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Coma corrector and Newtonian collimation

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#1 raal

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Posted 22 August 2018 - 01:10 PM

In another thread, member X3782 expressed concerns about being able to enjoy a quality mirror while having unavoidable errors in scope alignment (collimation).

 

Then I said that coma corrector will take care of that issue and gave some proposterous numbers on which I based my claim, but the numbers were wrong because I made the wrong setup of the simulation in OSLO, so I promised to post the right numbers once I get it right.

 

X3782 also mentioned something that coma correctors are very sensitive to decentering, thus collimation error from scope flexing with variable elevation.

 

So, lets see what happens.

 

When the scope flexes with elevation, it's the same thing as mirror tilt, as the axis of the scope doesn't match the optical axis any more. But there's more. You can have a mirror tilt while the axis of the focuser with CC will still point straight at the center of the mirror. I was simulating another case;

Let's say that if the focuser is on the side of the scope, parallel to ground, then scope flexing will "sink" the focuser towards the ground in parallel translation, thus focuser axis will not point straight at the mirror center.

I guess this ends up being just pure decentering.

 

The OSLO setup does contain a mirror tilt, but only to allow the image to hit the focal plane, while the focal plane and coma corrector (focuser), is being de-tilted and kept parallel to the scope axis, so it is pure decentering with the image steered off-axis to be get centered with focal plane center (focuser axis).

 

Attached File  12-5 f5 paraboloid tilted coma corrector not tilted.len   1.46KB   16 downloads

 

The decentering of focal plane center (focuser axis) is ~2.7mm, which is a substantially large collimation error.0

 

 

Here are the plots;

 

2.77mm focuser decenter 12.5" f/5 without coma corrector, focal plane diameter 14.2mm:

 

no corr.jpg

 

So, at center we have Strehl 0.81.

 

It can be seen here how coma arrows point in opposite directions, like pointing to somewhere in between. That is where the best spot is, at field height of 20%, which is ~1.4mm of 7.1mm field radius. It is virtually unspoiled, being Strehl ~1.

Here it is:

no corr best spot m.jpg

 

It sounds weird that the best spot is just 1.4mm above center, as collimation error is double that, at  2.77mm., but we have field curvature that is not centered any more with focal plane and I did refocus for minimum spot on axis, as it would be done in practice. I take this as field curvature and best focus do not cross in center of the focal plane any more, but 1.4mm away.

Which is really good, when you think of it.

 

 

Now with CC, same mirror.

My CC has magnification of 1.413. I wanted to keep the same TFOV for this presentation, so I increased the field stop radius. Focal plane now is 20mm in diameter.

 

First, let's see how CC works when centered.

Scale is changed so the Airy disk size would be the same on all plots:

 

corr centered.jpg

 

 

Now, with about the same decenter, 2.67mm:

 

with corr.jpg

 

We have the same Strehl in center, as without the CC, and the whole field is much better, being diff limited everywhere except just a little lower at far negative field edge, but we don't have a better spot than on-axis any more, anywhere in the field.

That has been lost.

However, as far as sensitivity goes, in is not worse on axis than without the CC and the image off-axis didn't explode into mess.

I chose this particular collimation error (~2.7mm) to keep on axis image at S=0.81.

 

What would be the conclusions from this?

Are collimation errors more or less critical with coma corrector?

 

One thing is for sure, stiff scope would be good in any case.


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#2 MitchAlsup

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Posted 22 August 2018 - 04:09 PM

One thing is for sure, stiff scope would be good in any case.

If you re-ran those experiments with 12.5 F/4 and 12.5 F/3 you would see how much harder it is to pull off these faster scopes.



#3 Starman1

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Posted 22 August 2018 - 04:39 PM

A recent discussion here on CN pointed out that with the new Paracorr coma corrector, the tolerances for focuser alignment (secondary error)

go down to 0.002D, where D is the diameter of the scope.

The Primary Axial error stays the same at 0.01778mm x f/r³

For an example of a 16" f/4 scope, for example, collimation tolerances are:

secondary--0.81mm

primary--1.14mm

Both of those are smaller than the typical size of a laser beam hitting the primary, so it seems an autocollimator is virtually essential to get the tolerances tight enough.

And it also means stiffness is paramount.            


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#4 X3782

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Posted 22 August 2018 - 06:06 PM

If I wanted to achieve "diffraction limited" performance, in reality there are multiple sources of aberration, not only this one tilt or misalignment, which will all sum up (quadratically or otherwise?) to degrade the image. So one needs to aim for significantly higher collimation tolerance than e.g. 0.8 or 1.1 mm I guess to leave ample room in the error budget for these other sources. For a F4 16 inch scope, this means eyeballing a mark located 1.6 m away from my eye with sub millimeter precision. I'm pretty sure with my eyesight I can't do that...... I can barely do that with 1 m. Also I keep wondering, how do you know that the mark on the mirror is so precisely placed, that presupposes the axis of the paraboloid and the center of the mirror coincide.

