Focal ratio confusion

[Finite]

Hi all, my poor old magnitude 25 brain is struggling with something I read in 'The Backyard Astronomers Guide'. Disussing Focal Ratio it says fast focal ratio scopes are useful for imaging, but when using the scope visually image brightness is only due to aperture and that focal ratio has nothing to do with it. Can anyone explain to my why that is? (please!)

cheers, John

[Atmos]

Nothing wrong with having trouble understanding this concept :)

When imaging the focal ratio is important because it means that you have more photons being concentrated into a smaller area (because of the shorter focal length). It isn't the whole story though.
If I use a KAF-8300 sensor with its 5.4 micron sized pixels on a 10"F/5 Newtonian it will perform virtually as "fast" as a 10" F/8 RC with a KAF-16803 with its 9 micron pixels.

Both telescopes are capturing the same number of photons as they are both 10" in diameter. As both cameras have different pixel sizes, even know the F/8 is technically a slower telescope it has been paired with a camera that has larger pixels.

So, in imaging, the "speed" of a system is to do with the sky coverage of each pixel (expressed in arcseconds/pixel) against the aperture.
To calculate the pixel coverage:

(Pixel Size*206.265)/Focal Length
(5.4*206.265)/1270= 0.877"/pix
(9*206.265)/2032= 0.914"/pix

The same principle works with visual astronomy. If I put a 5mm eye piece in the 10" F/5 I'll get a magnification of 254x. If I put an 8mm eye piece in the 10" RC I'll get 254x magnification. As both are the same diameter there is the same amount of photons at the same magnification.

Hope this helps John :)

[janoskiss]

@Finite That's not quite right. There are two ways to look at apparent brightness: surface brightness of an object or the overall brightness of an image (whether it's at the camera sensor or on your retina).

As far as the visually observed surface brightness of an object goes, for a given eyepiece a faster telescope will yield brighter views. Aperture does not matter: only f-ratio and the eyepiece focal length matter. Actually it's a combination of these that determines visual (surface) brightness: the exit pupil diameter = eyepiece focal length divided by f-number of scope = telescope aperture divided by magnification.

However, for the same exit pupil, a larger aperture telescope will yield higher magnification. Hence you will be able to see deeper and (if seeing allows) in more detail. If you are looking at an extended object, like a large gaseous nebula (think Orion or Carina) then it will take up more of your field of view at higher magnifications, so the image overall will appear brighter. But the apparent surface brightness of the nebula itself will still only depend on the exit pupil. It's perhaps a little counter-intuitive at first, till you think about it.

Or you can think of the Moon. Its surface will appear just as bright through 10x50 binoculars as through a 10" telescope (250mm aperture) at 50x magnification. But because the Moon will be 5x bigger in the latter case, the overall perceived brightness will be greater: you have 25x more light entering your eye from that much larger looking Moon. Note that the exit pupil in both these cases is 5mm. (Hope this make sense. ;))

Useful exit pupils fall in the range of 0.5mm to 7mm (from highest to lowest magnification and dimmest to brightest views). But in practice the range from 1mm to 5mm is more useful. Much below 1mm one tends to see no more detail (the image is just gets bigger, but also dimmer and blurrier). Above 5mm, your start running into the limitations of your own eye: how wide your pupil can open. If you're in your late teens to early 20s, nature gives you 7mm (or perhaps even a bit more). As you age this drops. I think for someone in their 40s, 5mm is average.

[barx1963]

