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azure1961p
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Re: How good are reflectors for resolving binaries? new [Re: 3c_273]
      #6057639 - 09/01/13 12:55 PM

Quote:

Really Good. Mostly!

My C-8, often excoriated because of its huge secondary (2.5, 63.5mm", 0.31% of primary aperture) and field curvature (~9", 228.6mm"), can deliver exquisite images, given a tranquil atmosphere. The diameter of it's Airy disc is 1.26", and first diffraction ring is 1.7". See

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

for how this is derived. The large secondary displaces light from the central disc to the rings, which is sometimes good. See

http://en.wikipedia.org/wiki/Airy_disk

for the gory details.

My C-8 is one of the old Ultimas, known for their excellent optics, and my telescope, with it's UO orthoscopics, leaves little to be desired in this respect. I actually use setting circles to find things with it.

On to what I've observed.

When both stars of a pair are close to the same brightness, The C-8 splits them very nicely. Especially with faint pairs. I've managed to make pairs like BU 394 (0.6" when observed), or BU 1313 (0.5" in 2010, observed in 2012) actually split or appear elongated.

What isn't so good is when the stars are around 1.2 - 1.9" apart, and the primary is 2+mv brighter than the secondary. Then the primary's first diffraction ring is right on top of the secondary, and the central obstruction is enhancing it's brightness. These are almost impossible for me to resolve.

Reflectors, with their inherently larger (both dollar and physical size wise) apertures, allow faint stars to be observed. The confusingly cataloged star L 44:

http://www.cloudynights.com/ubbthreads/showflat.php/Cat/0/Number/6010128/page...

might be a 12.5 - 13.9mv pair, 4" apart. I could see both stars in the C-8. My old Questar 3.5 (long since sold) would not have shown either star.




I completely agree a quality SCT can be a formidable doublestar instrument. Theory (and reality) would suggest the slightly smaller spurious disc and brighter rings could actually enhance sub arc second doublestar resolution.

Pete


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WRAK
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Re: How good are reflectors for resolving binaries? new [Re: azure1961p]
      #6057836 - 09/01/13 02:59 PM

I certainly agree with the solid statement of Tom and even included his observations of BU394 and BU1313 in my data set of limit observations - but I want to see myself how increasing CO shrinks the size of the Airy disk. For example I would expect a kissing pair with zero CO to get separated with 0.25 CO.
And then I want to check the limit of CO before it becomes destructive as I have learned happens when reducing the aperture of my C9.25.
I suspect so far that nothing positive happens any more above 0.25 CO and negative effects begin with 0.35 and exactly this I want to check with reality.
Wilfried


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azure1961p
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Re: How good are reflectors for resolving binaries? new [Re: WRAK]
      #6057949 - 09/01/13 04:09 PM

Wil,

I'm curious - your room reducing your aperture in the 9.25 SCT I'm guessing to see the effects of an enlarged CO. The reduced aperture would reduce resolution. Perhaps its best to leave aperture at 9.25" and simply experiment with CO silohuettes or masks. If Im misunderstanding you please clarify.

I think we are all in agreement however that at a specific seperation per aperture the illuminated first diffraction ring can be detrimental to fainter secondary companion visibility.

I'm clouded out here on my three day weekend off or Id be certainly doing doubles these evenings. Oh well.

Pete


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fred1871
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Re: How good are reflectors for resolving binaries? new [Re: 3c_273]
      #6058380 - 09/01/13 10:04 PM

Quote:



My C-8, often excoriated because of its huge secondary (2.5, 63.5mm", 0.31% of primary aperture) and field curvature (~9", 228.6mm"), can deliver exquisite images, given a tranquil atmosphere. The diameter of it's Airy disc is 1.26", and first diffraction ring is 1.7". .....

When both stars of a pair are close to the same brightness, The C-8 splits them very nicely. Especially with faint pairs. I've managed to make pairs like BU 394 (0.6" when observed), or BU 1313 (0.5" in 2010, observed in 2012) actually split or appear elongated.

What isn't so good is when the stars are around 1.2 - 1.9" apart, and the primary is 2+mv brighter than the secondary. Then the primary's first diffraction ring is right on top of the secondary, and the central obstruction is enhancing it's brightness. These are almost impossible for me to resolve. ......





I'd overlooked Tom's note (given in part, above) when it appeared. Looking at it now, I see some matters needing clarification.

