Wednesday 21 November 2018

The binocular summation factor

A lot of ink has already been spent on this subject since many astronomy enthusiasts are wondering what the actual gain is observing with both eyes instead of only one. Let me begin by saying that this whole discussion is fairly pointless because observing with both eyes is a completely different experience than observing with only one. The feeling of total immersion that not even a 150° eyepiece can ever offer, the strange 3D-effect, the joy and relaxation of using both eyes… Personally, even if there were no light gathering gain at all I’d opt for a binoscope, regardless the expense. On the other hand there are people who’re having difficulties observing with both eyes. And finally there’s the big unknown factor: the human brain, which is both unpredictable and personal.

So what’s the use of me writing this article? Because we astronomy enthusiasts have the unstoppable need to quantify everything. How much more can you see with a 14” telescope compared to a 10”? How does a refractor compare to a Newtonian (please, no, not again…)? Or… how much more can you see with both eyes? So here I go… explaining my 2 cents on this, for what they’re worth.

The misconception

Unfortunately very little real scientific study, if any at all, has been carried out to shed some light here. That is to say, a study that has been performed from an astronomical and not a medical point of view. Back in 1965, Campbell and Green published their renowned study in which they concluded that detection improves by a factor of 1.41 (√2) when using both eyes instead of only one. This figure has since also been adopted by part of the astronomical community. A factor of 1.41, or an actual detection gain of 41%, implies a telescope diameter gain of 19%. In other words, an 18" binoscope would be more or less equal to a 21" monocular telescope. Given that it is generally considered that you need at least a 30% increase in aperture (or 14% in diameter) to get any visible difference at the eyepiece, the real detection gain between an 18" mono or an 18" bino would be marginal and hence not worth the expense. Compare it to a C8 vs. a C9.25. The awe that one experiences when observing with a binoscope would therefore merely be an illusion, created by the larger perceived field of view and the beguiling 3D-effect.

But is this really so?

After having observed with a big binoscope for 2 years and a half and having done direct comparisons between mono and bino several times during every observing night (a binoscope is put in focus one eyepiece at a time), I daresay that all of this is pure nonsense.

First of all, the Campbell and Green study was a medical study, not an astronomical one, and it was intended for "normal" eye use. Citing it for binocular detection under astronomical conditions is therefore absurd, to say the least. Pirenne already concluded in 1949 that there is no such thing as a single binocular summation factor, but that binocular summation greatly increases with deteriorating conditions. The darker it gets, the better you see with both eyes.

I’ve also read an article of someone who claims to have performed a limiting magnitude test with a pair of binoculars and found an actual detection gain of 0.2 magnitudes. This is , if you ask me, a very dubious statement because there is no clarification as regards to the method, nor the reference stars used. An 18” telescope has a theoretical magnitude limit of 17. A 25” (twice the aperture) has a limit of 17.7. Therefore, if you’re going to do such a test with an 18” binoscope, you need a field of view which contains stars of mag. 17, 17.1, 17.2 and so on. You also need a perfect sky with a perfect atmosphere. When sky conditions are less than perfect, or worse, average, the limiting magnitude difference diminishes somewhat due to a brighter background and hence reduced contrast. So what is the real difference between an 18” and a 25” under a certain sky? You’d have to put both telescopes next to each other in order to find out and point to a star field which contains the right reference stars with the right magnitudes. And even then, we all know how tricky limiting magnitude tests can be with the naked eye, let alone with a telescope, or two scopes with a different exit pupil.
What I can already state with great certainty, is that when closing one eye many of the fainter stars simply disappear, or become very hard to see. I’ll also give an example in my observation of M76 (see below).

What does real science tell us?

- The extent of summation depends on stimulus contrast and duration (Bearse and Freeman, 1994)
- There is significant summation at low contrast (Banton and Levi, 1991)
- At low contrast, the level of summation is greater than could be expected by probability summation alone (Simmons and Kingdom, 1988)
- Summation depends on the complexity of the task, with simple tasks (detection) displaying far greater summation than complicated ones (pattern recognition) (Frisen and Lindblom, 1988)

Here’s the link to the article where I got this information and which also contains the links to the various studies I mentioned:

When you read them more carefully, you come to the conclusion that there’s still a great deal of uncertainty about the extent of binocular summation. Still, these studies lead us to believe that the binocular summation factor in the total dark (greatly) exceeds the 1.41 factor under "normal" conditions.

What does experience in the field tell us?

Drop a binoscope at a star party and see where all the people are flocking.

Seriously though. I've made a few direct comparisons between my 18" binoscope and big monoscopes. On the picture below you can see the 18" bino with in the background two high-quality 20" scopes, one of which was an f/5, coincidentally the same focal ratio as the bino. According to the 1.41 theory, these scopes should yield more or less similar performances. In reality, however, the 20" were no match at all for the binoscope, which brought out details in faint objects which you could only dream of in the monocular telescopes. This was confirmed by all present (about 20 people - all experienced observers).

