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WRAK
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Reged: 02/18/12

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Re: Putting the "Rule of Thumb" to test [Re: fred1871]
      #5569469 - 12/13/12 03:31 PM

Quote:

... +/- 20mm isn't too bad related to a 140mm aperture - though I'd like to see it closer. Down at the 50mm aperture level that variation tells us nothing useful. It's proportional, as I'm sure you know...



Thank you for pointing out the obvious, I already got some blind spots here. The average error relative to aperture at this data status is 23% and this is certainly too much - but there is a focal point on fixed aperture observations (including the infamous 60mm observation of Delta Cyg) and these are almost always to some degree dubious.
I found the mentionded Napier-Munn article on the web and will study it with interest.
Wilfried


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WRAK
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Re: Putting the "Rule of Thumb" to test new [Re: WRAK]
      #5574313 - 12/16/12 03:09 PM

I found the article of Napier-Munn "Model to Predict the Resolution of Double Stars" very interesting and I like the approach of statistical analysis of single observations. I modified the described algorithm of Napier-Munn giving the probability of splitting a specific double with a given aperture to providing the required aperture for reaching a 50% splitting probability for easier comparison with my other calculations - this did not give convincing results with my small data set (average error too huge to be mentioned here) and the behavior of the algorithm ist not gracious as for some parameter values it provides no solution for a 50% probability.
But the approach of statistical analysis of individual more or less "limit" observations encouraged me to resume my own efforts in this direction - I meanwhile got down to an average error in required aperture of 13mm (partly by eliminating 3 Lewis observations with statistically obvious deviation) and I am optimistic to get eventually to a single digit average error. My main problem remains the tiny data set available to me but I hope to solve this issue during the next year with a lot of limit observations with my iris diaphragm.
Wilfried


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astroneil
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Re: Putting the "Rule of Thumb" to test new [Re: WRAK]
      #5575531 - 12/17/12 11:12 AM

Nae buttin' in like; but here's an 'infamous' quote fae Michael E. Bakich,(second in command at 'Astronomy' magazine.

"The Dawes limit is certainly only a guideline...Using this formula, my 4-inch f/15 Unitron should, at best, split a double star with a separation of 1.14 arcseconds. In May of 2,000, on a night where the seeing could only be described as "legendary," I was able to obtain a clean separation between a pair of double stars only 0.9 arcseconds apart. This observation was from my backyard in El Paso with six other people, three of whom were seasoned observers."

Source: The Cambridge Encylopedia of Amateur Astronomy, 2003. CUP, pp240.

Stick that in yer pipe and smoke it.

Eye.

Edited by astroneil (12/17/12 11:13 AM)


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WRAK
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Re: Putting the "Rule of Thumb" to test new [Re: astroneil]
      #5575792 - 12/17/12 02:17 PM

Quote:

...Stick that in yer pipe and smoke it...



Thanks for your input - there are always amazing observation reports.
Some remarks:
1. "The Dawes limit is certainly only a guideline" ... this is certainly correct as the Dawes limit is an empirical value to be considered as 50% probability for a split in the form of an 8. The only fault here is the missing indication of a standard deviation range in the sense of a Gauss distribution
2. To obtain a clear split of a 0.9" double with a 4 inch refractor is according to the confirmed theory of diffraction pattern rather impossible as the spurious disks should overlap - may be it would be wise to recheck the advertised data on this double
3. I am disappointed that this observation was not done with a 60mm/f15 refractor
4. The above mentioned meaning of the Dawes limit as 50% chance for a split is valid for all so called limits for resolution - so a limit is no limit but a value with a 50% probability for a split according to the defined properties (for example a clean separation for Rayleigh) and can be taken seriously only with a given average error or standard deviation.
Wilfried


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fred1871
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Re: Putting the "Rule of Thumb" to test new [Re: WRAK]
      #5576437 - 12/17/12 09:17 PM

Neil, interesting input, though I'm hesitant to credit it at face value - so my thoughts were pretty much in the direction Wilfried has offered.

Perhaps I'd have been more inclined to believe the claim if it were, as Wilfried suggests, a 60mm f/15 refractor
I hear those things are made by the Harry Potter telescope company, and even muggles can get the use of them - and they outperform anything else you can buy .....

More seriously, diffraction theory doesn't allow for what's claimed. And "theory" as you know is a strong word in science, though a dismissive term in common usage.

