Jump to content


Photo

Delta Cyg reloaded

  • Please log in to reply
36 replies to this topic

#1 WRAK

WRAK

    Apollo

  • -----
  • Posts: 1188
  • Joined: 18 Feb 2012
  • Loc: Vienna, Austria, Europe

Posted 30 June 2012 - 09:30 AM

2010 I started with double star observing for 2 reasons: Heavy light pollution is not such a problem and a vast number of interesting objects is available. End of summer/begin of autumn is the Cyg constellation in my southwest/west frame of view and one of the very interesting double star targets in this constellation is STF 2579/Delta Cyg. I tried to split this double with my short 120mm refractor with mostly not very stable seeing several times without success and finally with a bit of luck concerning seeing I identified a stable bright spot in the first diffraction ring as the companion and I could repeat this result 2011 - I was very satisfied as according to the data in the Struve catalogue (1.8" +2.9/7.9mag) this was quite a good result and seemed to be confirmed by textbook diffraction theory: Calculating yellow light lambda with the correct 580nm (and not 550nm as used in calculating the Rayleigh Limit) I get an Airy disc diameter of 2.43" and for the second minimum 4.44". This means a diameter for the brightest part of the first diffraction ring of about 3.44" and a radius therefore of 1.72" which corresponds very well to the indicated 1.8" separation.

In preparing my Cyg sessions for this season I started with searching for all potential targets in the diverse double star catalogues (including especially of course WDS) and found that I was in ignorance of the actual data of Delta Cyg not only of the different separation of 2.7" but also of the magnitude of the companion (but here I am always a bit unsure if I should really trust WDS as there are at least some errors especially concerning mag2 to find here). But while the difference in magnitude only changes the difficulty level for splitting I was really frustrated by the difference in separation as this made my observation questionable. So I will have to recheck this very concentrated this year.

I have also looked at other observation notes (for example http://www.carbonar....nus/delta.html) and found here notes on clear splits with for example an 8" reflector (giving first minimum 1.46", second 2.67" and third 3.88") with the companion on the second diffraction ring giving a separation of about 1.6" and then a fantastic note with an 63mm refractor (giving first minimum 4.63" and second 8.46") also with a split on the first diffraction ring (somehow I feel like a fool that it should be so easy to split Delta Cyg with a refractor this small) - this observation would give a separation of 3.27".
Next an observation with an 150mm reflector (giving first minimum 1.95", second 3.56", third 5.18" and fourth 6.79") near the third diffraction ring meaning with a bit of interpretation a separation of about 2.9".

So what is going on here? I would have thought that the textbook formulas for the diffraction pattern should be useful for a reasonable estimation of the separations of close doubles. Either this is not the case or all (excluding may be the last) mentioned observations including especially my own are not valid or the textbook 2.7" are not correct.

With desperation
Wilfried

#2 azure1961p

azure1961p

    Voyager 1

  • *****
  • Posts: 10466
  • Joined: 17 Jan 2009
  • Loc: USA

Posted 30 June 2012 - 09:51 AM

I would imagine when you get into the details that fine that discrepencies are going to arise. I do love Delta Cygni. Busted it even when it was a wholelot closer [1.8"?] years ago with my 8". Seeing has made the companion elusive through my 70mm but that particular site I used to observe from was terrible due to local seeing environment.

Yours in an interesting post Wilfried and Im impressed that you have done the math for the diffraction ring spacings and such but as I said, I think when you cut the wire that fine you are going to get a lot of conflicting data. This isn't to say you should ignore it and embrace ignorance, but I think its a *data peril* when you refine your observations to that degree. I am interested to see how others weigh in on this. Ed, also known as Edz would probably have good specifics here.

Your observations are interesting and again a beautiful object.

