90x Per Inch!!...How?

[andrew s]

17 minutes ago, vlaiv said:

No it is not. I think you are confusing things here.

Look at this image:

I think you are thinking in terms of dashed lines here but you need to look at their sum rather than individual Airy patterns. At some point, when patterns are close enough, their sum is larger than the dip formed by individual patterns and dip disappears.

Not at all I am looking at the sum. The Rayleigh criteria refers to the size of the dip being 20% of the peak hight.

Humans may or may not be able to see the dip at the prescribed 20% some may not be able to see 30% other clearly 10% . Remember this is subjective reporting. Can anyone reliably estimate 20% drop in intensity?

Technical , if you narrow the individual PSFs ( e.g. by adding a central obstruction) then they can be closer before the dip is at the 20% limit.

Regards Andrew 

Edited August 18, 2020 by andrew s

[vlaiv]

3 minutes ago, andrew s said:

The Rayleigh criteria refers to the size of the dip being 20% of the peak hight.

We can say that having separation of  0.81 of airy disk diameter rather than 1.0 airy disk diameter is certain not to produce dip at all, right? (0.42 lambda is sigma of intensity based gaussian approximation, so at FWHM would be at 0.42 * 2.355 = 0.9891 which is 81% of 1.22 lambda)

In that sense - there is a hard limit that premium optics can't out resolve.

[andrew s]

1 minute ago, vlaiv said:

We can say that having separation of  0.81 of airy disk diameter rather than 1.0 airy disk diameter is certain not to produce dip at all, right? (0.42 lambda is sigma of intensity based gaussian approximation, so at FWHM would be at 0.42 * 2.355 = 0.9891 which is 81% of 1.22 lambda)

In that sense - there is a hard limit that premium optics can't out resolve.

Sorry I don't agree. Have you looked at the link I posted?

Regards Andrew 

[vlaiv]

5 minutes ago, andrew s said:

Sorry I don't agree. Have you looked at the link I posted?

Regards Andrew 

I have now and I'm well aware of central obstruction "boost" in high frequencies. I'm failing to see what this has to do with pushing "premium" optics beyond theoretical limits.

Even rather large central obstruction creates very small boost in high frequencies over perfect unobstructed aperture.

We can easily show that central obstruction reduces peak intensity of airy PSF compared to unobstructed, and hence difference in peak and dip is even more pronounced (contrast loss - harder to see).

 

[andrew s]

2 hours ago, vlaiv said:

I have now and I'm well aware of central obstruction "boost" in high frequencies. I'm failing to see what this has to do with pushing "premium" optics beyond theoretical limits.

Even rather large central obstruction creates very small boost in high frequencies over perfect unobstructed aperture.

We can easily show that central obstruction reduces peak intensity of airy PSF compared to unobstructed, and hence difference in peak and dip is even more pronounced (contrast loss - harder to see).

 

We will have to agree to disagree. 

The basic points I am making are three fold.

1) The Rayleigh criteria is arbitrary. The is no physical law dictating the 20%. It is a practical place to put the cutoff but it could have been set at  18% or 22% . It was a free choice.  Hence it is possible to detect "dips" at less than 20%.

2) Humans may or  may not be able to detect dips at 20% depending on their eyesight. 

3) I don't  think humans when judging if something is resolved or not applies the 20% limit.

The reason I pointed this out is that just restating the Rayleigh limit as what can or cannot be resolved is misleading when considering visual astronomy. 

The point about the obstruction in the link was that the second diagram in the section on "Theoretical inconsistency " shows how the MTF is cut of at 1.1 rather than 1.0. See the red square 32% CO solid plot.

If you disagree with my 3 points fine, however, in my understanding they are correct.

Regards Andrew 

 

Edited August 18, 2020 by andrew s

[vlaiv]

57 minutes ago, andrew s said:

We will have to agree to disagree. 

I don't think we necessarily disagree.

