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azure1961p
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Shrinking diffraction pattern revealed?
      #5595725 - 12/30/12 09:13 AM Attachment (37 downloads)

Droller a little time back had made the comment that fainter stars with their inherently smaller spurious discs also seemed to have diffraction ring(s) that were comparatively smaller in step with the reduced size. This was countered by some including myself as it was understood these are fixed properties of the pattern regardless of magnitude and governed by aperture.

The link below (if you scroll down till you see golden diffraction pattern illustrations ) actually fully supports Drollere!!!

This means the classic diffraction profile is all wrong and that the normally VERY shallow diffraction ring profile is actually not a flat slumpy wave but a raised set of concentric rings CONVERGING WITH the shrinking fainter spurious disk profile.

If this is correct this tosses a lot of things up in the air for reconsideration on when a telescope actually keeps resolving finer and finer resolution levels as the light fades compared to when this advantage might drop off as the graininess of fainter light obscures these gains.

Here's the link:

http://www.handprint.com/ASTRO/ae3.html#resolution

Here's the quote:A threshold explanation for the changing angular size of the disc does not explain the fact that the first diffraction ring contracts around this decreasing disc, becoming slightly thinner and separated from the disc by a constant or slightly narrower first gap (diagram right, C). It does not keep the same diameter regardless of the star magnitude, which would produce in very faint stars a visibly enlarged first gap around a much reduced Airy disc (diagram right, B).

Pete

Edited by azure1961p (12/30/12 09:23 AM)


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Cotts
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Re: Shrinking diffraction pattern revealed? new [Re: azure1961p]
      #5595848 - 12/30/12 10:32 AM

Ah, nuts. Here we go again.

The author of the article you linked (yes, I read the entire article) states the "fact" you quoted with absolutely no corroborating evidence, citations in the scientific literature, data, math or images of actual stars through actual telescopes (his nice CG images just don't amount to any sort of empirical data or science....).
In fact he drops this 'fact' and those three images in to the article with no connection to the rest of the article - just this one paragraph out of the blue...

Trouble is, his 'fact' is nothing more than an anecdote and anecdotes are neither evidence nor good science.

Dave


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Asbytec
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Re: Shrinking diffraction pattern revealed? new [Re: azure1961p]
      #5595865 - 12/30/12 10:42 AM

That is a controversial find, Pete. I would like to hear an explanation as to why or maybe find another reference to get another perspective. This seems to imply Raleigh's Airy disc does not apply to dimmer stars as the first minimum appears changed. Did you hear the thunder clap?

Another, possibly related, concept is the smaller Airy disc of obstructed scopes. (Yes, Airy, not spurious from what I can tell.) You can see this in the graph in the link below from Amateur Telescope Optic.net and an explanation follows. Remember, I do not think he is discussing a smaller spurious disc as we might believe. He states then graphs a smaller Airy disc more than once.

http://www.telescope-optics.net/obstruction.htm

"Obstructed aperture has significantly better contrast transfer - even from that of a perfect aperture - in the right half of MTF frequency range (i.e. for details smaller than about 2lambdaF linear, or 2lambda/D in radians. Even in the left half of the graph (range of resolvable low contrast details), obstructed aperture has an edge.

The reason is the effect unique to CO (at least in its extent), namely, the reduction in size of the Airy disc caused by it. The linear disc reduction is closely approximated by a factor (1-coD^2) for obstructions of ~D/3 and smaller, and by a factor (1-coD^2+coD^4) for larger obstructions, up to ~0.7D. Good approximation for the 1st minima reduction ratio for any obstruction size is 1-2^n... Apparently, the overall smaller diffraction pattern and brighter central disc give to the obstructed aperture an edge in contrast transfer efficiency with respect to spherical aberration error of near identical nominal energy loss from the Airy disc."

What's key here is the terms "brighter central disc" and "first minima reduction." Remember, the total light from the diffraction pattern does not change, it is simply redistributed into the rings. That still happens. So, the only way the Airy disc can be brighter is for it to be smaller. Weird.

For example, in a 6" scope obstructed 30%, the first minimum is no longer at 1.22. It is at 1.11 as plotted in his chart, or roughly (1-coD^2). Or, 1 - .3^2 = 91% of the standard Airy disc theory (1.22 * 91% ~ 1.1.) There is more to absorb, but that's what explains the higher frequency contrast improvement with a CO, a smaller and brighter Airy disc as I read it...and not a smaller spurious disc.

Since both dim stars and obstructions result in intensity fall off in the Airy disc, maybe the two phenomenon are related. However, some of the intensity fall off with a CO is caused by an increase in diffraction as well as a small amount of loss in photon flux. I think Raleigh did his work on Airy discs using an unobstructed scope. All this time, I thought the Airy disc was base solely on aperture and wavelength for all scopes.

Need to read more on this. (My apologies to the moderator and Mr Cotterell. )

Edited by Asbytec (12/30/12 11:08 AM)


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Cotts
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Re: Shrinking diffraction pattern revealed? new [Re: Cotts]
      #5595914 - 12/30/12 11:09 AM

If the 'fact' of a shrinking diffraction pattern with diminishing magnitude but constant aperture is true then this table from the article needs another column with some scale factor included for the magnitude of the target star..



feature dimension (k) in λ/D radians peak
illuminance percent of
total light
radius of
maximum diameter of
maximum
Airy disc 0 0 1.0 .
first gap 1.22 2.44 0 83.8%
first ring 1.64 3.28 0.017 .
second gap 2.24 4.48 0 91.0%
second ring 2.66 5.32 0.0041 .
third gap 3.24 6.48 0 93.8% the theoretical Airy disc and diffraction rings
of a "point" light source in a circular aperture
third ring 3.90 7.80 0.0016 .
fourth gap 4.24 8.48 0 95.3%

It doesn't copy and paste well here on CN....

He goes on to say:

"Visual Resolution (With Eyepiece). The resolution delivered by the objective to the image surface is only one part of the total optical system. Visual recognition of the artifact, or any dimensional feature on the image surface, depends on its image size relative to the resolution of the eyepiece/eye combination.

Unlike the angular width, the linear dimension of the diffraction artifact on the image plane scales only with relative aperture, independent of aperture and focal length:

Ρo = kλNo millimeters

where k is the dimensional of the feature radius or diameter taken from the table above. For example, the linear diameter of the Airy disc (at λ = 0.000555 mm) in an /8 telescope is 2.44 x 0.000555 x 8 = 0.011 mm.