Pete

#3 Bonco

Bonco

    Gemini

  • *****
  • Posts: 3455
  • Joined: 17 Apr 2006
  • Loc: Florida

Posted 30 June 2012 - 03:36 PM

Don't be concerned about being a "fool" if you didn't see it. Double star observing of difficult pairs involves many variables beyond your control. Delta can be fickle and while I've viewed it in a 3 inch scope, I've on occasion had no success with a 6 inch. I too have written in my log of observered splits that I later crossed out in my log because I learned the original observations were false. This happened on a couple of occasions with a newly purchased 3 inch scope. The problem is it would put bright spots on the first diffraction ring creating a false companion. The lens has been replaced and I now have confidence in the scope.
Best wishes, Bill

#4 blb

blb

    Aurora

  • -----
  • Posts: 4529
  • Joined: 25 Nov 2005
  • Loc: Piedmont NC

Posted 30 June 2012 - 05:52 PM

Just a thought, try to estimate the position angle. That alone will rule out a bright spot on the defriction ring that is not the companion star.

#5 azure1961p

azure1961p

    Voyager 1

  • *****
  • Posts: 10466
  • Joined: 17 Jan 2009
  • Loc: USA

Posted 30 June 2012 - 09:52 PM

Don't be concerned about being a "fool" if you didn't see it.


I dont believe I indicated that I had any such concerns. Such is observing. Thanks for your support though.

Pete

#6 WRAK

WRAK

    Apollo

  • -----
  • Posts: 1188
  • Joined: 18 Feb 2012
  • Loc: Vienna, Austria, Europe

Posted 01 July 2012 - 03:22 AM

Just a thought, try to estimate the position angle. That alone will rule out a bright spot on the defriction ring that is not the companion star.


This is a procedure I meanwhile use on a regular base as tool to verify my observations - but the main question remains: Are the diffraction pattern formulas of use for estimating close separations? In my coming observation sessions I will give this aspect special attention.
Wilfried

#7 azure1961p

azure1961p

    Voyager 1

  • *****
  • Posts: 10466
  • Joined: 17 Jan 2009
  • Loc: USA

Posted 01 July 2012 - 07:15 AM

The patterns should be. So long as radii and diameter arent confused this should work, alas the discrepencies though.

Pete

#8 blb

blb

    Aurora

  • -----
  • Posts: 4529
  • Joined: 25 Nov 2005
  • Loc: Piedmont NC

Posted 01 July 2012 - 09:24 AM

...but the main question remains: Are the diffraction pattern formulas of use for estimating close separations?


Does not a stars predominate color change a little with a stars spectral type? Is not the formula based on the wave length of a stars light? I think the answer is YES to both questions, so the radii would be a little different for each star, correct? That means you must know the spectral type of each star observed and do the math for each target object, correct? Assuming there are no published errors, and we know that there are, and your willing to do the math, this could be a guide for those realy close doubles.

#9 Bonco

Bonco

    Gemini

  • *****
  • Posts: 3455
  • Joined: 17 Apr 2006
  • Loc: Florida

Posted 01 July 2012 - 02:37 PM

Just a thought, try to estimate the position angle. That alone will rule out a bright spot on the defriction ring that is not the companion star.


This is a procedure I meanwhile use on a regular base as tool to verify my observations - but the main question remains: Are the diffraction pattern formulas of use for estimating close separations? In my coming observation sessions I will give this aspect special attention.
Wilfried

That's how I discovered my false observations. I later compared my estimate of PA with published values...Thus I crossed out the observation in my log. :foreheadslap: Thanks, Bill

#10 WRAK

WRAK

    Apollo

  • -----
  • Posts: 1188
  • Joined: 18 Feb 2012
  • Loc: Vienna, Austria, Europe

Posted 01 July 2012 - 02:51 PM

... Does not a stars predominate color change a little with a stars spectral type? ...That means you must know the spectral type of each star observed and do the math for each target object, correct? ...

