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Long-f/ratio instruments and insensitivity to defocus –– amendments to the "scientific proof"

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#1 Max Lattanzi

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Posted 05 April 2021 - 04:26 AM

Hi Everyone!

 

I know this has been long overdue but, as John used to sing, "life is what happens to you while you're busy making other plans". So, fast forward and here we are today.

 

As a note: I have been hinting this already in the past more than once and, as a matter of fact, my intention was to write this up as a corollarium of the still-to-come side-by-side observation between a highly corrected 5" f/9.25 apo and an equally highly corrected 5" f/31 achromat, reporting in detail the different observational experience. 

 

This was two years back now, and Covid matters did not help us in making this test (we have to put together instruments that are presently distant). So, in the end, I've decided to nonetheless put this down -- the test mentioned above being nothing else but an occasion, not the core of the matter. This having clarified, let's move on.

 

It's going to be necessarily a bit long, but I hope plain and clear.

 

We all know this has been a controversial question for a long long time -- having on one side the users of long-focus instruments, who keep reporting tranquillity of images and insensitivity to defocus, which constantly increase together with the increase of focal ratio; and on the other side the many who, not having first-hand experience of those instruments, nevertheless keep commenting that the above is impossible because a theoretical scientific “proof" was given that long-f/ratio instruments carry no advantage whatsoever as per insensitivity to defocus.

 

Last time this happened was in the now locked-down thread on "Tolerable CA in Achros" (https://www.cloudyni...ros/?p=10952430). The thread lockdown prevented me to offer an explanation to Bob recalling the "proof". This is to be also intended as a reply to that.

 

Previously, some posts were also touching the matter in the “Jules Verne Refractor and a D&G 5” f/31”

(see post 82 and following at https://www.cloudyni...s/?p=9464989). 

There again a reference was made to this theoretical scientific “proof”, which supposedly demonstrate  that long-f/ratio instruments do not have any insensitivity to defocus; once more, despite the empirical evidences of the users of these instruments.

 

To accomodate this seeming discrepancy between theory and practice, all sort of explanations have been made up over the years.

 

It has gained widespread consensus the one claiming that the difference is given by the fact that, being the lens in long-focus instruments located higher than in the short-focus one, it suffers less from ground turbulence. This "fact" (which, incidentally, cannot be utilized to explain the difference in behaviour of long-focus Newtonians!) is true and false at once — so, basically, irrelevant.

 

It is true in its trivial meaning: if the ground is not in thermal equilibrium and/or the observer is not careful in his/her own thermal interaction with the instrument, of course the farer the lens from both, the better.

 

It is false in claiming to be the response to the issue above: it is enough to set up a simple falsification experiment, e.g., by utilizing a taller pier and bringing the two lenses at the same hight to immediately see very clearly that, even though now the two lenses are side-by-side, the behaviour of the long-focus and short-focus still clearly differ.  The same happens when the instruments are used horizontally in terrestrial tests. Here, again, the lenses are nearby, still the instruments behave differently according to their f/ratio.

 

But how could this be possible, if here is an authoritative "proof" with a lot of nice scientific formulas and graphs that clearly (or, maybe, allegedly) shows otherwise...?!

 

So, let's now have a look at this "proof" and see together where and how it is incorrect; more precisely it is incomplete, truncated and, as a consequence, incorrect. And it can be utilized to "proof" exactly the opposite of what it claims to demonstrate.

 

And that, therefore, there is no contradiction between theory and practice.

 

In all this, no mathematical formulas or computer generated graph will be needed, but mere logic, which has a crucial importance in dealing with all demonstrations in general, and scientific one in particular. And that constitutes the slippery banana peel in that page.

 

OK, enough: let's read together the "proof" (you may find it, with graphs, formulas, etc, at https://www.fpi-prot...reer/seeing.htm — I am copying it for easy reference). I shall be commenting only the Depth of Focus Analysis, given that the same logic amendments can be applied to the other part of the "demonstration".

 

Please note that the author speaks of Newtonians, but of course the demonstration is valid for any prime focus image, no matter if lens or mirror generated. Here we are talking refractors, so let it be lens.

 

<<..

 

Depth of Focus Analysis

 

An independent method that corroborates the previous ray tracing result is to calculate the depth of focus for the two telescopes, and compare it to the shift in the best focus position that is induced by bad seeing. Sidgwick provides a formula for calculating the depth of focus as:

 

Depth of focus = 4*(1.22*lambda*(Fˆ2)), where F = focal ratio and lambda = wavelength of light. This formula, and similar ones, are also mentioned by Suiter.

 

The important thing to note is that the depth of focus changes with the square of the focal ratio, F. Thus, a f/10 telescope has four times the depth of focus of a f/5 instrument (i.e., (10/5)ˆ2).

 

This looks good for the long focus telescope until you also look at how much the atmosphere affects the focus shift for the two telescopes.

 

Table 1 shows the amount of best focus shift for three different "air lenses" of varying optical power. OSLO was used to derive these numbers. The important thing to notice is that the f/10 telescope has four times more focus shift than the f/5.

 

In fact, this focus shift varies by the same ratio as the depth of focus does — the ratio of the focal ratios squared. This exactly neutralizes the benefits of the greater depth of focus.

 

"Air lens" strength     150 mm f/5          150 mm f/10
weak                     0.021 mm            0.082 mm
moderate                 0.056 mm            0.227 mm
strong                   0.069 mm            0.275 mm

 

Table 1. Shift in best focus for atmospheric "air lenses" of varying strength.
 

..>>

 

 

And here the "demonstration" stops.

