44 replies to this topic

[Mad Matt]

I like those diagrams, esp. the second one, but I am a lawyer, so I am easily impressed by diagrams ... 

The most significant spread is the one for the Pentax - due to it's 20x60 format, the Adler Index shows a peak, but due to it's narrow fov, the Adler Field Shows a drop - not surprisingly !

So my question would be: do you really gain much by including the fov, or is the result so predictable that you can as well just leave it?

Pinac

This is a very valid question. I think most of use that have experience with different size binoculars automatically account for the field of view. I was hoping including the FOV would account for "anomalies" such as the 20x60 and to a lesser extent 7x35 Superwides which are surprisingly useful for astronomy even though they have a low Adler Index value.

 

Ok, one last chart, then I quit

 

If I use the formula:

 

Adler Field Index = [Magnification] * ( SQRT( [Aperture] ) + [FoV in degree] )

 

then the FOV at lower magnification more significant. I think multiplying the FoV is pretty "unfair" to the Pentax 20x60. I find, in practical use, that a smaller FOV at higher magnification is less of a concern. Of course that is objective so I will simply leave it at that.

 

Edited by Mad Matt, 30 November 2016 - 08:48 AM.

[GlennLeDrew]

I deleted scribblings made before closer study....

 

By the way, Matt, don't quit so quickly.   

Edited by GlennLeDrew, 30 November 2016 - 11:55 AM.

[GlennLeDrew]

And after a closer look... I think the green trend line, where the aperture and FoV are multiplied together and then taken the square root of, is more in line with my own internal rating system. Not to say that this is necessarily the best way to implement FoV, but it's far superior to your first stab at the matter. Being a wide field nut, where AFoV is a crucial feature, this scheme already is to me an improvement on the Adler index.

[Mad Matt]

And after a closer look... I think the green trend line, where the aperture and FoV are multiplied together and then taken the square root of, is more in line with my own internal rating system. Not to say that this is necessarily the best way to implement FoV, but it's far superior to your first stab at the matter. Being a wide field nut, where AFoV is a crucial feature, this scheme already is to me an improvement on the Adler index.

Thanks Gken, the green line is the original formula and I feel it fits better to my observation... then again, I am also a AFOV junky

I am only unsure on the Pentax 20x60. I have never looked though them so I can't say how they would compare to anything to the left or right of them in the chart.

Edited by Mad Matt, 30 November 2016 - 12:36 PM.

[GlennLeDrew]

Well, just reading of the soda straw-like AFoV of a mere 44 degrees for the Pentax 20X60 causes me to recoil in horror. That more than justifies its decrementing. Such a restricting field stop is utterly unnecessary, except for the specious desire to claim very good edge-of-field sharpness.

 

If we were to impose similar thinking on our own visual systems, we should all be wearing cylindrical 'blinders' that restrict the field of vision to just a couple of degrees. But in the same way our awfully poorly resolving peripheral vision is so useful (indeed, crucial to survival), a bino's outer field need not be sharp in order to do good work. In most instances our own vision is the limiter, where the instrument's off-axis aberrations are dominated by the eye's own very poor off-axis resolving power. Don't gaze far off axis, and you don't notice the poorer imagery out there. This is certainly not asking too much for a *handheld* bino at any rate, where target centering is so easy and natural. But even for mounted instruments aberrations are a fair price to pay for the extra field. Other factors such as eye relief permitting, of course.

 

In any event, a deliberate hobbling of field that does not derive from considerations of eye relief, but instead is to *artificially* improve edge-of-field definition, is just not on in my books. The Pentax 20X60 makes not the slightest blip in piquing interest or curiosity as an instrument I'd consider to use.

[KennyJ]

As I've tried to imply in previous responses in this interesting thread, and in spite of the last one being nothing more than a little bit of attempted humour on my part with a reference that goes back well over a decade, when I once started a thread about BINOCULAR AROMAS which attracted around 100 replies within a few days, whether or not Matt's charts and graphs represent anything which should be considered "truly objective", I honestly think there is some value to the effort.

 

Anyone who considers either TFOV or AFOV to be belonging purely to "subjective aspects" of binocular viewing is certainly not looking through them with the same hopes and expectations as I do.