The textbook diffraction pattern formulas are based on the wavelength of monochrome colors and all stars are a source of a whole spectrum of light depending on the spectral type - so far I have found no guideline how to handle this discrepance because this would mean that we don't see a single diffraction pattern but several overlapping ones. The simplest approach is certainly to choose an average value which means 580nm for yellow light - and depending on the spectral type this average value should be moved up (when more red) resp. down (when more blue).
But somehow it should work - especially if there exists such a tool as a diffraction micrometer even if seldom used because it seems cumbersome.
But the position of the companion in the diffraction pattern should allow an easy good enough estimate of the separation - so the above reported discrepances for Delta Cyg with values form 1.6 to 3.3" seem curious and therefore a reason for further investigation.
Wilfried

#11 WRAK

WRAK

    Apollo

  • -----
  • Posts: 1188
  • Joined: 18 Feb 2012
  • Loc: Vienna, Austria, Europe

Posted 12 October 2012 - 10:03 AM

Yesterday I had the opportulnity to observe Delta Cyg again (this time with a 140mm refractor) and could split it without any problems with a magnification of x140. This time I checked also the position and with estimated 225° it was close enough to the WDS catalogue position of 220° to be considered as confirmed. The diffraction ring pattern was rather unstable so I could not determine the exact position in the diffraction pattern and therefore not calculate the estimated separation - but compared with the separation of Eps Lyr at the same magnification I think 2.7" is maybe a bit too close and about 3" is more realistic.
Out of curiosity I also varied the aperture to see how far I could go down in apterture and still split Delta Cyg - the result (as reported in another thread about testing the rule of thumb) was somewhat below 100mm. Maybe a night will come with brilliant seeing - then I will try again if I can go below this value because the above mentioned splitting of Delta Cyg with a 63mm refractor is still kind of a challenge for me.
Wilfried

#12 drollere

drollere

    Surveyor 1

  • *****
  • Posts: 1588
  • Joined: 02 Feb 2010
  • Loc: sebastopol, california

Posted 12 October 2012 - 05:15 PM

i've been intrigued by the effect of the diffraction rings on the airy disk of companion stars.

i can see a much reduced but still distinct airy disk in isolated single stars down to about magnitude 9 using my 12" SCT. however if an 8th or 7th magnitude star is within the visible diffraction rings (or even just outside the faintest ring) of a brighter primary star, then the airy disk appears to be "dissolved" into a small fuzzy cloud. i have seen the diameter of this cloud appear larger than the airy disk of the brighter companion, which means the apparent brightness of the fainter star can be reduced by much more than the listed catalog difference.

the light from the two stars is "incoherent" (uncorrelated) so there should be no diffraction interaction between the two sources. but the diffraction rings seem to have an "erosive" effect on the fainter source, and this effect may clearly extend beyond the circumference of the faintest ring; this also suggests that it is not merely a form of reduced brightness contrast.

this again points out the difficulties with a single "rule of thumb" in close pairs: a 2 magnitude difference in a double star will have different effects depending on the number of diffraction rings around the brighter star. the brightness contrast will be reduced, but also the visibility of the seeing robust and evenly illuminated airy disk. in all situations, a disk is much easier to see than a fuzzy blob!

#13 fred1871

fred1871

    Viking 1

  • -----
  • Posts: 916
  • Joined: 22 Mar 2009
  • Loc: Australia

Posted 12 October 2012 - 08:15 PM

Interesting commentary, Bruce, and a good point. A secondary star sitting on a first diffraction ring will be a lot harder to see than one in the first dark interspace between spurious disk and diffraction ring, or one outside the first diffraction ring (and the first ring has over twice the light transferred to it compared to the second).

The effect will be more obvious with an obstructed telescope - your 12-inch SCT has, what, 35% obstruction by diameter? So about 37% of the star's light is transferred from the disk to the rings, comparted to about 16% with a refractor or other unobstructed design. So the rings are over twice as bright. Little wonder that a relatively dim secondary that falls on the first diffraction ring will have its appearance changed as you describe.

This helps to explain why unobstructed optics do better on larger delta-m doubles - less light in the rings, the lesser star has more contrast/visibility if it falls on the ring. So there's less interference of a relatively bright diffraction ring overlaying a dimmer disk plus ring(s).

And, yes, it does suggest a further modification might be needed to the 'rule of thumb'. My thoughts at the moment are that it'll likely be non-simple.