 

Please do note that I am buying the demonstration “as such”, thus not entering into any meta-analysis of the way in which OSLO makes simulations and, more important, was here utilized by the author. It could be done, as I personally have a lot of remarks on the severe reductionist way in which such a simulation was carried out; but it would be really long and complex and, further, that is not the crucial point. The banana peel is much easier to spot.

 

So, at this point, without going any further, the author derives the following:

 

<<..

 

Conclusion

 

Telescopes of equal aperture are affected the same by atmospheric turbulence, regardless of focal ratio.

 

The error in the hypothesis is that it was assumed that the same atmospheric distortion will cause the same shift in the best focus position in the two telescopes, and this is not true.

 

While the high f-number telescope does enjoy a greater depth of focus, unfortunately the shift in best focus caused by turbulence is also greater.

 

In fact, the two are locked together; the instrument with four times greater depth of focus also has a four times greater linear shift of the best focus position.
 

..>>

 

That's it.

 

"Unfortunately" (to quote the author), in his enthusiastic demonstration of what is true and what true is not, he overlooked that the "focus shift" seems to "neutralize the benefits of the greater depth of focus" of the longer f/ratio instrument only if we examine the images at the focal plane the size they are.

 

But, in the 150 f/5 instrument we have a focal length of 750mm, which produces at the focal plane an image of any object (its turbulence-induced focus-shift included) that is half in linear size (and 1/4th in area) than that of a 150 f/10, whose focal length in 1500mm. And the gap obviously keeps increasing vis-à-vis an f/15 (FL=2250mm), and so forth for longer f/ratio instruments.

 

Now, let's see if we can make good use of good old layman logic and common sense.

 

• Say, I am testing the stability of two mounts with a slam test, and report that they are "equal", but I've tested one looking into the telescope at 100x, and the other at 200x, would anyone consider this test actually valid?

 

• Say, I am testing two telescopes sharpness, and report that they are "equally sharp", but the image in the first is at 200x while in the second is at 400x, would anyone consider this as a valid test to actually assess the sharpness of the two instruments?

 

• Say, I am testing the sharpness of two photographic lenses and, to do so, I print the picture of the first at 10x15cm (4x6"), while the picture of second at 20x30cm (8x12"), would anyone consider this as a valid test to assess their actual respective sharpness?

 

• Say, I am testing the amplitude of the oscillation of two objects (let's say two undermounted telescopes shaken by the wind), and I report that the mounts are "equally capable" because they shake the same *to my eye*; but, alas, I am observing one of the instruments at five meters, while the other is at ten meters from me… would anyone consider this a valid test?

 

 

I may go on, but I guess by now the slip in logic -- the banana peel -- is clear to everyone.

 

In the demonstration above, the author obliterated (or simply forgot) that was drawing hasty conclusions by evaluating images of different linear size; images that, during the astronomical observation, need to be enlarged differently (in a 2:1 ratio in that case; 3:1 if the comparison was with a f/15 instrument; and so forth).

 

And apparently all the many readers of the "essay" -- maybe seduced by the beautiful graphs and formulas (all things that make so much "scientific paper") -- failed to notice this (involuntary) sleight of hand in the demonstration logic.

 

So, if now we enlarge the image of the f/5 instrument to match the magnification of the f/10 (or f/15, etc.) one, we are again enlarging the amplitude of those focus-shift effects that seemed to have been equalized in the truncated "demonstration" above.

 

And we shall be able to see again that the longer f/ratio instrument -- whose larger prime focus image needs to be enlarged less -- re-gains and retains its inherent defocus advantage (read: larger insensitivity to defocus and tranquillity of images).

 

As easy as this.

 

 

In the end, let's reconsider the list of the various advantages that the author rightly reports for a long-focus instrument:

 

<<..

There is a long list of valid reasons why high f-number telescopes often perform better than faster ones. Some important reasons are:

 

a) Slower (i.e., high f-number) optics are exponentially easier to fabricate to the same accuracy as faster optics.  [CHECK -- correct]
 

b) As already mentioned, the greater depth of focus of the high f-number telescopes makes them easier to precisely focus.   [CHECK -- correct]
 

c) High f-number telescopes have a larger region of the focal plane that is diffraction limited, so off-axis performance is better. (...)   [CHECK -- correct]
 

d) Slower optics are easier to collimate accurately, and there are less detrimental optical implications to slight misalignments.   [CHECK -- correct]
 

e) Many eyepieces perform better with a higher f-number.   [CHECK -- correct]
 

f) When comparing two Newtonian reflectors, slower scopes usually have smaller secondary mirrors. While the difference in image quality between, say, a 15% and 20% obstructed telescope is hard to detect, it would be a contributing factor.   [This does not apply to refractors, so no comment]

 

If you happen to be observing through two telescopes of the same aperture on the same night, and the longer focus telescope is performing better, some of the reasons stated above are likely to be the explanation.
 

..>>

 

 

Well, I hope that now -- having finally matched (correct) theory and (correct) practice -- we can amend the hasty conclusion of the author and happily add to all the points listed above (and others not mentioned):

 

z) Slower instruments (i.e., high f-ratio) produce final images that are less affected by atmospheric turbulence, showing larger insensitivity to defocus and increased tranquillity.

 

Q.E.D.

 

 

Happy Easter to you all

-- Max


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#2 alan.dang

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Posted 05 April 2021 - 05:41 AM

Great post.

#3 Jon Isaacs

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Posted 05 April 2021 - 06:34 AM

But, in the 150 f/5 instrument we have a focal length of 750mm, which produces at the focal plane an image of any object (its turbulence-induced focus-shift included) that is half in linear size (and 1/4th in area) than that of a 150 f/10, whose focal length in 1500mm. And the gap obviously keeps increasing vis-à-vis an f/15 (FL=2250mm), and so forth for longer f/ratio instruments.