 

A laser collimator I guess has a multi-mode diode laser inside, this produces an elongated and highly divergent beam spot because of the way a laser diode chip resonator is arranged. This beam is collimated with some prism + aspheric lens, or a tilted lens, mounted in the device to create a roundish beam. This type of beam has the problem that, as it propagates though the air it changes shape because the multiple spatial modes that overlap in the beam interfere with one another, so the apparent "center" of the beamspot at one location will not be the same at another, there is an uncertainty of order the spot size diameter or larger. The beam often does not have a Gaussian intensity profile, only the eye is tricked into assuming the center of the laser beam spot has the highest intensity, because of the logarithmic response the human eye has against light. I think +/- 1 mm alignment precision over 1.6 m or 3.2 m should already be (quite) difficult to achieve on a consistent basis, I could not say yes that is a reliable way to do that. Also how can one be sure the laser beam is going exactly through the center of the collimation lens, there must be some diffraction....?

 

The other option would be to simply give up this ambition, and say, good enough is good enough...... or to get a young person with very good eyesight to collimate. The seeing etc. will anyway never allow a 16 inch telescope to get close to the diffraction limit.... I have to admit, I'm not able to get the maximum performance out of my 16 inch F4.5 Dob for many reasons, I'll work on that in the next decades when I hopefully will have more time......


Edited by X3782, 22 August 2018 - 06:26 PM.


#5 X3782

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Posted 22 August 2018 - 06:38 PM


It sounds weird that the best spot is just 1.4mm above center, as collimation error is double that, at  2.77mm., but we have field curvature that is not centered any more with focal plane and I did refocus for minimum spot on axis, as it would be done in practice. I take this as field curvature and best focus do not cross in center of the focal plane any more, but 1.4mm away.

Which is really good, when you think of it.

 

Thanks, the simulations look nice. I love my TMB Supermonocentrics, it has a field stop diameter of 2.5 mm. The "best focus" is not within my field of view anymore bawling.gif.

I think the eyepiece has mild field curvature as well, so I can no longer get best image on-axis or anywhere else I guess......


Edited by X3782, 22 August 2018 - 06:50 PM.


#6 Starman1

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Posted 22 August 2018 - 07:46 PM



If I wanted to achieve "diffraction limited" performance, in reality there are multiple sources of aberration, not only this one tilt or misalignment, which will all sum up (quadratically or otherwise?) to degrade the image. So one needs to aim for significantly higher collimation tolerance than e.g. 0.8 or 1.1 mm I guess to leave ample room in the error budget for these other sources. For a F4 16 inch scope, this means eyeballing a mark located 1.6 m away from my eye with sub millimeter precision. I'm pretty sure with my eyesight I can't do that...... I can barely do that with 1 m. Also I keep wondering, how do you know that the mark on the mirror is so precisely placed, that presupposes the axis of the paraboloid and the center of the mirror coincide.

 

that the center marker may be inaccurate is a given.  Modern methods of making mirrors, however, pretty much guarantee the axis of the paraboloid and the center of the mirror coincide.

 

A laser collimator I guess has a multi-mode diode laser inside, this produces an elongated and highly divergent beam spot because of the way a laser diode chip resonator is arranged. This beam is collimated with some prism + aspheric lens, or a tilted lens, mounted in the device to create a roundish beam. This type of beam has the problem that, as it propagates though the air it changes shape because the multiple spatial modes that overlap in the beam interfere with one another, so the apparent "center" of the beamspot at one location will not be the same at another, there is an uncertainty of order the spot size diameter or larger. The beam often does not have a Gaussian intensity profile, only the eye is tricked into assuming the center of the laser beam spot has the highest intensity, because of the logarithmic response the human eye has against light. I think +/- 1 mm alignment precision over 1.6 m or 3.2 m should already be (quite) difficult to achieve on a consistent basis, I could not say yes that is a reliable way to do that. Also how can one be sure the laser beam is going exactly through the center of the collimation lens, there must be some diffraction....?

 

the best lasers have aperture stops that not only guarantee a small round spot on the mirror, but also produce diffraction rings like a star image that provide additional cues in collimation.  Achieving collimation to better than the dot size on the mirror is possible.  And some lasers are well collimated themselves.  You're correct to point out that even the best lasers will not result in the precision necessary.  For accurate collimation, an autocollimator is essential.

 

The other option would be to simply give up this ambition, and say, good enough is good enough...... or to get a young person with very good eyesight to collimate. The seeing etc. will anyway never allow a 16 inch telescope to get close to the diffraction limit.... I have to admit, I'm not able to get the maximum performance out of my 16 inch F4.5 Dob for many reasons, I'll work on that in the next decades when I hopefully will have more time......

 

good seeing is always a matter of being in the right place at the right time.  I've seen nights of sub 0.5" seeing that allowed my 12.5" to resolve to the limit, however.  Alas, such nights are not common.

It was good to know I was collimated and had cooled optics when it happened.


Edited by Starman1, 22 August 2018 - 07:48 PM.

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#7 X3782

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Posted 23 August 2018 - 07:29 AM

 

that the center marker may be inaccurate is a given.  Modern methods of making mirrors, however, pretty much guarantee the axis of the paraboloid and the center of the mirror coincide.


the best lasers have aperture stops that not only guarantee a small round spot on the mirror, but also produce diffraction rings like a star image that provide additional cues in collimation.  Achieving collimation to better than the dot size on the mirror is possible.  And some lasers are well collimated themselves.  You're correct to point out that even the best lasers will not result in the precision necessary.  For accurate collimation, an autocollimator is essential.


good seeing is always a matter of being in the right place at the right time.  I've seen nights of sub 0.5" seeing that allowed my 12.5" to resolve to the limit, however.  Alas, such nights are not common.