First, Tom quotes the diameter of the Airy disc and the first diffraction ring (1.26", and 1.7"). He then proceeds to discuss observations he's made of pairs at particular separations - but a separation is a radius, not a diameter.

So, using Tom's numbers, the first (bright) diffraction ring will be 0.85" from the centre of the star, not 1.7" from it. Consequently, pairs at 0.85" (spread plus or minus a bit) will be in the first bright diffraction ring. The second diffraction ring will centre around 1.4" (see below).

Second, he refers to pairs at separations of 1.2" -1.9", uneven by 2+ magnitudes, being so placed that "the primary's first diffraction ring is right on top of the secondary". Nope - can't happen - not with an 8-inch telescope that's operating at full aperture.

To have the first diffraction ring centre somewhere around 1.4"-1.7" requires a 4-inch to 5-inch aperture. And, in any case, a diffraction ring that's so wide it has effects from 1.2" to 1.9" (one ring!) is something I've not seen in a good telescope in reasonable seeing, even with my C9.25 that has a bigger CO factor than a C8.

That leaves the location of the second bright diffraction ring to be considered. Because it's around 1.4" (spread, so plus and minus) from the primary, that fits for Tom's observational experience.

That would suggest a very enhanced second diffraction ring. In an unobstructed system, the second ring will have a maximum brightness around 5.5 magnitudes dimmer (~1/200) than the star producing it. Ring enhancement from a 31% CO will brighten that; and less than perfect optics will brighten it further. Looking at Dick Suiter's table in his Star Testing book, 2nd edition, a 31% CO with 1/6-lambda (whole system optics) - about as good as it usually gets- effectively slightly more than doubles the amount of light in the rings, so if we assume roughly proportional brightening of 1st and second rings, that would produce a 2nd ring maybe near 4.5 magnitudes dimmer than the star.

A secondary star in such a ring should however be visible as a brightening in the ring, if seeing is good, collimation is good etc etc, and optics as prescribed, assuming it's around 2 to 3 magnitudes dimmer than the primary - it also loses extra light from the disc into its rings.

Quite a few different scenarios can be constructed here, as we vary this factor or that. And consider interference effects of a star image on another star's diffraction ring. But I think the overall picture is that
(a) it can't be the first diffraction ring at ~1.5" hiding the secondary star with an 8-inch aperture
and (b) the second diffraction ring seems pretty bright, from the description.

Anyone someone want to do some more exact estimates of the least possible brightness of the second ring....? And run some varied-factors scenarios?


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Asbytec
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Re: How good are reflectors for resolving binaries? new [Re: WRAK]
      #6058508 - 09/01/13 11:50 PM

I suggest you try that and continue exploring the topic.

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WRAK
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Re: How good are reflectors for resolving binaries? new [Re: fred1871]
      #6059631 - 09/02/13 04:36 PM

Quote:

...In an unobstructed system, the second ring will have a maximum brightness around 5.5 magnitudes dimmer (~1/200) than the star producing it. Ring enhancement from a 31% CO will brighten that...



I am not sure about this but it seems that while CO makes the first ring brighter it makes the second ring fainter and surprisignly the third ring is then actually brighter than the second ...
I also do not fully understand what it visually means that the diffraction rings have specific delta_m's compared to the central disk - does it mean that a secondary with the same delta_m simply disappears in the ring (making it maybe a tad thicker in its position) or is such a secondary to see without troubles as the brightness of the diffraction ring is distributed in the ring.
Will certainly have a look myself at this question - but don't have so far a good idea for a quick size change CO maks construction for my refractor.
Wilfried


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fred1871
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Re: How good are reflectors for resolving binaries? new [Re: WRAK]
      #6059946 - 09/02/13 08:26 PM

Wilfried, thanks for the reminder - from what I've now looked at, the change in intensity of particular rings depends on the ratio of obstruction. So I'll need to rework the numbers, according to various CO percentages, starting with the CO for a C8. There's a simple version of the relative changes in Suiter (2nd edition, p.165) - 25% obstruction enhances the first and third rings relative to unobstructed, 50% obstruction enhances the rings in order 1, 2, 3 again (linear progression). I'll try to calculate some (rough) numbers.

This won't change some of the points I've made earlier. The first diffraction ring can't intrude on a C8 at the separations quoted; and something (what?) affects the visibility of fainter secondary stars in a particular zone that approximates to the second diffraction ring. Puzzles continue.


