Bartel star test, it's a good read and fundamentally sound.
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### #22 Joe1950

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Posted 26 August 2018 - 10:58 PM

Good points, as usual, Norme! The star test is not easy and can be misleading. It takes a good deal of experience to get good with it.

Ideally, having someone with you who is good at it, explaining it as you are doing it would be the best situation.

Mel has good practical information on rating scopes. I like what he says here (from his site)

• Mirrors that can sustain 35x to 50x per inch of aperture I rate as excellent.
• Mirrors that sustain 25x to 35x per inch of aperture I rate as good.

Sometimes you hear claims of super sharp images at 100x per inch or more. Maybe, I guess. I've never been able to push a scope that high with any improvement in observed detail.

Thanks, Norme!

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### #23 Asbytec

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Posted 27 August 2018 - 12:21 AM

At the risk of going off topic, star testing can be challenging but it'll click with time. Correction, astig, coma, zones, turned edge and snap test and magnification (in focus) all exhibit some behavior we can recognize.

Whats hard is quantifying it, just a rough guess of excellent, good, or poor. We've had long discussions of magnification, it depends on the object. I think Mel means a star. Even stars can take 100x per inch in any scope, really. Jupiter can't...in any scope.

More to topic, I think we start out star testing at very specific defocus. We don't really have to except for the shadow break out. You wanna know where that happens, so you need to know how much defocus we are seeing. And to compare test images, it helps to match the defocus shown.

Other than that, general scrolling through focus is a good technique if we're familiar with the behavior each or a combination of aberrations exhibit.

Edited by Asbytec, 27 August 2018 - 12:29 AM.

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### #24 Oregon-raybender

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Posted 27 August 2018 - 01:29 AM

You can test this by using lens design software, simply move the image plane (thickness from best focus, just add another surface) to yield 10 waves of pure power. Look at the fringes and Point Spread Function (PSF) to show what the star image will look like. The real values can be tested to what the software says, they should match.

Starry Nights

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