It was good to know I was collimated and had cooled optics when it happened.

 

Do the axis of the paraboloid and the axis of the mirror coincide to less than 0.5 mm? I see for example that the diameter of my 8" mass produced mirror varies by 0.2-0.3 mm or so because it is rough cut...... it doesn't seem to be exactly round.

 

The main reason why the laser alignment is less precise than eye is because, even if one puts in an aperture, or reduces the aperture size, or makes it very round or knife-edge like, the laser beam continues to contain a certain number of spatial modes, not just one. In the far field 1-2 meters away, you see interference between these numerous modes that may look concentric, but in reality are behaving more unpredictably and often quite differently compared to an incoherent white light source that we have in everyday life.

 

Light from a candle or starlight contains countless numbers of  wavelengths and spatial modes that are superimposed in a truly random way, so when you let this beam pass through an aperture, it is the aperture and the aperture alone that defines how the beam will behave in the far field. So it behaves like classical ray tracing, straight lines, but with the added contribution of interference, so you get well behaved Airy rings that can be analyzed by Zernike formulations and so on. Multimode lasers on the other hand contain a small number of modes that are superimposed on each other, not necessarily in a symmetric way, so they interfere in a more unpredictable way. In the white light analogy, it is like letting light though a sequence of off-axis apertures that are not well aligned stacked on top of each other (this is a doubtful metaphor, it is not exactly like that). so light is sequentially scattering on iris A B C D E F G etc., but iris A and B are not on the same axis. So in the far field, the contribution from each stacked aperture interfere, the center-of-the-pseudo-Airy-ring actually drifts transversely as it propagates longitudinally. This is counter-intuitive if one is used to thinking of images propagating in straight lines. So I think +/- 1 mm precision over 1.6 m long OTA is already quite challenging and not always reproducible, although if you look only at the laser pattern you may think there is no problem.

 

One interesting experiment is to use a neutral density filter to really reduce the laser intensity, and look carefully. Then at some point, one may realize that the beam is not really homogeneously round, and this shape changes as one moves nearer or further from the laser source. Normal white light has actually quite nice characteristics, as used in Foucault tests and so on.

 

In Zygo interferometers etc. I guess a single-mode HeNe laser etc. are used that have only 1 single TEM00 Gaussian mode that avoid these problems. Nevertheless I would imagine that in high frequency small spatial modes, the laser will start to produce unwanted fringing, so classical white light sources are preferred to study them. Actually if you just look at the special case of Newtonian mirrors, the classical testing methods have a lot going for them it looks like.


Edited by X3782, 23 August 2018 - 08:03 AM.


#8 Starman1

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Posted 23 August 2018 - 09:00 AM

I can tell you what you say is true for most lasers.  It is not, however, true for all lasers.

There have been times when I was very careful to attain near-perfect registration of the laser and a following barlowed laser

when the autocollimator indicated no residual error at all, which is better than 0.01" accuracy.

As for determining the optical center of an out-of-round mirror, I have nothing to suggest.

Comparing tool collimation with star collimation is about all you could do in that case.

Center markers are rarely placed with 0.2-0.3mm precision anyway.



#9 X3782

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Posted 23 August 2018 - 11:26 AM

I can tell you what you say is true for most lasers.  It is not, however, true for all lasers.

There have been times when I was very careful to attain near-perfect registration of the laser and a following barlowed laser

when the autocollimator indicated no residual error at all, which is better than 0.01" accuracy.

As for determining the optical center of an out-of-round mirror, I have nothing to suggest.

Comparing tool collimation with star collimation is about all you could do in that case.

Center markers are rarely placed with 0.2-0.3mm precision anyway.

 

The spot on the mirror is located 1.6 m away from the autocorrelator, a lateral movement of 0.01 inches = 0.25 mm corresponds to arctangent(displacement/distance)= 0.00016 radians = 33 seconds of arc (is that right)? I think this is equivalent to the ability of eyeballing Jupiter on a Telrad, recognizing by naked eye that Jupiter is not a point but a disk, and slewing the telescope from one edge of this disk to the other by naked eye without any telescopic guidance, just by turning a knob; it is equivalent to seeing a legal A4 piece of paper at a distance of 1 km. Is it really possible to align to this precision by naked eye autocorrelator, in my case I cannot distinguish a mark moving by more than say 2-3 minutes of arc = 1-1.5 mm, and that is only for the first clear reflection that I strain to see, not to mention the additional passes which get progressively more difficult to distinguish.... the possible tilting of the mirror in the autocorrelator in the focuser, the unknown precision on the position of the sticker mark, etc.

