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How good are reflectors for resolving binaries?

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#151 DesertRat

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Posted 14 November 2013 - 11:13 AM

Norme,
Interesting comparisons - however the energy graphs posted here for increasing obstructions are seriously flawed. The 70-90% obstruction graphs show a central disk almost the same intensity as the first diffraction ring. This is clearly false.

Perhaps you would like to revisit the code that created these graphs?

Glenn

#152 Asbytec

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Posted 14 November 2013 - 12:10 PM

Glenn, I grabbed that from an earlier SA thread, don't know how it was created or what code was used. Still interested in the complex interplay between near monochromatic coherent and incoherent light with human physiology. It's far more complex that imagined.

#153 DesertRat

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Posted 14 November 2013 - 12:25 PM

I see. It could be that code was only looking at the diffraction rings - don't know.

Here is an animation of increasing obstruction. Even with an increasing obstruction the central spot will remain brighter than anywhere else. This graphic is normalized so it does not show the whole image getting dimmer as more light is cut out. Also it is displayed at gamma 2 so the rings appear brighter than they actually are. The actual eyeball response is very difficult to model. Not only are everyone eyes different, but the response in general cannot be described by a gamma only.

The animation does clearly show the central spot getting smaller with increasing obstruction as expected.

Glenn

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#154 WRAK

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Posted 14 November 2013 - 02:22 PM

I think Norme's graph refers to the distribution of peak intensity and is in this context correct. It is amazing how quick peak intensity of the central disk drops with increasing CO values. I am not sure about the weight of animations in terms of proof for anything but the visual impression of the animation for CO 0.8 looks very much like what I have seen when experimenting with extreme CO values. The same or even larger amount of energy in the first diffraction ring seems to give due to the larger surface of the ring compared to the central disk the impression of less brightness. This is one aspect I have so far not been able to check with my CO experiments: Which amount of CO is necessary to "erase" a fainter companion sitting on the first ring - this would then give an empirical evidence to the term of delta_m between central disk and first ring.
Wilfried

#155 DesertRat

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Posted 14 November 2013 - 07:48 PM

I think the original animated plot above is faulty. First it has a problem near zero, there is a singularity there in computations and maybe whoever created it did not deal with it well. Or maybe its a graphic of rings only? Not sure, but I would not base any conclusions based on that graphic.

Even with an 80% obstruction the central spot will be clearly brighter than the diffraction rings. See attached animation. It shows the airy profiles for a 150mm scope with varying obstructions in green light with the actual angular spread shown in arc-seconds.

I would not question your findings however. For a large obstruction seeing has to be very very good for it to be in any way beneficial in splitting a binary. This is a known but little discussed difficulty of large obstructions. When seeing is mediocre, turbulence will scramble all that extra energy in the rings along with the central spot to yield a mess.

Glenn

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#156 Asbytec

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Posted 14 November 2013 - 08:21 PM

For a large obstruction seeing has to be very very good for it to be in any way beneficial in splitting a binary. This is a known but little discussed difficulty of large obstructions. When seeing is mediocre, turbulence will scramble all that extra energy in the rings along with the central spot to yield a mess.


Intuitively, that makes sense as long as the ring structure is visible. Seeing here in the tropics is outstanding, enough so that the actual brightness of the second and third thinner rings can be seen at times. Other times, they are more disrupted by even the least disturbance, but even out to the fourth ring can be seen.

Interestingly, I feel reducing my own CO down to about 30% (from 38%), I lost the fifth ring all together on stars bright enough to show them and the fourth seems less bright. That was the extend of visible improvement, and maybe a little improvement on lunar diffraction effects.

Planetary /might/ be better, but it was not immediately obvious. Sketches seemed to improve over time, but that could be conditions or experience rather than CO improvement. Maybe that light loss in the fifth ring and the almost invisible 4th ring was redistributed to the central disc. Maybe the inner rings are unnoticeable dimmer, too.

The jury is still out on unequal doubles, and really on close doubles too. But some observations, particularly of 7 Tau suggest both a split /possibly/ below Dawes and the extent of the dark space seen (in excellent seeing) suggests a closer split is possible. Still need to do a sampling of splits just below Dawes down to about 0.7" arc to see if most can be split.