I will try and explain the idea as I think about it.
Firstly, imaging uses a camera that accumulates an image. the longer you collect light the brighter the image. Your eye doesn't work that way. It simply responds to the light coming in right now. So imaging systems and visual systems work quite differently.
With an imaging scope, the focal ratio determines the size of the image on the sensor. A long focal length scope, for example an 8" at f10 (typical SCT) will have a focal length of 2000mm and will produce a quite large image compared to a much faster 8" at f5 with a focal length of 1000mm. The amount of light being collected is exactly the same as the aperture is 8" in both cases BUT the amount of light being collected by each pixel on the sensor is more with the faster scope. So it can collect the light in a shorter time (hence it is faster!) This has benefits as guiding is easier, the sensor will stay cooler, so less noise and you can get an image quicker or get a deeper image in the same time.
As your eye cannot accumulate light like a camera, the f ratio no longer matters (as far as the overall brightness of the image is concerned) the only factor is how much light is collected, which is a function of aperture. Having said that, the eyepiece that you use will vary the "magnification" of the object you are looking at. If you increase the magnification with a shorter focal length eyepiece, it spreads out the light over a greater area, in effect reducing the surface brightness of the object, but not the overall brightness. However (just to complicate matters) higher powers also have the effect of darkening the sky background which can make dim objects "pop" into view as the contrast improves.So often times for visual observers, particular objects require an ideal amount of power to be seen best, and you sometimes have to try a few eyepieces to find the one that works the best on that object in your scope.
I have tried not to get to technical with the above, hope it helps!!

Malcolm

[N1]

I might add that the lower power limit (i.e. upper exit pupil limit) only applies to obstructed optics. Unobstructed, there is no penalty for going as wide TFOV and low power as your eyepieee case permits.

[janoskiss]

That's not so. The light from a distant point-like object enters the eye from the eyepiece as a beam of definite width = aperture / magnification. That beam width is what is called exit pupil. If the beam is wider than the pupil of the human eye, it will simply not fit in the eye. You still get an image but if you go wider you are throwing light away (using a smaller effective telescope aperture). That's got nothing to do with obstructions in the optical path. It's easy to show this diagrammatically using basic geometric optics.

Something like this:
http://www.jayandwanda.com/digiscope/pupils/basic_scope.gif

[Finite]

Thanks guys, I'm a bit the wiser now. Still trying to assimilate some of that though.

So visually - let's use f/10 sct's as examples - if we have a 8" and a 16" side by side and focussed on the same celestial object, using different eyepieces to produce the same magnification in each scope, is the image going to be brighter in the larger scope than the 8", though the image is the same size in appearance (assuming the viewer has a healthy pupil dilation)?

I hope that makes some sense...?

[Atmos]

The 16" will slaughter the 8" :)

[Finite]

Love the comment Colin! By the way, it was easier to me to understandthan your first 😀. . Would it be simply a better resolution of the same object then, it would also be brighter to look at? The tract in the book kind of threw me.

I understand how an increase in magnification makes the image dimmer, and how a focal ratio is calculated, how a imaging device builds up the light over time exposure, the very basics etc. Beyond that I'm wading through murky waters, so I thanks guys for the input. I also saw written recently that the way f ratio works in a telescope is different to how it works in a camera. I'll have to look that one up, as I'm pretty sure it's the same principle.? Both are effectively lenses.

[AEAJR]

Yes! That is the advantage of aperture, gathering more photons which gives you a brighter and potentially more detailed image.

An object at 200X looks about the the same in every scope regardless of FR or aperture.

The eyepiece you would use to achieve 200X would differ from scope to scope based on the Focal length of the scope but the image size would be the same.

[Atmos]

At the same magnification you will get the same FOV but the image will be brighter. Remember, focal length increases linearly (A*x) where as aperture (light gathering power) increases at A^x. So a 16" will gather 4x the amount of light than an 8" but only have twice the focal length given the same f/ratio.

Basically, bigger scopes make brighter images :)

[barx1963]

I could be wrong, but my understanding is that they are exactly the same, focal length divided by aperture. The main difference is that in most cases, the f ratio is fixed in a telescope, while it is variable in a camera lense.
There is a discussion here https://en.wikipedia.org/wiki/F-number

Malcolm

[Somnium]

the only difference i know of in this area is that photographers refer to the focal ratio as the aperture where astronomers, correctly, refer to the objective diameter as the aperture. this can be a source of confusion but i don't think it has much to do with this.

[julianh72]

f-number is exactly the same for a telescope or a camera lens: Focal Length divided by Aperture. As you say, camera lenses typically have a variable f-number, by using an adjustable diaphragm to reduce the aperture (and zoom lenses also have an adjustable focal length).

What differs is the common usage of a single measurement to describe a camera lens versus a telescope. A 200 mm camera lens has a focal length of 200 mm; if it is f/4, this implies a maximum wide-open aperture of 50 mm. A 200 mm telescope has an aperture of 200 mm, and will typically have a focal length somewhere between 1000 mm (e.g. an f/5 Dob) to 2000 mm (e.g. an f/10 SCT).