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WRAK
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Re: How good are reflectors for resolving binaries? new [Re: fred1871]
      #6060435 - 09/03/13 03:11 AM Attachment (17 downloads)

There is a table from Lord's paper on resolving unequal binaries with values for different CO - maybe of interest.
Wilfried


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fred1871
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Re: How good are reflectors for resolving binaries? new [Re: WRAK]
      #6060656 - 09/03/13 09:05 AM

Thanks, Wilfried. A useful table, as it shows the changing amount of light transferred into the 2nd and 3rd rings, according to changes in CO size. The first ring keeps growing in intensity as the CO increases, but the relative amount of light in rings two and three is changeable - at 0.2 CO and 0.33 CO the 3rd ring is brighter than the second; at 0.4 CO and zero CO the 2nd is brighter than the third.

I'll look further at how this can affect unequal doubles. But it does indicate that your experiments with a diaphragm on your SCT, having the effect of increasing the CO as you stop down, brings in variations in the diffraction rings' appearance and relative brightness, so it can affect the visibility of faint companions in particular positions from to the primary. And, as your aperture changes as the CO is changed, the position of each ring will vary, as well as its intensity. That increases the difficulty of isolating individual factors with diaphragm use. Your new thought, putting various sizes of CO via masks on the refractor, has the advantage of keeping aperture constant.


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Asbytec
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Re: How good are reflectors for resolving binaries? new [Re: fred1871]
      #6061106 - 09/03/13 02:01 PM

Fred, might the deltaM of the rings tell us something of the deltaM required to detect the companion located very near that ring?

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fred1871
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Re: How good are reflectors for resolving binaries? new [Re: Asbytec]
      #6061746 - 09/03/13 09:53 PM

Yes, it should - the delta-m of the rings, included in the Lord table, should suggest the degree of interference (bad pun) with visibility of the secondary star.... if delta-m is greater for the star than for the ring, the star will be lost in the ring, and if it's close to the same delta-m for star and ring it'd be very difficult to be sure that a slight ring brightening is a secondary star rather than a seeing artifact. Sidgwick is quite pessimistic on this - using the old term for a minor secondary star (comes), he remarks - "A comes much more than 1 mag fainter than its primary will be imperceptible if its image falls on the first ring...".

An interesting feature of the changing relative brightness of difffaction rings 2 and 3 is that, for a CO of 0.33, the second and third rings are fairly similar, the third ring in this case being slightly brighter. Both, of course, are dimmer than the first ring, but can interfere with visibility of secondary stars where delta-m is large.

I'll write another (not too long ) item on all this later today if I get time; for the moment, interesting features are the change in location (radius) of rings with CO changes, and (from Sidgwick and others) a need to factor in the increased width of the rings with CO.


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Asbytec
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Re: How good are reflectors for resolving binaries? new [Re: fred1871]
      #6062032 - 09/04/13 01:31 AM

Fred, exactly what I was driving at. If the first ring is 3 magnitudes fainter, maybe a star less than 3 magnitudes fainter can be seen. Maybe not. I have no idea, but it might be another interesting aspect to explore. It turns out, 42 Ori has a ~3 mag difference. That's interesting.

It may be that the star will have to generate enough contrast to separate itself from the bright ring. Is one magnitude brighter than the ring sufficient, or must is be only 1 magnitude fainter than the primary? For a .33D obstructed, the second and third ring are pretty bright, too, but they are extremely thin. The first and dimmer fourth rings both have some width to them. If memory serves, the second and third rings are actually slightly less intense than an obstructed aperture. (Normalized, I think.)

Above, the third is dimmer than the second. I wonder if that is for an un-aberrant aperture. One may be brighter than the other depending on the amount of spherical aberration present.

This subject always begs the question, is the difficulty due to sheer brightness gradient or does interference patterns change the brightness of a point source in the vicinity of another. Surely the pattern of interference is much more complex than for a single point source. Certainly at the minima of the primary some destructive interference is going on. I wonder if that affects the brightness of a companion star in that vicinity...and /if/ the companion's interference affects the primary, even.

And can a little bit of adverse seeing manipulate both wave fronts so that - lucky snapshot - constructive interference can form an image of the secondary if only for an instant as the primary's first ring fades at that location?