This diffraction limited image dimension must be compared to the minimum physical width that can be separated by the observer's eye with the assistance of a specific eyepiece, defined as:

Re = eRv/206265 millimeters

where Rv is the visual resolution limit (in arcseconds, converted to radians by division by 206265) and e is the eyepiece focal length (in millimeters). Thus the minimum width that can be resolved with a 10 mm eyepiece, given a visual resolution limit of Rv = 120 arcseconds, is 10 mm x 120"/206265 = 0.0058 mm.

Comparison of the two widths shows that the linear diameter of the Airy disk (0.011 mm) is roughly twice the width of the resolution limit (0.0058 mm), and therefore would be easily visible in an /8 optical system with a 10 mm eyepiece. However this might not be the case if the eye were fully dark adapted and the pupil aperture larger."

If the diffraction pattern radii change with magnitude then the entire quote above becomes incorrect without a correction factor for magnitude. There is no such factor mentioned. The article is self-contradictory.

He then quotes Sidgwick: "The visible extent of the disc, like the number of rings visible, varies for a given instrument with the brightness of the source, although the discs are in fact the same size, irrespective of brightness."

Another self-contradiction.

Unless someone comes up with a reference in the scientific literature (blogs and self-published internet articles are NOT scientific literature - there's no peer review process) then we are stuck with what standard optical physics say - that the radius to the first minimum, the first maximum and any subsequent minima and maxima are determined by wavelength of the light and the diameter of the aperture. Period.

Dave


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azure1961p
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Re: Shrinking diffraction pattern revealed? new [Re: Cotts]
      #5595965 - 12/30/12 11:39 AM

Yes there would seem to be contradictions debasing the validity of the shrinking diffraction pattern statements. Heh, and so well illustrated too.
Gotta run for now

Pete


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Cotts
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Re: Shrinking diffraction pattern revealed? new [Re: Asbytec]
      #5595982 - 12/30/12 11:47 AM

Norme, you bring out a good point about obstructed optics. The Rayleigh factor to the first minimum is 1.22 in an unobstructed scope and 1.11 in a 30% according to the source you quote (a non-peer-reviewed source but we'll let that go). Assuming that this is true is there a further reduction of this factor with magnitude as well?. No source I have ever read on the topic mentions this specifically and gives it a name and an empirical value for obstructed or unobstructed scopes.. Even the article the OP linked doesn't come to grips with this factor.

It's easy to simply say Rayleigh's factor varies with magnitude without quantifying this variance. And no one has done so. Because if they had, it would be part of the standard literature of optical physics. And it isn't.

I propose an Experiment.
Use your own telescope, stopped down to a small aperture - say 10mm - pointed at a 1st magnitude star and with enough magnification to clearly see the diffraction pattern (which will be huge at this aperture). A reticle eyepiece would be very helpful. Or a video recording device. Find some neutral density filters which can be placed over the aperture to vary the intensity of the light entering the telescope, mimicking varying magnitude. You could make the light monochromatic with a 58 green filter and then use a variable polarizing filter. Observe or video the diffraction pattern. It will either expand and shrink like a circular accordion or it won't. I'll try this at the Winter Star Party with my 6" refractor and post he video here.

Actual science where we eliminate extraneous variables and examine only magnitude. Sounds like a fun experiment.

Dave


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Asbytec
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Re: Shrinking diffraction pattern revealed? new [Re: Cotts]
      #5596005 - 12/30/12 11:59 AM

A possible connection above is drawn from Amateur Telescope Optics.net which appears to collaborate the idea the Airy disc is not a set size across all scopes of equal aperture. Diffraction (redistribution of light away from the Airy disc) around a CO does, while lower photon flux (dim star) might, play a role. The calculation of 1-coD^2 is an approximation for light loss due to the obstruction area.

"The effects of obstruction are: (1) reduction in light transmission by a factor of (1-coD^2), resulting from pupil obscuration, and (2) transfer of energy out of the Airy disc - mostly to the first bright ring."

Eerily similar affects and eerily similar reduction in Airy disc size and reduction in the radius to the first minimum.

http://www.telescope-optics.net/obstruction.htm

If so, that seems related and consistent with the claims made on that site. Maybe not, just saying it's possible for the Airy disc, itself, NOT to always be related to frequency and aperture (as Raleigh claimed using an unobstructed scope.) So, what drives it's size in both cases one more credible than the other, apparently?

I worked the math in your reply and found the Airy disc diameter on the focal plane of my own scope to be 0.016mm at f/13 using a factor of 1.11 (as opposed to 1.22.) It turns out, that requires 13x per inch (coincidence?) to magnify the Airy disc to 0.015mm. Apparently, this is just enough for it to be seen in the eyepiece, as I understand his intent. Truthfully, this was true at 1.22, as well.

Edit: Sorry, Dave, just read your post. Yea, peer review is nice. And I have read nothing on it, either, until now. It's interesting at least.

An experiment? Man, Pete, more ground breaking work (or reworking someone else's stuff) But, remember those controversial images Brian posted? There seemed to be some argument over a very tiny discrepancy. Some guys swore there was a change in the first ring. Maybe there is, but it's for the more advanced Optics classes.

Edited by Asbytec (12/30/12 12:17 PM)


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fred1871
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Re: Shrinking diffraction pattern revealed? new [Re: Asbytec]
      #5596853 - 12/30/12 08:00 PM

Hmmm... a few thoughts on this.

1. The link given by Pete at the beginning is to one of Drollere's own web pages. So it's not too surprising that he supports his own view.
Scroll to the bottom of the page for the author name; this page is part of bruce's web site.

2. There's a difference between how things look and the real diffraction pattern. That's why the Airy disc looks smaller with fainter stars - it has to do with how the eye perceives (and its limitations). Fainter stars look smaller.

3. I'm wondering if there's a confusion here between the angular size (angle subtended) by an image, and the linear size of the image. The angular radius, as Sidgwick and others point out, depends only on aperture, D; whereas the linear radius is a function of F/D, the focal ratio.

So if you try to work things out on the basis of the linear size of the diffraction image you've introduced focal length via the back door, instead of keeping to the significant issue which is the angular size of the diffraction image.