[janoskiss]

You could always stop down your telscope's aperture to increase the f-ratio in exactly the same way as is done in a camera lens. But you very rarely want to do that because normally you want all the light you can get.

But the same goes really for camera lenses when it comes to astrophotography: you normally want the aperture wide open to collect as much light as possible (unless your lens performs very poorly at full aperture; much like a badly figured telescope mirror that can typically also be improved by masking its edges).

[Finite]

Thanks everyone, I get it I think. I got hung up on thinking f10, no matter what size aperture, meant that the image is going to be the same level of dimness but with an improvement in resolution. All great info, I haven't learnt a lot in my 50 yrs (just ask my wife). Colin, this you submitted resonates with me, thanks.



I am thinking of going SCT again for the goto capability. I am rubbish at star hopping and my eyesight is getting a bit long in the tooth perhaps. Before it goes (or before I go) I would like to sight a galaxy in person. Yep haven't seen one,- own galaxy and its satellites not included that is.

I really appreciate the help from all of you who have contributed. :thumbsup:

[janoskiss]

Your "camera lens" for visual astronomy is not just the f-whatever telescope but the combination of telescope, eyepiece and the lens inside your eye. The way others have explained it probably makes the most intuitive sense: for a given magnification, a larger aperture will yield an intrinsically brighter image (both in terms of surface and overall brightness).

That's true until you hit the limitation of your own eye's aperture. Beyond that you gain nothing upon increasing the telescope's aperture. Roughly around 1m or 40" is the largest useful telescope aperture for visual astronomy (so you still have plenty of room for aperture-fever beyond 23" ;)).

[barx1963]

John
I am seeing a 20" dob in your signature, is that correct?
If you are no good at star hopping you could fit out that dob with an Argo Navis system for a lot less $$$ than a go to SCT and you will be seeing galaxies all night long.

Get in touch with Gary if you are not sure about the fittings required, he will surely be able to help.

Cheers

Malcolm

[N1]

Thankfully, not everybody seems to think so
http://www.vixenoptics.co.uk/Pages/sg_2.1x42.html
http://www.televue.com/engine/TV3b_page.asp?id=102

"Throwing light away" and "using a smaller effective telescope aperture" by stopping down the exit pupil with your own pupil is of approximately zero consequence in unobstructed optics. In fact, stating it like that is misleading, because it suggests that the image will be darker. Wrong. The image simply stops getting brighter, and that is because it's the same brightness as what you see unaided, only magnified (for extended objects that is - point sources like stars do look brighter because their light is not being spread out over the magnified area). So if you want super widefiled, go for it. Unless of course your scope has a secondary mirror. You see, the exit pupil is just a small image of the entrance pupil - the telescope's objective. So enlarging it enlarges everthing in it as well, such as the secondary' image. And when its size gets close to your own pupil size, while the outside of the exit pupil is being cropped away by your own pupil, well you get the idea. "Lowest practical power" is strictly a problem of obstructed optics.

Apologies to the OP for moving off topic a bit here.

[Finite]

Interesting. I'd not seen a aperture limit put on for visual. Using the Naperville Astronomical Association Telescope calculator gives me max 32mm eyepiece for going wide with the 23" (not usable as of yet) dob, and 28mm with the up-and-running 20" dob. Given my estimated pupil size being 50 yrs age.

[Finite]

[/QUOTE]Apologies to the OP for moving off topic a bit here.[/QUOTE]

No problem on my part Mirko, I'm thoroughly enjoying the discussion, happy for it to range, it's relevant.

[Finite]

Hey Malcolm, :thanx: I shall look into that. I must confess to not having explored that idea. Argo Navis = push-to I think from memory, and when I finish this post I'll do a search.