Re Delta Cygni itself, it's not a pair I can do much with observationally from my location, as it rises only about 10 degrees above my northern horizon. Seeing at that altitude, plus atmospheric dispersion, makes life difficult.

However, given the listed delta-m for Delta Cygni (c. 3.4 mags), and separation (2.5" 2011, 2.7" by ephemeris), spltting it with less than a ~100mm aperture exceeds (does better than) the limit my version of the rule of thumb would indicate. Hmmm. :question:

Small scopes follow a different rule, and do better than mid-size? Or are we comparing small unobstructed scopes with mid-size obstructed ones?... We know big ones do relatively less well, as seeing has more effect in imposing limits....

So the rule may vary by aperture class as well. Ok - more thinking needed ....

#14 azure1961p

azure1961p

    Voyager 1

  • *****
  • Posts: 10466
  • Joined: 17 Jan 2009
  • Loc: USA

Posted 13 October 2012 - 12:17 AM

Bruce and Fred,

Nice points made here. I dont think there is going to be any clear cut rule, or *limit* or simple formula that will account for a secondary involved with the primaries rings and minima that amply forecasts difficulty to a prospective observer. Itd be so much more straight forward if the rings and such never existed but there in is the charm and challenge.

I think at best a fair rule of thumb is the best one can hope for if these matters were hashed out in any mathematical way that suits the greater general body of oservers. I think a kind of Dawes for unequal doubles is impossible. Its noce food for thought but its too steeped in variables to simplify and generalize.

Bruce, I like your close observations and questions raised with regard to stellar diffraction pattern appearances.

Pete

#15 drollere

drollere

    Surveyor 1

  • *****
  • Posts: 1588
  • Joined: 02 Feb 2010
  • Loc: sebastopol, california

Posted 13 October 2012 - 01:26 AM

fred, i was thinking of a specific example where the secondary appeared to be *outside* the diffraction rings. it was 6 cas (STT 508), currently listed at 1.5" with mags. 5.66 and 7.95 ... delta mag. 2.29.

in my 12" SCT a 6th mag. star usually shows two rings, and the radius of the third dark interval (outer border of 2nd ring) would be at about 1.2". so i observed no *visible* overlap between the primary diffraction artifact and the secondary. this is what made the effect especially intriguing. could there be diffraction "erosion" even in an area where no ring is visible?

to your other points, i do think a "rule of thumb" needs to be fitted to the specific type of scope, for reasons you mention, and to the observer's skill. i have tried phrasing my rule in units of the rayleigh limit (aperture specific), but i haven't really tested how well that performs across different apertures (2 of my 10" scopes are down for repair or rebuilding).

anyway, to wilfried's query, "is the diffraction pattern useful to estimate the separation of close pairs?" my answer would be "probably not", because the patterns of two stars seem to interact in ways that degrade the image of the fainter star.

herschel used the airy disk diameter to judge distances, within a few diameters' separation, and i think that method would be more reliable, provided you have some way to state definitively the visual diameter of the airy disk for the specific magnitude of the primary star. the gaussian formula says all airy disks are exactly the same diameter in the same aperture, independent of stellar magnitude: there is no formula to estimate by how much the disk of a 2nd and 6th magnitude star will differ in apparent diameter.

#16 Cotts

Cotts

    Just Wondering

  • *****
  • Posts: 4949
  • Joined: 10 Oct 2005
  • Loc: Toronto, Ontario

Posted 13 October 2012 - 09:53 AM

"the gaussian formula says all airy disks are exactly the same diameter in the same aperture, independent of stellar magnitude: there is no formula to estimate by how much the disk of a 2knd and 6th magnitude star will differ in apparent diameter. "

To be clear, the gaussian formula says that the radius to the first minimum in the diffraction pattern is the same at a given aperture. This is the so-called Airy disc. the radius of the visible portion of the Airy disc changes with magnitude at a given aperture and is often referred to as the central spurious disc.