4. Introducing a central obstruction (CO) doesn't change the spacing of the pattern, but it does change the distribution of light with more light in the rings and less in the central disc.
As well, as Sidgwick notes, "the diameters of the disc and rings are slightly reduced, while the rings are relatively thicker and noticeably brightened at the expense of the disc. The interspaces being unaffected, the apparent brightness of the rings is increased still further by contrast." [my italics]

There are similar descriptions in, from memory, Rutten and van Venrooij, Suiter, Argyle, etc etc.

One difficulty is that writers on this don't always clearly distinguish between changes in the energy distribution of the diffraction image on one hand, and the change in visual appearance mediated by the eye, on the other.

Edited by fred1871 (12/30/12 08:22 PM)


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Asbytec
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Re: Shrinking diffraction pattern revealed? new [Re: fred1871]
      #5597083 - 12/30/12 10:48 PM

Linear! Okay, that might be the confusion.

"The linear disc reduction is closely approximated by a factor (1-coD^2) for obstructions of ~D/3 and smaller..."

However, nothing in that discussion involves focal length. But, that does not mean the linear dimension cannot change if brightness is reduced with a constant relative aperture. For example, the spurious disc can look smaller by a factor of 1 - coD^2 (area of the aperture normalized to 1 minus the approximate area of the obstruction) since that is the same equation describing the loss of photon flux, as I understand it.

So, while the first minima radius might not actually change, the illusion might make it appear to be different. This could be caused by the shape of the PSF at the first maximum peaking a little closer to the peak intensity. If the first ring appeared to peak a little earlier than the normal wave, this could give the impression the first minima was smaller.

Yea, maybe that is what they are saying: the shape of the PSF is different while the actual radii are unchanged. This could give a visual (and photographic) impression of a smaller star. So, Brian's images of this phenomenon would have shown this if someone measured (and someone did) the apparent radii accurately enough. So, it seems that argument was correct on both sides, they just crossed in their definitions.

That makes sense to me and clears up a lot of confusion: the discussion between actual and apparent (linear and angular) dimensions caused by increased diffraction due to a CO (light loss and redistribution of the PSF.) CLICK! I think that's it. Stars actually DO appear smaller in obstructed scopes, if they are dimmed and diffracted by the central obstruction. (A filter would not have the same effect.)


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azure1961p
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Re: Shrinking diffraction pattern revealed? new [Re: Asbytec]
      #5597107 - 12/30/12 11:07 PM

Well then that makes my OP rather silly!

Thank you Norme and Fred and Dave.

So it was a misinterpretation on one persons part of the reduction taking place ie; linear versus angular.

Interesting and enlightening.

Pete


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Asbytec
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Re: Shrinking diffraction pattern revealed? new [Re: azure1961p]
      #5597173 - 12/30/12 11:48 PM

No, I disagree Pete. The Airy pattern DOES change with image brightness (if dimmed by an obstruction.) This explains why Raleigh did not notice it in an unobstructed scope, probably confusing him to no end if it did. It also validates the MTF, to many folks chagrin.

Droller was correct in this sense, Brian's images should have shown this effect. It actually does appear to shrink the diffraction pattern (even though the true first min remains constant and determined by aperture and wavelength only.) The mystery of the "shrinking diffraction pattern" is solved.

For me, raising the issue once again solves the mystery. The first ring DOES shrink toward the Airy disc - visually.

Edit to above: Brian's images would have shown this effect if he compared images between obstructed and unobstructed scopes on the exact same scale. All of Brian's images should have included this affect, and measured to the same size, since his scope is obstructed.

So, the question is, did the author of the link in Pete's post misspeak claiming magnitude plays a role? Or did he mean dimming caused by diffraction, "It does not keep the same diameter regardless of the star magnitude, which would produce in very faint stars a visibly enlarged first gap around a much reduced Airy disc?" When folks say Airy disc, they should mean "the" Airy disc.


Edited by Asbytec (12/31/12 03:57 AM)


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Asbytec
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Re: Shrinking diffraction pattern revealed? new [Re: Asbytec]
      #5597363 - 12/31/12 04:05 AM

But, then again, thinking more about this...

If diffraction is the cause of the Airy disc, then changing the diffraction pattern SHOULD change the actual Airy disc radius and the radius of each ring.

So, in this sense, the shrinking of the actual Airy disc could be - in fact, should be - very real. And it's probably caused by the effects of the CO which are dimming effects caused by diffraction and obscuring light. I am convinced of it, how can that not be sensible?

Not sure this happens with magnitude, though, but the effect is associated with dimming the star's image.

The implication is Raleigh only applies to unobstructed scopes just like it does only to 6th magnitude stars. And it means higher resolution is possible not because of a smaller spurious disc, as we might have thought, but due to an actual reduction of a brighter Airy disc radius. This is consistent with higher resolution MTF.

It also means, for double star observations, an obstructed scope seems to have a higher maximum frequency response by a factor of 1 - coD^2, the same factor reducing it's angular dimension to 1.11 lambda/D. When normalized for the smaller Airy disc, a 6" scope gains about half an inch in aperture in terms of real high frequency resolution from .92" arc to .84" arc...a new Raleigh limit of sorts. Bold claim? Maybe, my reading is still preliminary.

"However, despite its smaller central maxima, which correspondingly increases its limiting stellar resolution, the theory states that obstructed aperture has cutoff frequency identical to that of a clear aperture, regardless of the size of obstruction. And it seems to be controversial. With the MTF of imaging system being Fourier transform of its PSF, it cannot produce two or more different outcomes for a given PSF. And that is exactly what cutoff frequency independent of the size of central obstruction would imply....In effect, an aperture D with central obstruction coD acts as a larger aberrated aperture..."

http://www.telescope-optics.net/obstruction.htm

Not exactly sure what the above (and the rest of the explanation) means yet. There may be implications for Dawes and Sparrow, too. But, there is some more reading to do on maximum spacial frequency.

Edited by Asbytec (12/31/12 07:26 AM)


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Cotts
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Re: Shrinking diffraction pattern revealed? new [Re: Asbytec]
      #5597669 - 12/31/12 10:21 AM

Quote:

No, I disagree Pete. The Airy pattern DOES change with image brightness (if dimmed by an obstruction.) This explains why Raleigh did not notice it in an unobstructed scope, probably confusing him to no end if it did. It also validates the MTF, to many folks chagrin.

