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Shrinking diffraction pattern revealed?

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#26 azure1961p

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Posted 06 January 2013 - 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

#27 freestar8n

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Posted 07 January 2013 - 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

#28 Asbytec

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Posted 07 January 2013 - 10:09 AM

...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.

...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.

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.

#29 freestar8n

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Posted 07 January 2013 - 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

#30 Asbytec

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Posted 07 January 2013 - 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.

#31 freestar8n

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Posted 07 January 2013 - 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

#32 Asbytec

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Posted 07 January 2013 - 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. :lol:

#33 GlennLeDrew

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Posted 09 January 2013 - 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.

#34 fred1871

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Posted 10 January 2013 - 01:46 AM

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.

#35 Asbytec

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Posted 10 January 2013 - 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.

#36 FlorinAndrei

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Posted 20 January 2013 - 06:23 PM

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.

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.

#37 azure1961p

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Posted 21 January 2013 - 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

#38 freestar8n

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Posted 21 January 2013 - 11:38 AM

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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