 

Kenny

[Mad Matt]

Kenny, I missed the aroma thread but since you brought it up... I did nearly gag when I opened up my BA8's for the first time. Luckily whatever it was has dissapated

Now the question is... How can I quantify stink?

Edited by Mad Matt, 01 December 2016 - 12:22 AM.

[karstenkoch]

Kenny, I missed the aroma thread but since you brought it up... I did nearly gag when I opened up my BA8's for the first time. Luckily whatever it was has dissapated

Now the question is... How can I quantify stink?

http://futurama.wiki...i/Smell-O-Scope

An excellent question for Professor Farnsworth.

[Fomalhaut]

Because it doesn't satisfy the energy-equation, the Adler-index is physically incorrect and therefore should be considered obsolete!

Proof of this statement as well as suggestion of an alternative index which does not contradict the energy-equation plus further conclusions => see article linked below.

The discussion developping beneath the article results in a general approach and shows how a new index could look like and also how it could be practicably tested by observation.

http://www.cloudynig...for-binoculars/

Chris

Edited by Fomalhaut, 01 December 2016 - 05:17 AM.

[Mad Matt]

Great article and discussion Chris. Many thanks! A lot to digest there

[Mr. Bill]

So, boiling this down for us simple minded.....

[Fomalhaut]

So, boiling this down for us simple minded.....

 

There isn't anything to be boiled down, pre-digested and simplified.

 

All the problems and findings are clearly exposed in the article. 

Proofs are given by means of (simple) maths in order to be counterargued either on the same level or at least not without having carefully read the chain of arguments provided: The author doesn't  intend to repeat what is already written down. 

 

One of the main findings is that the so-called Adler-index does NOT work for calculating relative differences in stellar magnitudes being perceived by using different binoculars (even not if of same built quality).

Most questions which may arise are already answered  -  either in the article or in the discussion following it.

 

New questions are welcome.

 

Chris 

[Mad Matt]

Ok, time for more diagrams... problem is, I am even starting to confuse myself. 

 

Lets take a close look at the three indexes.

 

My understanding of Bishop's factor is that is was intended to be a very simply way of comparing the astronomical performance of binoculars.

 

Adler felt that the more weight should be given to magnification so he used the square root of the aperture which results in magnification getting more weight.

 

Here is a little background information on Bishop and Adler

 

My understanding is that Fomalhaut (Fankhauser) takes the index to a new level by introducing a logarithmic factor to the equation so it mathmaticaly relates to the theoretical limiting magnitude of a perfect binocular.  

 

This is an unscaled comparison of the Bishop, Adler and Fankhauser

 

 

Just for comparison (and I am not sure if this really adds value) in this chart I have scaled the values to be coincidental at the 10x50 size.

 

 

I still haven't figured out what the charts are trying to tell me so I need a little time to think about this and digest a little more.

Edited by Mad Matt, 02 December 2016 - 09:06 AM.

[Fomalhaut]

My understanding is that Fomalhaut (Fankhauser) takes the index to a new level by introducing a logarithmic factor to the equation so it mathmaticaly relates to the theoretical limiting magnitude of a perfect binocular.  

.....
 
I still haven't figured out what the charts are trying to tell me so I need a little time to think about this and digest a little more.

Hi Matt,

So far I feel myself pretty well understood.

One thing which you can see in your two last diagrams IMO is, that Adler underrates the bigger binoculars (by dissatisfying the energy equation, according to which e.g. a 20x100 binocular has to be 4 times as performant as a 10x50 of same quality).

IMO this underrating has not been very noticeable yet - mainly for the following reason:
There are very few really big binoculars with image quality on the same level as e.g. Nikon SE12x50 or Fujinon 16x50. Most of the big ones tested+rated have been of Chinese origin and their too low Adler-Indexes haven't been conspicuous enough because compared to their relatively low real performance per size.

Chris

Edited by Fomalhaut, 03 December 2016 - 08:32 AM.

[Mad Matt]

Thanks Chris, that adds clarity. 

[Pinac]

Matt,

stupid question maybe, but: what has now really been gained ?