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WRAK
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Re: How good are reflectors for resolving binaries? new [Re: Asbytec]
      #6062068 - 09/04/13 02:39 AM

As already stated - I am not so sure about this (delta_m for rings equivalent to delta_m binary). I have found so far no precise description how this delta_m is calculated - I assume from the relation of the energy distribution. But this would mean the delta_m refers to the whole ring and not a single point of the ring. So the same delta_m would mean that the secondary is easy to detect when sitting on the ring because he is then brighter than the overlapping part of the ring.
Wilfried


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WRAK
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Re: How good are reflectors for resolving binaries? new [Re: azure1961p]
      #6062128 - 09/04/13 04:46 AM

Quote:

...I'm clouded out here on my three day weekend off or Id be certainly doing doubles these evenings... Pete




Pete, your equipment (200mm Nexton with 35mm CO) would allow some interesting experiments with aperture masks. First you could easily do limit observations regarding resolving doubles (at least a very solid elongation bordering on a rod) by reducing the aperture. Even with 120mm aperture you have still only 0.3 CO. Second you could combine this with enlarging systematically your CO and thus observe how this changes the diffraction pattern and the resolution for a given double up to the simulation of a C8 with 70mm or even larger CO.
Wilfried


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Asbytec
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Re: How good are reflectors for resolving binaries? new [Re: WRAK]
      #6062244 - 09/04/13 07:54 AM

Thanks for the reminder, Wilfried. I had forgotten you addressed that topic.

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3c_273
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Re: How good are reflectors for resolving binaries? new [Re: Asbytec]
      #6063038 - 09/04/13 05:01 PM

To get back to Fred's detailed analysis, which is also supported by the papers cited in my original post, my problems with 1.2 - 1.9" separations are based on observations, and I took the separations from the WDS which usually gets it right. The stars might have closed up a bit, or, more likely, the secondary is much fainter than its WDS magnitude.

I've found the WDS magnitudes to be all over the place. Try observing a few of the Jonckheere pairs. The vast majority, but not all, are 2mv fainter than their published WDS magnitudes.

So. It's quite possible that my inability to make out a secondary at slightly over an arc second is that it's enmeshed in the primary's diffraction pattern. In some stars, this can be quite large. Sirius is now at 7" separation, way over the Airy radius of the telescope, but I can only see the Pup in moments of Pickering 9 seeing, and with an occulting bar stuck in the focal plane of my eyepiece.

Theoretically, the arguments in the optics texts are accurate, but the atmosphere, star brightness, and how well trained your eye is can yield somewhat untheoretical results.


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fred1871
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Re: How good are reflectors for resolving binaries? new [Re: Asbytec]
      #6063385 - 09/04/13 09:02 PM

Norme, you've quite a few matters/questions regarding the diffraction rings. Regarding the visibility of a star on the first bright ring of a primary - how bright it can be relative to the primary and still be seen is difficult to estimate. Sidgwick, who I've quoted above, is pessimistic; Taylor in the Argyle book is somewhat pessimistic.

With regard to 42 Ori, the issue is whether the companion star is on the diffraction ring or in an interspace. That will depend on the aperture of the telescope, which determines where the spaces and rings fall. More on that, and 42 Ori, in a later note.

The relative brightness of rings, as I've indicated, depends on CO. The numbers are different for different CO proportions. Using Lord's data, and comparing 0.33 CO with zero CO: the first diffraction ring is brighter with 0.33 CO, the second diffraction ring is dimmer with 0.33 CO, and the third diffraction ring is similar with each (a tiny bit dimmer with zero CO).

There are other differences - the spacing of rings and interspaces changes with CO. I've used the figures in Lord's table (via Wilfried) to calculate relative spacing of the centres of dark and bright rings in the diffraction patterns, again for zero CO and 0.33 CO.

Interestingly, the percentage increase in location of the centre of each ring (dark or light) relative to the centre of the preceding ring (light or dark) is smaller for 33% CO than for zero CO.

So, for zero CO,
1st dark
1st bright +34%
2nd dark +36%
2nd bright +20%
3rd dark +21%
3rd bright +14%
These are increases relative to the previous ring (dark or light)

EDIT: I've now corrected this table (first percentage increase) from an earlier error.

And, for 0.33 CO
1st dark
1st bright +47%
2nd dark +50%
2nd bright +13%
3rd dark +14%
3rd bright +16%

Edit addition: In some respects, the numbers are misleading; the positions of the 1st bright ring and others beyond that change only slightly; the biggest change is the reduction in the size of the central disc, and the position of the centre of the first dark ring as the Lord table shows. The first dark ring is centred closer to the central point of the diffraction image (1.098 units, compared to 1.220 units for zero CO). Both disc radius and first interspace centre are reduced about 6%, but the centre of the first bright ring is less than 2% closer to the centre of the diffraction image.