Dave

#17 drollere

drollere

    Surveyor 1

  • *****
  • Posts: 1588
  • Joined: 02 Feb 2010
  • Loc: sebastopol, california

Posted 13 October 2012 - 12:14 PM

"the gaussian formula says all airy disks are exactly the same diameter in the same aperture, independent of stellar magnitude: there is no formula to estimate by how much the disk of a 2knd and 6th magnitude star will differ in apparent diameter. "

To be clear, the gaussian formula says that the radius to the first minimum in the diffraction pattern is the same at a given aperture. This is the so-called Airy disc. the radius of the visible portion of the Airy disc changes with magnitude at a given aperture and is often referred to as the central spurious disc.

i waited for the other shoe to drop, until i realized ... there is none.

to be clear: there is no formula to estimate by how much the disk of a 2nd and 6th magnitude star will differ in apparent diameter, and therefore there is no systematic or rigorous way to apply the airy disc component of diffraction artifact to the estimation of the separation between double stars, which is the topic. (having excluded the use of the diffraction rings for measurement purposes for the reasons explained in my post.)

and while i'm here ... pete, i appreciate your acknowledgement of my interest in the diffraction artifact as visual evidence, but in fact the core of my testimony is simply: PILE ON THE MAGNIFICATION. you can't see the complexities of the diffraction artifact unless you're down in pinhole exit pupils, and you'll never get to pinhole exit pupils if you follow the planetary observer's advice to use "only the magnification that the seeing allows."

ah, so dainty, so civil, this acceptance of allowable limits! well, we are buccaneers and pirates, we double star tribe; we use magnification like torture with an "AR AR AR!", and "enough" is however much is required to get the testimony we seek.

#18 Cotts

Cotts

    Just Wondering

  • *****
  • Posts: 4949
  • Joined: 10 Oct 2005
  • Loc: Toronto, Ontario

Posted 13 October 2012 - 05:26 PM

Bruce, the only thing we are mixing up between us is nomenclature. Can we agree on the following? To be clear.

Diffraction Pattern: the entire thing we see when examining a star including a central disc and one or more rings and, in our imaginations at least, the dark spaces between the rings.

Airy disc: the disc whose radius to the first minimum of the gaussian function is determined by the aperture of the telescope only. The entire Airy disc is not visible for the vast majority of stars.

Spurious disc: that portion of the Airy disc which is actually visible.


You and I both agree that there is no formula for relating magnitude and the radius of the spurious disc as defined above. There most certainly is a 'formula' relating magnitude and the radius of the Airy Disc - specifically, the Airy disc size is constant for a given aperture without regard to magnitude or telescope type.

Dave

#19 azure1961p

azure1961p

    Voyager 1

  • *****
  • Posts: 10466
  • Joined: 17 Jan 2009
  • Loc: USA

Posted 13 October 2012 - 11:29 PM

Bruce,

I agree the magnification needs for proper or optimum stellar diffraction pattern study is far higher than typical planetary observations might dictate.

Pete
{Ar Ar]

#20 WRAK

WRAK

    Apollo

  • -----
  • Posts: 1188
  • Joined: 18 Feb 2012
  • Loc: Vienna, Austria, Europe

Posted 14 October 2012 - 04:15 AM

...there is no formula for relating magnitude and the radius of the spurious disc ...
Dave

Dave, I agree insofar as I also don't know of any written precise formula but already Airy considered this topic to some degree in his work "On the Diffraction ..." and gave at least formulas for specific parameters:
"The rapid decrease of light in the successive rings will sufficiently explain the visibility of two or three rings with a very bright star and the non-visibility of rings with a faint star. The difference of the diameters of the central spots (or spurious disks) of different stars ... is also fully explained. Thus the radius of the spurious disk of a faint star, where light of less than half the intensity of the central light makes no impression on the eye, is determined by [s = 1.17/a], whereas the radius of the spurious disk of a bright star, where light of 1/10 the intensity of the central light is sensible, is determined by [s=1.97/a]."
As the Airy disk is defined as mathematical function there has to be also a formula to define the radius of the spurious disk at the threshold of detection for a given aperture (and therefore given resolution limit) and a given brightness of a star because this would be "simply" the part of the gaussian profile above this threshold - even if only as approximation.
The question remains if such a formula would be of any practical value and maybe it is sufficient to know according to our Prof. EdZ in his paper about "Resolution" that bright stars might take up to 85% of the Airy Disk and mag 6 ones about 50-60% and fainter ones even less.
Wilfried