Droller was correct in this sense, Brian's images should have shown this effect. It actually does appear to shrink the diffraction pattern (even though the true first min remains constant and determined by aperture and wavelength only.) The mystery of the "shrinking diffraction pattern" is solved.

For me, raising the issue once again solves the mystery. The first ring DOES shrink toward the Airy disc - visually.

Edit to above: Brian's images would have shown this effect if he compared images between obstructed and unobstructed scopes on the exact same scale. All of Brian's images should have included this affect, and measured to the same size, since his scope is obstructed.

So, the question is, did the author of the link in Pete's post misspeak claiming magnitude plays a role? Or did he mean dimming caused by diffraction, "It does not keep the same diameter regardless of the star magnitude, which would produce in very faint stars a visibly enlarged first gap around a much reduced Airy disc?" When folks say Airy disc, they should mean "the" Airy disc.





I have now made my 'device' for testing the magnitude 'theory'. I took the barrel from an old 1.25" eyepiece and screwed in a #58 Green Wratten filter and then a pair of polarizing filters. The outer (furthest from the telescope) polarizing filter is rotatable on its threads - I have marked 'max' and 'min' points with yellow tape to make working in the dark easier. This contraption will be duct-taped (hey, I'm Canadian....) to a cardboard holder which fits over the objective of my 6" refractor. I will video the results with my Canon T3i camera and a 2x barlow.

My methodology isolates only one variable - the intensity of the light hitting my telescope's objective lens. By using one star - Sirius probably - I avoid the problem of the differing spectral classes of stars as well as any atmospheric differences from place to place in the sky. By using the #58 filter I will be working with monochromatic light.

And while I'm here- I've gone to some physics texts online, reading about light going through a vertical slit which is the simpler analogue of light going through a circular aperture. The pattern of light and dark bands is probabilistic in nature. Any given photon could end up anywhere in the pattern. As you admit more and more photons they follow the same probabilistic paths to a position somewhere in the diffraction pattern. Adding photons is equivalent to increasing the intensity of the light but no matter how many photons pass through the slit they strictly, exactly and invariably obey the statistical distribution determined by the size of the slit and the wavelength of the light. At no point in my reading did any author mention that the distribution pattern varies with the intensity of the light. None. Zero. Because it can't. Because at the individual photon level - the faintest light imaginable - the pattern is already determined.

Changing to a circular aperture won't change this.

Regarding obstructed apertures vs. unobstructed: It would be great if someone else did some actual star test videos of the diffraction pattern of their telescope with some sort of variable obstruction. It would be interesting to see the diffraction pattern changes and whether or not the radii to the various minima/maxima change or not.....

Dave


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Asbytec
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Re: Shrinking diffraction pattern revealed? new [Re: Cotts]
      #5597817 - 12/31/12 11:49 AM

That's a fair statement on the probabilities of photon distribution. I understand the basic concept and what you say gives me pause to consider it.

Testing the magnitude aspect will be interesting. My hypothesis is you won't find a difference as the filter induces no (or very negligible) additional diffraction. But, it will still be interesting to read your results. After all, that is the original question. Upon reading that comment again, I am not sure that is the contest the author was discussing. It was under the "CO affects" context of his thread.

It would be great if someone could actually photograph and scale some results using obstructed and unobstructed apertures. I think there might actually be a measurable difference. After all, it's possible an obstructed scope is no longer a two slit problem with a given set of probabilities. The original diffraction occurs by the aperture, that's the two slit problem. Add an obstruction, and you change to a 4 slit problem. There are two more "edges" or slits adding to the diffraction and altering the probabilities. I suspect, anyway.

Interesting, none the less. Happy New Year, Dave, et al.

Edited by Asbytec (12/31/12 12:09 PM)


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azure1961p
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Re: Shrinking diffraction pattern revealed? new [Re: Asbytec]
      #5598407 - 12/31/12 05:17 PM

Diffraction pattern imaging is always awful. The light is too dim and the movement even on good night is too much to get the resolution needed to measure. I've never in my life seen a decent CCD image of a stellar diffraction pattern through a telescope. It's for ever smeared. A shame really. Unlike lunar, planetary and deepsky where imaging is king, the visual observer still is at the head of the pack.

Pete


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azure1961p
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Re: Shrinking diffraction pattern revealed? new [Re: Asbytec]
      #5598408 - 12/31/12 05:17 PM

Diffraction pattern imaging is always awful. The light is too dim and the movement even on good night is too much to get the resolution needed to measure. I've never in my life seen a decent CCD image of a stellar diffraction pattern through a telescope. It's for ever smeared. A shame really. Unlike lunar, planetary and deepsky where imaging is king, the visual observer still is at the head of the pack.

Pete


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Cotts
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Re: Shrinking diffraction pattern revealed? new [Re: azure1961p]
      #5598547 - 12/31/12 06:42 PM

Nevertheless, I will try. Who knows, the combination of Florida Keys seeing and the pretty much perfect optics of my scope I might get a positive result....

Dave


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Asbytec
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Re: Shrinking diffraction pattern revealed? new [Re: Cotts]
      #5598733 - 12/31/12 08:53 PM

Yea, good luck. There may be something to it. Living on a tropical island, we normally get very good seeing too when the tropical weather heads south for the winter. Interesting to see your results.

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azure1961p
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Re: Shrinking diffraction pattern revealed? new [Re: Cotts]
      #5598769 - 12/31/12 09:21 PM

Quote:

Nevertheless, I will try. Who knows, the combination of Florida Keys seeing and the pretty much perfect optics of my scope I might get a positive result....

Dave




It could make the difference. Here though in the northeast and this time of year... It's a steep wish. On a separate note I was going to run my DBK 21 on jupiters moons to see if I could document the effect of flare reduction via thermal fans . Tonight was a wash as its cloudy plus I'm under the weather. Might be able to tomorrow? At any rate your odds are markedly better than mine.

Pete

Ps: I've got a variable polarizer that'd mount to my Dbk to dim the star and considerably. Too, I've got a W58. Fly in the ointment again is the seeing here. But I will perform the experiment!

Edited by azure1961p (12/31/12 09:44 PM)


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Asbytec
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Re: Shrinking diffraction pattern revealed? new [Re: azure1961p]
      #5598794 - 12/31/12 09:43 PM

Here is something I am digesting (the portion of explanation between the quote above.)