Alternatively a 12 - 16" Skywatcher is not out of reach. There's probably a good argument for me to not go too over the top with expense. (I know I've got a couple of big dobs, but only relatively recent purchases, which were too inexpensive to ignore. With the 20" purchase I was travelling the South Island when it popped up on TradeMe here in NZ. The dob owner lived in an out of the way place in the Southern Alps and needed to move due to health reasons. Cue an urgency to sell and I had the ability to drive to him to get it pretty much there and then. So for less then the price of recoating the 23" dobs mirrors I struck a deal. The 23" also needs a focuser and replacement turntable base on the mount. The 20" was a good buy, I just finished collimating it tonight but my hired help (15 yr old son) to take it outside has gone to sleep! Looks a good viewing night too. I'll likely just move the 23" dob on once I'm happy with the performance of the 20".

Now it's me hijacking my own thread. I apologise to the contributers.

[barx1963]

John
I have a 20" and installed the Argo myself. Very easy and Gary is a wealth of info and help.

His website is here http://www.wildcard-innovations.com.au/

Malcolm

[ausastronomer]

Plenty of incorrect information in this thread :)

The joys of the internet. At least before the internet you had to buy books and read them and fortunately most authors had some idea what they were on about

Cheers
John B

[ausastronomer]

Absolute A grade crapola.

Cheers
John B

[ausastronomer]

Absolute A plus grade crapola

Cheers
John B

[Finite]

Aha, I see some peer review coming in. I hope there's not going to be a fight in the playground :)

Malcolm I went and had a look through that website after your note on Argo Navis, it and Servocat looks the thing. I hope to catch up with Dave from Hamilton who has a bit to do with mirror making, perhaps find out with his help how good the mirror is in my scope/s. (Hi Dave if you read this :hi:)

[AEAJR]

John,

You took exception to my post. I see you picked one sentence out of context of the entire post and took it out of the context of the post before it, which I was responding to.

But perhaps I am wrong. I am open to education. Please help me.

A 200X image will be the same size no matter what scope you look through. The brightness and possibly the detail will differ from scope to scope based on aperture but the size will be the same. In other words 200X is 200X

If I was not clear, I was referring to the size of the image or the apparent magnification.


Do you disagree?

[N1]

Thank you John for your comment, well reasoned as usual. Of course it should read "eyepiece case", not eyepieee case, my mistake. Thanks for pointing it out and apologies for any confusion.

[ausastronomer]

Hi Ed,

The image size isn't "about" the same it's "exactly" the same at equal magnification, irrespective of aperture. But that's the only thing that's the same. To be honest for someone trying to get their head around something they don't understand, I didn't think you post was very clear, particularly when you put that single sentence in an isolated paragraph.

Cheers,
John B

[AEAJR]

Thanks John. I will try to be more careful in future posts.

[ausastronomer]

Your spelling isn't the problem. The premise contains incorrect information.

Obstructed or unobstructed is irrelevant in this case as Steve already tried to point out to you. The links you provided are also irrelevant in the context of obstructed / unobstructed.

Cheers
John B

[N1]

You obviously did not read them before making your "crapola posts".

[janoskiss]

What people think does not matter. The laws of physics matter. In this case basic high school or first year uni physics depending on what country you're from and how much your government invests in science education (geometric optics is the main topic in any case). The problem with going too wide with a large aperture telescope is two fold. I'll try to illustrate by example.

Let's say one goes for 20x magnification with an 8" ~= 200mm (amongst friends) aperture telescope, with an f5 focal ratio (focal length = 1000mm). The eyepiece to use will have an FL of 50mm. The exit pupil will be 10mm, which will not fit into the human eye. What will fit into the average human eye is about 5-6mm. Allowing for little side-to-side head movement, let's say 5mm.

Issue #1. At 20x you will not be able to tell the difference between the views from a 4" scope and an 8" scope based on brightness alone. The views you get at 20x will be about the same as far as brightness goes. So you'd be wasting your money/effort with 8" of aperture if you just want to view the sky at 20x; and you'd be throwing ~75% of the light away (it'd be hitting your iris and not making it to the retina). But it's worse than that:

Issue #2 (more important). If the starlight comes out of your eyepiece as a 10mm wide beam, your eye's pupil (5mm wide) is acting as an aperture stop. The perimeter of your eye's pupil is not as nice near-perfect circle as a telescope lens or mirror, but has natural roughness to it (take a look). You will get diffraction artefacts from the light having to graze past the edge of your pupil. (Reduced contrast, unusual looking flares/spikes.) It'll be as if your telescope lens' or mirror's edge was badly chipped. And you will also get reflection artefacts from the light hitting your iris. So at low magnifications you will get much sharper and more contrasty views from a smaller scope that is better suited to your eye. For the present example: at 20x, a 4" apo will outperform an 8" apo (and probably even a 6" apo in practice).

