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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Putting the RoT to test – state of affairs [Re: WRAK]
#6431723 - 03/27/14 05:29 AM

Current state of affairs:
- Mr. Royce has now started the production of my 8" DK scope. This means that from about mid summer I should be able to cover the aperture range up to 202mm myself. After a sufficient number of observations in the range 150 to 200mm aperture (with a reasonable range of central obstruction between 0.25 to 0.33) I will then redo the statistical analysis with some adaptions of the model structure. Looking forward to it
- I have started now to repeat sessions several times if possible (though I had few opportunities to do so lately) to get a wider range of limit observations to cover better the spread reality of required minimum apertures for resolving a given double. This also means that I no longer consider a small standard deviation as quality parameter for my RoT algorithm – to target is not to get it as small as possible but as realistic as possible
- A realistic target seems to be to that the RoT value minus the 3-fold standard deviation should be the "competitive" lowest possible value for ideal conditions with nearly 100% of all observations above this value. For the simple case of equal bright doubles up to +6mag we have found by experiment this "hard" limit of resolution defined as observation with confident correct estimation of the position angle to be at about 0.5 Rayleigh or 0.6 Dawes criterion. This means that the standard deviation should be around 14-16% to match this range. A RoT value of for example 100mm would then mean that the realistic lowest required aperture assuming perfect conditions would then be 60mm and that even under not this good conditions 140mm should be enough (but with unavoidable possibility of non resolution with really bad conditions)
- I am now aware of an unavoidable bias in my data set as the registered observations in the upper range of used apertures by me plus the addition of difficult "third party" observations with fixed apertures tend to reduce the recorded spread compared to reality. I have currently no idea how to handle this and tend to ignore it – with a reasonable large total number of limit observations this effect will hopefully be neglectable
- It is certainly no longer correct to assume a symmetrical deviation around a RoT mean value as the negative deviation is definitely limited by laws of optics while the positive deviation is defined by seeing conditions and basically open ended as there are situations where no amount of aperture will allow resolution. But as working hypothesis it might be sufficient to stay with the assumption of a symmetrical standard deviation to avoid too much complexity in the RoT model
- But important to note: This asymmetry seems to get stronger with increasing faintness of the companion – a tad of haze in combinaiton with some light pollution is enough to eliminate a faint star against the background, so the threshold for non resolution is for faint stars much lower than for bright ones. Thus I have started to record the current telescope magnitude limit at the beginning of each session in the field of my target area on a regular base. If my current TML is for example +11.8mag for my 140mm refractor it is futile to try to resolve a companion of +12mag regardless separation. Next day with for example TML of +12.2mag I might at least try if wide enough. So far no idea how to handle this.
Wilfried

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drollere
Pooh-Bah

Reged: 02/02/10

Loc: sebastopol, california
Re: Putting the RoT to test – state of affairs [Re: WRAK]
#6433559 - 03/28/14 12:07 AM

wilfried, i hope your new royce scope is everything you expect. i found i had to make several "improvements" to mine in order to get it operating effectively.

i will say, the effect of the first magnitude ring shrinking in diameter with a fainter star (smaller airy disk) appears most clearly in my royce DK, so i'll be curious if you notice it -- del CYG is a really unmistakable example of it.

i think i commented in another thread on your RoT analysis, but i'll mention again that a correlation coefficient gives you no information on the validity of a level sensitive prediction, because you can simply double or triple all the predicted scores and get exactly the same correlation with the observations you want to predict.

the problem with the TML is interesting, because it is really a visual and not an instrument parameter. for example, the standard calculation for it requires you to put in your pupil aperture PA and your naked eye magnitude limit, which is just assumed in the aperture based formula:

2.61 + 5*log(D) ... is really .... NEML - 5*log(PA) + 5*log(D)

in particular, i am unsure how aperture interacts with a physiological limit like this, because the physiological limit being predicted here is your averted vision (rod) threshold, whereas the limit of interest to a double star astronomer is the foveal threshold, and not just for detection but for small interval angular resolution. this means the other complicating factor is magnification, which reduces image brightness as it increases angular scale.