There is some psychological improvement as well knowing peak intensity moved very close to the standard 80%.

Wonderful animations, by the way. Now, how the eye responds to the logarithm of intensity is weird.

#157 azure1961p

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Posted 14 November 2013 - 08:41 PM

Glenn thanks for clarifying - your points are appreciated.

Wilfreid, perhaps then better seeing is needed to more accurately assess larger COs?

Interesting points made here.

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#158 WRAK

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Posted 15 November 2013 - 05:09 AM

Glenn, your input is appreciated very much as new ideas stimulate the discussion but I think a "competition" with animations does not help much to answer the question of the effects of CO regarding resolution of unequal binaries.
Besides your animation shows near 20% intensity for the Airy disk with CO 0.8 and this is wrong at with this value it is already only ~10%, else green light is 510nm and not 550nm as indicated in the graph but 550nm is anyway the usually used value for average visual impression.

To get nearer the question of visual brightness of especially the first ring in terms of magnitudes I would be happy to find a paper discussing this topic with some scientific background. For example the information given on http://www.telescope...obstruction.htm is quite comprehensive but the CO dependent energy distribution within the diffraction pattern does not help very much as it seems quite complicated to "translate" energy values in a spot (spurious disk) and in a ring into differences in magnitude.
Chis Lord's paper on resolving unequal binaries includes a table with delta_m values but I did not find any explanations how he got to this values and so far I was not able to confirm or falsify these numbers neither theoretical nor emperical.
For zero CO he gives a delta_m of 4.39 - does this mean that a companion with +6.39mag sitting on the first ring would disappear if the primary is +2mag bright?
I still have to wait for a good opportunity to get empirical evidence here - for my 140mm refractor I need a double ~1.3" with delta_m ~3 to have a good chance for resolving with zero CO and then I can apply different sizes of CO to see when and if the secondary disappears. Bad news here is that I did not find this many candidates with such parameters - currently I wait for an opportunity to observe STT457 in Cep with a delta_m of 2.16. Could get interesting - will the companion disappear between CO 0.4 and 0.5 or may be earlier or even not at all?
Wilfried

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#159 DesertRat

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Posted 15 November 2013 - 12:13 PM

Wilfried,

I'm not competing with any animations. I was simply correcting the original posted animation as it was incorrect.

I'm confident the last posted animation is correct. Photometric peak searches on high definition simulated star images yield a ratio for an obstruction of 0.8 as 0.1294 with respect to the unobstructed case. The Bessel expression used in my last posted animation shows it as 0.1296. That's close enough I think.

Glenn

#160 DesertRat

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Posted 15 November 2013 - 12:56 PM

Norme,

The diffraction rings do not need to be 'visible' to detract from an obstructed scopes performance in dodgy seeing. In fact in larger scopes and 'continental' seeing the diffraction rings are rarely visible. However the energy is still there and given turbulence impacts the scopes performance in a negative way in terms of contrast transfer. Think of an obstruction as a high pass filter, and when increased displays increasingly more noise.

I envy the tropical seeing you enjoy! I'm lucky to see fragments of the first diffraction ring in my C14.

Finally, you stated earlier "As I understand it, light is pretty much coherent in modest amateur scopes.". What evidence or reference do you have for this? I have never seen an image of a binary star that would suggest coherence, from any scope. But if you have any evidence I would sorely like to see it.

Glenn

#161 azure1961p

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Posted 15 November 2013 - 03:53 PM

Well coherence here I think is being used in the way of stating medium apertures will more often yield a stable diffraction pattern
Than a larger aperture which can be quite a bit more demanding. Not to suggest large aperture is taking a back seat to resolution just that its more condition needy to get the same apparent stability in the pattern for average seeing conditions.

Pete

#162 Asbytec

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Posted 15 November 2013 - 09:25 PM

Glenn, yes, that's the interesting thing about doubles for me. The rings do not have to be visible to affect contrast transfer, so it seems to imply energy is affecting the companion in some way. This was kind of the core of my question earlier. Is it energy or glow from the brighter primary.