I'd certainly agree about getting elongation, perhaps notched, with a 4-inch f/15 refractor at 0.9". Of course, we'd need to know that the double in question was at 0.9" at the time of the observation - in case that was an old measure, and the pair had widened by the time of the observation.

Ne'ertheless, welcome to the discussion. I'm hoping a few more folk, from wherever, might be "buttin in".

So, feel free to offer more miraculous splits. I get the occasional one myself, and with no help from smoking anything nor from "a wee dram" as the Scots would have it. Though I find these miraculous observations more often happen with uneven pairs, where the rules are still uncertain. The even pairs are very law-abiding.

And I'm still hunting for the fabled SW Burnham 0.2" double seen with a 6-inch telescope. I'm working my way through his General Catalogue of Doubles (the 1900 version - only his own discoveries). So far, no definite find, though plenty of tough examples. Does anyone know which double it was that keeps being mentioned - without identification? as the 0.2" pair found with the 6-inch....

I have found several cases where Burnham writes along the lines of "thought it was likely double with the 6-inch, but it was single with 18.5-inch and/or 36-inch" - and the star in question is not listed as a double these days in the WDS. Which suggests it was a false impression - indeed, Burnham remarks on this view himself, saying it was the likely explanation in several cases where follow-up observations found no sign of a second star. Working at the limits is tricky.


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astroneil
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Re: Putting the "Rule of Thumb" to test new [Re: fred1871]
      #5576785 - 12/18/12 03:32 AM

Quote:

Neil, interesting input, though I'm hesitant to credit it at face value - so my thoughts were pretty much in the direction Wilfried has offered.

Perhaps I'd have been more inclined to believe the claim if it were, as Wilfried suggests, a 60mm f/15 refractor
I hear those things are made by the Harry Potter telescope company, and even muggles can get the use of them - and they outperform anything else you can buy .....

More seriously, diffraction theory doesn't allow for what's claimed. And "theory" as you know is a strong word in science, though a dismissive term in common usage.

I'd certainly agree about getting elongation, perhaps notched, with a 4-inch f/15 refractor at 0.9". Of course, we'd need to know that the double in question was at 0.9" at the time of the observation - in case that was an old measure, and the pair had widened by the time of the observation.

Ne'ertheless, welcome to the discussion. I'm hoping a few more folk, from wherever, might be "buttin in".

So, feel free to offer more miraculous splits. I get the occasional one myself, and with no help from smoking anything nor from "a wee dram" as the Scots would have it. Though I find these miraculous observations more often happen with uneven pairs, where the rules are still uncertain. The even pairs are very law-abiding.

And I'm still hunting for the fabled SW Burnham 0.2" double seen with a 6-inch telescope. I'm working my way through his General Catalogue of Doubles (the 1900 version - only his own discoveries). So far, no definite find, though plenty of tough examples. Does anyone know which double it was that keeps being mentioned - without identification? as the 0.2" pair found with the 6-inch....

I have found several cases where Burnham writes along the lines of "thought it was likely double with the 6-inch, but it was single with 18.5-inch and/or 36-inch" - and the star in question is not listed as a double these days in the WDS. Which suggests it was a false impression - indeed, Burnham remarks on this view himself, saying it was the likely explanation in several cases where follow-up observations found no sign of a second star. Working at the limits is tricky.




"And you shall not bear false witness against your neighbour." Exodus 20:16

Take the matter up with him and not me. He's got a physics background so I'm sure his reply will be interesting.

Merry Christmas to you and yours.
Nelly


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WRAK
Pooh-Bah


Reged: 02/18/12

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Re: Putting the "Rule of Thumb" to test new [Re: astroneil]
      #5577445 - 12/18/12 02:53 PM

"If yer quote another one you have taken own responsibility" WRAK 18:12
Best wishes
Wilfried


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7331Peg
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Re: Putting the "Rule of Thumb" to test new [Re: fred1871]
      #5578204 - 12/19/12 12:13 AM

Here's a little something to spice up the conversation -- using stars that are closely matched in magnitude:

Using a 3.8" Dolland refractor, which by the good Reverend's own forumula results in a Dawes limit of 1.20", that same Reverend Dawes measured the separation of Xi Librae(magnitudes are 5.2 and 4.9)in 1831 at 1.15" at a magnification of 295x.