"This linear PSF is obtained in OSLO by reducing (clear) aperture by 10% and adding the obstruction; this means that the linear PSF of the obstructed aperture is enlarged by 10%, but its angular size remains unchanged due to unchanged focal length (makes no difference to scale the entire system down, which would give to the obstructed aperture 10% smaller linear PSF, but also as much smaller focal length, with the angular PSF unchanged), Yet, according to the MTF theory, the former will have 10% higher cutoff frequency, given as D/lambda; (cycles per radian; related to the linear resolution as D/lambda=1/lambdaF lines per mm, being the focal length and F the focal ratio), i.e. as much better limiting MTF resolution. Evidently, there is no basis for such difference in their respective PSFs. If the two PSFs are nearly identical, as they are, their actual MTF resolution limits should also be practically identical."

http://www.telescope-optics.net/obstruction.htm

So, he reduces clear aperture by 10%. This increases the Airy disc size relative to the original clear aperture. Then he adds an obstruction, reducing the Airy disc. The PSF of the larger clear aperture and the smaller obstructed aperture are the same.

Then explains, I think, there is no basis for them to be different, "Evidently, there is no basis for such difference in their respective PSFs." (This was in response to some questions over Fourier transform and two possible outcomes mentioned earlier.) In other words, the two Airy discs are the same: smaller obstructed and larger unobstructed apertures have the same level of resolution due to the "shrinking" of the Airy disc. "...their actual MTF resolution limits should also be practically identical."

This means two equal apertures, one obstructed, will have Airy disc of differing angular size, as I read it. One might trust that such a work with a high degree of detail, math and understanding might be credible. I doubt if a crank could make this up. Plus, adding additional diffraction would seem to change the outcome of the probability distribution (the Airy pattern.) In fact, it does. That IS the method of redistributing light from the central maximum into the rings. So, based on what little I know, I trust he is correct. The Airy disc shrinks due to the obstruction effects of diffraction and dimming.

Now, does that apply to just dim stars, too, with less energy? I'd think not, because the energy is in the wavelength not the intensity.

Edited by Asbytec (12/31/12 09:51 PM)


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Asbytec
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Re: Shrinking diffraction pattern revealed? new [Re: Asbytec]
      #5600954 - 01/02/13 10:25 AM

I just split 31 Tau in about 8/10 seeing. It is rated at 0.8" sep. My scopes theoretical Dawes limit is 0.77", just 0.03" difference.

At this sep, I am supposed to see a barely detectable 5% contrast difference. However, I could make out a distinct dark space. Not a black space like 52 Ori (1.2"), but a distinct dark space that was unmistakable.

It seems more than 5% contrast even if the sep is just slightest bit larger than the Dawes limit. I think this means my Airy discs were indeed smaller. In my 150mm aperture/.28D CO, the Raleigh limit is about 0.85" (black space at 28% contrast) and Dawes 0.72" (barely seen dark space at 5% contrast.) Both figures were corrected for the obstruction effects.

I would estimate contrast seen between 5% and the much more distinctly seen black space at Raleigh's 28% contrast. What I need to do is find a star at Raleigh limit (0.92" and 0.85") and see the difference.

Interesting. It could mean, however, I have exceptional ability to detect contrast at the threshold of human vision. Maybe, but I doubt it...not these aging eyes.


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fred1871
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Re: Shrinking diffraction pattern revealed? new [Re: Asbytec]
      #5603491 - 01/03/13 06:33 PM

I did think about point by point replies to various issues raised here, then decided it'd be briefer to write a book on these things, then decided there was no need 'cos the books are already available.

I don't think there's a need to re-invent the wheel on diffraction theory. The attempts above that suggest there is are confusing what we see (visual perception and its limits) with what's extremely well-established regarding diffraction, and questioning it on a basis of not knowing enough about how images are seen - air steadiness, observer variations (a biggie), particular qualities of the telescope used, etc. And the limits on what we can see of what is there - cameras are useful in extending vision, to make the point that we don't always see as much as we think of what is there and "visible" (if you're a camera).

Norme - the way the eye sees a pair at the Dawes Limit does NOT reflect the 5% contrast difference that is the case here. That's because of the form of the diffraction image and the way it is partly seen by the eye. The relative illumination of the diffraction disc does decrease from the centre to the first minimum (minimum is singular, despite some writers - "minima" is the plural)- however it does NOT look that way through the telescope. It looks quite different and of much greater contrast and different form. That's not news. You'll find discussion of it written in the 1800s; it's described in some detail in Sidgwick, writing in the 1950s.

Where we might get some new understandings (maybe?) is in terms of perception - what do we see, and what are the limits of vision on various kinds of doubles. Hence the discussion of "rules of thumb", the Haas project on uneven doubles, etc etc

So, yes, there are things we can usefully discuss.
That includes discussing diffraction images for a better understanding of the ideas, and applying that understanding to what we see. And noting when there are curious or interesting variations to what we might expect, followed by "why is it so". Plenty of room for discussion.

I will comment on one matter - in the case of dimmer stars - that has to do with perception, and simply reflects the limitations of the eye as illumination decreases. It does not change the diffraction pattern. It does change how (and to what degree) we can see it.


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Asbytec
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Re: Shrinking diffraction pattern revealed? new [Re: fred1871]
      #5603671 - 01/03/13 08:40 PM

Fred, thanks for the insight on how the eye perceives contrast on close doubles. I understand we only see part of the pattern and simply extracted the 5% contrast drop to the visual. I am new to double stars and will add that bit of information to my experience.

Yes, we've known about the laws of diffraction for a long time and they are grounded in good science. Not really trying to reinvent the wheel, but trying to understand the wheel. The sites cited above seem pretty clear the pattern does change with a CO. They state it explicitly. Relative to my basic understanding, that was quite a surprise.


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FlorinAndrei
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Re: Shrinking diffraction pattern revealed? new [Re: Asbytec]
      #5607673 - 01/06/13 01:27 AM

The central portion of the diffraction pattern (the solid disk in the middle, the Airy disk), does decrease when the central obstruction (the secondary mirror) increases, all else being equal. But the decrease is not due to the fact that fewer photons enter the system. It is purely a change in the way light is diffracted, the maximum and minimum points are placed at slightly different angles.

As the obstruction becomes bigger and bigger (all else stays the same), the minima of the diffraction pattern (the dark rings) move slightly towards the center - the whole figure appears to "shrink" somewhat. At the same time, more and more energy is being poured into the outer maxima (the outer bright rings) which become much brighter.

