Binocular Scalability (1 Viewer)

I came up with this thing that relates binocular models to one another based on their magnification and exit pupil. I think I came up with something that is telling, but I am not sure.
For instance, my calculations say that a 15x56 is a scaled up version of a 12x50 is a scaled up version of a 8.5x42. Or that a 10x50 is a scaled up version of a 7x42.
Has anybody else ever gone through this exercise?

Really interesting stuff here Quincy, and nice write up. I really appreciate the graph. This is kind of a different measure for twilight factor, which is (magnification * objective_diameter) ^ 0.5. That calculation always seemed too simple to me though; I like yours a lot more.

I hope others who know more about optics than me can chime in.

Welcome to birdforum by the way!

Hello Quincy88, and welcome to the binocular forum! If I'm not mistaken, you're referring to scaling the objective up or down, keeping a constant focal ratio, and re-using the same eyepiece, resulting in a series of binoculars with the same exit pupil. This used to be quite common, and you'd especially see it with certain Porro series. For example, Nikon's well-known SE series was available in 8x32, 10x42, and 12x50. All scaled up objectives. A similar progression is 6x30, 7x35, 8x40, and 10x50. This made a lot of sense from the manufacturing perspective because companies could basically re-use the same prisms and eyepieces for several different models, and just make diifferent objectives and tubes.

peatmoss said:

Hello Quincy88, and welcome to the binocular forum! If I'm not mistaken, you're referring to scaling the objective up or down, keeping a constant focal ratio, and re-using the same eyepiece, resulting in a series of binoculars with the same exit pupil. This used to be quite common, and you'd especially see it with certain Porro series. For example, Nikon's well-known SE series was available in 8x32, 10x42, and 12x50. All scaled up objectives. A similar progression is 6x30, 7x35, 8x40, and 10x50. This made a lot of sense from the manufacturing perspective because companies could basically re-use the same prisms and eyepieces for several different models, and just make diifferent objectives and tubes.

Click to expand...

I think this scaling exercise is more trying to evaluate the low light performance of binoculars.

As an example, with everything else equal, if you put a 8x32 and a 10x40 on a tripod at twilight, you should get an equally bright image, but you'll be able to resolve more detail with the 10x40 because of the higher magnification. But what if you had a larger objective on the 8x binocular? How much larger would you have to go to resolve as much detail as the 10x40 (given your pupil can dilate large enough to use the larger exit pupil)? If I did my math right, Quincy's formula calls for about an 8x36. The twilight factor formula calls for an 8x50. Now the question is, which is more accurate?

Thank you coopershawk. That is much closer to what I developed.

Quincy,

Welcome to the forum.

Do you have an idea what performance criteria and light levels these formulae might relate to?

You might want to check out the article Holger Merlitz wrote on binocular performance and target detection. He explores the work done by Zeiss and more particularly Berek from Leica (Leitz) on the limit of detail detection and threshold for object detection respectively. He also includes other studies on pupil diameter. You can download it from this page. http://www.holgermerlitz.de/bino_performance/bino_performance.html

Coopershawk is right the twilight factor is somewhat simplistic. That formulaic relationship between objective diameter and magnification is not much use to most here. It approximates to the Zeiss apparent acuity results for young conscripts at light levels that are roughly equivalent to moonlight.

David

quincy88,
Unfortunately my two computers couldn't open this file, post 1.
Binocular Scalability.

Numerous binoculars, both Porro and roof prisms use the same back end and different objective tubes.
The only real problem is that the higher the magnification, the more carefully aligned they need to be.

Is there a simpler pdf file that my computers can read.
Or just list any formulae you may have.

I am not computer literate.

Binastro,
Good Luck.
This has been edited for grammar and clarity from the original, but largely identical.
-q

Thanks Quincy,
I need to reread it, and I needed stronger glasses.
For some reason with this computer I cannot edit texts, so have to get it right first time.

For faintest star magnitudes or visibility at night, then I have found that the simple formula 10x50 = 500, and 7x35 = 245 very closely matches real observations.
This is confirmed by other observers.
In other words a 10x50 shows stars twice a faint as an identical type 7x35 binocular side by side. I.e. a 0.8 magnitude gain.
This is for point like stars.

For extended objects like nebula things are more complex.
But a 20x60 may show nebulae completely invisible in a 10x50.
With light pollution a 12x45 usually shows more than a 10x50, when they should be similar.

In daylight or twilight one is into a different realm entirely.

So one has to match formulae to empirical observations.

One has to take into account that some binoculars are vignetted, say a 12x50 Alpin is about 12x42.
And transmissions vary.

So different formulae will apply to different light levels and whether the object is extended or point like.
And possibly to different observers.

Quincy88,

As others have pointed out, depending on the task and the lighting conditions, different figures of merit apply. And of course there are all the other constraints when comparing e.g., similar quality of instruments, vision of observer, entrance pupil of observer >= exit pupil of instrument, etc.

However, I am sorry to be dense, but it seems to me that your scaling factor has the wrong sensitivity with respect to aperture and magnification compared with my experience and most other figures of merit. Let me try to explain. Let A be aperture or objective size and let M be magnification. The binoculars on each of your curves have the same value of A^2/M. I'll call this your derived figure of merit or scaling factor. Other common figures of merit or performance figures are

• A/M or exit pupil
• (M*A)^1/2 or twilight factor
• M*A or Bishop figure
• M*A^1/2 or Adler figure

The Bishop figure and Adler figure are more commonly used in astronomy and the Bishop figure is obviously just the square root of the twilight factor common in binocular advertising. I find that Adler figure most closely agrees with my experience using binoculars for astronomy.

