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- The nominal luminous power of the binoculars: (1 Viewer)

Rico70

Well-known member
As everyone will know, there is still no simple formula that describes the ability of binoculars to lighten civil twilight and part of nautical twilight. And therefore, that can indicate the luminous power of the instrument, or at least the nominal one.
The twilight factor indicates the ability to read the detail in very low light conditions, which correspond to the brightness of the astronomical twilight (the darkest one), or technically from about 0.3 to 0.003 cd/m^2 or even, from the moonlight to about the night.
In this case, therefore, the Zeiss engineers used an inconsistent term to name this factor. A term that has often confused users, since in practice the twilight factor has nothing to do with twilight or even with twilight binoculars.
In fact, for example, all 10x35 and 7x50 binoculars will have the same twilight factor 18.7 = √(10x35) = √350 = √(7x50).

But will a 10x35 binocular really have the same ability to "lighten the twilight" that has a 7x50?

Obviously not! Thus, the twilight factor will be completely unsuitable for describing the light power of binoculars.

So I tried to reason on the question, and gathering all the knowledge and experiences, I first hypothesized and then found that in fact both the enlargement and the pupillary surface of the binoculars, both contribute in proportional way to increase the ability to lighten the observations in the twilight (as described above) and in very shady situations of equal environmental brightness.
The magnification multiplies the amount of light in the eye, in proportion to the apparent superficial increase of the observed object, in the same way as the larger surface of the exit pupil, increases the luminous flux directed towards the eye. In this way, both values ​​concur together to increase the visibility of the objects observed, and the most suitable factor to represent this capacity, can be expressed with a formula that equals the magnification and the pupillary surface, like their product, providing so also a nominal value, numeric and indicative of the "light power" of the binoculars.

For example: 8x56 = 8x(π((56/8)/2)^2) = 8x((56/8)^2x0.7854) = 8x(38.484...) = approximately 308 (where 0.7854 is an abbreviation of Pi).
Thus, 7x50 = 7x(π((50/7)/2)^2) = 7x((50/7)^2x0.7854) = about 280 and 10x35 = 10x((35/10)^2x0.7854) = about 96. This indicates consistently the true difference of the luminous power in the twilight, between a 7x50 and a 10x35 (considering them of equal optical quality and total transmittance).

Logically, the resulting value is considered as nominal because it uses the nominal values ​​of the format and does not count the transmittance or the various optical qualities involved. But basically this formula can also be simplified a lot and adapted to the simplest calculators, excluding the Greek Pi from the calculations and replacing the exit pupil with the value of the aperture, directly using the format data.
Also in this mode, the calculation will always find proportionate and consistent results between the various binoculars exposed to the formula:

Nominal luminous power (pln) = Aperture^2/Magnification

For example: 8x56 = 56^2/8 = approximately 390, but also 7x50 = 50^2/7 = approximately 360 and 10x35 = 35^2/10 = approximately 120. Where, 360/120 = approximately 280/96.

Over time I have been able to do various experiments in various circumstances of ambient light and so I could see that the results of this formula are actually consistent with reality and can be very useful for cataloging the differences in brightness between the various formats.

For example, each 10x28 binocular has a nominal light output of 78 pln. Every 10x36, of 130 pln and every 10x70, of 490 pln.
Similarly, each 8x25 binocular has a nominal light output of 78 pln. Every 8x32, of 128 pln and every 8x56, of 390 pln.

Thus, up to 80 pln, fall the less bright or low power binoculars. Between 120 and 180 pln, those of medium power and between 340 and 500 pln, the brighter ones, often considered even the true crepuscular binoculars.
 
Rico,

Interesting line of though. Do keep in mind that 'brightness' is a visual perception and not a photometric value. Any metric that relies on the binocular parameters alone will have very limited value. Even readily measured visual parameters like the effective acuity will have severe limitations, as Köhler and Leinhos discovered.

David
 
That's right foss, that's very interesting.

Binastro, is exactly 1/4 of Pi (not complicated)


Interesting line of though. Do keep in mind that 'brightness' is a visual perception and not a photometric value. Any metric that relies on the binocular parameters alone will have very limited value. Even readily measured visual parameters like the effective acuity will have severe limitations, as Köhler and Leinhos discovered.
Hi David, you said well, but I used the term "luminous power" figuratively. This calculation serves only to evaluate the ability of binoculars to lighten images during twilight. But obviously it would have been more correct to use the term "twilight power", since it is in those circumstances that it can be used.
Since Zeiss came before me, I have to differentiate ;)

Anyone of you who is an expert in calculations and would like to make serious tests to confirm or refute the formula, I am very interested in the results. Thanks
 
Rico,

Magnification can only make a target look bigger. It cannot amplify it's luminance. Making a target bigger simply makes it more visible, which can be perceived as brighter.