He included this comment: "Occasionally divided. Fine night. Measures very good."

He measured it again in 1834 at 1.17".

For comparision, the senior Struve came up with these figures:

1825: 1.15"
1832: 1.22"


Using the same refractor to measure Zeta Cancri (magnitudes of 5.3 and 6.3), Dawes recorded a separation in 1831 of 1.09" at a magnification of 226x and included this comment: "Discs just separated when steady. Decidedly elongated with 140."

Again, for comparison, the elder Struve measured the separation at 1.05", also in 1831.

Data for Dawe's measurements comes from pages 82 (Zeta Cancri)and 87 (Xi Librae) of "Micrometrical Measurements of the Positions and Distances of 121 Double Stars, taken at Ormskirk, during the years 1830, 1831, 1832, and 1833", which was published in Volume 8 of the Royal Astronomical Society's journal, Philosophical Transactions, which can be found HERE, starting on page 61.

So it would appear that the good Reverend Dawes beat his own limit at least a couple of times.

Cheers,

John



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WRAK
Pooh-Bah


Reged: 02/18/12

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Re: Putting the "Rule of Thumb" to test new [Re: 7331Peg]
      #5578338 - 12/19/12 03:13 AM

John, thanks for the comments and especially for the link - very interesting.
"So it would appear that the good Reverend Dawes beat his own limit at least a couple of times" - this has to be necessarily so because his "limit" is calculated as average value derived from many observations so about 50% of his own observations have to be below his "limit". To know the average error would be of high interest - this way we could calculate the probability of a resolution of for example 10% below Dawes limit.
Wilfried


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7331Peg
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Re: Putting the "Rule of Thumb" to test new [Re: WRAK]
      #5579077 - 12/19/12 02:47 PM

At this late date, I'm afraid it would be a bit difficult to determine the average error -- but I certainly understand your point. That was part of the reason I included Struve's measurements -- they at least provide a reference point as well as a basis for comparison.


John


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astroneil
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Re: Putting the "Rule of Thumb" to test new [Re: 7331Peg]
      #5580139 - 12/20/12 06:51 AM

John,

In an age where men are sending space probes to Mars and uncovering the deepest secrets of the Universe, amateur astronomers on the cutting edge of double star research are looking to Dawes for answers.

Isn't it ironic that it's not the Apo or Newtonian, Maksutov or SCT that is setting the standards, but a humble, early 19th century spy glass, built with a token nod to optical theory.

Regards,

Neil.


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WRAK
Pooh-Bah


Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the "Rule of Thumb" to test new [Re: astroneil]
      #5581191 - 12/20/12 05:59 PM

I don't think anybody is looking for answers from Dawes - diffraction theory is the base of the discussion here and the Dawes limit is a potential starting point for any usable Rule of Thumb for splitting of double stars with unequal brightness and doubles with a primary fainter as +6mag.
Some errors are certainly not avoidable here as the Dawes limit is derived from observations with fixed aperture size and with advertised data for doubles less then perfectly exact corresponding to the available methods then - both factors together let expect an error range of 10% or more but even this is good enough for a starting point.
I think I am now at an interesting point of investigation with a multi step approach giving an average error of less than 10mm in required aperture but my data set is still far too small to take this seriously. Most interestingly statistical analysis of limit observations does not suggest any exponential effect of magnitude differences (especially not 2.512 as base as one would expect) but the effect of decreasing separation is exponential as one would expect.
I asked Napier-Munn for use of his raw data to counter check these results but so far without positive response.
Wilfried


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fred1871
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Reged: 03/22/09

Loc: Australia
Re: Putting the "Rule of Thumb" to test new [Re: WRAK]
      #5581725 - 12/21/12 12:06 AM

My reply is much the same as Wilfried's, first off - Dawes is a starting point but not a final answer. Dawes already had Airy's work on diffraction available by the time he came up with what we call the Dawes Limit, long after his early observations that John mentioned above. And I find it interesting Dawes does better than predicted using a smallish telescope - later he used larger scopes more typically around 6- to 8-inch aperture. And didn't do quite as well per aperture?

Wilfried, is the mentioned 10mm average error in aperture consistent over a range of apertures, or does it apply at some particular point? 10mm on 60mm is much bigger than 10mm on 150mm. Sorry to keep harping on this...