Points to take home:

1. The reduction of the central disk is very slight. It takes a gigantic obstruction to achieve a fairly meager reduction.

2. By the time the central disk is significantly reduced in size, the surrounding rings have become very very strong, degrading the overall performance of the system.

Even an obstruction 95% the size of the aperture does not produce a much smaller Airy disk, it just makes the outer rings extremely bright.

The overall shape and size of the diffraction pattern does not depend AT ALL on the brightness of the star. In the same telescope, all stars generate diffraction patterns of EXACTLY the same size and shape. However, faint stars appear, to the human eye, to generate smaller patterns for the simple reason that the outer part of the pattern is less bright, and hence less visible if the star is faint.

The Airy disk APPEARS to become smaller when the star is less bright (because its edge is so dark), but in reality the diameter of the first minimum (the first dark ring) remains exactly the same for all stars in a given telescope.

This is nothing new, it's just basic optics. There's nothing here to experiment or discover.

All of the above is very well illustrated on telescope-optics.net - take a look at the Point Spread Function in figure 106 (the PSF is basically a section through the diffraction pattern, indicating its brightness at different distances from the center):

http://www.telescope-optics.net/telescope_central_obstruction.htm

The parameter "o" is the size of the central obstruction as a fraction of total aperture. Notice how the zero points of the curve (the dark rings of the diffraction pattern) move closer to center as "o" becomes smaller, but at the same time the outer maximum points (the bright rings) become taller and taller. Also notice how it takes a pretty big obstruction (0.4x the total aperture) to achieve an unimpressive reduction (maybe 20% or so) in the size of the Airy disk, at the price of a large increase (2x or more) in the brightness of the surrounding rings.

Also see here:

http://www.hoflink.com/~mkozma/obstruction.html

The phenomenon is also discussed in the book "Star testing" by H.R. Suiter.

Finally, you could download Aberrator and calculate the PSF at different sizes of central obstruction, but the software is old and quirky, so it may require some coaxing until you figure out the right song and dance to make it work.


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Asbytec
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Re: Shrinking diffraction pattern revealed? new [Re: FlorinAndrei]
      #5607688 - 01/06/13 01:56 AM

Beautiful reply, Florin. I suspected it had to do with altering the pattern of diffraction. That just made sense.

Yes, the difference seems slight. For example (and very preliminary), I was able to exceed the theoretical Dawes from 0.77 to 0.74" arc (figures as reported, anyway.) That is a slight difference, and may be able to push a tiny bit more. Anyway, the diffraction affects are about 92% of the full Airy disc, that should give a little better hi freq resolution. Indeed, that /appears/ to be the case in the real world.

Quote:

The overall shape and size of the diffraction pattern does not depend AT ALL on the brightness of the star.



Correct. I think that was a misread of the original thread (and entirely my fault, I misread it remembering an earlier debate on the subject.)

To me, the revelation 1.22 Lambda didn't apply to obstructed scopes was enlightening. It meant that the shrinking apparent size of the spurious disc was not responsible for the increased resolution. In fact, the central disc is smaller and less light is scattered into that smaller area. So, its really 'brighter' than otherwise.

I read Suiter and was not sure whether he mentioned this clearly. In fact, probably read right over it.

Thank you for the additional link and the reply. This may be basic optics for those who care to read beyond Raleigh, but it was surprising news to me. Thank you, Florin.


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azure1961p
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Re: Shrinking diffraction pattern revealed? new [Re: Asbytec]
      #5608103 - 01/06/13 11:14 AM

Florin thanks for the clarity here and others too. It was interesting and revealing however to question it and to that end at least on my end much was gained. Again my appreciation.

Pete


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freestar8n
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Re: Shrinking diffraction pattern revealed? new [Re: azure1961p]
      #5609654 - 01/07/13 05:39 AM

I'm not sure if this thread mentions it, but most of these discussions assume the eye is a perfect, linear detector - and therefore the physical diffraction pattern is what is "seen" by the human visual system. Instead, here is a quote from an FAQ on gamma correction by Poynton:

"Human vision has a nonlinear perceptual response to luminance: A source having a luminance only 18% of a reference luminance appears about half as bright."

This means that a diffraction pattern with a range of brightness including a central peak will not correspond to the actual irradiance distribution on the retina, but a nonlinear version of it. If the eye were looking at a smooth sine wave modulation, for example, the human would not perceive a sine wave, but something with wider troughs and flattened at the top - which corresponds to the addition of higher spatial frequencies. This means you have a nonlinear imaging process when you include the perceptual component - and MTF does not apply.

In addition, it means that the perceived size of the central spot in relation to the other rings will depend in a complicated way on the overall scene and can't be deduced from diffraction theory or simulations.

In a situation like this, involving a variety of human subjects and a variety of objects (in this case, unequal double stars of varying brightness and separation) you would really need to do empirical tests. It may be possible to predict the perceived appearance of the Airy pattern by applying a gamma of 0.4 to the distribution prior to measuring the perceived size of the central spot and how doubles might appear.

It's also important to know if and when a gamma of 0.4 is effectively included in an image. If the video display itself includes this gamma to compensate for the visual system, then you need to know if it should be present - or not - in any simulation of a diffraction pattern. When you show a plot of the profile of an Airy pattern, this will always be linear - and therefore will not match the perceived profile - unless a gamma is applied first to distort the plot.

Frank


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Asbytec
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Re: Shrinking diffraction pattern revealed? new [Re: freestar8n]
      #5609857 - 01/07/13 10:09 AM

Quote:

...the human would not perceive a sine wave, but something with wider troughs and flattened at the top - which corresponds to the addition of higher spatial frequencies.



I am sure you are correct. However, if that flattened top was at a specific distance, that's where the eye would see it. That is where the irradiance distribution would be at it's peak. So, while the eye might not see a smooth and gradual brightening, allowing for a broader trough, it should still detect the peak at a specific frequency. Diffraction puts that peak at it's given radius. And it does seem you could squeeze those "flatter tops" closer together.

Quote:

...it means that the perceived size of the central spot in relation to the other rings will depend in a complicated way on the overall scene and can't be deduced from diffraction theory or simulations.




If I understand, you are discussing the spurious disc. It does appear it can differ in apparent radius between one person and another depending on their individual contrast sensitivity. That /should/ create a variable sized trough between the spurious disc and the first ring, but it shouldn't change the radius of the first ring.