57 minutes ago, andrew s said:

1) The Rayleigh criteria is arbitrary. The is no physical law dictating the 20%. It is a practical place to put the cutoff but it could have been set at  18% or 22% . It was a free choice.  Hence it is possible to detect "dips" at less than 20%.

Indeed it is, we can create other criteria based on actual MTF and call those rules. Maybe one I suggested - when stars are separated at twice FWHM - as that leaves no dip in curve.

What is important is that both criteria have same underlying physical reality (I know that in the light of what you have pointed out this is up for discussion and I will address it below) - there is maximum spatial frequency and it depends on diameter of aperture.

1 hour ago, andrew s said:

2) Humans may or  may not be able to detect dips at 20% depending on their eyesight. 

Quite correct, but this is "one way" street - they can undershoot but they can't overshoot - they can't see what is not there. If we take above criteria where there is no dip in the graph - well, then no one can see the dip. Psychological reasons excluded.

1 hour ago, andrew s said:

3) I don't  think humans when judging if something is resolved or not applies the 20% limit.

I totally agree, but we can derive a criteria where they don't have to judge anything being certain percent lighter or darker or whatever. We can do basic thing - test of equality. If two stars are separated so that space between them is at one point as dark as surrounding empty space - we will call that resolved (or clean split - as it is often called).

1 hour ago, andrew s said:

The point about the obstruction in the link was that the second diagram in the section on "Theoretical inconsistency " shows how the MTF is cut of at 1.1 rather than 1.0. See the red square 32% CO solid plot.

Ok, now I see what you mean - I totally missed that, but I wonder where is it coming from?

My concentration is lacking at the moment, so I can't really tell where is it coming from except that it is from comparison graph of 32% CO and 10% larger aperture with 1/4 wave spherical. My question is - why does such graph show first minima in Airy pattern to be in the same place when it should be 10% inward for larger aperture (or 10% outward for one with central obstruction)?

If we do Fourier optics simulation - we will get results consistent with dashed red line in right graph. Based on what theory / math / whatever do we need to consider this claim that maximum spatial resolution increases with central obstruction?

 

[andrew s]

@vlaiv I think we are quite close. On point 2) we still disagree.  The dip size is a continuous monotonic function as the PSFs get closer. There will be a dip at 40% , 20% 10% and so on to zero. I don't  see what you mean by you can't  see what is not there? Do you mean the dip jumps from 20% to zero ? Or something else.  I can envisage a photometer recording a 10% dip etc.

I will also review the link again to get back up to speed on his thinking so we can discuss it if you wish to. I am just off for a few days holiday so posting will be intermittent. 

Regards Andrew 

 

[Stu]

Just to add, I don’t believe any of my observations have been of double stars beyond the theoretical limits of the scopes I’ve been observing with. Zeta Herc in a 4” is probably the hardest I’ve done due to the brightness difference. I’ve got to 1.1” with the Vixen FL102S, thought I had gone tighter with the Tak but not sure.

[vlaiv]

11 minutes ago, andrew s said:

@vlaiv I think we are quite close. On point 2) we still disagree.  The dip size is a continuous monotonic function as the PSFs get closer. There will be a dip at 40% , 20% 10% and so on to zero. I don't  see what you mean by you can't  see what is not there? Do you mean the dip jumps from 20% to zero ? Or something else.  I can envisage a photometer recording a 10% dip etc.

I agree with dip size being a continuous monotonic function as PSFs get closer. As such, dip will hit 0 at some distance between PSFs centers - monotonic function does not cross origin and it won't hit zero only as distance between centers hits zero. Precisely, dip will hit 0 once height of PSF is at half maximum at the point where PSFs meet (provided that intensities of sources are equal). There is some separation of stars where there is no dip any more. If you look at last image I posted - third case still shows separation between PSF centers and there is no dip in function.