 

In my case in darkness and if I am tired, it can be several factors worse than the +/- 1-1.5 mm that I measured in a bright lab. With the colimation laser it is similar or worse. I'd like to be refuted, but I can't see how one can objectively get more than +/-1 mm using any of these techniques in a fully reproducible way, meaning, I can't get "diffraction limited" performance with my great mirror because I can't align with that accuracy. I need to be able to align the knobs so accurately that I can center the image on one side of the orbit of Io around Jupiter (corresponding to Strahl ratio=0.8) to the other side of its orbit by twisting the alignment knob (ratio=1.0), but if the OTA twists and I see the image of Jupiter jerking around, it shows the OTA doesn't have the rigidity to adjust that finely by far. The image has to be dead steady and smooth first of all, and then I can start to think about alignment.

 

When I used a perhaps much more robust way to align the mirror using more sophisticated equipment, and compared it with the other two normal techniques (and I used the most expensive amateur laser collimator for this), the convergence in no case was better than a few arc minutes equivalent or even worse. Laser's limited by diffraction, autocorrelator by the angular resolution of the naked eye, though the latter one is more precise. If we have two techniques which are equally imprecise, and compare the two, and we see an agreement, it just means both methods are imprecise. Just like, if we use a poor laser interferometer and measure the figure of a mirror and see no deviation from some reference value, we are mistaken to claim it is 1/12 wave precise.


Edited by X3782, 23 August 2018 - 01:17 PM.


#10 Starman1

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Posted 23 August 2018 - 04:29 PM

Obviously you have not used an autocollimator.  The 4 images produced are at varying distances from the eye, about 7 focal lengths in total.

When they are "stacked", you have lined up spots at those distances to coincide exactly with one another.

It is easy to see an error of 1/50 of the diameter of the center marker in the final stack (~0.01"), and if the collimation screws are precise enough, you can get even closer.

What size angular error is 0.01" at 7 focal lengths distance?

It is so precise a tool that differential contraction of the tubes in a truss dob as they cool can result in seeing collimation wandering all over the place.

I used that tool to gauge how much sag in the UTA and spider vanes occurred as I moved the scope up and down.  Once everything was tight enough, I could see literally zero

change until the scope pointed below 10°.  I have stops on the altitude axis to prevent the last 10° of movement now.

 

I admit, I did not counterweight the UTA so that placing a Paracorr and heavy eyepiece in the focuser on one side would not result in a rotational twist imparted to the poles.

But the poles are 32mm diameter and only 107cm long, and there are 8 of them, so the rotational twist is likely to be quite small.

I see no miscollimation of the optics at all in the star test after collimating with tools.  I've never been able to improve on tool collimation when checking using stars.

[I do, however, see astigmatism in the star images during the cooling of the optics, but it goes away when the optics reach thermal equilibrium.]



#11 X3782

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Posted 23 August 2018 - 05:47 PM



Obviously you have not used an autocollimator.  The 4 images produced are at varying distances from the eye, about 7 focal lengths in total.

When they are "stacked", you have lined up spots at those distances to coincide exactly with one another.

It is easy to see an error of 1/50 of the diameter of the center marker in the final stack (~0.01"), and if the collimation screws are precise enough, you can get even closer.

What size angular error is 0.01" at 7 focal lengths distance?

It is so precise a tool that differential contraction of the tubes in a truss dob as they cool can result in seeing collimation wandering all over the place.

I used that tool to gauge how much sag in the UTA and spider vanes occurred as I moved the scope up and down.  Once everything was tight enough, I could see literally zero

change until the scope pointed below 10°.  I have stops on the altitude axis to prevent the last 10° of movement now.

 

I admit, I did not counterweight the UTA so that placing a Paracorr and heavy eyepiece in the focuser on one side would not result in a rotational twist imparted to the poles.

But the poles are 32mm diameter and only 107cm long, and there are 8 of them, so the rotational twist is likely to be quite small.

I see no miscollimation of the optics at all in the star test after collimating with tools.  I've never been able to improve on tool collimation when checking using stars.

[I do, however, see astigmatism in the star images during the cooling of the optics, but it goes away when the optics reach thermal equilibrium.]

 

     I own one yes... the eye needs to identify and line up these spots lying at various distances between 1.6 to 10 meters away from my eye. My eyesight isn't good enough to split the center marker to 1/50, that corresponds to being able to see 30 arc seconds. The further it is, the more incredibly severe the requirement on the eye becomes.

 

     The massive stainless steel mounts for 3-inch mirrors with sapphire seats that I use on my day job which I mount with 1 inch stainless steel posts on a 500 kg, 300 mm thick stainless steel table have a precision of 2300 arc seconds per turn of the 130 threads-per-inch fine-threaded adjustment screw (I guess this kind of thing can't be used for long outdoors before dirt and contamination mess up the thread, a normal fine-thread UNF has 12 threads per inch, a coarse thread 7 threads per inch). 30 arc seconds is 1/80 of a turn of this very fine screw (or 1/700 turn if I used a fine-threaded UNF, or 1/1200 turn if I used a normal UNF). If the temperature changes by 10 degrees, the spring-loaded mount itself will deform and drift by 10 arc seconds (measured). The same mount made of aluminium will probably move 5 times as much, not including the fact that it is much less massive and probably less robust in design (no sapphire seats.... no 130 TPI adjustment threads....) than an optical table precision mirror mount where weight and cost are not issues. That's already larger than 50 arc seconds just for the primary mirror mount movement mechanism, without thinking of the (probably much larger contribution from) telescope OTA or the flimsy secondary mirror mount suspended in air, or the fact that the primary is just placed there, floating on 6 or 9 or so Delrin supports. I don't have much experience, but a good German equatorial mount weighing 20-30 kg has a periodic motion error before correction of around 30 arc seconds peak-to-peak as far as I understand, the dob mirror mount cells and secondary mirror mount suspended by thin vanes are by far not this massive or as precise.