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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the RoT to test – state of affairs [Re: drollere]
#6433752 - 03/28/14 06:31 AM

Quote:

... the problem with the TML is interesting, because it is really a visual and not an instrument parameter. for example, the standard calculation for it requires you to put in your pupil aperture PA and your naked eye magnitude limit, which is just assumed in the aperture based formula:

2.61 + 5*log(D) ... is really .... NEML - 5*log(PA) + 5*log(D) ...

Bruce, this is an interesting topic indeed and there is more in it but NEML, PA and D because with the same values for these parameters I get different "current" (means observed) magnitude limits. This might be also a problem with the reliability of advertised magnitudes for faint stars but mainly I think this has to do with transparency. A tad of haze has as far as I have observed no real effect on NEML (at least it would be hard to measure) but certainly an effect on the telescope magnitude limit as haze leads to some spread of the light of the star and the given brightness is then related to an area instead of a single point.
Wilfried

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WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the RoT to test – state of affairs [Re: drollere]
#6433774 - 03/28/14 07:06 AM

Quote:

... i think i commented in another thread on your RoT analysis, but i'll mention again that a correlation coefficient gives you no information on the validity of a level sensitive prediction, because you can simply double or triple all the predicted scores and get exactly the same correlation with the observations you want to predict. ...

Bruce, yes that's correct ... but then the standard deviation as the second quality parameter will explode. If the model with the best correlation coefficient has also the smallest standard deviation it is at least from a statistical point of view to prefer.
Wilfried

 Post Extras:
WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the RoT to test – state of affairs [Re: drollere]
#6436023 - 03/29/14 12:35 PM

Quote:

wilfried, i hope your new royce scope is everything you expect. i found i had to make several "improvements" to mine in order to get it operating effectively.

i will say, the effect of the first magnitude ring shrinking in diameter with a fainter star (smaller airy disk) appears most clearly in my royce DK, so i'll be curious if you notice it -- del CYG is a really unmistakable example of it...

Hope for the best regarding the 8" DK and will have a look at Del Cyg with it to check this impression.

Wilfried

 Post Extras:
WRAK
Pooh-Bah

Reged: 02/18/12

Loc: Vienna, Austria, Europe
Re: Putting the RoT to test – state of affairs [Re: WRAK]

My data set of limit observations has now grown to ~620 lines - to my regret still most of the observations below 140mm as my 8" Royce DK is still in production (will hopefully come in time for the observations of Delta Cyg to countercheck Bruce's impression regarding seemingly different diameter of first ring of primary and secondary).

Statistical analysis without changing the structure of the model resulted in somewhat different parameter values but else rather similar results compared with the analysis with about only ~130 limit observations. But the overall statistical quality of the model got somewhat worse with a correlation coefficient of now only 0.914 compared to earlier ~0.945. This seems a confirmation of my impression that several components of the model have to be enhanced to get better results.

Attached is a graph showing the relation between used apertures and proposed apertures - up to 140mm this seems rather straight forward. With 140mm we come into the realm of fixed apertures with enlarged spread due to the fact that we have to accept observations being on the "limit" because we have this impression but no proof for it.
We see the same effect with 150mm - here additonally with one obviously extreme overperforming observation.
Especially "off" are my own seriously underperforming 235mm observations. This might have several reasons working in combination:
- model does not work really good with large CO (in this case 0.38) as I know already
- seeing in my locations is usually not good enough to come near the optical potential of this scope (had it tested in an optical labor with a very good 0.95 Strehl result)
- collimation might be an issue as I have never seeing good enough to secure perfect collimation
- I do not like this scope very much for observing of close doubles so my own performance might be questionable here.

Overall I think this result is a good argument for my impression that fixed aperture observations are no good base for any serious conclusions regarding aperture limits for resolving doubles.
Wilfried

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