I can't offer proof for stellar light being coherent, in fact it's not. But, it's not entirely incoherent either, in how it behaves. For example, incoherent light (according to discussion here and here) really does not loose peak intensity in the presence of a CO as coherent does. So, that we do notice some intensity loss suggests a bit of coherent behavior. And FWHM is relatively unaffected for incoherent light, however if FWHM is affected with an obstruction then it would behave like coherent light even though it is nearly incoherent. And all of this behavior is overlaid by the human logarithmic response to intensity distribution. Complicated, in that it's nearly monochromatic. I am still trying to get my head around it.

"While there is no difference in a single point-source imaging between coherent and incoherent light with respect to the relative intensity distribution - as long as light remains near monochromatic - the resolution limit for a pair of point sources for the former varies with the phase difference between the two sources...Since, according to Van Cittert-Zernike Theorem, light arriving from stars is coherent in amateur-size telescopes, as long as it is near monochromatic, it is an interesting question how much this coherence factor, changing with the wavelength bandwidth and source OPD, influences the actual resolution limit in the field."

"Since deducting the CO area amplitude contribution and squaring the difference (in coherent light) produces different result than deducting energy from this area directly (in incoherent light), the entire annular aperture PSF will differ for the two, not only its central intensity. Considering that PSF-defined intensity distribution for point-source image determines contrast and resolution of extended objects as well, any significant difference in the annular PSF will imply significant difference in the effect of CO on overall performance."

My question is, "In general, CO effect modeled for incoherent light shows much less depressed central maxima, and nearly identical reduction in its width." Is this what we actually see? We obviously get to 80% intensity with a ~0.3D obstruction, so are we seeing 'behavior' consistent with coherent light for near monochromatic incoherent star light? And as such, does FWHM behave consistent with coherent light (affecting resolution), as well, by falling off more rapidly than with pure incoherent light?

"The actual light from astronomical objects is neither incoherent, nor coherent. It is generally closer to incoherent (partially incoherent), so the actual CO effect would be, correspondingly, closer to that indicated by the incoherent model. While this modeling for the effect of central obstruction in incoherent light is, as already mentioned, informal and approximate, it can be assumed that it is significantly smaller than in coherent light, simply because taking out energy originating from the obstruction area directly has significantly less of an effect than taking out the corresponding wave amplitude in coherent light."

Much of this technical discussion is over my head and I'm swimming for the surface to breath. :)

#163 DesertRat

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Posted 16 November 2013 - 12:32 AM

Norme,
We're straying off the OP comments - not your fault really - I'll share some of the blame!

I respect Vlads contributions in his website you linked to. I would love to see him publish his work in printed form some day as many of his graphics and discussions are unique and of much value to astronomers interested in telescope performance.

Coherent optics forms the basis for incoherent imaging. From the coherent model one can build a structure of expressions using sums of uncorrelated waves which describe very well the way images are created.

My question was with respect to a binary system. There is no coherence between 2 or more stars closely placed - their wavefronts are independent from each other. So there is no way the sum of the stars would yield a coherent interference pattern. If there was coherence the 2 stars could show alternately a bright max or a zero min or no difference at all depending on the phase difference between them.

In a microscope however, especially when its condensor iris is stopped down or when using laser illumination, coherent images are clearly evident. I've done a lot of work in that area, and in fact most of my code was written for coherent imaging. I know what it looks like and I have never seen myself or seen published any evidence of coherence for astronomical images in optical wavelengths.

When reading texts on optics its important to understand that some limitations discussed (like the utility of a MTF for example) apply to one or the other as they are meant to describe imaging in general - like everything from microscopes to telescopes as I mentioned.

But to answer your question - the PSF in my graphics above are what we would see for a coherent point source imaged in a narrow wavelength range. Full understanding requires reading Vlad's work in addition to several other texts and especially the limitations of the Van Cittert - Zernike theorem. For visual work the image should resemble the incoherent expectation, so the central max would not be diminished as much with increasing obstruction. Need to think about this one, I see your dilemma! :scratchhead:

Glenn

#164 Asbytec

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Posted 16 November 2013 - 02:16 AM

Thanks, Glenn...yea, I am a long way from anything beyond a faint understanding of how it all comes together. Just delving into the complex topic. Great point on the lack of coherence between two closely spaced stars, but the individual star has an essentially 'coherent' point source wavefront?