And re @Finite, as an aside, that's where the practical limit on size of scopes for visual astronomy comes in. For a 1m or 40" aperture scope you need to be at roughly 200x to take full advantage of it. Arguably you could get more out of a 1.2 or 1.5m but it's kind of getting to the limits of what one can do; it's battling against two opposing "forces": 1) human biology that left us with two limited aperture cameras in our heads and 2) the atmosphere which rarely allows for more than 400x magnification without everything looking like a boiling mess.

References
Halliday & Resnick, Fundamentals of Physics 10th ed., Chapt. 34.
Young & Freedman, University Physics 13th ed., Chapt 33.
... still pays to buy books ;) @ausastronomer --- for those who want to dig deeper:
Hecht, Optics (http://www.bookdepository.com/Optics-Eugene-Hecht/9781292021577).

[AEAJR]

Steve,

Great post. Much more useful than the blind sarcasm posted by someone else.

Seeing your reference notes it reminded me that I have my freshman physics text book on the shelf, Halliday & Resnick, Fundamentals of Physics.

I should pull that out and add it to my current reference material. I wonder how much has changed in 45+ years. I imagine the basics are still the same.

[janoskiss]

It's all the same. Basic physics has not changed in 100 years (most of it in much longer than that). You can pretty much do all undergraduate physics with old textbooks. Newer editions have just more colourful illustrations that's all. I actually like the old texts better. Quantum field theory is the first point of departure and that does not feature till you've decided you're going to be a physicist. And even that's 50 y.o.

Btw. you're right it's still Fundamentals and not Principles of Physics. Fundamentals was what I first referenced but my Internet search seemed to show otherwise, so I made an erroneous correction to my post. Thanks to you I've restored it now.

I think it's fair use if I post a relevant excerpt from Halliday & Resnick from one of the latest texts. (Halliday & Resnick have both passed on but their excellent textbook lives on and continues to be referred to as H&R.) I bet you will find the equivalent passage in your old edition. If you do and can take a photo and post it here, I would be ever so grateful.

[Finite]

Thanks Steve, that was useful information for me,- good to know re the visual limit and why. And also the fact that the perimeter of the pupil is flawed. Is that then a fault of the lens in the eye, or a fault of the edge of the pupil, or something else do you know? eg Would that still hold true with an older pupil as the pupil no longer dilates to the same degree as when in ones youth?

(I suppose a relevant comparison to what I'm getting at could be to digital camera sensor size and lenses, - how a aps-c sensor does not utilise (does not 'see') the optical edge of a camera lens, whereas a larger full-frame sensor does, and so the camera with the smaller sensor can get away with using a lesser quality lens yet still produce a pleasing result.)

Just let me know if I'm being too annoying, I won't be offended.

[AEAJR]

I never thought of the exit pupil exceeding the pupil of the eye as actually causing interference. I realized I would be losing light but never expected it could actually degrade the image.

I use a 38 mm 70 degree AFOV eyepiece in my 203mm dob for 31.5X. If I am doing the math right that would be about a 6.4 exit pupil. I suspect that at my main observation site that that is probably exceeding my pupil size.

I have never noticed any distortion but I do find that as I move my eye around I can see more in the view. Kind of like looking through a window where you take different angles to see peripheral areas. I figured that was the result of the light cone exceeding the pupil.

[N1]

Thanks for your post Steve. It helps illustrate my point. I'll try to explain.