#21 ziridava

ziridava

    Vostok 1

  • -----
  • Posts: 123
  • Joined: 17 Aug 2012
  • Loc: Arad,Romania,Eastern Europe

Posted 14 October 2012 - 06:43 AM

I used Delta Cyg to get the right focus before attempting to split 23 Aql on the 6-th of October,as reported here:

http://www.cloudynig...5/o/all/fpart/2

I understand my 125mm F/7 reflector is falling somewhere in the middle of the aperture range required to split Delta Cyg, computed with the ''rule of thumb''.
My magnifications for double stars are between 116x and 236x.
On that night I used 144x/Radian 6mm for Delta Cyg,it was very nice and clean split.
For me,the use of diffraction rings to measure separations is a bit confusing because the CO on my reflector is 28% and I know I don't see the first diffraction ring.
However ,the separation of the companion of 23 Aql seemed to be 10-15 % bigger than that of Delta Cyg. Still,23 Aql is a much more difficult double star than Delta Cyg.
Last year I had very hard time until I split Delta Cyg:I was ''young'' as double star observer.
This is my personal list of things important for succses-so they are important only to me.I come up with this list after two years since I fall in love with double stars:
-seeing
-quality of the objective
-personal skills
-aperture
-telescope type
-eyepiece,Barlow,mounting stability,ergonomics of observation-sitting or standing.

Please note this is a very personal list.
The aperture is ranking on my list where is ranking because I'm speaking about objects within the resolving power of the smaller telescope.
My biggest telescope yet is an 8 inch F/6 Dobsonian.

Mircea

#22 WRAK

WRAK

    Apollo

  • -----
  • Posts: 1188
  • Joined: 18 Feb 2012
  • Loc: Vienna, Austria, Europe

Posted 14 October 2012 - 07:16 AM

... Still,23 Aql is a much more difficult double star than Delta Cyg...Mircea

Depends certainly on a lot of factors - last time I visited 23 Aql I could go down to 80mm aperture and still split it. Delta Cyg limit for this was about 100mm so in terms of required aperture for splitting 23 Aql seems easier.
Wilfried

#23 drollere

drollere

    Surveyor 1

  • *****
  • Posts: 1588
  • Joined: 02 Feb 2010
  • Loc: sebastopol, california

Posted 14 October 2012 - 03:43 PM

You and I both agree that there is no formula for relating magnitude and the radius of the spurious disc as defined above. There most certainly is a 'formula' relating magnitude and the radius of the Airy Disc - specifically, the Airy disc size is constant for a given aperture without regard to magnitude or telescope type.


dave, i certainly understood you, and in my original post i clearly respected the dependence of the theoretical airy disk on aperture only. i am pushing back on your spurious distinction (pun intended).

the easiest route is for you to cite an authoritative modern source where your usage is respected. suiter (p.12) cites the rayleigh formula to calculate "the visual radius of the Airy disk". couteau (p.31ff) refers to "the Airy disk" as an *image* attribute. warren smith (p.192) speaks of point sources "imaged as an Airy disk." rutten & van venrooij (p.213) call "the central light spot the Airy disk." i can continue enumerating examples, but nowhere is the airy disk termed "spurious".

your may be referring to sidgwick (p.38ff), who applies the term "spurious disk" as a synonym for "Airy disk" -- "termed the spurious disk OR Airy disk" (emphasis mine) -- but sidgwick *never* (so far as i can find) contrasts the Airy disk (theoretical) with the spurious disk (visible). he simply acknowledges john herschel's coinage, adopted by airy, that signals the disk is not a *physical* or stellar disk (as herschel and other ancestors believed) but an optical one (as described, e.g., http://arxiv.org/pdf/1003.4918.pdf ... a nice historical summary). in fact, if you google "airy spurious disk" you can come up with several 19th century sources where the distinction is pounded into the ground.