 

     This method relies on the 2nd mirror in the autocollimator retaining a perfect 90 degree alignment with respect to the barrel of the focuser. To get 30 arc seconds, doesn't one need 10 micron (I'm not confident of this number, but Seran Wrap is 13 um thick) absolute displacement precision on this mirror, it needs to be within 30 arc seconds of perfect 90 degrees, implying between 89.992 degrees to 90.008 degrees. I don't know what this device is made of (not a low thermal expansion alloy it seems to me), but that must be extremely difficult. The focuser I guess doesn't have that kind of precision, I have a play of 150 micron (otherwise it won't slip smoothly in of course). Fitting two pieces of machinery together with this kind of precision is when, if I take a handkerchief and polish the metal interface to take the dust out, that is enough to send it out by 5-10 um.


Edited by X3782, 23 August 2018 - 07:17 PM.


#12 Starman1

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Posted 23 August 2018 - 06:08 PM

I use an autocollimator with a dual pupil, so I can line up secondary and primary separately.

I also use a Hotspot™ center marker, which can reveal extremely small errors in stacking.

I agree that attaining and holding collimation to perfection is simply not possible.

However, attaining sufficient precision is.  If you see perfectly round star images with uniform illumination of the diffraction rings at 40x/inch,

how are you likely to be able to improve on that?  And I see that all the time.



#13 X3782

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Posted 23 August 2018 - 07:34 PM

I think I have the same product yes, so I've spent 1000 USD on my alignment toys.

 

Precision means being able to resolve something, though that measurement may not be correct.

Accuracy means being able to resolve something, plus being able to move it to the known correct value.

Not being able to resolve means one sees zero, it is actually neither precise nor accurate, though there is a danger to assume it is precise and accurate.

 

Even illumination of the diffraction rings (which is a bit subjective criterion) is not an indication that the optical system has achieved 1/4 wavefront distortion, it can be much worse than 'diffraction limited' but still achieve that. The eye is not so very good at distinguishing levels of brightness, plus what we see is time-averaged, if the fluctuation of the image is rapid enough, the blur is integrated and averaged out in our brains and we will perceive that it is evenly illuminated, though at each instance in time, it is not. Given a more rigid mount and OTA, a more stable atmosphere, a more perfect figure of the optics, we will be able to further improve the alignment, and improve the "sharpness" of the image, and discover that, we were actually not working at the best possible potential of the optics.

 

The diffraction ring is an artifact caused by the diffraction of the light rays on the finite size of the optics, mostly the outer rim of the primary mirror. Even if you put a small obstacle in the light path, relatively little change will be seen in the evenness of the illumination if the eye is used. If you use a high-dynamic range CCD camera and measure the number of photons hitting each pixel and strictly equalize, you normally find how bad the eye is for this kind of use, especially when the image is shaking and so on. The word 'diffraction limited' is actually misleading, it makes people assume that just because they see the artifact (Airy disk, diffraction rings, etc), they are now limited in resolution. From the point that you start to see these effects (which were already seen in the optics of the 1820's), there is actually quite a ways deeper to go until the true limit in resolution is reached, just because starlight is such an ideal light source. In a lab environment, I will start to align coarsely and I will quite rapidly start to see the interference fringes, that is just the beginning and it can be hours of alignment of walking all the possible knobs and scanning the parameter space of alignments, before the best possible alignment which is the 'diffraction limited' resolution one, is reached.


Edited by X3782, 23 August 2018 - 08:02 PM.


#14 Adun

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Posted 23 August 2018 - 08:23 PM

 

Now, with about the same decenter, 2.67mm:

 

attachicon.gif with corr.jpg

 

We have the same Strehl in center, as without the CC, and the whole field is much better, being diff limited everywhere except just a little lower at far negative field edge, but we don't have a better spot than on-axis any more, anywhere in the field.

That has been lost.

However, as far as sensitivity goes, in is not worse on axis than without the CC and the image off-axis didn't explode into mess.

I chose this particular collimation error (~2.7mm) to keep on axis image at S=0.81.

 

What would be the conclusions from this?

 

 

I didn't quite get this part. Can you explain again?



#15 Vic Menard

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Posted 23 August 2018 - 08:27 PM

Precision means being able to resolve something, though that measurement may not be correct.

Accuracy means being able to resolve something, plus being able to move it to the known correct value.

In this case, I see "precision" as the alignment read. With a calibrated reference, it's hard to miss an alignment error as large as 0.02-inch. With a Cheshire alignment (HotSpot/bright Cheshire ring), the 0.02-inch read represents a 0.01-inch primary mirror axial alignment. Similarly, using a quality autocollimator (one that passes a rotation test), and carefully decollimating the primary mirror, stacking the 2 central reflections (HotSpot or perforated triangles give the best calibrated results, in my experience), the alignment read is similar to the Cheshire and the read error, again, is twice the actual focuser axial error. In each case, the error is discrete and the correction is obvious. 