I don't at the moment have data for calculating the effective width of diffraction rings for 0.33 CO. I do have numbers for zero CO.

Yes, spherical aberration will play into this. Discussion thus far is for un-aberrated apertures. Real telescopes have deficiencies, small or large, that will have an effect. Feed in your preferred level of SA

"Surely the pattern of interference is much more complex than for a single point source" - I can only agree. But I don't have at present a means to evaluate this in detail.

"Constructive interference" to make stars visible ("for an instant") on the first bright ring? - one can hope... but the images I see through telescopes more often have seeing artifacts that mimic star points.

Edited by fred1871 (09/05/13 03:54 AM)


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fred1871
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Re: How good are reflectors for resolving binaries? new [Re: WRAK]
      #6063391 - 09/04/13 09:05 PM

Quote:

As already stated - I am not so sure about this (delta_m for rings equivalent to delta_m binary). I have found so far no precise description how this delta_m is calculated - I assume from the relation of the energy distribution. But this would mean the delta_m refers to the whole ring and not a single point of the ring. So the same delta_m would mean that the secondary is easy to detect when sitting on the ring because he is then brighter than the overlapping part of the ring.
Wilfried




Wilfried, I thought the delta-m of the ring referred to the brightest part of the ring. The rings, like the central disc, have a gradation of brightness across width. Lewis (1914) gives figures for brightness levels across the disc and each ring as well, from which delta-m figures can be easily calculated, at least for the centre of each ring for unobstructed apertures and assumed zero aberrations.


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fred1871
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Re: How good are reflectors for resolving binaries? new [Re: 3c_273]
      #6063406 - 09/04/13 09:18 PM

Tom, see my revised details on diffraction rings, their brightness levels, and locations, above.

Re your C8 - the numbers for it will be close to the 0.33 CO.
For that aperture and 0.33 CO, the ring centres are as follows:
1st dark ~0.7" (=Rayleigh)
1st bright 1.0"
2nd dark 1.5"
2nd bright 1.7"
3rd dark 1.95"
3rd bright 2.25"

These numbers are based on the table Wilfried posted here, from Chris Lord's paper.

Interestingly, the 2nd dark ring (the dark interspace between the first and second diffraction rings) occurs in the middle of your "difficult" zone (1.2"-1.9"). If you don't happen to attempt pairs around that separation, but a bit each side of it, you might not see there's a clearer zone in that area.

Alternately, spread of the rings, due to atmospheric haze, stray light on the SCT corrector plate, dust on it, spherical aberration, figuring roughness on mirrors, zones in optical elements, or ??? - enabling light spread - might occur and hide the clear zone. A few years ago I saw an SCT that had nice looking star images but poor resolution of low contrast planetary detail, and checking further (star test) it appeared to have a lot of spherical aberration in the system. This smeared the diffraction ring pattern in focus as well.

Edited by fred1871 (09/05/13 01:42 AM)


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fred1871
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Re: How good are reflectors for resolving binaries? new [Re: 3c_273]
      #6063709 - 09/05/13 01:59 AM

Tom, a couple of other matters. We know, following Wilfried's interest in Jonckheere doubles, that older magnitudes for those are highly inconsistent and often wrong. But many of the magnitudes quoted in the WDS are from Tycho, so they should be pretty good. Many of the older magnitudes are also closer to accurate than the typical Jonckheere magnitudes. 'J' doubles are not typical of the photometry presently recorded in the WDS. No doubt the APASS magnitudes for fainter stars will find their way into the WDS as stars are identified.

Sirius - you're not dealing with diffraction patterns here, in trying to see The Pup - rather, it has to do with image spread and flare light. Sirius, as the brightest star in the night sky and a very uneven double as well, demonstrates these problems better than any other. But it's nothing to do with the diffraction pattern.

"untheoretical results"? - do you mean "theory" in the popular usage sense (speculation) or in the scientific sense (the best description we have that takes all the facts into account etc)?
Currently, we don't have a good theory for describing the visibility of secondary stars in very unequal doubles. We might get close to that at some time, and Wilfried's work-in-progress looks promising, along with some earlier studies that appear to give pointers in the right direction - but given the number of variables involved (including individual eyesight) I suspect any theory, which will need to be consistent with what we know of diffraction, will involve conditionals and approximations.


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