otherwise sidgwick talks about the "theoretical appearance" of "the disk" and all its various attributes "in theory", which i accept as modern usage.

this usage prevents any ambiguity: texereau (p.5) explicitly equates the *theoretical airy disk* with the *visual airy disk* when he says (in translation): "one should be familiar with this "ideal" star image, consisting of the "false disk" and surrounding rings ..." (quotes in original). here "ideal" and "false" have the same status because the "false" is one component of the "ideal"!

so i'm not confused about your usage; i'm asserting it is antiquated or obsolete, and a neologism to the extent that you use "spurious" as a contrast to "theoretical", when the original contrast was with "physical". there is no good reason not to follow sidgwick's and general modern usage when the "apparent" Airy disk is contrasted with its "theoretical" figure.

you tip your rhetorical intention, dear cotts, when you refer to the "imaginary" dark rings, which are patently not imaginary but perfectly visible -- and in certain situations reproducible in a camera. if you go down that path, then you must refer to the "spurious diffraction rings" and the "spurious diffraction artifact", since all parts of the artifact arise from the same physical process described by the same singular "theoretical function" ... they deserve the same name.

#24 drollere

drollere

    Surveyor 1

  • *****
  • Posts: 1588
  • Joined: 02 Feb 2010
  • Loc: sebastopol, california

Posted 14 October 2012 - 03:52 PM

Thus the radius of the spurious disk of a faint star, where light of less than half the intensity of the central light makes no impression on the eye, is determined by [s = 1.17/a], whereas the radius of the spurious disk of a bright star, where light of 1/10 the intensity of the central light is sensible, is determined by [s=1.97/a]."


excellent catch, wilfried, i had forgotten he put numbers on his visual threshold explanation.

in part i forgot it because i dismiss it as invalid. we've hashed this out in another topic, but the flaw is that you can see rings around the airy disk at magnitudes where a threshold explanation, applied to the *log* form of the bessel function (which yields perceived brightness; see the paper cited in my previous), falls above the peak intensity of the rings and therefore predicts they will not be visible. or, as sidgwick (p.39) says, "the rings are brighter than theory would indicate, the first ring being not much fainter than the disc itself."

this implies a fundamental problem with airy's "threshold" explanation, which makes it unreliable as a basis for correction.

#25 Cotts

Cotts

    Just Wondering

  • *****
  • Posts: 4949
  • Joined: 10 Oct 2005
  • Loc: Toronto, Ontario

Posted 14 October 2012 - 10:44 PM

"Do not confuse the definition of the Airy disk as the bright central dot in the diffraction pattern. This this term is very often confused in much of the literature in print. The Airy disk is measured out to the minimum of the first diffraction interspace. The central dot may be referred to as the spurious disk and is more easily understood described as the visible disk. The true measurement of the spurious disk itself is difficult. The measurement 5.45/D based on the wavelength of light (and specific only to yellow light at 550 nanometers) is out to the first minima. The edges of the central visible disk usually cannot be seen as the light falls off to zero towards the first minima as we move from the center of the central disk out into the first diffraction interspace where the minima occurs. "

The above is from Ed Z. It makes sense, it removes ambiguity from the nomenclature of these phenomena. He's done as much research on this topic as anyone and I, for one, support his view.

i haven't even read any of the books you mention. Allthose authorities, though, throw these terms arond in a very mixed up manner as you have pointed out with the difference between 'modern' and older experts.

And the spaces between the rings for virtually every star in the sky are spaces. Thus invisible. What star can you look at where the diffraction pattern is a continuum of light, visible to your eye with the rings brighter and the 'not-rings' are visible but less bright? Maybe Sirius - maybe. In the thousands of double star observations I've done there is blackness between the diffraction rings and between the spurious disc and the first ring, not just less light.

and don't call me 'dear'.

Dave






Cloudy Nights LLC
Cloudy Nights Sponsor: Astronomics