Yea, we may be off on a tangent, but I thought it might be applicable to discussing CO and particularly on doubles...and related to the topic. If it's not, forward any Moddie PMs to me, I'll apologize profusely, eat crow, and take the hit to my reputation for dragging the discussion here. :)

So, yea, why do we get less peak intensity if light is more incoherent than not. Actually, in good seeing I've peaked deep into the Airy disc realm and feel I can best Dawes with an obstruction. It's given me a new appreciation for that bit of high performance curve near max spacial frequency (and the PSF.) So, not sure what's going on down there.

Cheers, Glenn

#165 brianb11213

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Posted 16 November 2013 - 05:38 AM

the individual star has an essentially 'coherent' point source wavefront?

No, the stellar photosphere consists of a vast number of independent "transmitters"; putting enough distance between the stellar surface and the photon collector / detector to make the star appear as a "point" (angular diameter much smaller than the instrumental diffraction pattern) doesn't affect coherence.

What does make a difference - in an incoherent stream - is a tight waveband limit. The point here is that there is no difference in atmospheric disturbance caused by variations in refraction with wavelength so the image appears sharper. Most "white light" solar observers are well aware of the improvement in seeing when a narrow waveband (nebula type) filter is used but it appears that few deep sky observers know about this.

Yea, we may be off on a tangent, but I thought it might be applicable to discussing CO and particularly on doubles...and related to the topic. If it's not, forward any Moddie PMs to me, I'll apologize profusely, eat crow, and take the hit to my reputation for dragging the discussion here. :)

No need IMVHO. Interesting discussion often arises from going off at a tangent, but this is related rather than tangential.

FWIW my personal opinion is that low CO systems seem to suffer less from atmospheric turbulence than high CO systems of a similar aperture / resolving power / light gathering capacity. Theories about thermal disturbance of the air around the secondary don't seem to hold water as (a) thermal disturbance from the objective, which has much more thermal inertia, will completely mask them, and (b) the practical seeing advantage of a small CO persists when the scope is fully conformant with ambient temperature.

What really matters here is the stability (lack of turbulence) of the atmosphere for the whole light path from the top of the atmosphere to the light detector (be it animal or mineral) via the objective. The diffraction pattern is indeed modified by the central obstruction but the practical effects of this are usually quite small for COs of up to 30 - 35% providing that the seeing is fairly steady.

#166 WRAK

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Posted 16 November 2013 - 07:38 AM

I think I have meanwhile found how Lord calculated his delta_m numbers for the diffraction pattern: Translating the relation of peak intensity into magnitude differences.
Examples:
0.0 CO: Disk Peak=1, First Ring Peak=0.0175, Relation ~57, Delta_m based on LOG2.512 ~4.39
0.1 CO: Disk Peak=0.98, First Ring Peak=0.0206, Relation ~47.5, Delta_m based on LOG2.512 ~4.19
0.2 CO: Disk Peak=0.92, First Ring Peak=0.0304, Relation ~30, Delta_m based on LOG2.512 ~3.70
0.3 CO: Disk Peak=0.83, First Ring Peak=0.0475, Relation ~17.5, Delta_m based on LOG2.512 ~3.11
0.4 CO: Disk Peak=0.71, First Ring Peak=0.0707, Relation ~10, Delta_m based on LOG2.512 ~2.5.
The numbers do not meet exactly the numbers of Lord but to a good enough degree to assume that his reasoning was along this line.
While I don't want to suggest that these numbers are "true" (especially not without empirical evidence) the idea to use peak intensity numbers for calculating delta_m values makes sense for me as this would it make possible to directly compare the peak intensity of the first ring of the primary with the peak intensity of the central disk of the secondary.

I still hope that somebody with better knowledge of diffraction theory and better mathematical background than me comes up with a solid founded approach to determine delta_m within the diffraction pattern.
Wilfried

#167 Asbytec

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Posted 16 November 2013 - 09:03 AM

I think it's a great discussion and I appreciate everyone who contributes for contributing.

Wilfried, I still find your calculations above interesting. At 0.3D, I look for those unequal doubles in the range of deltaM ~3 in the vicinity of the first ring. Some closer and some wider, some dimmer and some brighter. I think there is something to the figure calculated (more or less) at the angular separation of the first ring.