 

Although a simple thin beam laser is often used incorrectly, I've found that a good laser with a 1mm aperture stop can not only pass a rotation test, it can also provide excellent focuser axial error resolution, perhaps 0.02-inch with an optimally (matched) perforated primary mirror center spot.

 

Regarding the acceptable focuser tilt error for a Newtonian, I've saved a copy of a discussion I had with Nils Olof back in 2005. In his words:

 

"A back-of-the-envelope calculation - in mm:

the distance m from optical axis to where the coma is 0.071 waves RMS (The
Marechal criterion - with low-order sph abb this is 1/4 wave, for coma it is
1/2.5 wave) is approx F^3 * 0.0106 - at this distance the defocusing due to
focal axis tilt should be much smaller than coma (since they both increase
linearly, one point is enough). Let's say the P/V of defocusing error is
allowed to be 1/10 wave here (contributing some 15% of total), this makes th
e defocus 0.00044 * F^2 (Suiter) and the error d/L where d is pointing
error and L is focal length: d=L/(25*F) - without Paracorr! Divide this by
another 6 if you have one."

 

After this discussion, he updated his website, http://web.telia.com...olli/kolli.html  to include this alignment criteria (with some minor tweaks), scroll down to "Error type 1B - the optical axes are not parallel, but form an angle"



#16 X3782

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Posted 23 August 2018 - 08:47 PM

In this case, I see "precision" as the alignment read. With a calibrated reference, it's hard to miss an alignment error as large as 0.02-inch. With a Cheshire alignment (HotSpot/bright Cheshire ring), the 0.02-inch read represents a 0.01-inch primary mirror axial alignment. Similarly, using a quality autocollimator (one that passes a rotation test), and carefully decollimating the primary mirror, stacking the 2 central reflections (HotSpot or perforated triangles give the best calibrated results, in my experience), the alignment read is similar to the Cheshire and the read error, again, is twice the actual focuser axial error. In each case, the error is discrete and the correction is obvious. 

 

Although a simple thin beam laser is often used incorrectly, I've found that a good laser with a 1mm aperture stop can not only pass a rotation test, it can also provide excellent focuser axial error resolution, perhaps 0.02-inch with an optimally (matched) perforated primary mirror center spot.

 

Regarding the acceptable focuser tilt error for a Newtonian, I've saved a copy of a discussion I had with Nils Olof back in 2005. In his words:

 

"A back-of-the-envelope calculation - in mm:

the distance m from optical axis to where the coma is 0.071 waves RMS (The
Marechal criterion - with low-order sph abb this is 1/4 wave, for coma it is
1/2.5 wave) is approx F^3 * 0.0106 - at this distance the defocusing due to
focal axis tilt should be much smaller than coma (since they both increase
linearly, one point is enough). Let's say the P/V of defocusing error is
allowed to be 1/10 wave here (contributing some 15% of total), this makes th
e defocus 0.00044 * F^2 (Suiter) and the error d/L where d is pointing
error and L is focal length: d=L/(25*F) - without Paracorr! Divide this by
another 6 if you have one."

 

After this discussion, he updated his website, http://web.telia.com...olli/kolli.html  to include this alignment criteria (with some minor tweaks), scroll down to "Error type 1B - the optical axes are not parallel, but form an angle"

 

I'm sorry this is just my sickness that comes from occupation, I've seen too many instances where something is "assumed", then when you check it with an alternative method that has 10 times higher accuracy, it is found that one has underestimated by a factor of say 3-4, by explaining away errors that one sees. There is this magic factor 3 of underestimating errors that I have seen throughout even experts in most things, just because some error has been overlooked, and the power of some supposed cross-check method has been overestimated. One should start to get nervous when the argument runs like "suppose, assume, suppose, therefore it this so accurate". Psychological alignment is when we wish something to be accurate, and therefore look for ways we can prove it to be accurate, whereas in reality we should look for ways it can be inaccurate.

 

0.02 inch is now 0.5 mm. Is that peak-to-peak (maximum possible excursion under worst-case scenario), or full width at half maximum (most of the time it is inside this, but a significant number of non-negligible times it is outside). Is that the read, or the accuracy. If it is the accuracy, there must be a reference that one has absolute confidence in. If it is referenced against itself, that is already a dangerous thing to do to then claim it has such-and-such accuracy because I have moved parameter A and B and see no apparent change within my perception. Suppose the perception has not the sensitivity, or parameter C has been neglected, it is limited by one's poor imagination of noting possible error sources.

 

I know from experience that if I have a 400 um diameter optical fiber (which of course has a certain angular acceptance), and I try to fire a laser beam at it from say 2 m away, and I believe it to be aligned using reflections and eyeballing, and now check how much light is transmitted on the other end. I often see 1 to 10% of maximum transmission, just because looking at reflexes or eyeballing is not that precise as one may assume. Especially looking at coherent light is problematic, we assume it is acting like normal incoherent light, but it is not, so the possibilities of being mislead by optical illusions or diffraction effects is that much magnified. The diameter of the laser light is specified by 1/e^2 diameter, FWHM diameter, rms radius, etc. and there is a surprising difference in factors between them, which is again different from what person A or person B perceives. "Do not believe what you see" is the first thing one teaches a novice.