Looking at the sequence from your figure to the Adler figure, you give the most emphasis to aperture relative to magnification and Adler gives the least emphasis to aperture relative to magnification. Three binoculars I have used extensively for astronomy are 7x50, 10x30, and 15x45. All three are of reasonably high quality. The 10x and 15x are image stabilized but for testing and comparison at night I used all three tripod mounted.

If I use your figure for the three I get 50^2/7=357 for the 7x50, 45^2/15=135 for the 15x45, and 30^2/10=90 for the 10x30. so the expectation would be that the 7x50 would be vastly superior with the other two lagging behind but the 15x45 better than the 10x30.

Using the Adler figure I get 7*50^1/2=50 for the 7x50, 15*45^1/2=101 for the 15x45 and 10*30^1/2=55 for the 10x30. When I tested the binoculars under dark skies I found that the 10x30 performs as well as the 7x50 and the 15x45 is vastly superior. I judged this both by the faintest stars I could detect and by the detail I could see in deep sky objects.

In other words, I can give up exit pupil at higher magnification and increase what I can see. Further, the advantage I gain from more magnification increases faster than the penalty I pay for smaller exit pupil. That's why the Adler figure is a better representation than the Bishop or twilight figure. Of course if I can use a larger aperture and more magnification that is even better, but then there are other issues like mounting, portability, field of view, etc.

Again, perhaps my astronomy experience is unrelated to the low light scaling you are considering. And if I am misinterpreting your math or intent I apologize.

Alan

Everybody,
Thanks for taking the time to think about my idea.

Alan,
Your math is the correct distillation of the idea presented. You saw what I was getting at before I did. You called it a 'figure of merit,' I like that. Attached is a derivation of that figure for anyone else who is interested.
Based on the empirical evidence in your write-up it seems that the figure of merit that is presented here doesn't have much application when comparing binoculars for astronomy.
-q

Quincy88,

The metric that is the starting point of your proposed figure-of-merit is the so-called relative brightness factor (to within a constant scaling), see for example:

http://www.backcountrychronicles.com/binoculars-relative-brightness-twilight-factors/

Peter.

Hey peter,
Can you elaborate a little? I don’t think I understand what you are saying. Isn’t this relative breightness factor defined as (do/M)^2? If so, then the scaling factor is the inverse of magnification, which isn’t a constant and is defined by the specific model...

Everybody,
Any birders out there with experience with several binocular models? Comparing twilight, or low light, performance of various standard models? Alan has demonstrated that empirical observation of my figure of merit doesn’t apply well to astronomy. Or hunters?
Keep it coming. I’m learning a lot!
-thanks, q

Quincy,

Did you have a read of that article I mentioned in post #6.

I'm not a regular twilight user but there have been numerous occasions when I've taken, 4 or occasionally 6 binoculars and compared their performance as night falls, by moonlight and even by the street light glow from the town near by. How i would rank each comparison depends very much on the target luminance and what facet of performance I'm looking for.

Generally, perceived brightness appears to be principally governed by the binocular transmission levels at the short end of the spectrum. It is particularly evident at the top end of the mesopic range when the residual light will usually be strongly blue shifted. Provided the pupil of eye isn't limiting I 'd suggest exit pupil is the next to come into play as first the blues and then the reds start to fade. The level of detail would be the next consideration. That is clearly driven primarily by magnification through the photopic range, but through the mesopic becomes increasingly apparent that target contrast is most critical. That can be reduced by an inadequate exit pupil of course, but the contrast of the target itself becomes increasingly important determining factor in failing lighI. I was surprised to find that visibility improves disproportionately with magnification.

I've mentioned this old story on the forum a few of times before. I had a binocular to review and decided to see how it performed in low light. I put up a black and white line chart in the flower bed at the bottom of the garden and used 4 of my own binoculars for comparison. As the light faded I'd noted the loss of colour and level of detail on the line chart with no real surprises and was about to pack up when I noticed some movement in the shadows at the foot of the hedge with my 7x36. I couldn't make out what it was at all. With my 8x42 I was sure it was a cat from it's outline and could see it's tail moving. With the 10x56 I could not only make out some of it's features, but I could easily see the mouse it was stalking.

I don't remember the exact numbers from the line chart now but it was something like a two fold improvement between 7x and 10 x towards the end of the test when the light levels were probably in the scotopic range. With the cat and mouse comparison it was something like 20 to 50 fold. I've used this kind of comparison many times now with binoculars ranging from a 6x30 to a 15x110 and over a wide luminance range. The benefit of magnification on low contrast targets can be seen in the mesopic range but greatly increases as the light falls further.

Your figure of merit ranks the 7x36 slightly better than a 10x56 and a lot better than a 10x42. That is totally contrary to my observations, particularly on low contrast targets. Given my age and the variety of binoculars and targets I've used it's probably not surprising that none of the usual mathematical methods exactly match my needs, but the development of Bereks work described in Holger's paper is closest, by some margin, to reflecting my experience of binocular comparisons in low light.

David