Re the data used by Tim Napier-Munn - no doubt some of the results in the raw data will be of use, but I find most interesting his graph for the 356mm aperture, which fits fairly well with my old suggestion of the RoT for significantly obstructed reflectors. The graph for 80mm and 203mm indicate under-performance for their sizes compared to the RoT and compared to my own experience.

That the magnitude differences don't follow a log scale (as per magnitude 2.512) is perhaps surprising but I'd come to a similar conclusion. Separation, however, I'd agree does appear to follow a model that's beyond linear - I'm wondering how much effect here is increased difficulty from seeing, as well as light spread, diffraction ring interference, and approaching the (diffraction) limits of the particular aperture.

Seeing in particular can make a huge difference. There are pairs I can't see one night in apparently steady conditions, and another night, looking similar on seeing, the pair is obvious. SW Burnham commented on the same experience. It does make finding the limits more difficult, because seeing appears to affect uneven pairs much more than even ones.


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WRAK
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Re: Putting the "Rule of Thumb" to test new [Re: fred1871]
      #5581861 - 12/21/12 04:25 AM

Fred, the average error in relation to the calculated required aperture is 10,85%. You are right, seeing is all important but how you handle this depends on the intended use of the RoT model - I see it as tool for selecting doubles for sessions and then you have given the advertised data for the doubles, your scope and light pollution on your site. Seeing and possible other factors should therefore covered by the indicated average error.
The proposed model for small telescopes means refractors from 60mm to 150mm (work clearly still in progress) works as follows: Required aperture rA for a split is
1. If sep larger 10" then rA = derived from TLM modified by light pollution (this part is not yet implemented)
2. Else base is Dawes limit (116/sep) - this covers the beaten path of equal bright pairs up to +6mag
3. If delta-m >1 or m1 > 6 then rA = Dawes + f(delta-m) = 7.82302995069649*(m2-m1)/sep^0.814655479470003 else zero - this covers delta-m
4. If m1 > 6 then rA = Dawes + f(delta-m) + f(m1) = 8.28247140956849E-02*(m1+31.0737334876114)/sep^-0.999405092970208 else zero - this covers faintness of primary above +6mag
5. If m2 > 9 then rA = Dawes + f(delta-m) + f(m1) + f(m2) = 19.7728649102522*(m2-8.84688581507273) else zero - this covers increasing faintness of the secondary
6. If NELM < 6.5 then rA = Dawes + f(delta-m) +f(m1) + f(m2) + f(NELM) = 2.33967425240235*(6,5-NELM)^2/6,5 else zero - this covers light pollution.
The resulting rA is to be interpreted as 67% chance to split a spedific double within a 11% range of this value.
The unwieldy numbers are the result of a statistical analysis - different runs produce slightly different values with similar final result so there is no theoretical optical background for this numbers.

Some examples for NELM of 3 means rather heavy light pollution:
23 Aql 3,2" +5,3/8,3mag -> 68mm with error compared to obervation of 2mm
STT216 2,2" +7,38/10,28mag -> 133mm with error 13mm
STF2482 1,6" +9/10,2mag -> 123mm with error 17mm

Some examples for NELM of 6 means no light pollution (advertised data from Lord's paper mentioned earlier):
STT279 2,2" +7/9mag -> 77mm with error 2mm
STT140 2,8" +7/9,5mag -> 87mm with error 12mm
HO161 2,9" +7/11mag -> 155mm with error 5mm.

These examples were selected by chance and 4 of 6 values are within the expected range and therefore within the expected probability range.
Wilfried


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astroneil
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Re: Putting the "Rule of Thumb" to test new [Re: fred1871]
      #5582855 - 12/21/12 05:13 PM

Quote:


More seriously, diffraction theory doesn't allow for what's claimed. And "theory" as you know is a strong word in science, though a dismissive term in common usage.






That's tosh as well.
There's a whole bunch of reasons why this project is downright silly. But here's one specific objection for ya.
Angular resolution (in radians) is approximated by Lamda/D. For the Dawes limit Lamda is set at 562nm. But an average human eye can detect radiations as low as 390nm. Doing the math (which I'll leave for you to do) shows that you can resolve stars down to a smidgen lower than 0.8".
Sticking a blue or violet filter on an eyepiece would easily allow a 0.9" split in a 4-incher and compounded still more if the stars are already bluish.

I believe Mike Bakich; it was something about the way he said it, unambiguously and plainly. And with several witnesses.