 

 Max:

 

Some years ago, I did the analysis my own way, before I had seen Bryan Greer's work. I used the standard depth of focus equation and used depth of field to model the defocus.  The result was that the greater depth of view focus of the longer focal length scope scope exactly equal to the the greater shift in defocus caused by the shift in the depth of field. 

 

But I am wondering why image size enters into the analysis.  The analysis says they are equally out of focus which is independent focal length and only dependent on aperture.  The image is smaller but so is the Airy disk and the depth of focus equation is about diffraction limited performance. At equal magnifications, the airy disks have the same angular sizes.  

 

The depth of focus equation says that the depth of focus is range in which a perfect optic remains diffraction limited.  What my analysis said was the for a given amount of seeing induced defocus as modeled by shift in the depth of field, the two optics had identical responses, both had the same reduction image quality.  

 

This was essentially Bryan's conclusion. 

 

Here is a thought experiment:  

 

I have a 5 inch F/6 with it's is sensitivity to depth of focus and attendant depth of field.  Now I install a 5 X Powermate.  The light cone is that of an 5 inch F/30 and if I focus after the Powermate, the depth of focus and depth of field are those of an F/30 instrument. 

 

However, the mere addition of a Barlow cannot change the sensitivity to seeing induced defocus.

 

The same is true of a Mak-Cassigrain.  The primary mirror is probably about F/3, the magnifying secondary is F/5, just as in the previous case, the light cone is that of a F/15 instrument but the primary mirror is F/3. This is fundamentally no different than an F/3 optic with a 5X Powermate.

 

How are these light cones distinguishable from the light cones of 5 inch OA Newtonian of F/30 or F/15 in terms of on-axis performance?    

 

Jon


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#4 sg6

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Posted 05 April 2021 - 07:53 AM

I suspect the "insensativity to defocus" is that within the depth of focus field the focus is never "good". It is always a little fuzzy so instead of a sharp well defined focus you now get a long but less well defined "focus".

 

Easy enough to show on a refractor if you have a ray trace program you plot the chromatic focal planes and the focal planes caused by spherical aberration. The result is that you end up with a length around the theoretical focal plane with the light from both aspects comes to a "focus". The result being a somewhat non-sharp image.

 

If you adjust the focuser up and down that depth of focus length nothing gets much worse but neither does it get much better. So it is "insensative" to focus, and therefore "defocus". Makes it "easy" as since it is broad just about anyone can "focus" their scope. Awful for AP or wanting a sharp image as it is never quite sharp enough.


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#5 Max Lattanzi

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Posted 05 April 2021 - 07:56 AM

Hi Jon,

 

Good to hear from you.

 

Nop, it doesn’t quite work that way. Yes, you get at the eyepiece a light-cone of the same angle of an f/30 (so the eyepiece does work better), but not with the same defocus features (and others, as well — e.g., adding a 5x powermate to a f/6 refractor does not change at all its color blur making it a f/30 equivalent tout-court).

 

That is not a primary focus.

 

What you are actually doing there — both with the 5x powermate and with the 5x secondary of a Cassegrain — is to magnify the defocus of that f/6 or f/3, basically making the situation 5 times worse. That is why the focus in a f/2 => f/10 SCT is so critical. Nothing in comparison with a f/10 primary focus — being it refractor or newtonian, but primary.

 

Get yourself, say, a 4” f/15 Mak (or whatever diameter and/or Cassegrain variant you want) and compare it with a nearby 4” f/15-native refractor (no matter if achro or apo), and you will see immediately by yourself that their defocus differ of an order of magnitude.

 

That’s why on the former everyone runs to get a 1:10 microfocus reduction, while on the latter is not needed.

 

— Max


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#6 hyia

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Posted 05 April 2021 - 08:27 AM

Hello Max,

 

I have enjoyed your many posts and incredible photos here over the years.  Thank you for sharing.  I have no doubt that your experience with regards to long focus vs short focus is true.

 

I am skeptical that it is due to increased depth of focus.  With regards to the "proof" previously given, I do not rest my belief upon that.  So, showing any error in that proof, if possible, has no effect.  My logic is as follows:

 

1.  The telescope itself does not create the aberration of the image.  It exists before it reaches the telescope.

2.  The aberration cannot be considered as a mere defocus.  If I look at a star in poor seeing, the image boils, has spikes, etc.  It does not simply look like a star test oscillating in and out.  So, the belief that if I could freeze time and re-focus that I would have a good, in focus image is curious.  This is why I find the "proof" mentioned above as being insufficient. 

3.  It follows then that if I take an aberrated image that, even if the long focal ratio scope renders it perfectly, it is not going to be any better.

 

My practical experiment would be as follows:  Take a picture of Jupiter and place it in your field a set distance from your long and short focus scopes.  Focus each scope to best focus.  Then, either smear some petroleum jelly over the picture or place a glass block in front and again view through each telescope.  You seem to be claiming that the long focus scope will yield a better image?  

 

Point #2 which I give above, namely that the effects of seeing cannot be thought of as a mere de-focus and I rest my logic upon, may be wrong.  I am not too determined to find a "proof" here because I do not doubt your actual experience in any way.  As I said, I am simply skeptical that it due to the issue of de-focus.   

 

Best Regards.


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#7 Jon Isaacs

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Posted 05 April 2021 - 08:27 AM

Hi Jon,

 

Good to hear from you.

 

Nop, it doesn’t quite work that way. Yes, you get at the eyepiece a light-cone of the same angle of an f/30 (so the eyepiece does work better), but not with the same defocus features (and others, as well — e.g., adding a 5x powermate to a f/6 refractor does not change at all its color blur making it a f/30 equivalent tout-court).

 

That is not a primary focus.

