F ratio rule, how solid?

[Shibby]

So I think image brightness depends on f/ratio.

Don't think that's in dispute any more. But, with the longer FL (same f/ratio) scope in your example, you are gathering more signal. Either higher resolution or, binned, more signal per "superpixel" for the same scale of image.

[ollypenrice]

Yes, field of view increases at smaller f-ratio (which is the real reason for using it in my opinion), so you get photons from parts of the sky you wouldn't have at higher f-ratio. But providing your object of interest fits within the FOV then it gets the same number of photons from the same aperture in the same time irrespective of f-ratio.

NigelM

Nicely put, though the bit in brackets (my emphasis) is a puzzle. Wouldn't a fast f ratio be something you'd want when choosing an instrument of a given focal length?

Olly

[Looking Up]

I think, although I may be wrong, that the f ratio of a telescope is first and foremost a pure division of focal length by aperture but this is not a measure of the amount of light that it will transmit. Mirrors, vanes, secondary obstruction, glass, filters etc all absorb or stop light. A better measure would be a T number, this would give a figure of the actual light transmitted through the scope, to allow calculation of more accurate exposure time figures.

[Demonperformer]

I woke up thinking about this one this morning (sad, I know) and, although I don't have anything like the math to support my thinking, if I wanted to put a different point of view, I think I would start with something along these lines.

Stars don't follow the rule - as I understand it that is because they are 'point sources'.

If I take a photograph of a double star, I now have two point sources and so neither of them would follow the rule either.

However, every double star has a minimum aperture that will separate them, below which the light is no longer arriving as a point source, but the light merges to form a blob.

What about when I am taking a photograph of a dense open cluster – one of those described as a ‘hazy patch’ in the manuals? If I am using a large aperture all the stars become resolved into point sources and so the rule does not apply. But if I am using a small aperture scope, I no longer have point sources, but an extended ‘hazy patch’, to which I have to apply the rule.

Extrapolating that argument one step further, if I were to take a photograph of M101, I would now have how ever many hundreds of millions of what are still point sources, the light from which would actually form a blob on my sensor because I cannot separate them into point sources. However, if I had a large enough aperture, I would be able to resolve M101 into individual point sources, and thus the rule would no longer apply.

So it is not so much a case of the rule breaking down at large apertures, it is just that objects move from one category (extended sources) to the other category (point sources) as aperture (and resolution) increase.

Am I making any sense?

[dph1nm]

Stars don't follow the rule - as I understand it that is because they are 'point sources'.

Unfortunately images of stars are not point sources. They have a finite angular size due to both the atmosphere and the telescope optics. So in fact they behave just like very small galaxies (in fact, because of this, there is a magnitude faintward of which it becomes impossible to distinguish an image of a galaxy from that of a star).

I suspect some of this "stars behave differently from galaxies" comes from wide field imaging where the seeing is grossly undersampled. Here, if you double the image scale, stars remain essentially single pixels whilst galaxies double in size. However, if you well-sample the seeing then doubling the image scale also double the number of pixels a star covers i.e. it behaves just like a galaxy.

NigelM

[FraserClarke]

However, if I had a large enough aperture, I would be able to resolve M101 into individual point sources, and thus the rule would no longer apply.

So it is not so much a case of the rule breaking down at large apertures, it is just that objects move from one category (extended sources) to the other category (point sources) as aperture (and resolution) increase.

Am I making any sense?

You want to be careful here -- you might open up a whole new world of pain

As you say, these 'rules' are applicable in different regimes. Once you start considering resolution as you are, you can work out that, for point sources, the sensitivity can go as the fourth power of the diameter (absolutely nothing to do with focal ratio). So that means that a telescope which is twice as large, is 16 times more sensitive to point sources. That's one reason why building a big telescope (e.g. a 40m telescope) gives you such a massive gain in sensitivity -- it's 600x more sensitive than an 8m telescope. It's a rule which most professional astronomers are not yet familiar with...

This D^4 rule only applies though if you can reach the diffraction limit of the telescope. That means it works for telescopes <6 inches (where atmosphere doesn't matter (so much)), or for big professional telescopes with full adaptive optics systems running which can correct the seeing. In between, it breaks down as you can't reach the diffraction limit of the telescope due to the atmosphere (as Nigel says).

But, if you're interested in sensitivity to point sources (i.e. stars), an F/100 100mm telescope is 16x more sensitive than an F/1 50mm telescope. So f/ratio isn't everything

[Looking Up]

But, if you're interested in sensitivity to point sources (i.e. stars), an F/100 100mm telescope is 16x more sensitive than an F/1 50mm telescope. So f/ratio isn't everything

I risk sounding dumb here but I can't see how this can be true! A 1mm objective v a 50mm objective, the larger must gather/focus many more photons, making it much more sensitive. Am I wrong?

[FraserClarke]

I risk sounding dumb here but I can't see how this can be true! A 1mm objective v a 50mm objective, the larger must gather/focus many more photons, making it much more sensitive. Am I wrong?

Nope, I just wasn't clear enough when I wrote F/100 100mm -- I meant 100mm diameter not 100mm focal length...