I've also had the opportunity to compare the 18" bino to a 27" mono and this turned out to be a clash between more or less equals in terms of light gathering power and the perception of detail. Elaborating on this experience would be inappropriate, however, because there were no neutral observers present.

I’d also like to add some notes about a very intensive comparison I've made on various objects, observing with both and with only one eye. These observations were done by me, with my eyes and with my sky conditions. I do not wish to generalise these results in any way but suppose that they give an indication of what one might expect.

Overall, a nice way of putting it is that with binocular vision I can easily see with direct vision what I can only perceive with averted vision in mono. Closing one eye, not only a nebulous object becomes fainter and loses detail, but several faint stars disappear as well or become hard to see.

  • NGC246 (104x with OIII filters): In mono the nebula shows an opening towards the south-east. With both eyes, the nebula not only becomes significantly brighter, but the opening fills with nebulosity, making the overall aspect of the nebula decisively round.
  • NGC7009 (285x without filters): In mono the ansae are faintly visible. In bino they become evident and even show hint of detail. The internal structures of the nebula look much more pronounced and the overall blue-greenish hue becomes striking. A noteworthy difference.
  • NGC604 (285x without filters): In mono there were maybe three or four stars within the nebula that could be identified with absolute certainty. In bino an entire cluster appeared.
  • NGC1491 (104x with OIII filters): The difference was not that large, in a sense that what was there in bino was also there in mono, albeit fainter and with averted vision.
  • M76 (285x without filters): Here’s an interesting observation. In bino I noticed a tiny little star in the northern arch of the eastern wing, next to the more obvious mag. 14 star. It was there and easily visible, also with direct vision. When I closed one eye it simply disappeared. Well, I still thought I saw it but am pretty sure that this was an illusion because I had just seen it with both eyes open. After taking some time with one eye closed, looking around and then trying to spot it again, I couldn’t see it. Also the mag. 14 star was difficult with one eye, by the way.
    Coordinates: 01423079 +5134386, mag. 15.264

I'd like to present this sketch which is a direct comparison between mono and bino of planetary nebula NGC1501, just to give you an idea:


Over time I've grown to the conviction that detection with a binoscope increases by a factor nearing 2, or an aperture increase of 41%. Hence an 18" bino would have the light gathering power of a 25" mono. It's difficult to put a real number on it because the binoscope offers vastly enhanced contrast, whereas the bigger monocular scope offers better resolution (but suffers more from bad seeing). It may even be possible that this factor increases somewhat beyond a factor of 2 because, when observing at the limit as we astronomers do, it is far less likely that a "false" light signal is accepted as "true" by both eyes simultaneously.

This figure should not be taken as an absolute. I’m not a scientist, nor do I wish to present my findings as a general guideline. It’s just an impression after years of experience with making direct comparisons and hearing comments from people who’ve actually observed with binoscopes.

Surface brightness

It may be that a binoscope brings objects with an extremely low surface brightness within reach, which remain impossible with any telescope, not even a 30”. An 18” binoscope offers the theoretical light gathering power of a 25” mono but with the exit pupil of an 18”. This means that with an 18” binoscope you can go as low as 65x and still retain a 7mm exit pupil. With a 30” scope, you’re limited at 108x. Therefore it may be possible that very large and extremely faint objects are visible in the 18” bino and not even in a 30”! With my bino I’ve observed planetary nebula Purgathofer-Weinberger 1, under an SQM20.9 sky. I’m not sure whether this would be possible with monocular telescopes… It’s probably an interesting point for discussion.

Making binoscopes… or not?

But if all of this is true, why aren't there more big binoscopes around? Why is there only one manufacturer left (for as far as I know and apart from a few home-builders) that offers them commercially? The answer's very simple: it's not about cost as such because, even though the expense for a quality bino's significant, my binoscope cost me less than a 25" Obsession. The real problem is that a big binoscope's awefully difficult to make. Alignment needs to be precise up to a nanometer and stability needs to be such that both tubes remain absolutely motionless regards to one another, no matter how you move the scope. Every single binoscope is a new adventure in which you're never sure which problems may arise. Even with all of his experience, Mr. Otte spent 15 months building mine whereas he had stated 3-4 months initially. Furthermore, big binoscopes are incredibly bulky (mine's 145cm wide and weighs in at about 150kg) and are impossible to assemble by yourself, whereas you can easily assemble a 25" Dob on your own. I've given up on hauling my bino to star parties because it's simply too much of a hassle.

In brief, a (big) binoscope is commercially unfeasible.


I have no commercial interests (actually, Mr. Otte has recently retired) and I live happily on my hilltop under the stars. Therefore I have no reason to boast the results because I couldn't care less about what other people think. These are simply my impressions and thoughts, with my scope and eyes. Hopefully they may be useful to others.

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