 

What you are actually doing there — both with the 5x powermate and with the 5x secondary of a Cassegrain — is to magnify the defocus of that f/6 or f/3, basically making the situation 5 times worse. That is why the focus in a f/2 => f/10 SCT is so critical. Nothing in comparison with a f/10 primary focus — being it refractor or newtonian, but primary.

 

Get yourself, say, a 4” f/15 Mak (or whatever diameter and/or Cassegrain variant you want) and compare it with a nearby 4” f/15-native refractor (no matter if achro or apo), and you will see immediately by yourself that their defocus differ of an order of magnitude.

 

That’s why on the former everyone runs to get a 1:10 microfocus reduction, while on the latter is not needed.

 

— Max

 

It actually does work that way.  You are focusing at primary focus since the magnifying mirror/barlow is before focus.  

 

The devil is in the details.  With most Cassigrains, you are focusing by moving the primary mirror.  When you focus this way, the amount you move the primary mirror depends on the focal ratio of primary mirror and the magnifying barlow/mirror causes the shift in focus to increase.

 

However, if you are focusing after the Barlow/Magnifying mirror, something that is not as common, then the depth of focus is related to effective focal ratio of the light cone you are focusing on.  

 

And this is the situation that is analogous to the long focal length refractor.

 

Look at how depth of focus is derived. It depends on the focal ratio,the angle, of the light cone you are focusing on. 

 

If you want to see this, just stack up a few Barlows in a fast scope and focus by moving the eyepiece rather than the focuser.  It's an experiment worth doing.. 

 

Jon


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#8 Max Lattanzi

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Posted 05 April 2021 - 08:47 AM

(...)

2.  The aberration cannot be considered as a mere defocus.  If I look at a star in poor seeing, the image boils, has spikes, etc.  It does not simply look like a star test oscillating in and out.  So, the belief that if I could freeze time and re-focus that I would have a good, in focus image is curious.  This is why I find the "proof" mentioned above as being insufficient. 

(...)

Point #2 which I give above, namely that the effects of seeing cannot be thought of as a mere de-focus and I rest my logic upon, may be wrong.  I am not too determined to find a "proof" here because I do not doubt your actual experience in any way.  As I said, I am simply skeptical that it due to the issue of de-focus.   

Hi Hyia, and thanks for the appreciation.

 

You are right : the whole phenomenon cannot be reduced and explained as mere defocus analysis vs the angular size of the Airy disk. It's more complex than that (I did say that was buying the proof "as is", despite not being in agreement with it).

The defocus does contribute, but all the advantageous points mentioned above are at stake.

 

-- Max


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#9 Max Lattanzi

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Posted 05 April 2021 - 08:56 AM

It actually does work that way.  You are focusing at primary focus since the magnifying mirror/barlow is before focus.  

 

The devil is in the details.  With most Cassigrains, you are focusing by moving the primary mirror.  When you focus this way, the amount you move the primary mirror depends on the focal ratio of primary mirror and the magnifying barlow/mirror causes the shift in focus to increase.

 

However, if you are focusing after the Barlow/Magnifying mirror, something that is not as common, then the depth of focus is related to effective focal ratio of the light cone you are focusing on.  

 

And this is the situation that is analogous to the long focal length refractor.

 

Look at how depth of focus is derived. It depends on the focal ratio,the angle, of the light cone you are focusing on. 

 

If you want to see this, just stack up a few Barlows in a fast scope and focus by moving the eyepiece rather than the focuser.  It's an experiment worth doing.. 

 

Jon

Yes, I was thinking exactly about focusing the primary mirror in a Cassgrain. Or, which is the same, having a barlow in the focuser. And it behaves as I told you.

 

Now you are suggesting something like putting a Powermate inside the focus (i.e., inside the telescope) and keeping it totally independent from the focusing  mechanism, which is an interesting idea. Worth an experiment, certainly.

 

We have a mechanical device (thought for something else) that can reproduce that, furthermore by putting the barlow not at a fixed distance but in a range. Let me have a look.

 

Cheers,

-- Max


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#10 KBHornblower

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Posted 05 April 2021 - 09:18 AM

This thread has me scratching my head.  I just did textbook-style ray tracing calculations with objectives of the same aperture but different focal lengths.  Starting with them sharply focused I placed the same thin lens in front of each one to force a defocus.  The ratio of the blur circle to the Airy disk in each one was the same, so I concluded that at the same magnification (different eyepiece of course) the appearance would be the same.

 

For now I am too lazy to try to decipher the verbalizations of conflicting opinions.



#11 Jon Isaacs

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Posted 05 April 2021 - 11:39 AM

Here is some more information concerning where you focus.

 

This comes from a thread about the focal plane shift in SCTs caused by thermal changes.  It's a thread initiated by John Hayes..  This is where I step in to address this issue:

 

https://www.cloudyni...p/#entry8498289

 

This where John agrees with me:

 

https://www.cloudyni...-2#entry8499671

 

https://www.optics.a...le/john-b-hayes

 

Jon



#12 Max Lattanzi

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Posted 05 April 2021 - 01:43 PM

Yes Jon, I read your post.

 

But what I am trying to get through is that, no matter your defocus formula, you are not reproducing the physical characteristics of a native f/30 system, but merely amplifying 5 times an f/6.

 

If that were the case, you (me, everyone) could get yourself a 150mm f/6 achromat, put behind (or internally) a powermate 5x (or any 5x barlow of your choice) and have at the focal plane the full chromatic correction of a native f/30, instead of merely enlarging 5 times the focus blur of its native f/6.

 

Which brings me also to comment your remark on the angular dimension of the Airy disk, which I realise I overlooked to do before.