Quote:

When you show a plot of the profile of an Airy pattern, this will always be linear - and therefore will not match the perceived profile - unless a gamma is applied first to distort the plot.



Makes sense. Thanks for the link, something new to absorb.


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freestar8n
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Re: Shrinking diffraction pattern revealed? new [Re: Asbytec]
      #5609935 - 01/07/13 10:54 AM

MTF requires a linear shift invariant system. If you input a sine wave and you output other frequencies than that sine wave, you do not have a linear system and MTF does not apply. If your input signal includes f and 2f frequencies, the transform will not treat them distinctly and instead will convert the f to f, 2f, 4f; and convert the 2f to 2f, 4f, 8f... The nonlinear induced harmonics will then combine - so that the output is no longer related by a simple transform of the input frequencies. Any partial coherence of the terms will further complicate the result due to interference dependent on phase.

When it comes to imaging double stars with a linear ccd, MTF has more of a chance to apply - but when it comes to human perception of the image - the nonlinearity and other factors are a departure from the assumptions that allow Fourier optics to apply.

With regard to the spurious disk - I am describing the perceived appearance of the Airy pattern - and I'm saying it will appear to have a larger central spot relative to the first ring, and the rings will have narrower width - but the diameter of the rings will be unchanged. This effect will depend on the intensity of the pattern, and may change when two different intensities are near each other. I think that is consistent with what people "think" they see, and it can be explained by the known nonlinear response of the eye - so there is no magic here.

In some sense - when it comes to visual/observational astronomy at an eyepiece - I don't know how you distinguish a perceived effect from a true effect - since if you faithfully record what you see, you will be including the nonlinearity and other artifacts of perception.

Frank


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Asbytec
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Re: Shrinking diffraction pattern revealed? new [Re: freestar8n]
      #5610125 - 01/07/13 12:24 PM

I agree, Frank, not sure how to separate what we do see from what we should see. Perception is reality, I guess. It does help to be aware of some illusions, such as mach bands. But, I think it's difficult to be aware of the eye's behavior in all cases.

You are definitely more knowledgeable that me on the higher order transformations. I never doubt you are correct, just try to apply what I understand against what you write. But, for my own purposes, at the moment, MTF is a useful approximation I can understand.


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freestar8n
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Re: Shrinking diffraction pattern revealed? new [Re: Asbytec]
      #5610283 - 01/07/13 02:00 PM

Hi Norme-

MTF is definitely useful and applied all over the place - but it does have caveats, and textbooks that talk about it and derive it in detail will describe its limitations. I think it is useful to describe general imaging behavior of a system, but it should never be used to make a comparison of one imaging system to another different one - particularly without the object specified. I think it should be used as a guide in design, but never referred to as something rigorous and deterministic about an imaging system.

The details I refer to are easily found in textbooks on Fourier optics, and they are not in the fine print. But they are not described in Suiter or in typical amateur web pages on telescope optics.

For a human studying a double star in an eyepiece with changing atmospheric conditions, I think it is particularly complex and ill-suited to simple theory - regarding CO, nonlinearity, and personal preference.

I place particular value on what users actually report, in terms of what optics they used to split stars with confidence. If they don't know the star ahead of time and they estimate its PA, separation, and magnitudes roughly correctly - that is good evidence they really observed it. And if they have an impression that fainter stars have smaller central spots than brighter ones, and that helps split them cleanly or something - I wouldn't be concerned if it didn't match a simplified linear view of the whole system.

Frank


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Asbytec
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Re: Shrinking diffraction pattern revealed? new [Re: freestar8n]
      #5610894 - 01/07/13 08:55 PM

Its often best to observe with little knowledge of the PA and maybe the companion, IMO and for exactly the reason you suggest. If a companion is visible, reporting where it is can be confirmation. When picking a double to observe, usually I limit myself to sorting they by separation only. When a difficult companion is clearly seen, there is little trouble picking the correct PA for a successful split. It's enjoyable.

Yes, the interplay of light and human sensitivity is highly complex, especially for the many with little knowledge beyond the Raleigh limit. I am peeking into that realm. Its interesting if not complex. A perfect example is this thread and others. I was unaware lambda/D did not apply across all scopes - only unobstructed ones. On human perception of color on Jupiter is another area dealing with human sensitivity. One can learn to see color on Jupiter.

Believe it or not, my whole investigation into the realm beyond Raleigh was fueled by that "effective aperture" thread. How do telescopes actually do what they do and what limits can be realized or pushed back. Then observation at that limit becomes a challenge. It's quite pleasing to succeed at observation near the limits of both man and machine.

Always a pleasure, Frank. The mere mention of, "Fourier optics" implies some advanced study beyond simple web page illustrations and often lacking among casual observers and even critical observers like myself. Next thing you know, we'll all be grinding 6" APO glass.


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GlennLeDrew
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Re: Shrinking diffraction pattern revealed? new [Re: Asbytec]
      #5614643 - 01/09/13 10:47 PM

One important fact to bear in mind is this. At lower surface brightness, diffraction patterns for dimmer stars could appear to be smaller due to the eye's lower resolving power at lower light levels.

A test for this using the eye as the detector should be devised so as to instantaneously vary the image brightness, and not introduce some slow interval over which a change is effected. Or better yet, devise an artificial star target so that an array of closely spaced, *identically sized* holes have ND filters installed for the control of brightness.

But I feel this test will only be confirmatory of what physics tells us; image brightness by itself in no way alters the scale of the diffraction pattern.

On the matter of what happens with a changing central obstruction, I'm not sure myself, and for my own edification an experiment would be useful. Some way to quickly flip a circular obstruction into and out of place in front of a refractor's objective would be one way to approach a visual comparison.

My only unknown in the matter is this. Does the CO in effect act like a superimposed smaller aperture, creating an angularly larger diffraction pattern superimposed on the angularly smaller pattern produced by the larger aperture (which would result in a more 'smeared' pattern)? If this does not occur--and all I've seen on the matter points to merely a redistribution of energy in the existing, non-obstructed pattern--then the whole business of altering scale of the diffraction pattern via a central obstruction is moot.