#168 DesertRat

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Posted 16 November 2013 - 11:25 AM

Brian,

If I understand what Norme is asking we have this. The experimental evidence of CO effect on the PSF implies the distribution is more like the expected coherent behavior. At least across the distance from the central max to the first minimum - or possibly even a lesser distance. To answer that requires some computations using the Van Cittert Zernike theorem.

If the star was really incoherent the drop in PSF max due to obstruction is entirely different and much smaller. Thus the question Norme is asking.

Complicating matters is this: the intensity of the central max is highly dependent on wavelength. The power goes as the inverse square of wavelength. So the central max in blue light would be significantly brighter than red, taking into account the spectral distribution of the star.

On seeing - yes a CO makes seeing more of a limiting factor, for the reasons I stated above. Even if the outer rings are not visible, common with larger scopes, there is enough energy there that in the presence of turbulence the image is more negatively impacted with increasing CO.

Glenn

#169 Asbytec

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Posted 16 November 2013 - 01:16 PM

Yes, that's exactly the question, the apparent coherent behavior...if indeed it is apparent rather than normal incoherent behavior. Or something in between.

On seeing. Seems that tropical excelent seeing has finally arrived, even with a CO. Sirius just sat there as a disc and rings - sometime a bit dusturbed. Amazing sight, just wanted to share the moment. No confirmed pup sighting, though. Straying back toward the topic, "darn CO!" :)

#170 WRAK

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Posted 16 November 2013 - 01:49 PM

Checked my data set and found several observations from Fred, Norme, Roberto and myself with delta_m ~3 at or near the first diffraction ring. I found also an entry from Roberto for AC15 1.25" +5.13/8.96mag meaning delta_m of 3.8 directly on the first diffraction ring (with 152mm and zero CO within the calculated numbers).
Only one entry in my data set is outside the above calculated values: Bill's observation of Gam Equ with CO near 0.3 but delta_m of 4 - but this is a case with open questions regarding the advertised data.
Wilfried

#171 DesertRat

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Posted 16 November 2013 - 03:10 PM

Sirius just sat there as a disc and rings - sometime a bit dusturbed. Amazing sight, just wanted to share the moment.

Now you are just making us envious! I use to live in a semi-tropical clime and the seeing was clearly much better than here in the desert southwest. Your statement above just hurts!

On coherence
Just to be clear to anyone reading here - we are discussing the concept of spatial coherence. If one were to place 2 pinholes or slits in the intercepted star beam (Young's experiment) the contrast in the resulting inteference pattern beyond would be a measure of the degree of spatial coherence. Best done with color filter. I suspect it is fairly coherent in that respect. One could get a handle on it, if not measure, by estimating the contrast in the bands seen with a ronchi eyepiece.

I think it fairly safe to model these PSF's as above - which assumed coherent, single wavelength light. Doing the incoherent pattern is relatively easy, partial coherence somewhat more difficult.

Glenn

#172 WRAK

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Posted 16 November 2013 - 04:28 PM

To make things a bit more realistic we should may be include the factor quality of scope in terms of Strehl.
Formula for calculating max. CO for target peak intensity depending on Strehl:
max. CO =(0.6-0.6*Peak Intensity/Strehl)^0.5.
Example for target peak intensity 0.85 with given Strehl 0.95 (not perfect but very nice scope) results in max. CO = 0.25.
Example for "target" (nobody would want this) peak intensity of 0.1 with given Strehl 0.95 results in max. CO = 0.73.
Wilfried

#173 Asbytec

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Posted 16 November 2013 - 08:52 PM

Glenn, my apologies. Last thing I want is to inflict pain, well most of the time, anyway. I lived 100 miles north with exceptional nightly seeing, this new location had yet to prove itself. I've been very fearful about moving away being a horrible mistake. So, to see a really good night was a relief of mammoth proportions. Being retired, seeing alone is enough to make me move back. So, yea, it was great to finally 'see' it after fretting over something so important to us.