David
 
Exactly, the surface brightness does not change. But as the surface of the image changes on the retina, it increases quadratically the number of retinal receptors involved in the observation of that object. And this creates a real improvement in the vision of that object. For example, 10x binoculars increase 10 times the linear size of the objects observed, but also 100 times their surface on the retina.
Of course all this, you already knew, without me repeating it, but you also do two calculations and two practical tests, please.
 
Rico,

The data from both Berek and Leinhos show that the advantage due to magnification above about 0.3cd/m2 is essentially proportional to magnification and not proportional to target area. Below 0.3cd/m2 there is a progressive cooperation in signalling amongst the rods which enhances sensitivivity at the expense of acuity and gradually swings the binocular parameter in favour of the exit pupil. For acuity at least, magnification becomes a negative factor mathematically according to Leinhos. It is the region between these to states which is approximated by the twilight factor calculation. Their formulas actually describes the performance of the eye, not the binocular's function.

I do understand that you are trying to calculate a rather different metric. I just don't believe it's possible to achieve your goal without also modeling the dynamics of the physiology of the eye, while factoring in the spectum of available light, and only then, the physical properties of the binocular.

I have spent a little time trying to establish the relevance of Leihos and Berek's studies to my own observations with various magnifications and exit pupils. Both appeared to work, but with some reservations. Both papers acknowledge the importance of an undefined transmission factor to their equations, but as far as I can tell they did not consider the how the transmission spectrum might alter performance as the colour balance of ambient light shifts, particularly after sunset. To be fair, coating technology was in it's infancy when those sudies were conducted. It seems clear to me that the resulting filtering not only alters effective acuity and threshold of detection, but also very obviously perceived brightness through much of the mesopic range. It's certainly beyond me to come up with that kind of formula I'm afraid.

David
 
The twilight factor is a simple nominal calculation, just like mine. But that refers to the detail reading at low ambient brightness and therefore takes more into account the magnification. But that factor is also useless to understand the power or the ability of the binoculars to be able to lighten the twilight as if it were day. Twilight-binoculars have this ability to lighten twilight and show us a "brighter" image than that seen with the naked eye. Of course, it is the magnification value that does this, but without an exit pupil appropriate to the iris, it would be impossible.
In my formula I simply gave the right weight to the exit pupil. I removed the square root (which serves no purpose) and simplified the calculation using only the nominal data of the format.
I did not enter either the transmittance, or the color-cast, but neither did the individual user variables, because it would be too "scary" and unthinkable for 99% of the common binocular users.

This is essentially a simple formula, to be able to differentiate the nominal twilight power of the binoculars by inserting only the format data in the calculation. Nothing more.

With me it works (but not only with me - I experimented with friendly guinea pigs), and I also use it to determine the equivalent formats (to those I've already tested), reversing the formula like this: 8x binoculars that diameter of opening must have, to be equivalent for example to a 10x36 binoculars?
8x opening = √(36^2/10x8) = 32 mm

That is, the two 8x32 and 10x36 formats, will have the same ability to lighten the image in the twilight.


David, did you do some practice tests?
 
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Rico,

You're not going to like this.

I did this comparison reasonably deep into the mesopic transition to try to ensure my own pupil diameter did not affect the results greatly. I also did the comparison using directions towards farmland to minimise the effect of light pollution from the nearby town.

I have done twilight comparison looking at level of detail or the threshold with these and other binoculars several times, but never intentionally looking for brightness. Obviously it is hard to eliminate predudiced with binoculars you know, but I repeated this comparison in random order several times to at least convince myself I was being as objective as possible.

In order of apparent brightness high to low.

10x42 pln = 176.4
7x36 pln = 185
8x42 pln= 220.5

I should point out that the 10x42 probably has the best transmission around 450nm and the widest AFOV both of which will affect brighness perception. The 7x36 advantage over the 8x42 is harder to explain. Neither excel in the blue and they have a similar AFOV, but it could be that the 7x36 advantage in the longer red may have tipped the balance. I guess you would also expect someone with a different opsin profile to arrive at different conclusions.