 

I did not get into it, but that is one of the many points on which I disagree regarding the capability of that modelling simulation to actually reproduce what is observed at the focal plane of a telescope.

 

You see, as you rightly say, the angular size of the Airy disk is solely dependent on the diameter of the objective. Fine. But if you analyse telescopes behaviour only like that, you find yourself into some unexplanatory paths.

 

Just to name one: a regular BK7/F2 achromat.

 

When focused at 546nm has a C-F defocus of about F/1850, where F is here the focal length. Now, if the angular size of Airy were the only variable at play, we would have the consequence that a 150 f/15 — which has the same angular size Airy but three times the focal length — would have three times the chromatic aberration of a nearby 150 f/5 (same angular size of Airy but 1/3 of focal length).

 

But, as we all know, here is the physical size of the Airy disk that also gets into the picture, physical size that increases with the native f/ratio and allows the C-F defocus to be better contained into the Airy physical disk of the 150 f/15 rather than in the one of the 150 f/5. And, again, if you add a 3x barlow to that 150 f/5, its C-F defocus remains identical, i.e., you won’t transform it into the nearby 150 f/15. For some geometrical characteristics yes, for some physical not. So, globally, not.

 

-- Max


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#13 daquad

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Posted 05 April 2021 - 06:59 PM

Yes Jon, I read your post.

 

But what I am trying to get through is that, no matter your defocus formula, you are not reproducing the physical characteristics of a native f/30 system, but merely amplifying 5 times an f/6.

 

If that were the case, you (me, everyone) could get yourself a 150mm f/6 achromat, put behind (or internally) a powermate 5x (or any 5x barlow of your choice) and have at the focal plane the full chromatic correction of a native f/30, instead of merely enlarging 5 times the focus blur of its native f/6.

 

Which brings me also to comment your remark on the angular dimension of the Airy disk, which I realise I overlooked to do before.

 

I did not get into it, but that is one of the many points on which I disagree regarding the capability of that modelling simulation to actually reproduce what is observed at the focal plane of a telescope.

 

You see, as you rightly say, the angular size of the Airy disk is solely dependent on the diameter of the objective. Fine. But if you analyse telescopes behaviour only like that, you find yourself into some unexplanatory paths.

 

Just to name one: a regular BK7/F2 achromat.

 

When focused at 546nm has a C-F defocus of about F/1850, where F is here the focal length. Now, if the angular size of Airy were the only variable at play, we would have the consequence that a 150 f/15 — which has the same angular size Airy but three times the focal length — would have three times the chromatic aberration of a nearby 150 f/5 (same angular size of Airy but 1/3 of focal length).

 

But, as we all know, here is the physical size of the Airy disk that also gets into the picture, physical size that increases with the native f/ratio and allows the C-F defocus to be better contained into the Airy physical disk of the 150 f/15 rather than in the one of the 150 f/5. And, again, if you add a 3x barlow to that 150 f/5, its C-F defocus remains identical, i.e., you won’t transform it into the nearby 150 f/15. For some geometrical characteristics yes, for some physical not. So, globally, not.

 

-- Max

Max, the angular size of the Airy disc, as we all know, is strictly a function of the aperture.  And the linear size of the disc is strictly a function of the focal ratio.  So a 6" f/5 with a 3X barlow will produce an Airy disc that is the same size (in millimeters) as that of a 6" f/15 native focal length.  And, as Jon has noted, if you focus the f/5  by moving the eyepiece only, (i.e. holding the barlow stationary) the depth of focus will be the same as that of the 6" f/15 refractor.

 

Now for another thought experiment.  Given the above.  Will not the variation in focus of the f/5 be linearly mapped onto the f/15 barlow focus?   So any small change in the focus at the f/5 focus will be magnified 3X with the barlow.  In other words, the instrument with 3X the greater depth of focus will, in fact, have 3X the linear shift in focus.   

 

All those checks you indicated in Post #1 are the more likely reasons that long focal ratio instruments seem to tolerate the seeing better than the short focal ratio ones.

 

Dom Q.



#14 KBHornblower

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Posted 05 April 2021 - 08:48 PM

This thread has me scratching my head.  I just did textbook-style ray tracing calculations with objectives of the same aperture but different focal lengths.  Starting with them sharply focused I placed the same thin lens in front of each one to force a defocus.  The ratio of the blur circle to the Airy disk in each one was the same, so I concluded that at the same magnification (different eyepiece of course) the appearance would be the same.

 

For now I am too lazy to try to decipher the verbalizations of conflicting opinions.

Addendum:  Here are details of my thought exercise with the number-crunching.

Suppose we have a 100mm f/10 scope, that is, focal length is 1m.  Focused image of a star is an Airy disk subtending 1 arcsecond, thus linear diameter of 5 microns or 0.000005m.  Now we defocus it by placing a hypothetical thin lens of 10,000m focal length just in front of the objective.

 

Objective fo = 1m

Thin lens  fs = 10,000m

 

1/f = 1/fo + 1/fs, where f is the shifted effective focal length

1/f = 1 + 1/10,000

f = 1 - 1/10,000 to an excellent approximation

 

The focus is thus shifted by about 100 microns.  With the f/10 light cone this gives a ray trace blur circle of 10 microns, about twice the size of the properly focused Airy disk.  With a suitable eyepiece this change would be clearly visible.

 

Now we go to a 100mm f/5 objective.  Focal length fo is 1/2 m.  Airy disk same angular diameter but half the linear diameter, or 2.5 microns.  With the same thin lens just in front of the objective,

 

1/f = 2 + 1/10,000 = 2(1 + 1/20,000)

f = 0.5(1 - 1/20,000) = 0.5 - 1/40,000

 

The focus is thus shifted by 25 microns (see the inverse square of the focal ratio in action), so the blur circle with the f/5 light cone will be 5 microns, still twice the size of the Airy disk.  With twice as strong an eyepiece to give the same magnification, we should see the same appearance.