To be fair, I am equally envious of your (Brian, et al) grasp of the topic at hand. It's almost painful, too, to be so behind in the knowledge with a long hard road ahead. :)

On coherence as it relates to doubles, it does seem each star has many emitters therefore the light arrives not in phase. It's not a laser. But the idea of spacial coherence is interesting, being two individual points close in angular separation and possibly physically close on astronomical scales.

The distance between them, of course, dwarfs the wavelength of light, but can they somehow be coherent in that the wavefront might arrive almost as if from a single source? The two slit example you mention is the same wavefront arriving the detector and seems not to dissimilar to two closely spaced sources whose wavefronts experience very similar seeing and aberration en route to the focal plane.

Can the wavefront leaving one source arrive in phase and on time with a wavefront from the companion source? Is that a form of coherence? It seems the same could be said for many emitters on a single star. Some waves from different emitters are bound to arrive in phase (for a given color.)

#174 fred1871

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Posted 16 November 2013 - 08:55 PM

Checked my data set and found several observations from Fred, Norme, Roberto and myself with delta_m ~3 at or near the first diffraction ring. I found also an entry from Roberto for AC15 1.25" +5.13/8.96mag meaning delta_m of 3.8 directly on the first diffraction ring (with 152mm and zero CO within the calculated numbers).
Only one entry in my data set is outside the above calculated values: Bill's observation of Gam Equ with CO near 0.3 but delta_m of 4 - but this is a case with open questions regarding the advertised data.
Wilfried


Wilfried, looking through my observation files of difficult pairs, from the 140mm refractor, I'm finding various doubles on or near the first bright ring with a delta-m in the 2.5-3 range. The same delta-m range applies for the more difficult pairs that fall into the Rayleigh gap - the first dark interspace, closer to the primary's disc. I find it interesting that there's an approximate matching between a closer companion in a dark space, and a slightly wider one on a bright ring, in terms of delta-m.

Wider again, beyond the first bright ring, around the 1.7" to 2.0" separation, several pairs with delta-m in the 3.5 to 4 range were seen. (For 140mm, the 2nd bright ring is centred about 2.2"). So, clear of the first ring, and slightly wider, delta-m can unsurprisingly be larger and still allow a visible star.

On the matter of Gamma Equ, we're still in the dark so to speak, until there's a new measure.

With regard to another of the doubles on the Haas list, 42 Ori, I've been looking at the complete data file, where before I had only some of the measures, and will shortly (later today?) offer a revised commentary on that one. 42 Ori has had various discussions in a few threads here in the past.

I did a revision recently on BU 9 (in the "From Dolphins to Dogs" thread) where I discovered that having the complete data set changed to some degree the overall picture, compared with what could be deduced from a partial data set. Likewise with 42 Ori, the full data set suggests a different pattern.

#175 Asbytec

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Posted 16 November 2013 - 09:36 PM

Fred, with my own limited double experience, I find the delta mag on or inside the first ring to require a brighter companion than say about mag 3, too. I don't know the delta M required, it might even change nightly. But it seems delta mag 3 is a bit optimistic if not a close approximation. It is interesting this delta mag limit seems to hold into the first dark inter-space and possibly decreasing closer to the primary. It's one of the fascinating mysteries of doubles. What makes the so difficult? Surely glare from the primary, diffraction plays a role somehow, as does personal acuity and our physiological response along with observing conditions and optical performance.

BU 1030 is a real mystery in that each visible disc should retain much of it's angular size even being fairly dim. In appearance, however, the pair appeared to be two very closely separated pin points. Surely each star affects the other in many ways with a delta mag of ~1.9. That they 'appeared' to be very close pin points, both neatly tucked inside a faint ring structure, with a dark space was astonishing, really.

On 42 Ori, that was one of those long duration observations that finally led to the correct 'guess' to the companion's location. There was discussion about how conditions might sweep the first ring long enough to get a good look at the companion (hampered by the CO effect on the first ring and maybe reduced intensity of the central disc.) I am not sure, but then sometimes it seems the only explanation, this allowed a lucky guess to be correct. It's becoming clear, to me, steady ring structure in good seeing is preferable for doubles. Man, fighting that distorted ring and all the seeing artifacts simply makes resolution a real chore on difficult doubles, so not sure the 'ring sweeping' effect is preferable.






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