We will take this point to be limit of resolving. It will have some numerical value associated with it. This value will depend on aperture of telescope and no observer can claim to see the dip if stars are at this separation or closer. No matter how good their optics. This was my point. There is physical limit to what certain aperture can resolve. Take larger aperture and it will show the dip because PSFs themselves will be narrower - Airy disk will have smaller diameter.

18 minutes ago, andrew s said:

I will also review the link again to get back up to speed on his thinking so we can discuss it if you wish to. I am just off for a few days holiday so posting will be intermittent. 

Yes, I would like that. It is very interesting claim and I simply can't figure out where it is coming from - but would like to know what sort of reasoning lead to it.

[andrew s]

5 minutes ago, Stu said:

Just to add, I don’t believe any of my observations have been of double stars beyond the theoretical limits of the scopes I’ve been observing with. Zeta Herc in a 4” is probably the hardest I’ve done due to the brightness difference. I’ve got to 1.1” with the Vixen FL102S, thought I had gone tighter with the Tak but not sure.

Thanks, good to have some data.  I thihk it is more often obvious with linear features where it seems common to see features below the limit e.g. divisions in Saturn's rings. Here it seems the visual system can discriminate finer contrast differences when they are extended.

Regards Andrew 

. 

[Stu]

1 hour ago, andrew s said:

Thanks, good to have some data.  I thihk it is more often obvious with linear features where it seems common to see features below the limit e.g. divisions in Saturn's rings. Here it seems the visual system can discriminate finer contrast differences when they are extended.

Regards Andrew 

. 

On that front, I’m afraid I’m with @mikeDnightin terms of having seen the Alpine Rille in my Tak FC100DC, something which does seem to cause some consternation amongst folk on here. I saw it as a bright white line, broken in one or two places if I recall correctly. Only seen it twice, so the illumination has to be exactly right, but I’m sure I’ve done it, largely because I also know when I HAVEN’T done it which is a good check in my mind.

[CraigT82]

3 hours ago, vlaiv said:

Psychological reasons excluded.

Thesee psychological reasons could be significant. One's belief in what one's scope is capable of is directly proportional to cost of scope! 

[andrew s]

3 minutes ago, CraigT82 said:

Thesee psychological reasons could be significant. One's belief in what one's scope is capable of is directly proportional to cost of scope! 

Expectation bias is a major issue in many areas. Just look at HI FI as an example. However, my working hypothesis is to accept all visual observations at face value and look for scientific evidence to support such claims.

Regards Andrew 

[Stu]

6 minutes ago, andrew s said:

Expectation bias is a major issue in many areas. Just look at HI FI as an example. However, my working hypothesis is to accept all visual observations at face value and look for scientific evidence to support such claims.

Regards Andrew 

That sounds like a very reasonable approach Andrew.

I endeavour to always give honest opinions of what I see at the eyepiece. I know, having failed for many years on Zeta Herc, that I am now genuinely seeing it rather than imagining it! I saw it first in larger scopes (210 Mewlon and 8” f8 dob, and having seen it, and knowing what to look for, it then became easier to see in my 4” fracs, and also my Heritage 150p)

I have yet to see Sirius B, whereas by now (after 20 plus years of observing) it would be quite easy to claim that I had spotted it, so again hope that my observations are believable.

[Stu]

19 minutes ago, CraigT82 said:

One's belief in what one's scope is capable of is directly proportional to cost of scope! 

That can certainly appear to be the case! 😉. I’ve had to accept though that Zeta Herc looked better in my £199 Heritage 150p than either of my lovely, and expensive fluorite refractors!

[CraigT82]

6 minutes ago, Stu said:

That can certainly appear to be the case! 😉. I’ve had to accept though that Zeta Herc looked better in my £199 Heritage 150p than either of my lovely, and expensive fluorite refractors!

Well I for one am extremely glad that far Eastern optical manufacturing is at such a good level!   

[John]

12 minutes ago, Stu said:

... I know, having failed for many years on Zeta Herc, that I am now genuinely seeing it rather than imagining it!.....