If your last unscaled chart is correct, all three indices now follow basically the same pattern, but show just slightly different values, and the shape of the curves is virtually the same.

So maybe one of the indices is more correct than the other in terms of absolute values, but for the purpose of comparing binos, all three indices give basically the same answer (whereas in your previous charts, where the Pentax in your Matt index was "punished" for its narrow fov, this was not the case).

Or have I just lost track of what you were trying to do ?

[GlennLeDrew]

Matt,

For your second chart on post #38, where you chose a 10X50 as the common point for 'normalizing', you must provide three separate Y-axis scales; one for each of the plotted curves. A single, incorrect scale can lead to the "I'm not sure what the chart is trying to tell me" head scratching.

[GlennLeDrew]

Pinac,

When the same two fundamental variables of aperture and magnification are the foundation of a series of formulae, then naturally the *trends* among these formulae track similarly. If normalized at both the low and high values for the data set (by introducing a scaling factor), all curves will overlap. The only matter in question is that of the absolute values and what they most closely represent.

[Mad Matt]

Matt,

For your second chart on post #38, where you chose a 10X50 as the common point for 'normalizing', you must provide three separate Y-axis scales; one for each of the plotted curves. A single, incorrect scale can lead to the "I'm not sure what the chart is trying to tell me" head scratching.

Unfortunately I am using google sheets to do this and the charts it generates are limited in there complexity. That is why I included both scaled and unscaled charts in my post.

 

Actually what I need is an interactive chart that let you set the any of the binoculars as the scaling factor.

 

If I set the scale to normalize at 16x56 and show only the straight progression through 25x100 you see the differences more easily. 

 

 

I think it is obvious that at scale, the differences are smaller and to be honest I think that at this level the quality of the instrument will have a great impact on how the values compare to real life. I need to compare the limiting resolution of my BA8 (stoped down to 80mm) and Docter Vario to see how much of a difference in real life quality makes. I have not done a scientific comparison yet but in my casual observations under mediocre skies, I don't see a huge difference between my BA8 (22x85) and Docter Vario (at 20-25x80). 

 

Coming back to my original idea of factoring in the FoV into the Index... I am wondering If using the Bishop Index as the base purely for simplification would be a better idea as it is a subjective value and is more closely aligned to the Fankhauser. Useing Fankhauser would of course work but I see it as a true mathematical representation of the limiting magnitude and I doubt "diluting" it with the subjective factor of FoV would add benefit.

[Fomalhaut]

I am wondering if using the Bishop Index as the base purely for simplification would be a better idea as it is a subjective value and is more closely aligned to the Fankhauser. Using Fankhauser would of course work but I see it as a true mathematical representation of the limiting magnitude and I doubt "diluting" it with the subjective factor of FoV would add benefit.

Yes, my equation #(1): Index F = (m^2 * d^1)^(2/3) represents the relative limiting magnitudes of faintest stars visible (m-> binocular's magnification and d-> objectives' diameter).

In the discussion following my article (see post #18), I derived my general equation #(4):

F = (m^a * d^b)^[2/(a + b)]; (a and b being general weighting exponents)

Holger Merlitz (following Berek's law) and independently and similarly Nils Olof Carlin, have both come to the differing result that based on contrast considerations, magnification m should be weighted slightly less than diameter d.

I applied my above mentioned general equation #(4) on Carlin's results, in my post #26, and could so
calculate his weighting exponents in my formula to be a = 2 and b = 3.
Therefore, if his and Holger Merlitz's derivations were correct, then my equation #(5) would be valid:
F = (m^2 * d^3)^[2/(2 + 3)] = (m^2 * d^3)^[2/5]
(see my last post #26 in the discussion which followed the article).
Matt, I wonder how this curve fits in the other ones...

In my post #18, I had also suggested how exactly any of these formulae could be tested independent from variation of optical quality.

Obviously, my article and the following discussion have turned out to be a lot more comprehensive than merely proving Adler's index not to be able to represent the real visible limiting stellar magnitude-differences of stars as shown by different binoculars...

Chris

Edited by Fomalhaut, 04 December 2016 - 04:21 AM.