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fred1871
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Re: Shrinking diffraction pattern revealed? new [Re: GlennLeDrew]
      #5614822 - 01/10/13 01:46 AM

Quote:

My only unknown in the matter is this. Does the CO in effect act like a superimposed smaller aperture, creating an angularly larger diffraction pattern superimposed on the angularly smaller pattern produced by the larger aperture (which would result in a more 'smeared' pattern)? If this does not occur--and all I've seen on the matter points to merely a redistribution of energy in the existing, non-obstructed pattern--then the whole business of altering scale of the diffraction pattern via a central obstruction is moot.




Glenn, that's a pretty good description - "the CO in effect act like a superimposed smaller aperture, creating an angularly larger diffraction pattern superimposed on the angularly smaller pattern produced by the larger aperture" - of what is known as Babinet's principle, the complementary apertures theorem. Christopher Taylor (Argyle book, again!) describes it in relation to observing double stars with reflectors.


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Re: Shrinking diffraction pattern revealed? new [Re: fred1871]
      #5614927 - 01/10/13 06:15 AM

It does seem a good description, but the CO, from studying this topic, I believe is referred to a "negative" aperture. It does not diffract in the way the full aperture will, it has an opposing effect.

As the wave passes the CO, it diffracts into the wavefront from the center outward (for lack of a quantum explanation) to combine with the diffraction from the "positive" aperture's outer edge. Apparently, it does so in a way that first minimum has a different location.

It does seem the original first minimum would still form where it is supposed to. However, the introduction of a second set of peaks and valleys cause interference to cancel at a different radius rather than superimposing a larger Airy disc upon the original. The CO is not forming an Airy disc, only the original positive aperture is. To smaller extent the rings are affected, too, with CO size. Some tighten, some expand - then reverse as CO exceeds some diameter.

I'd have to gruel through that reference again to more fully understand. It did mention a "negative" aperture and that would be the simplistic way I understood it to work.


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FlorinAndrei
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Re: Shrinking diffraction pattern revealed? new [Re: freestar8n]
      #5633726 - 01/20/13 06:23 PM

Quote:

This means that a diffraction pattern with a range of brightness including a central peak will not correspond to the actual irradiance distribution on the retina, but a nonlinear version of it. If the eye were looking at a smooth sine wave modulation, for example, the human would not perceive a sine wave, but something with wider troughs and flattened at the top - which corresponds to the addition of higher spatial frequencies. This means you have a nonlinear imaging process when you include the perceptual component - and MTF does not apply.

In addition, it means that the perceived size of the central spot in relation to the other rings will depend in a complicated way on the overall scene and can't be deduced from diffraction theory or simulations.




That's a valid and subtle observation. However, there's one important thing to note here:

Whether the detector is linear or not, it doesn't matter, the positions of the maxima and minima remain the same.

In other words, a linear detector and a non-linear one will see the darkest parts and the brightest parts of the diffraction figure in the exact same spots. The only thing that gets skewed is the intermediary stuff, the half-bright portions of the pattern. But the max and min markers do not move at all - those are set in stone by the telescope.

I believe the most important result of the eye's non-linearity is the familiar look of the Airy disk, which appears to have a rather constant brightness almost all the way to the edge - while in reality the center is much more bright than the rest.

I don't think the eye's non-linearity makes a big difference for the shape of the rings - they are just too thin for a difference in the slope of the brightness curve to matter that much. Maybe a tiny difference, yes, the eye might be making them a bit more flat and fat than they really are. Oh, and they appear far more bright than they really are; in reality, they are quite faint when compared with the central disk. But overall shape and size is basically the same.

Based on all of the above, I would not throw the MTF overboard just yet.

Quote:

My only unknown in the matter is this. Does the CO in effect act like a superimposed smaller aperture, creating an angularly larger diffraction pattern superimposed on the angularly smaller pattern produced by the larger aperture (which would result in a more 'smeared' pattern)? If this does not occur--and all I've seen on the matter points to merely a redistribution of energy in the existing, non-obstructed pattern--then the whole business of altering scale of the diffraction pattern via a central obstruction is moot.




I wrestled with that metaphor for a long time, myself. It's quite tempting. I came to the provisional conclusion that it is not an appropriate metaphor.

The reason is - a simple scalar sum of two diffraction figures from two separate circular edges would almost never exhibit hard minimum points (zeros), except by sheer luck. But the point spread function of any obstructed telescope does exhibit zeros in the middle of each dark ring. Indeed, it's just the same old point spread function of an unobstructed scope, but with a shorter central peak and taller outer peaks (also, the minimum points are shifted a tiny amount inwards).

So, it's not the sum of two simple diffraction figures, but is a thing on its own, a separate, different phenomenon. The metaphor I use to satisfy my intuition is that the outer and inner edge "work together" to create the new diffraction figure.

Just another case showing that wave physics is non-intuitive.

Edited by FlorinAndrei (01/20/13 06:38 PM)


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azure1961p
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Re: Shrinking diffraction pattern revealed? new [Re: FlorinAndrei]
      #5634218 - 01/21/13 12:30 AM

An interesting thing I noticed with the brightening of the spurious disc to a central peak is that in 7/10 seeing its seen clearer at 400x than 550x through my 8". The Dawes notch and such can be still good at 550x but that starry point of light at the peak central area of the disc tends to flatten a bit in contrast. High mags beyond 40x per inch can seem to help on determining desperation details even out to 80x per inch but the light profile of the central airy disc area appears to plateau . Seems to look less starry and more disc like.

Pete


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Re: Shrinking diffraction pattern revealed? new [Re: FlorinAndrei]
      #5634768 - 01/21/13 11:38 AM

Quote:

But the max and min markers do not move at all - those are set in stone by the telescope.




I just noticed this reply. Yes, the radii of the rings are unaffected by the nonlinearity - but the apparent size of the central disk could be strongly affected. When you look at a bright star in comparison to a dim one, your eye compresses the dynamic range - and does a lot of other stuff too - so it would be perceived as having a larger central disk. The perception is nonlinear, and for visual work, it's the perception that matters - not the irradiance on the retina. When you apply a gamma to the Airy pattern to compress it, the fwhm will increase with intensity - and that would affect the size of the central spot and the ability to split a close double.

MTF assumes everything is linear - so when the perception is known to be nonlinear, it's hard to say that the MTF is still useful - particularly when comparing a bright scene to a faint one, where the MTF would theoretically be identical, but the change in visual response would make the effective mtf's very different. And when you have a bright star near a faint one, you are perceptually rescaling as you move your eye around - and who knows what that does to the "mtf."

Frank


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