 

In this thought exercise the thin lens is a stand-in for transient air pockets that momentarily deflect the incoming rays by the same angles.  Thus I stand by my finding that the shorter scope is no more sensitive to poor seeing, provided all other variables are controlled.  It is indeed more sensitive to a given movement of the eyepiece, which is not in dispute.


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#15 daquad

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Posted 06 April 2021 - 08:46 AM

Addendum:  Here are details of my thought exercise with the number-crunching.

Suppose we have a 100mm f/10 scope, that is, focal length is 1m.  Focused image of a star is an Airy disk subtending 1 arcsecond, thus linear diameter of 5 microns or 0.000005m.  Now we defocus it by placing a hypothetical thin lens of 10,000m focal length just in front of the objective.

 

Objective fo = 1m

Thin lens  fs = 10,000m

 

1/f = 1/fo + 1/fs, where f is the shifted effective focal length

1/f = 1 + 1/10,000

f = 1 - 1/10,000 to an excellent approximation

 

The focus is thus shifted by about 100 microns.  With the f/10 light cone this gives a ray trace blur circle of 10 microns, about twice the size of the properly focused Airy disk.  With a suitable eyepiece this change would be clearly visible.

 

Now we go to a 100mm f/5 objective.  Focal length fo is 1/2 m.  Airy disk same angular diameter but half the linear diameter, or 2.5 microns.  With the same thin lens just in front of the objective,

 

1/f = 2 + 1/10,000 = 2(1 + 1/20,000)

f = 0.5(1 - 1/20,000) = 0.5 - 1/40,000

 

The focus is thus shifted by 25 microns (see the inverse square of the focal ratio in action), so the blur circle with the f/5 light cone will be 5 microns, still twice the size of the Airy disk.  With twice as strong an eyepiece to give the same magnification, we should see the same appearance.

 

In this thought exercise the thin lens is a stand-in for transient air pockets that momentarily deflect the incoming rays by the same angles.  Thus I stand by my finding that the shorter scope is no more sensitive to poor seeing, provided all other variables are controlled.  It is indeed more sensitive to a given movement of the eyepiece, which is not in dispute.

Nice nuts and bolts explanation, KB.

 

Dom Q.



#16 Max Lattanzi

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Posted 06 April 2021 - 10:37 AM

Max, the angular size of the Airy disc, as we all know, is strictly a function of the aperture.  And the linear size of the disc is strictly a function of the focal ratio.  So a 6" f/5 with a 3X barlow will produce an Airy disc that is the same size (in millimeters) as that of a 6" f/15 native focal length.  And, as Jon has noted, if you focus the f/5  by moving the eyepiece only, (i.e. holding the barlow stationary) the depth of focus will be the same as that of the 6" f/15 refractor.

 

Now for another thought experiment.  Given the above.  Will not the variation in focus of the f/5 be linearly mapped onto the f/15 barlow focus?   So any small change in the focus at the f/5 focus will be magnified 3X with the barlow.  In other words, the instrument with 3X the greater depth of focus will, in fact, have 3X the linear shift in focus.   

 

All those checks you indicated in Post #1 are the more likely reasons that long focal ratio instruments seem to tolerate the seeing better than the short focal ratio ones.

 

Dom Q.

Yes Dom, be assured that I follow your calculations.

 

Still, for the sake of everyone, if things are really all equal, you may wish to complete your reasoning and explain to Mr James Smith — who, having read your lines, enthusiastically added a 5x powermate to his 150 f/6 (CA index=1, see table attached) with the certitude of having as a result a hi-res planetary instrument, thus matching the color correction of his two friends, Mr Bob Johnson and Mr John Williams, who brought to the gathering a 150 f/15 (CA index=2.5) and a 150 f/30 (CA index=5) —, why he alas found himself with the correction of his good old f/6; with zero improvement in chromatic aberration and the image still plagued by an unacceptable chromatism; only requiring an eyepiece 5 times bigger (i.e., 18mm instead of 3mm) to reach the same 300x magnification.

 

Also Bob Johnson, seduced by the idea, added a 2x barlow to his 150 f/15, but found out that the level of CA correction didn’t change at all, and was a far cry from the 150 f/30 (*) of his friend John.

 

Incidentally, still flabbergasted and disappointed, James Smith also made a test by removing a (maybe faulty) 5x Powermate and added three nice brand new 2x barlows in cascade sure of reaching a stellar f/48 correction. Much to his chagrin, the outcome did not change.

 

I guess they are eager to understand why their results seem not match with the demonstration above.

 

Thanks,
— Max

 

 

(*) Now it exists — we recently added a custom made one nearby the D&G 5” f/31

 

 

 

gallery_224509_12397_50894.jpg


Edited by Max Lattanzi, 06 April 2021 - 10:38 AM.

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#17 daquad

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Posted 06 April 2021 - 12:39 PM

Yes Dom, be assured that I follow your calculations.

 

Still, for the sake of everyone, if things are really all equal, you may wish to complete your reasoning and explain to Mr James Smith — who, having read your lines, enthusiastically added a 5x powermate to his 150 f/6 (CA index=1, see table attached) with the certitude of having as a result a hi-res planetary instrument, thus matching the color correction of his two friends, Mr Bob Johnson and Mr John Williams, who brought to the gathering a 150 f/15 (CA index=2.5) and a 150 f/30 (CA index=5) —, why he alas found himself with the correction of his good old f/6; with zero improvement in chromatic aberration and the image still plagued by an unacceptable chromatism; only requiring an eyepiece 5 times bigger (i.e., 18mm instead of 3mm) to reach the same 300x magnification.