Edited by X3782, 23 August 2018 - 09:16 PM.

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#17 Vic Menard

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Posted 23 August 2018 - 08:51 PM

0.02 inch is now 0.5 mm. Is that peak-to-peak (maximum possible excursion under worst-case scenario), or full width at half maximum (most of the time it is inside this, but a significant number of non-negligible times it is outside). Is that the read, or the accuracy.

It's a simple, linear, tolerance (measured relative to the reference).



#18 X3782

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Posted 23 August 2018 - 09:25 PM

"Simple linear tolerence" already makes me nervous (and what is the reference in this case, normally the reference has to be factor 3-4 more precise or accurate than the thing that you want to measure, otherwise the actual error is a quadratic or linear sum of uncertainties).

If it is 1 sigma error = 1 "standard deviation" error (which is often used), then it means

68% of the time it is within the specified +/- 0.5 mm. 32% of the time, it is outside. If it is quality control cutoff set to +/- 0.5 mm as upper limit, we have a reject rate of 32%.

95% of the time it is within +/- 1 mm.

99.7% of the time it is within +/- 1.5 mm

 

If we repeat the Newtonian alignment procedure 1000 times, and see only 3 cases where the error was as large as >+/- 1.5 mm due to whatever mishap, only then are we allowed to say, the tolerance of this procedure is robustly +/- 0.5 mm one standard deviation error. If we see 5% of the time this happening, the actual error is +/- 0.8 mm. This assumes we have some reliable calibration method to compare to which is say 3-4 times more precise or accurate compared to the thing we want to measure. And the interesting thing is, in many cases, one sees times when the alignment precision is more than +/- 1.5 mm inaccurate, though mathematically it is impossible to have such a "quality control failure rate" which should be vanishingly (<=0.3%) small, if indeed the tolerance is +/-0.5 mm. Because we have underestimated.

 

If instead the story is that one tried to align and achieved 0.5 mm as a best case champion data for a highly skilled person in a particularly good day when he/she made no mistake, or the story is that we have established a credible logic why a certain method is "in principle" 0.5 mm accurate if everything were perfectly done without any mistake, normally it means the actual "tolerance" of the procedure is e.g. 3 times larger than that, like 1.5 mm. And so most of the time, the telescope will not achieve strict diffraction limit. Normally the rule of thumb is, if there is an engineering requirement as an upper limit ("I must get +/-0.5 mm to get diffraction limit"), and somebody proves this is possible at the very limit of sensitivity, and there is a complicated reasoning why this is so, then it can be that "I wish it to be 0.5 mm, it ought to be 0.5 mm, and therefore it is 0.5 mm".

 

Then the factory or project gets overwhelmed by the high failure rate.


Edited by X3782, 23 August 2018 - 10:49 PM.

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#19 Starman1

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Posted 24 August 2018 - 01:07 AM

OK, you're trolling.

Arguing that we simply cannot achieve the collimation precision necessary to get "diffraction limited" performance from the optics simply doesn't agree with experience.

If we cannot achieve it, then no telescope can ever perform that well, and yet they do.

So are we just lucky, or are the tolerances for collimation and good images simply looser than assumed?

Maybe a bit of both.  But the tools, if accurate, and used correctly, can get you there.



#20 X3782

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Posted 24 August 2018 - 05:10 AM

OK, you're trolling.

Arguing that we simply cannot achieve the collimation precision necessary to get "diffraction limited" performance from the optics simply doesn't agree with experience.

If we cannot achieve it, then no telescope can ever perform that well, and yet they do.

So are we just lucky, or are the tolerances for collimation and good images simply looser than assumed?

Maybe a bit of both.  But the tools, if accurate, and used correctly, can get you there.

 

Sorry about that, didn't mean to troll.... My point is that "diffraction limited" means for example that the star images are really tiny, like a few micron diameter on the focal plane, depending on the F-number of the optics.

 

The alignment tolerances to achieve this are extremely, really small, like a fraction of an arc minute when the telescope apertures get to >12.5-15 inches and small f-numbers; and there is an error budget that has to be carefully added up. The old professional instruments 50-100 years ago etc. are really massive and look like tanks even in the 10-16 inch regime, and the collimation instruments are exceedingly complicated, even for relatively small aperture telescopes. They used a tripod-mounted telescope to align a telescope.

 

Now this technology comes down to our amateur level, and they have been "downsized", made very light, and very simple and low cost by factor 10-100. In fact the Dobsonian was initially a very low cost instrument that did not care so much about precision. The question I have is, perhaps this means we are not achieving the same level of precision for example with a 12 inch or 16 inch compared to what is actually needed to get to diffraction limit, as the old extremely massive instruments? All these instruments, like a handheld diode laser, are relatively new inventions. I design and build lasers for a living, I think I know where the dangers are, and I am wondering whether these problems have been really carefully studied.

 

But we've also learned that perhaps a significant number of people are insensitive even if the star image blows up by factor 10, to few 10's microns or even larger, far from the diffraction limit, which is for example what you get if you don't use a coma corrector.

