44 replies to this topic

[Mad Matt]

So there has been a little talk here lately on numerically rating different sizes of binoculars for astronomical usage. As noted by others here, I find the Adler Index ( Magnification x SQRT(Aperture) ) to be useful for mathematically comparing different sizes of binoculars.

 

There is one thing that I think is missing in the Adler index and that is the size of the field of view. Since, at least for me, a wider field of view at a specific magnification does increases my enjoyment factor I thought adding in the FOV to the calculation my be beneficial:

 

Magnification x SQRT(Aperture*FoV) [FoV expressed in degrees]

 

Fo the sake of comparison, I would like to call this the Adler Field Index... Not sure if "Mad Matt Enjoyment Factor" would be generally accepted 

 

This is how the Adler Index and Adler Field Index compare with several generic examples and my collection:

 

 

As you can see this gives more weight to wide angle designs and makes them more comparable. As you can see my 6x50 Frankenbino and 8x32 have very close Adler Field Index values. This is actually what I am seeing in the field. Also the difference between the Aspectem Vario at 40x and the UWA's is what I "feel" behind the eyepiece.

 

Any ideas, thoughts or reservations. If this has already been thought up and discussed then please post a link. I would like to see any conclusions made in previous discussions.

Edited by Mad Matt, 28 November 2016 - 12:31 PM.

[Rich V.]

Good thoughts, Matt.  Though the Adler Index represents "visibililty of stars" regardless of FOV, I can see how factoring in FOV may make a better "viewing experience" index.  But then again, taking into account other factors will also increase this.  EdZ included contrast, transmission and lack of aberration in his BPI (Binocular Performance Index).

 

This can always get more complicated, though, as one might also include illumination of the exit pupil and flatness of field as factors.   

 

This all affects the overall viewing experience...

 

Rich

[Pinac]

Matt,

I think I agree with Rich. I like the idea of your Mad Matt Enjyoment Factor   but would assume that if you add to the Adler index only FOV as an additional factor, this will only be useful when you compare binos with similar "quality" images. Assuming you compare Swaro, Zeiss, Leica and Nikon only (and other first class binos, e.g some from Kowa or Meopta) I guess a table like yours would be useful. But as soon as you include "second best" instruments, EdZ's idea to include various other factors might bring more.

Or what do yo think ?

Edited by Pinac, 28 November 2016 - 02:28 PM.

[Mad Matt]

Yes, a qualitative assesment is always better. I remember reading about edz's index but the problem with that is that it requires actually looking thru them

I wanted something that refects what I have noticed in the field but can be applied to future purchases. What may actually be interesting is to factor in the price under the assumption the better binocular will be more expensive. Take for example the two 16x56 in the list. The numbers put them very close but the price difference is considerable for "only" a 10 point advantage of the Swaro's. By all accounts swaro's are worth the money so should factoring in the price give them a higher point score?

Edited by Mad Matt, 28 November 2016 - 01:34 PM.

[KennyJ]

As I opined at the time ( it must be here in the Archives somewhere from all those years ago ) as regards more accurate representations, I thought EdZ's Binocular Performance Index ( BPI ) was a definite improvement upon both the Adler Index and the even simpler Bishop formula of straight Magnification x Aperture.

 

I also commented at the time that none of these formulae can be really accurate without taking into account sheer quality of the binoculars included, and fine and comprehensive an effort as EdZ's was, it must be remembered that very few, if any really top quality all-round binoculars, such all those roof prism models from leading manufacturers such as Swarovski, Zeiss, Leica and Nikon, were ever tested by EdZ.

 

I applaud Matt for this attempt at provding an alternative formula, but again, sheer quality surely must be taken into account.

 

For example, if my Strathspey 20x90 were entered into the table, even allowing for it's true magnification of 18x and reduced effective aperture of 82mm, it's MFI ( Matt's Field Index ) would total a very respectable looking 282, placing it  higher than a Doctor 20x80 and a Fujinon 16x70 FMT SX, even for those users who can see the Fuji's full field of view.

 

Somehow, I seriously doubt if a side by side real world comparison between those three models would bear this out.

 

Kenny

[Mr. Bill]

Aesthetics is hard to quantify.....I propose Mr Bill's Eyeball Index....

 

BT binoculars add another dimension with interchangeable eyepieces.

[GlennLeDrew]

Of note is the halving of the range in values among the binos listed after incorporating the FOV as a variable. This results in a diminution of raw performance in depth of penetration as a factor, shifting importance not insignificantly to the expansiveness of the view. In this scheme the humble eye, with its ~150 degree FOV and 7mm iris, rates at a respectable 32, or 1/4 as 'good' as an 8X32 bino (Matt index of 126.)

 

If different instruments have the same AFoV, this factor should null out, I think. In other words, if doubling the aperture at given exit pupil exactly halves the TFoV, the 'immersiveness' is unchanged by my way of looking at it. And so the AFoV might be a better variable to use instead of the TFoV.

