Daylight resolution tests show a detection increase up to 16% (I haven't got the link right now). But the heart of the matter is that the reality at the telescope is quite different, allowing for a much more significant increase of resolution with a binoscope.
I have asked Mr. Otte for advice and will quote his response here:
Let me start with Pirenne's study, which compares what you see with one vs two eyes. It appears to depend greatly on the amount/intensity of light that's being used. At a probability of 50% that you see a signal with one eye, you get a probability of 75% with both eyes. This is 1.5x more and hence the summation factor is 1.5. With a probability of 60% you get the notorious summation factor of 1.4 and with a probability of 1 (daylight) you get a summation factor of 1.
Now continue with your reasoning. The surface of your mirrors is 509 sqin. With a factor of one, that would mean a diameter of 25.4in or 1.41x linear. With a factor of 1.41 this becomes 360 or 21.3in diameter. With a factor of 1.5 this is 339 or 20.8in diameter, etc.
In short, if you assume the total surface as X and interpret the summation factor Y as just Y of the total light, the bigger the factor results in an ever smaller mono mirror, whereas during daylight you'd get a mono mirror twice as large. Let's agree that this is not the correct way to look at this.
This doesn't mean that Zarenski hasn't got a point. His reasoning is this: if the summation factor is 1.4, then you see 1.4 times more with both eyes (or mirror). So you have to multiply the surface of one mirror by 1.4, which corresponds to a diameter of 21.3, or 1.18x. This, however, does not correspond to the observations of people who observe with a big binoscope.
What seems to be the problem?
1) As I quoted in the first paragraph, there is no such thing as one and the same binocular summation factor. It largely depends on how you measure, which parameter you measure, resolution, detection etc. I've seen factors well above 2 in scientific literature.
2) There's a major confusion going on. Amateur astronomers translate the factor directly into the size of mirrors. This is something that vision scientists will never do, and with good reason too. Simply put, they look at how much better you see with both eyes compared to one. From their perspective it is total nonsense to translate this into how big that one eye would be, compared to two. We only have one eye and it doesn't get a bigger surface in order to do a comparison. In short, they completely refute the INTERPRETATION that Zarenski gives on the summation factor. Scientists would never translate the factor to how big a comparable, single surface would be. This is, understandably, an obsession of amateur astronomers. As I said, if with two 18in mirrors you don't get further than a 21.3in mono, would it still be worthwhile? Also for a telescope builder, why bother with all the fuss if a marginally larger monoscope will do?
3) It isn't clear at all whether there is a linear connection between the surface increase of a single mirror and what you'll see. Of course, if you put a camera behind it, you'll catch twice the number of photons with a mirror twice as large. But what about our brain? In Pirenne's study you see that the intensity of light doesn't have a linear curve. But no-one's doing any research about this, because vision scientists do this primarily from a medical perspective, eye abberations etc. No-one seems to be interested to know what one eye sees more with more light.
These considerations were enough for me to cast some serious doubt on the simplistic approach of "there's a summation factor of 1.4 which translates in a diameter increase if 1.18".
What I saw myself was completely different. Hence I started measuring myself. And these measurements have been confirmed over time by others (including you). It matters whether you're looking at point sources, or much fainter, extended objects such as galaxies. Everything confirms that the equivalent of two mirrors is much more than the notorious 1.18 factor. You've even quoted 27in. But which binocular summation factor would fit that??? And is this actually important???
I couldn't agree more. I know what I see with my instrument and I could call in many witnesses about how much more an 18" bino shows compared to a 20" mono, which according to Zarenski should be more or mess equal. I could call in the owner of the 27". I could call in Bruce Sayre or Andrea Boldrini, whose magnificent 24" binos were the inspiration for mine. This entire discussion is therefore completely useless. As I said... see where the longest queues are during a star party. That's proof enough.
Edited by PeterDob, 06 September 2017 - 05:18 AM.