David

P.S. Something to consider that might help future investigations. I've previously done some simple test on myself and family on the ability to distinguish changes in luminance with and without binoculars. Using three or four subjects it's difficult to have much confidence in how relevant it is, but there were a couple of key points. The time taken between comparisons is absolutely critical. The difference between less than one second and 10 seconds reduced sensitivity to differences by three fold or more and that got worse with increased time. A more experienced observer did significantly better than a less experienced one.
 
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Hi, David. I try to summarize, to see if I read correctly.
I have done twilight comparison looking at level of detail or the threshold with these and other binoculars several times, but never intentionally looking for brightness.
... and did you find that 10x42 is brighter than 7x36 which is brighter than 8x42?

In fact, it sounds a little strange. Because it's all upside down.

Maybe you focused more on the details and not on the brightness of the scene? Or is your 10x42 better than 8x42?
In general, between 175 and 220 pln there is no big difference. But could your binoculars have different qualities?
 
Hey Rico,
I came up with this same concept some months ago. I wrote a thread on it that you can check out here:
https://www.birdforum.net/showthread.php?t=367485
Funny how similar ideas can pop up in different places spontaneously. You did a far better job than I did describing this formula though. Our fellow forum members worked to convince me that this is not a valid way to describe low light performance in binoculars, but I do still keep it in the back of my mind.
Typo was there to offer helpful commentary on that thread as well. Thanks again, Typo.
There are some good resources linked in that thread.
 
Hi, David. I try to summarize, to see if I read correctly.

... and did you find that 10x42 is brighter than 7x36 which is brighter than 8x42?

In fact, it sounds a little strange. Because it's all upside down.

Maybe you focused more on the details and not on the brightness of the scene? Or is your 10x42 better than 8x42?
In general, between 175 and 220 pln there is no big difference. But could your binoculars have different qualities?

Rico,

Yes the brightness ranking was 10x42 > 7×35 > 8×42, and as I explained, I took the greatest care I could, under the circumstances, to judge apparent brightness alone. The ranking would be different if I was looking at detail or threshold of detection.

Yes these binoculars are from different manufactures, with different properties, including the transmission spectrum, which will filter the available light and alter brightness perception. If I'd used different models, done the comparison half an hour earlier, was thirty years younger, or had different genetics I might have had quite a different result. That's the problem we all face, one size doesn't fit all. :-C

David
 
Hey Rico,
I came up with this same concept some months ago. I wrote a thread
Quincy, that's exactly it! We have arrived at the same result. I like it.
I've been working on it for a couple of years now (maybe 3) and I've noticed that it works.
Beautiful also your table with scalable values. ;)

I have read your thread now and as I see here, it seems that David is always focused on reading details in low light, but not of brightness in civil twilight, where this formula applies. Like ailevin the astronomer, also ...
https://www.birdforum.net/showpost.php?p=3766323&postcount=10

Do not lose faith in what you have already reasoned and discovered, because it is a considerable intuition that works.
I have dozens and dozens of experiences with various models and formats. For example, my 25x70 Porro-prism with a diaphragm of 40mm (25x40) is slightly brighter than my 10x25 pocket. And when I saw it, it was fantastic.

The most useful application of the formula is perhaps that of the equivalence between the various formats, especially during the choice of binoculars.

Have you already experimented?
 
Rico,

The reason many experimental theories fail is that the variables have not been identified, quantitated or controlled. You have systematically ignored them so yours was doomed from the start.

Much of my 35 years as a working scientist has been about identifying and investigating variables. Old habits die hard. Inevitably over that time the subject of observer bias has frequently cropped up. I must have coached a dozen teams and possibly a hundred individuals in the skills and precautions necessary for objective observation. Now I'm retired my daily rates are very reasonable. ;)

David
 
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Hi David,

How on earth is that possible ? :cat:
In every metric the 8x42 should come out on top .....
Is the 7x35 markedly better quality than the 8x42 ?

Chosun :gh:

CJ,

Much of the apparent brightness difference is probably due to the level of mismatch between the transmission spectum and the ambient light, but other factors are likely to play a part as well. It was most obvious with the 10x42, which was clearly the brightest, in spite of the disadvantage of the smallet exit pupil. There are colour differences with the other two which could possibly explain a difference, but it's much less obvious why the 7x36 appeared brighter.

David
 
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