Far too suspicious you lot.

Edited by astroneil (12/21/12 05:33 PM)


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fred1871
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Re: Putting the "Rule of Thumb" to test new [Re: astroneil]
      #5583156 - 12/21/12 08:20 PM

Okay, Neil, so the Michael Bakich quote had to do with observing through a blue filter (say, 430nm), so that the Rayleigh Criterion becomes 0.9", as per the description. The context of the claim wasn't given, if that's the basis for it.

Likewise, we could observe through a red filter, and the resolution becomes a lot worse than Rayleigh or Dawes.

The discussion we've been having is posited on an agreed wavelength point, roughly where the human eye is most sensitive in photopic mode. Sensitivity is much lower at blue wavelengths, and at red, hence the convention.

So, yes, if I use my 140-mm refractor with a narrowband blue filter, as per Bakich's 4-inch Unitron, I can increase its resolution compared to non-filtered use. So I might expect to see elongation on a 0.4" double (even components) instead of my current unfiltered limit of ~0.5" for elongation? If it's a bright double the light loss won't be a killer.

Suspicious? - I'd say properly sceptical. Such as when one observer claims to split a pair with 120mm that wasn't split by experienced observers under very good seeing with bigger, including much bigger - 400mm and 600mm - scopes. We're inclined to doubt in such a case. And when someone appears to say that diffraction theory isn't accurate - because they've shifted the goal posts, something we discover later - we unsurprisingly question the claim until it becomes clear what its real status is.

There is, incidentally, a nice illustration of resolution by wavelength in a series of images by Damian Peach, reproduced in Bob Argyle's Observing and Measuring Double Stars 2nd edition - Gamma Virginis in May 2005, imaged with a C9.25 at three wavelengths - Red, Green and Blue. Red is an oval smudge, green an elongated image (Sparrow Limit?), and blue a neat close resolution. The pics are accessible on the internet as well.

However, it doesn't change the basic story. It's a difference that works better with imaging rather than visual observing, because cameras can do things eyes can't in terms of relative sensitivity. And it's not going to help much for the visual observer with very uneven pairs where the secondary star is pretty dim.

A side point re cameras - Rainer Anton, in writing about "lucky imaging", suggests using red filters to reduce atmospheric seeing effects. This implies that resolution limits are more adversely affected by seeing at short wavelengths than there are gains via higher resolution at the shorter wavelengths. Which fits with adaptive optics on huge telescopes being used at Red/near-IR wavelengths for that reason. And, yes, there's a whole collection of issues to discuss there.


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astroneil
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Re: Putting the "Rule of Thumb" to test new [Re: fred1871]
      #5583162 - 12/21/12 08:27 PM

Eye

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


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azure1961p
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Re: Putting the "Rule of Thumb" to test new [Re: astroneil]
      #5583326 - 12/21/12 10:44 PM

If adding color filters did anything to apparently increase angular resolution levels perceived, it was more than likely the dimming of the spurious disk to the point only its brighter centers showed and hence appeared smaller. Using a violet or blue violet filter on many a star would dim it substantially but the diffraction pattern never changes size.

Pete


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Astrojensen
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Re: Putting the "Rule of Thumb" to test new [Re: astroneil]
      #5583620 - 12/22/12 06:14 AM

Hi Neil

I somewhat disagree with you here. The sensitivity of the eye in the blue end of the spectrum is extremely low. It drops to below 10% already at 470 nm when photopic vision is used, which is what we want to use when looking at doubles, and is near zero at 400nm. It is thus not impossible to drastically improve resolution with a deep blue or violet filter, but the number of equal doubles bright enough to benefit from said filtration is very small. It must also be remembered that as our eyes age, they get increasingly yellow and opaque to blue light. This is why older observers tend to see less false color in achromats.

In theory, it's an interesting technique, but in practice, it has many limitations and is thus hardly useful.


Clear skies!
Thomas, Denmark


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Astrojensen
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Re: Putting the "Rule of Thumb" to test new [Re: azure1961p]
      #5583623 - 12/22/12 06:20 AM

Quote:

Using a violet or blue violet filter on many a star would dim it substantially but the diffraction pattern never changes size.




That is actually wrong. They DO change size with wavelength. The spurious disk ALSO change size with changing brightness.


Clear skies!
Thomas, Denmark


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