[Jon Isaacs]

I think one has to decide what it is one is quantifying.  As I understand it, the Adler index tries quantify the faintest star visible so that binoculars of different apertures and magnifications can be compared.

 

I am not quite sure what Matt is trying to quantify, it seems like it is something that is actually quite subjective...

 

Myself, I think of binoculars and scopes as tools, magnification, field of view, exit pupil, these are variables that are matched to the task at hand..  

 

 

Jon

[MartinPond]

People can have different standards...

Somehow, having a field of uniform geometric flatness and sharpness

to the edge don't seem to figure into the numbers.  The concept of "more is more"

seems to leave quality by the wayside, or at least...assumes perfection in all units.

Flat, sharp to the edge, high contrast. Those are my top attributes....and they definitely

don't just come automatically with the size or power or afov....

[Mad Matt]

Just to add clarification. This is intended to be a tool for purely mathematical (or quantified) comparison not an assessment of quality. It is supposed to serve the same purpose as the Adler index and other mathematical comparisons. It of course MUST assume that the quality of the compared binoculars is the same. I think it is obvious that in reality, that is not the case. It is by no means meant to replace a subjective test

 

For those who would like to play with this a little I have created a public spreadsheet that you can download as Excel and try yourself: https://docs.google....dit?usp=sharing

 

I've added a few binoculars and the naked eye for comparison.

 

 

As you can see, it does not apply very well to the 2x56 which ignore the math and simply provide very enjoyable views

Edited by Mad Matt, 29 November 2016 - 10:07 AM.

[Mark9473]

Matt, it looks to me like what you're determining here is to what extent the view qualifies as "richest field".

The Adler index gives the depth dimension, i.e. how deep can you see, what is the faintest star.

You're adding size in the perpendicular direction - knowing how deep you can see, how much of that depth is in your view.

 

I like the approach you've taken.

Perhaps a future refinement would be to factor in transmission losses (in rough classes, say 5% - 15% - 25%) as well as to decrease the contribution of the outer FOV that is unsharp.

[Mr. Bill]

Also off axis aberrations and ghost reflections should be part of the equation.

[Mad Matt]

Guys... those are all great ideas but they are qualitative assessments (judgements of quality) which are subjective. Edz pretty much has those covered in his BPI (see link in post #2 from Rich V.)

My idea here is provide a better base of comparison then the Adler Index using only the manufactures technical details. I want to use it on binoculars I can't look though (or cant find direct comparison reviews) in oder to compare general astronomical performance. Performance for me also includes the FoV which is simply what I am missing from the Adler index.

Edited by Mad Matt, 29 November 2016 - 11:35 AM.

[GlennLeDrew]

Matt,

Just for further exploration, try adding a column or columns based around AFoV instead of TFoV, as either or both of linear and areal consideration. Graphing all these indices (including Bishop's and any others) would provide a ready visual comparative assessment of the trends.

[Mad Matt]

Good idea on the graph Glen! I'll see what is can put together.

On the AFOV vs TFOV... I tried that with both ISO and simple AFOV and the numbers are different but the difference between the values remained constant. If my basic math knowledge is not failing me it is because AFOV has magnification as a component and that is already in the calculation. Using AFOV just makes the numbers larger.

Edited by Mad Matt, 29 November 2016 - 11:58 AM.

[KennyJ]

As the charts grow increasingly complex, it may be worth adding at least a decimel point or two for comparitive aromas of the various models!

[Jon Isaacs]

Guys... those are all great ideas but they are qualitative assessments (judgements of quality) which are subjective.

 

 

Matt:

 

As an engineer/research scientist type, the question is just what does this number mean?  What is it a measure of? In a technical field, this might be called a figure of merit.

 

The Adler index is a measure of the faintest visible star and there's an analytical or at least empirical model behind this index.

 

What exactly are you quantifying that can be precisely defined, that is not subjective?   If two instruments both have the same index, just what does it mean?

 

For example, 10x50s with a 6 degree FoV have an index of 178.2.  20x50's with a 1.5 degree FoV have an index of 178.2, they are equivalent.  Just what does that mean?  In what way are they equivalent? 

 

What is it a measure of?  Can you define it?

 

For me, 10x50s with a 6 degree TFoV and 20x50s with a 1.5 degree TFoV are very different instruments and have very different capabilities, I don't see an equivalence.

 

Jon

[Mad Matt]

Here is my first attempt at a chart. I had to normalize the values to a percentage of Min and Max values in order to get comparable numbers. I have also narrowed the data set down to some common binoculars. I had to make up a "perfect" 20x80 with a 3,5° FOV to mark the upper end as 100% (Naked Eye is 0%)

 

I hope this is starting to make sense now   

 

 

 

Edited by Mad Matt, 29 November 2016 - 03:22 PM.

[Mad Matt]

And here is the data behind the chart

 

 

 

Edited by Mad Matt, 29 November 2016 - 03:23 PM.

[Mad Matt]

<snip>

 

The Adler index is a measure of the faintest visible star and there's an analytical or at least empirical model behind this index.