 

Also Bob Johnson, seduced by the idea, added a 2x barlow to his 150 f/15, but found out that the level of CA correction didn’t change at all, and was a far cry from the 150 f/30 (*) of his friend John.

 

Incidentally, still flabbergasted and disappointed, James Smith also made a test by removing a (maybe faulty) 5x Powermate and added three nice brand new 2x barlows in cascade sure of reaching a stellar f/48 correction. Much to his chagrin, the outcome did not change.

 

I guess they are eager to understand why their results seem not match with the demonstration above.

 

Thanks,
— Max

 

 

(*) Now it exists — we recently added a custom made one nearby the D&G 5” f/31

 

 

 

attachicon.gifgallery_224509_12397_50894.jpg

I don't see what anything you said here has to do with depth of focus in short vs. long focal ratio scopes.  No one doubts that a barlow cannot improve the color correction of an achromat. 

 

KB's. Jon's and my argument is simply that long focal ratio scopes are no less immune to the effects of bad seeing than short ones.  Your initial post was to prove this claim false.  The inability of a barlow to correct chromatic aberration in an achromat is common knowledge and irrelevant to the depth of focus issue.

 

Dom Q.


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#18 KBHornblower

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Posted 06 April 2021 - 03:46 PM

Well said, Dom Q.  My misgiving about this thread concerns digressions into other variables and poorly focused discussion thereof, leading to confusion.


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#19 Jon Isaacs

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Posted 06 April 2021 - 04:27 PM

Yes Jon, I read your post.

 

But what I am trying to get through is that, no matter your defocus formula, you are not reproducing the physical characteristics of a native f/30 system, but merely amplifying 5 times an f/6.

 

If that were the case, you (me, everyone) could get yourself a 150mm f/6 achromat, put behind (or internally) a powermate 5x (or any 5x barlow of your choice) and have at the focal plane the full chromatic correction of a native f/30, instead of merely enlarging 5 times the focus blur of its native f/6.

 

 

Max:

 

This has nothing to do with coma or chromatic aberration, these are aberrations of the objective.  Forget about this, this is not what this thread is about.

 

The issue here is depth of focus and how that is derived.  It is derived from the angle of the light cone.  This is changed by a Barlow, it is changed by a magnifying mirror.  

 

Get back to what you wrote here:

 

"Yes, I was thinking exactly about focusing the primary mirror in a Cassgrain. Or, which is the same, having a barlow in the focuser. And it behaves as I told you.

 

Now you are suggesting something like putting a Powermate inside the focus (i.e., inside the telescope) and keeping it totally independent from the focusing  mechanism, which is an interesting idea. Worth an experiment, certainly.

 

We have a mechanical device (thought for something else) that can reproduce that, furthermore by putting the barlow not at a fixed distance but in a range. Let me have a look."

 

Cheers,"

 

Barlows, Powermates and magnifying secondary mirrors are all before the focal plane, that is how they work, the diverge the light cone so that that it is analogous to a slower focal ratio.

 

https://en.wikipedia...iki/Barlow_lens

 

"The Barlow lens, named after Peter Barlow, is a diverging lens which, used in series with other optics in an optical system, increases the effective focal length of an optical system as perceived by all components that are after it in the system."

 

330px-Barlow_lens.svg.png

 

Think about placing the focuser so B doesn't move relative to A (the objective) and the eyepiece moves relative to A-B.  

 

This means you are focusing on the slower light cone.

 

It's an easy experiment to try.

 

Jon


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#20 KBHornblower

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Posted 06 April 2021 - 07:05 PM

I just added a sanity check to my thought exercise, using the f/5 with a Barlow lens at 2x.  The final focus shift was 100 microns, same as the straight f/10.



#21 infamousnation

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Posted 06 April 2021 - 10:43 PM

To be honest, since you have an equation that states depth of focus is equal to lambda times focal length squared times some constant, I’m not sure saying anything more is necessary as long as you can prove that equation is true.

 

If it is true then it is also true that increasing focal length will increase depth of focus, because that’s what the equation represents.

 

So I would say either prove that equation true, or prove a similar one is true. To do so you would need to precisely define depth of focus, then probably draw a triangle that shows how having a larger angle of convergence results in a smaller depth. 

 

 

It always just seemed obvious to me that parallel rays have in infinite depth where as sharply converging rays will go out of focus in a fraction of a wavelengths distance.


Edited by infamousnation, 06 April 2021 - 10:44 PM.


#22 KBHornblower

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Posted 07 April 2021 - 08:44 AM

The greater depth of focus with longer focal ratio is not in question here.  It appears that there are some of us who assert that the greater depth makes the long scope less sensitive to the ill effects of poor seeing.  If they think it is an inherent optical characteristic, it appears that they have misunderstood or miscalculated something.  If such is the case, I have not yet attempted to ferret out the error.  I am not even certain whether or not such an assertion is actually being made in this thread, because of digressions into other variables.  I presented my thought exercises and so far no one has found any mathematical fault in them.


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#23 Jon Isaacs

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Posted 07 April 2021 - 09:14 AM

To be honest, since you have an equation that states depth of focus is equal to lambda times focal length squared times some constant, I’m not sure saying anything more is necessary as long as you can prove that equation is true.

 

If it is true then it is also true that increasing focal length will increase depth of focus, because that’s what the equation represents.

 

So I would say either prove that equation true, or prove a similar one is true. To do so you would need to precisely define depth of focus, then probably draw a triangle that shows how having a larger angle of convergence results in a smaller depth. 

 

 

It always just seemed obvious to me that parallel rays have in infinite depth where as sharply converging rays will go out of focus in a fraction of a wavelengths distance.