 

We have recently seen that some high volume mirror manufacturers claim very high precision figures that are 'diffraction limited', even adding data sheets, and as many people including me in CN have found out, the precision is actually perhaps not as high as all that. Or even, significantly worse. When we add up all these imprecisions, in the mirror, in the alignment, in the rigidity of the telescope structure, etc. I don't see how one could claim diffraction limit is achieved so much in every day use. My point is that perhaps in all these cases, there is underestimation.

 

For me the laser and alignment part particularly hurt, because that is my speciality. I guess the mirror opticians see how mass produced optics have their shortcuts and limitations, I have the same opinion here. For me an alignment device of less than a few arc minutes has to cost 10000 USD at least in the economy version and mounted on a tripod with two telescopes and three different ways to cross check because of how easy it is to mess it up. There is usually a professional who is trained to do nothing but alignment, and 30 arc seconds is a level that often they will refuse to guarantee. Because this is at a level where temperature drifts even on a concrete floor start to play a non-negligible role. The claim is that the same level of precision is reached with a 400 USD device. I like this device, I studied it. But if really 400 USD trumps 10000 USD, then nobody would buy the 10000 USD.


Edited by X3782, 24 August 2018 - 05:59 AM.

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#21 Jon Isaacs

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Posted 24 August 2018 - 05:58 AM

But we've also learned that perhaps a significant number of people are insensitive even if the star image is few 10's microns or even larger, far from the diffraction limit, which is for example what you get if you don't use a coma corrector.

 

 

One simple test of star size is splitting close doubles.  When the seeing is sufficiently stable, the Dawes limit is within reach for my generic 10 inch GSO Dobsonian.  It gets more difficult with larger scopes because of the excellent seeing required but have split a double close to the Dawes limit with my 13.1 inch F/5.5.

 

Jon



#22 Jon Isaacs

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Posted 24 August 2018 - 06:03 AM

 

the best lasers have aperture stops that not only guarantee a small round spot on the mirror, but also produce diffraction rings like a star image that provide additional cues in collimation.

 
Not the perfect picture but it tells the story.  
 
4895267-Howie Glatter Laser at 2.2 meters.jpg
 
Jon
 
 

 



#23 Jon Isaacs

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Posted 24 August 2018 - 06:42 AM

The Primary Axial error stays the same at 0.01778mm x f/r³

For an example of a 16" f/4 scope, for example, collimation tolerances are:

secondary--0.81mm

primary--1.14mm

 

 

I am confused here. I am trying to make the equation for the primary axial error work out, I can't get it to work out.  What is f and what are the units, what is r and what are the units?

 

Also, for the primary, the radius of the coma free region is 0.7mm.  I was under the impression that the primary axial error needed to significantly less than the radius of the coma free region.  

 

:question:

 

Jon



#24 X3782

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Posted 24 August 2018 - 08:51 AM

 

 
Not the perfect picture but it tells the story.  
 
 
 
Jon

 

 

Thanks. I checked, a nickel is 21.2 mm diam lol.gif  So the first diffraction ring is 8 or 9 mm full diameter or so, second ring 14 or 15 mm. The question is how precisely you could subdivide this spot looking only by naked eye as it propagates.

 

The argument was that I think subdividing by a precision of 0.25 mm (1/83 of a nickel) and finding the "correct" centroid is a goal that I would not be comfortable with. If I do the alignment 1000 times, I believe there will be much more than 3 cases where one would be off by 0.75 mm (1/27 of a nickel) assuming a Gaussian statistical distribution of errors. So I do not accept the 0.25 mm tolerance.

 

1/21 of a nickel is what I would dare to give as a repeatable tolerance, but only grudgingly, meaning I am confident if I align 1000 times with this laser spot, I might be off by 1/7 only in 3 cases or so. Once every year on a bad day, if I align every day.

 

Because the "roundness" of the beam is not that perfect to be able to divide this coherent beam spot by 1/40; actually if you look carefully, there is a rectangular component in the beam, areas of darker and brighter parts in the circular fringe to the top and the bottom; the main beam also may have 2 or 3 spikes running horizontally, it is hard to see from the photo because it is overexposed with respect to the main beam. The resonator is a rectangular semiconductor junction, the original beam is highly elliptical that is shaped by an aspheric lens, then there is a circular aperture. So if you took a photo of this using a CCD laser beam profiler, and tried to fit a round Gaussian function on it, you will see how it deviates from that, and then one has to calculate the transfer function and see how precisely the centroid can be determined. The problem is that, when you look at this profile at various distances from the laser beam, the shape is slightly changing and the centre-of-gravity will appear to shift, which surprises a lot of people who are used to dealing with white incoherent light.

 

One interesting thing to do is to look with sunglasses etc., and rotate the laser beam device. Then I think you will see that the laser beam is not perfectly round, there are features inside the beam profile that appear to follow the rotation.......


Edited by X3782, 24 August 2018 - 09:31 AM.


#25 ad701xx

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Posted 24 August 2018 - 10:56 AM

Just a minor correction.

 

The coin pictured is a dime. I measured one I have handy at 17.6mm.




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