 

What exactly are you quantifying that can be precisely defined, that is not subjective?   If two instruments both have the same index, just what does it mean?

 

For example, 10x50s with a 6 degree FoV have an index of 178.2.  20x50's with a 1.5 degree FoV have an index of 178.2, they are equivalent.  Just what does that mean?  In what way are they equivalent? 

 

What is it a measure of?  Can you define it?

 

For me, 10x50s with a 6 degree TFoV and 20x50s with a 1.5 degree TFoV are very different instruments and have very different capabilities, I don't see an equivalence.

 

Jon

 

Just to reiterate: 

 

Adler Index =          [Magnification] * SQRT([Aperture])

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

 

As far as I know there is no direct mathematical correlation of the Adler Index and the theoretical limiting magnitude of a binocular. I don't have access to Alan Adlers original article but my understanding is that the formula simply correlated well with his observations. My intention is to simply add another dimension to that correlation. 

 

As explained, the point is to factor the FOV into the Adler index. That is all the formula does.

 

Yes that makes the 10x50 6° and 20x50 1.5° identical but in your example, the 20x50 would have an impressive Adler # of 141 compared to 71 of the 10x50... the Adler # would suggest that the 20x50 is the better binocular, but with a 30° FOV is it providing a better view?

 

Bringing the FoV into the calculation helps determine not only the faintest visible star but also a larger FoV showing more stars. The 20x50 would show only 1/4 the FoV of the 10x50 and, although it will go deeper, I don't believe the total amount is stars shown will be what the Adler # leads you to believe. 

Edited by Mad Matt, 29 November 2016 - 03:58 PM.

[GlennLeDrew]

Matt,

By normalizing all data sets you suppress the divergence in the trends. This makes all indexes track identically. It's the divergence that we *want* to see, in order to appreciate how the different schemes scale.

 

Incorporating TFoV is something of a red herring, in that the general trend among binos has TFoV increasing as aperture decreases. This is a compensatory factor, in that the decrease in aperture/gain in field is accompanied by a more or less similar decrease in stars seen per unit true solid angle. In other words, over the limited range of exit pupil typically encountered, and if we initially take the AFoV to be reasonably similar, a not very dissimilar number of stars is seen in a random field for *all* instruments. The wider TFoV for the smaller instrument does not result in more stars being seen.

 

Hence my suggestion to discard TFoV and adopt AFoV. This latter quality has a more pronounced impact on the impressiveness of the image. In terms of both the 'majesty factor ' and the number of stars seen. As to star numbers, realize that going from an AFoV of 50 degrees to 65, about doubles the sky area and hence the star count. At first blush, a rating for a 10X50 with 65 degree AFoV that perhaps doubles that for a 10X50 at 50 degrees might be going in the right direction... Or if this results in an unwieldy and overly large range from binos small to large, the square root of this doubling, or 1.41 might be better. 

 

As to AFoV, if unknown, simply multiply magnification and TFoV for a good enough first stab.

[Jon Isaacs]

Yes that makes the 10x50 6° and 20x50 1.5° identical but in your example, the 20x50 would have an impressive Adler # of 141 compared to 71 of the 10x50... the Adler # would suggest that the 20x50 is the better binocular, but with a 30° FOV is it providing a better view?

 

Bringing the FoV into the calculation helps determine not only the faintest visible star but also a larger FoV showing more stars. The 20x50 would show only 1/4 the FoV of the 10x50 and, although it will go deeper, I don't believe the total amount is stars shown will be what the Adler # leads you to believe.

 

It is my understanding that the Adler Index attempts to quantify the faintest star visible in a particular binocular.  That means if two binoculars have identical Adler Indexes, both binoculars would go equally deep.  The faintest star is something that is measurable and subject to analysis. 

 

When you ask if the view is better, that is not an objective question, that is a subjective question.  It is dependent on a number of factors.. 

 

Glenn suggests that you are trying to put a number on the "majesty factor", a subjective factor, or possibly the number of stars seen in the field of view.

 

I just want a definition of what you are attempting to quantify.  

 

Jon

[karstenkoch]

I agree with Jon.

Magnification affects brightness.
Aperture affects brightness.
FOV does not affect brightness.

Bringing the third variable into this factor mixes units of measure.

I think the Matt index is a two variable index with the Adler index on the x-axis and the fov on the y-axis. Now plot those points and do a two variable analysis. I don't think you can meaningfully collapse this data into a one-dimensional value.

Edited by karstenkoch, 30 November 2016 - 02:22 AM.

[Mad Matt]

Ok, the general acceptance to the idea by very well respected members (I mean that) is... ah well... how should I state this... everything but overwhelming?       

 

I will post one last diagram and then let this rest. 

 

 

EDIT: Ok, two diagrams... Added this one that is a little better in representing the spread. 

 

 

For me it was a nice thought exercise and I got to brush up on a few math skills I had not used in years so nothing lost 

Edited by Mad Matt, 30 November 2016 - 05:57 AM.

[Pinac]

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