 

As KB wrote, the greater depth of focus with slower focal ratios is not in contention. That's understood by all.

 

The contention here is that this somehow makes a longer focal length telescope less sensitive to seeing. 

 

The difficulty with this idea is that the greater depth of focus is counteracted by narrower depth of field, the net result being there is no effect.

 

I proposed a thought experiment to help understand why depth of focus depends on focal ratio and why depth of focus cannot be a factor in seeing senstivity..

 

Consider to telescopes:

 

A 6 inch F/30 

 

A 6 inch F/6 with a 5X Barlow/Focal extender.  The important thing about This scope is the Barlow is not inserted in the focuser, rather it is part of the OTA and focusing is done after the Barlow on the F/30 light cone. 

 

Both have the same depth of focus since both are focusing on the same F/30 light cone.

 

The conclusion is then the observation that merely adding a Barlow cannot affect a system's sensitivity to seeing.

 

An example of a similar arrangement are the modified Petzvals like the TeleVue NP-101, a 4 inch F/5.4. These use the opposite of a Barlow, a focal reducer-flattener. 

 

The objective itself is a rather slow ED doublet, estimated to be F/9-F/12. The reducer/corrector is fixed to the OTA and does not move.

 

Focusing is achieved in the usual fashion, after the reducer. 

 

Anyone who has spent much time with one of knows that the depth of focus is not forgiving easy focus of an F/11, it's the more sensitive focus of the F/5.4. 

 

At F/5.4, the depth of focus is 0.0025".  A human hair is normally thicker. At F/11, it's about 0.010".. no two speed needed.

 

Jon



#24 Max Lattanzi

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Posted 07 April 2021 - 10:00 AM

I don't see what anything you said here has to do with depth of focus in short vs. long focal ratio scopes.  No one doubts that a barlow cannot improve the color correction of an achromat. 

 

KB's. Jon's and my argument is simply that long focal ratio scopes are no less immune to the effects of bad seeing than short ones.  Your initial post was to prove this claim false.  The inability of a barlow to correct chromatic aberration in an achromat is common knowledge and irrelevant to the depth of focus issue.

 

Dom Q.

Well, Dom, I personally would find it quite relevant.

 

 

You see, my take since the beginning has been that enlarging a prime focus image X times (with an eyepiece, with a barlow, with whatever), does not produce an image identical (size apart) to the one natively that large at prime focus.

 

Your (and others) simulation -- trying to kindly explain that what I and others see is plainly wrong and/or nonexistent -- is based on formulas which calculates the Airy disks, and asserts that the two instruments should behave identically inasmuch as their respective Airy disks (both angular and linear) are calculated as perfectly matching after the enlargement.

 

Now, formulas are to be both descriptive and predictive. And, if valid, they are to be valid always, not only on odd days.

 

Mr James Smith, on the base of the results of your calculations -- supposedly describing what is exactly happening at the focus --, and given that the resulting linear Airy disks are calculated as being perfectly equal, is legitimately entitled to expect that -- given that the final Airy dimensions are now such to include not only the C-F defocus of the native f/30, but also the one of the native f/6 * 5x = f/30 equivalent -- his formerly-f/6 now-f/30 instrument should have the exact chromatic aberration level of the native f/30.  Not similar, exact.

 

While nothing of this happens, the CA remaining exactly the one of the original f/6. Only with an image 5 times larger.

 

And this happens both in even and odd days; and even on Sundays.

 

Therefore, if the description of what happens at the focus is not accurate (neither descriptive nor predictive) as per the C-F defocus, I am sorry but Mr Smith is understandably entitled to think that such a description is equally not accurate (neither in the description nor in the prediction) as per the behaviour of the seeing-induced defocus, no matter how nice the formula looks.

 

And, given that your humble servant (and not only him) has also repeated constant empirical evidences that a highly corrected 5" f/6 (triplet apo) is showing a severely more nervous and prone to defocus image than the nearby equally highly-corrected 5" f/31 (achro), which instead remains almost motionless and undisturbed, he is also understandably entitled to agree with Mr Smith perplexity.

 

And you cannot dismiss Mr Smith simply by telling him that "the inability of a barlow to correct chromatic aberration in an achromat is common knowledge", because:

 

a) this should not happen, IF f/30 native and f/6 * 5x = f/30 equivalent have the same linear Airy disk at the focal plane, AND what happened at prime focus has no importance; and

 

b) Mr Smith could equally well reply you that "the insensitivity of a high f/ratio instrument vis-à-vis a lower f/ratio one is also common knowledge"...

 

Forgive me, but here there seems to be a little impasse: on the one hand we have a heuristic theory that seems to accomodate two repeatedly constant empirical evidences (seeing-induced defocus and C-F defocus as being different in different f/ratio instruments); and on the other hand, we have a formula that does not seem to accomodate neither.

 

So, maybe, instead of systematically obliterating and dismissing repeated empirical evidences because they do not match with a formula,  we may think of a better descriptive formula and/or a more accurate and less simplistic modelling of the seeing behaviour vis-à-vis what is happening at a focal plane of the telescope?  Just a thought.

 

 

I hope I was able to explain why I would consider my remark as relevant.

 

Many thanks,
-- Max


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#25 KBHornblower

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Posted 07 April 2021 - 10:11 AM

Post #24 sums up my misgivings about digression into other variables.  Let me clarify a point.  My thought experiment assumed no aberrations of any type other than what poor seeing introduces.  That is, a reflector, a simple lens in monochromatic light, or a hypothetical apochromat made of unobtainium glass.

 

I would take empirically driven claims about less sensitivity to poor seeing in a longer scope with a grain of salt if the observer has not taken rigorous steps to control all the variables except the seeing.




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