Re issue 1: Assuming that the exit pupil of the 4" is at least that of the observer's eye, you are totally correct, you would not see a difference between the two scopes for brightness. That's exactly my point. If there was a penalty for allowing the exit pupil to become too large, the 8" should somehow suffer a loss in brightness, either compared to the 4" or compared to itself operating at higher power. It doesn't. Period. My arguments are being called irrelevant on here, when the only thing actually irrelevant is the light you are "throwing away". If one was to follow that logic, you'd also be "throwing resolution away" every time you use your scope below its highest practical power (seeing limits notwithstanding). You'd also be wasting all the light hitting the grass next to your scope, because you failed to bring a larger instrument. Of course you're not, it's just silly. As I said, "throwing light away" is a misleading argument, because it suggests you shouldn't be doing it*. That's what I take issue with.

Re issue 2. Yes, and that's why I said earlier it's of "approximately zero", not "zero" consequence. I acknowledge that the iris' edge is less than perfect and may introduce some diffraction artifacts. However, in practice the effect can be happily ignored. For example, when observing the Moon, the eye's pupil will be smaller than fully dilated, so it will encroach on the EP's exit pupil at a higher power than the telescope's "lowest practical power". If one was to follow your argument, full- disk, low power views of the Moon should be of mediocre quality at best in anything but small telescopes. They are not. They are actually quite good. Secondly, the iris stops down the light beam almost all of the time anyway. It's called life. If one was to follow your argument, people should be seeing said artefacts, and finding them obtrusive, whenever their pupils are the limiting factor to the amount of light their eyes receive, i.e. just about always. Yes, I do see some spikes on bright point like sources, but the are hardly obtrusive. Reduced contrast by using your eyes naturally? Gimme a break! For the avoidance of doubt, I'm not saying these artifacts don't exist, but I am saying that they are hardly a reason not to use as low a power as your eyepiece case permits. Importantly, we are talking about the effects of exceeding the maximum recommended exit pupil size here, not the difference between the optimum (2mm perhaps?) and say 10mm. Yes, that difference would be more than minor, especially for contrast and sharpness.

*The caveat to this, I think we all know and agree on, and it's what you appear to be wanting to avoid: Obstructed optics do have a low power limit. The effects introduced by the secondary absolutely dwarf anything I've seen myself having to discuss with you since my first post in this thread. I also note with interest that it has taken until now for anyone to produce the pupil-edge-diffraction argument. Not what I'd expect to see if it was the main, or even a significant, argument, sorry.

It's interesting how this discussion has evolved, considering my original argument. We've heard of digestion artifacts, been back to school, we've even gone travelling. However with the above in mind, I stand by every single word. Again, apologies to the OP for any unwanted diversion.

Further reading: Nagler, A. "Choosing Your Telescope's Magnification." Sky & Telescope (May 1991).

[janoskiss]

I get diffraction and reflection artefacts from my own eyes if I view bright objects at excessively low powers. The most likely culprit for the diffraction flares/spikes is the somewhat rough edge of the pupil. But maybe some people have more astronomy friendly pupils than others. :)

If the lens in the eye is not near perfect, its performance degrades also with increasing exit pupil; e.g., astigmatism is much more of an issue at lower powers. OTOH, too small an exit pupil also shows defects in the eye like the "floaters" which start becoming annoying somewhere in the range of 0.5 to 0.9 mm.

Using a large exit pupil however will most likely not unravel the very fabric of the space-time continuum and destroy the entire universe. The destruction may in fact be localized merely to our own galaxy. :P It's a risk I'm sometimes willing to take with a finder EP and so far I've gotten away with it (35mm in an f/4.7). But if I wanted to push it much further, and/or make the most of wide TFOV observing, a smaller scope or binoculars would be preferable. I sometimes wish I had not sold my ED80. At 15-20x it would be great widefield to go between hand-held binos and the 10" Dob. I could never get the hang of larger binos (70-100mm).

[Satchmo]

EDIT Just noticed this was the beginners section so just ignore if you're not yet competant with the relationship between magnification , exit pupil and aperture !

This discussion ties in with an add I saw the other day for Vixen 2X 40mm mini binoculars and prompts my usual rant about `unity brightness' and the human eye :)

Provided you fill the fully dilated pupil you cannot make an extended object brighter by increasing the size of the telescope . You can only make it appear larger by increasing the aperture . The increase in visibility of faint galaxies comes about because the resolution of the eye drops to one or two degrees at low light levels and filling the pupil with an(increasingly larger telescope only makes its apparent size larger and thus becomes visible . There is also an amplifying effect where the rods in the eye can be brought into play with averted vision though !