Honest opinion needed here Stu:

- Do you think I was imagining splitting Zeta Herc when I first reported it with my ED120 back in 2013 when the pair were closer ?

- Do my frequent reports of splitting Sirus with my 12 inch dob and my 130mm refractor seem plausible ?

I'm starting to doubt my observations currently

 

[andrew s]

6 minutes ago, John said:

Honest opinion needed here Stu:

- Do you think I was imagining splitting Zeta Herc when I first reported it with my ED120 back in 2013 when the pair were closer ?

- Do my frequent reports of splitting Sirus with my 12 inch dob and my 130mm refractor seem plausible ?

I'm starting to doubt my observations currently

 

Why on earth would you doubt it now. You would know if you ... 

Regards Andrew 

[John]

10 minutes ago, andrew s said:

Why on earth would you doubt it now. You would know if you ... 

Regards Andrew 

I was just being honest Andrew - hope that is OK ?

[jetstream]

1 hour ago, CraigT82 said:

Thesee psychological reasons could be significant. One's belief in what one's scope is capable of is directly proportional to cost of scope! 

When using the Heritage 130 sometimes I feel a degree of sadness... sadness because this scope competes with 2 refractors many times their price... on the other hand I get much pleasure from this telescope after accepting how much cash I blew on the others lol!

I love the H130...

[CraigT82]

4 minutes ago, jetstream said:

I love the H130...

Same... mine has seen off a Tal100RS, 102mm f/11 achro, skymax 127 and even a C8 (which might not have been the best example) all those were bought as 'upgrades' to the little newt but I always just preferred the view through the H130p and moved the others on. Maybe it's sentimental bias... as it was my first scope! 

[Stu]

34 minutes ago, John said:

Honest opinion needed here Stu:

- Do you think I was imagining splitting Zeta Herc when I first reported it with my ED120 back in 2013 when the pair were closer ?

- Do my frequent reports of splitting Sirus with my 12 inch dob and my 130mm refractor seem plausible ?

I'm starting to doubt my observations currently

 

No John, I don’t doubt your observations. Take Zeta Herc for example, it was only 0.2” closer and you had an extra 20mm aperture/resolution to play with so it seems eminently doable. I also suspect that your local seeing conditions are somewhat better than mine, in part because you have split Sirius and I’ve never managed it in a wide variety of scopes.

There have certainly been posts on the forum which I really don’t believe; I do recall one new starter claiming a view of the Pup on their first outing and I just didn’t find that credible. Impossible to prove obviously but I think where you have had repeated sightings, make clear reports and sketches (as I recall you doing for Zeta Herc I think)  then it all builds to credibility. Reported failures also help with this; as said, most of the time I fail to see the Alpine Rille in my Tak, it has only been on two occasions that it has been there which makes it much more convincing to me, and hopefully people reading the reports. So, I think reporting failures should be encouraged as it does then increase knowledge of what works and doesn’t work, and lends credibility to successful reports if that makes sense?

[Stu]

17 minutes ago, jetstream said:

When using the Heritage 130 sometimes I feel a degree of sadness... sadness because this scope competes with 2 refractors many times their price... on the other hand I get much pleasure from this telescope after accepting how much cash I blew on the others lol!

I love the H130...

Gonna love that 150p then Gerry

[mikeDnight]

I feel I've caught glimpses of the Pup in fleeting moments of good seeing, but then I really can't be certain. I've never been able to pinpoint it with any degree of certainty as the image never stops dancing all over the place, plus observing Sirius with prior knowledge of the Pup's position and distance from the primary has the potential for biasing my observation. Sirius always seems to be in a turbulent atmosphere from my site, so I'm seriously hindered by that. I may never see it for absolute certainty. It's a tough life!

Edited August 18, 2020 by mikeDnight

[Sunshine]

Wow, i left this thread for a few days now it has grown, i have a lot of catching up to do lol.