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:
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.
"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.
Happy Easter to you all