Its called `unity brightness' and its a concept that helps to understand human interaction with telescopes , where the eyes are not CCD chips , but limited by that physical bottle-neck of the iris.

A simple demonstration with our Vixen 2 X 40mm binoculars . At 2 X magnification ( and 7mm pupil ) we can't see more than 14mm of the 40mmm aperture due to the vignetting of the Iris. We have doubled the effective aperture over the unaided eye and are using 4 X the surface area of optic over the 7mm pupil but we have also increased the size of the image on the retina by 2X and hence reduced the surface brightness of the image by a factor of 4X .

The net result is a zero increase by unit area of light on the retina , and this relationship continues on adfinitum as we increase aperture .
tThis is just pure maths but the visibility of faint objects is further enhanced in the eye by the physiological nature of rods and cones . Theres good treatment of this subject and unity brightness in this article from Page 35 link below on extended objects ..avoid the maths if you are squeamish and stick to the text .

Point sources behave differently but in bad seeing even stars can start to behave like extended objects !

https://books.google.com.au/books?id=vG0QBwAAQBAJ&pg=PT46&lpg=PT46&dq=unity+brightness+and+telescope+s&source=bl&ots=cfZQ9kpanU&sig=vs8v_QNtC-4_KbxzANktZZ7OSsw&hl=en&sa=X&ved=0ahUKEwiRvpSwvezLAhUO62MKHfCKDi 4Q6AEIJTAE#v=onepage&q=unity%20brightness%20and%20telesc ope%20s&f=false

[N1]

I expect the 40mm aperture of the Vixens is the most efficient way to achieve their TFOV, i.e. the purpose of the large aperture here is a wide angle, as opposed to light gathering?

[Satchmo]

Hi Mirko The 2X magnification should give a large true field of view. The 40mm aperture is just there probably to make the binoculars large enough to hold as the most aperture you will be able to utilise with young eyes is about 14mm which wouldn't look so impressive in the advertising and they would be tiny . The relationship between magnification and aperture is magnification X exit pupil = aperture and pupil maybe open to 7mm when you are young.

[Finite]

Does the brain combine the images from both eyes, so is making use of 7 mm of pupil x 2, is that how you achieved the 14mm of the 40mm available through the binos?

[N1]

Hi Mark that would be quite neat actually. Imagine a pair of 2x14s for your shirt pocket :lol:
Would they need more strongly curved lenses perhaps?

John, I think what Mark means is that with an iris opening of 7mm, you'd be using 14mm of the 40mm, because aperture divided by power equals exit pupil. I won't comment on the bino effects because I don't know a lot about binoviewing. Steve et al. might be able to help.

[janoskiss]

@N1 It sounds like you and I were on the same page all along as far as the cold hard facts of the matter are concerned --- saying much the same thing but in conflicting sounding ways, and we may have somewhat different personal preferences too (which is a good thing; visual astronomy is all in the eye of the beholder after all).

I like Mark's analysis why they had to make it 2x40 instead of 2x14 - advertising and marketing! I could definitely go for a well made 2x14 or 3x20.

[janoskiss]

No, it's about the 2x magnification. Aperture / Magnification = Exit Pupil. In this case 14mm/2 = 7mm. Two eyes or one don't matter as far as exit pupil goes. If you wanted say 5x magnification, then the largest useful aperture would be 5x7mm = 35mm.

[Finite]

Ta, as you can see i'm no professor.

[janoskiss]

The human eye pupil size can be such a bottleneck that some people even resort to performance enhancing drugs for visual astronomy: http://www.aapos.org/terms/conditions/43

You will look pretty scary though to your fellow stargazers at the 5am tea break.

[Satchmo]

I've got to do those drops with a 30mm 100 degree apparent field eyepiece and a 24" F3.5 at least once in my life :)

[N1]

Steve, yes that has been my impression also. Visual sure is a subjective beast. Re destruction of galaxy, I'm sure it's nothing a beer or two couldn't fix/prevent :)

[Finite]

Update to something I posted earlier, - seen a galaxy now - Thanks to Dave Brock👌:thumbsup: