F ratio rule, how solid?

[ollypenrice]

I'm canvassing opinion on the F ratio rule and exposure time for an article. I gather there is a camp of dissenters who believe that at larger aperture it breaks down. If you are one of these doubters I'd love to hear from you!

By 'F ratio rule' I just mean exposure time going as the square of the F ratio irrespective of aperture.

Olly

[NickK]

Interesting. There's a limit on F-ratio and returning a sharp image. So perhaps F-ratios that are above dawes limit would be good? Some blurring can be removed by software processing but I'm suggesting optical.

[Ags]

Surely the laws of physics are well established in this regard? The density of photons delivered to the sensor is related in an absolute way to the F ratio. Stars do not obey the rule of course - stars in a 100mm F3.5 lens are four times brighter than stars in a 50mm F3.5 lens (although you are more zoomed in so you probably have a similar star count...).

[ollypenrice]

Well, I agree with the above and have always held it to be so but I wish I could pry out of someone the dissenting voice that I know is out there! I'm curious as to what the argument might be but I can't find anyone owning up to it. I have a draft article mentioning the F ratio rule as it is usually understood and I suspect that the dissenters will pounce on me afterwards, hence my desire to hear their arguments now.

Nick, presumably the issue with very fast F ratios is the depth of the focal plane and, by implication, its orthogonality?

Olly

[vdb]

I gather you know those articles:

f-ratio myth

Aperture, f-ratios, myths, etc. | Ask Craig | Stark Labs

Yves.

[Jessun]

The articles above really deal with S/N ratio, and not exposure time as such.

F-ratio IMHO is a simple optical number, and it determines how fast the focal plane collects photons. I don't immediately see these articles challenging that. They focus on what can be extracted from different images in terms of S/N ratio.

A fast scope will do more subs in a given time and that brings the noise down in the stack. So even if two subs from different f-ratio scopes can be processed to reveal similar S/N ratio the fast one does more subs and would in my book be the overall winner for achieved S/N ratio over a given time frame.

BUT as aperture grows the focal plane grows accordingly so the nicely illuminated sweet spot grows too, so larger and larger chips can be used before vignetting shows up. That's a clear bonus!

[davew]

I think that if you correctly state the laws of science in an imaging article then it doesn’t really matter what some people think. The problems seem to be “ In the detail “ but that will always be the case.

It’s quite likely that Robert Hooke in the late 17th Century had some ideas about it but I’m not a scholar and can’t say. I know the Iris Diaphragm is attributed to him. By the middle to late 19th Century they had it nailed down quite well so no real arguments available there.

Part of the problem lies in the terminology that’s banded about, in this case the word “Myth”. I can’t direct you to a particular document or thread but I get the impression it revolves around the often pushed theory that the faster the focal ratio the better. No matter what. Once accepted that f/r is all then it’s a small step to say that imaging at, say, f10 can’t be done.

Little gets said about camera noise, surface brightness, CCD response, background pollution, image scale, image size etc ( I use etc because I’m running out of ideas ) This leads to the assumption that a scope running at f4 will produce images that are twice as bright, less noisy and soooo much easier to process than any combination running at f5.6 for a given time.

Threads I’ve read about this go off in all sorts of directions once aperture is mentioned. Often focal length related and sometimes image scale.

It may also be worth mentioning that not all scopes are created equal. Just because a scope has near identical dimensions as another doesn’t mean the light coming out the back end is identical.

State your case and be damned. Just be sure to mention that you’d rather image a small Galaxy in a big R/C scope running at f9 than a 50mm camera lens at f1.8 !

Dave.

P.S. The words “ All things being equal “ can come in handy

[narrowbandpaul]

i posted this a while back, think it sheds some light (pardon the pun) on the issue raised by davew...

http://stargazerslounge.com/astro-lounge/77512-focal-ratio-vs-aperture-size.html

[ollypenrice]

More thanks. No dissenters have been flushed out so I think I'm basically closing their case. (I only know of them via hearsay but I wanted to cover all bases.) I'm in complete agreement with all that is being said here.

Olly

[Shibby]

I don't pretend to know much about optics, but I have read about the "f-ratio myth" in the past. It makes no sense to me. The argument seems to be that the S/N ratio is not affected by f-ratio, because the sky noise scales with the signal. Well, to me this is a bit like saying that a picture of a tree taken through fog won't offer better tree detail if the image is twice as bright - hardly profound? The article clearly states that with a lower f/ratio there are more photons hitting each pixel, I think that should be case closed.

One thing, though, that I don't fully comprehend due to my poor understanding of optics - perhaps someone could explain this to me - is that for a given aperture, the "same number of photons" enter the telescope, yet fewer photons hit each pixel. With longer focal lengths, are we ignoring more of them?

[terryf]

No, it's not that we are ignoring any of them, it's just that they get more spread out the bigger the F-ratio. So for a given aperture, a scope can collect a given number of photon per second from a deep-sky object. Now as the focal length gets longer (for this fixed aperture), the size of this deep sky object at the focal plane gets bigger (it equals the angular size in radians times the focal length) and so this fixed number of photons is spread out over a larger area so will appear to be more faint. Or it takes a longer exposure to collect the same number of photons per pixel. I keep trying to get my brain around all the S/N ratio stuff, but all I get is a headache

Terry

I don't pretend to know much about optics, but I have read about the "f-ratio myth" in the past. It makes no sense to me. The argument seems to be that the S/N ratio is not affected by f-ratio, because the sky noise scales with the signal. Well, to me this is a bit like saying that a picture of a tree taken through fog won't offer better tree detail if the image is twice as bright - hardly profound? The article clearly states that with a lower f/ratio there are more photons hitting each pixel, I think that should be case closed.

One thing, though, that I don't fully comprehend due to my poor understanding of optics - perhaps someone could explain this to me - is that for a given aperture, the "same number of photons" enter the telescope, yet fewer photons hit each pixel. With longer focal lengths, are we ignoring more of them?

[Shibby]

Thanks Terry, so unless we have a much larger sensor, the photons are effectively ignored right? As they fall outside the FOV of the sensor? Are they absorbed by the tube before reaching the focuser?

[dph1nm]

Oh, seeing as you ask. The arguments are quite simple:

(1) The number of photons collected from a DSO depends only on aperture (and exposure time) not focal ratio. That's physics.

(2) The depth of an image (i.e. the faintest objects which are detectable) depends only on the number of photons and not how they are spread over the imaging camera. That is true providing we don't add significant extra sources of noise such as read noise when we measure the signal.

NigelM

[dph1nm]

The article clearly states that with a lower f/ratio there are more photons hitting each pixel, I think that should be case closed.

So what I have never understood is why people think the number of photons per pixel such a fundamental quantity. A DSO has a fixed size in seconds of arc, not microns! If I display my images at a fixed angular scale then all this f-ratio-makes-a-difference stuff becomes irrelevant.

NigelM

[dph1nm]

The density of photons delivered to the sensor is related in an absolute way to the F ratio. Stars do not obey the rule of course

Actually they do if they are resolved (by the detector). And if they are not resolved (i.e. your pixel is bigger than the PSF) then you actually lose depth by going to smaller f-ratio. This would also apply equally well if you pixel size was larger than a DSO (which can happen with faint galaxies and wide fields). This is why you cannot arbitrarily image to any depth you like with 1mm scope by just going to an incredibly small focal ratio!

NigelM

[rfdesigner]

I would agree.. all else being constant.

Problem is, no matter how hard we try, when is anything constant?

Derek

[Shibby]

(1) The number of photons collected from a DSO depends only on aperture (and exposure time) not focal ratio. That's physics.

You're quite right (assuming that DSO isn't cropped by the detector)

So what I have never understood is why people think the number of photons per pixel such a fundamental quantity. A DSO has a fixed size in seconds of arc, not microns! If I display my images at a fixed angular scale then all this f-ratio-makes-a-difference stuff becomes irrelevant.

I take your point, that does make sense. But, and please forgive my ignorance on the subject, but you are gathering less total photons with a longer focal length unless you increase the size of the detector, right? (just checking). And once you have achieved the image scale you want of your DSO (or the optics/seeing/sensor size can cope with) then it is desirable to have lower f-ratio (ok, yes, by increasing aperture) or increase exposure time... so not "irrelevant" as such, I think that's just a semantical argument though.

[Ags]

Actually they do if they are resolved (by the detector). And if they are not resolved (i.e. your pixel is bigger than the PSF) then you actually lose depth by going to smaller f-ratio. This would also apply equally well if you pixel size was larger than a DSO (which can happen with faint galaxies and wide fields). This is why you cannot arbitrarily image to any depth you like with 1mm scope by just going to an incredibly small focal ratio!

NigelM

Yes that is quite true - stars are just one case of a DSO that is smaller than one pixel. The same principle seems to apply in our eyes as star brightness seems constant regardless of magnification - presumably the star image is always falling on the same number of receptors.

[davew]

As I see it these conversations will wander off at a tangent every time and I suppose I’m partly responsible.

Do we take the original question at face value or do we think there’s a hidden agenda ? If the first then I don’t see how a lens of any size doesn’t comply with the laws of physics. If the second, then it’s correct that a large aperture will collect more photons than a small aperture. The real question is what we want to do with them.

If we put aperture and time together then how can we ignore F/R ? That brings us straight onto F/L, image scale, size and I’ll stick an etc in again.

My own view is how big is the thing up there I want to image and as I’ve only got one camera, what focal length am I going to use ? It’s at that point when I decide on aperture and F/R.

Real world….. I want to take a quick snap of M82. I want it reasonably big on my laptop screen within the field of view of the camera. I decide 2000mm F/L might be good.

Which scope do I use ? 100mm lens running at f20, 200mm lens at f10 or maybe 400mm at f5? What the heck, I’ve got loads of dosh so I’ll go for the FASTEST and BIGGEST I can get my mitts on. Remarkably the arcsec/pixel doesn’t change so I’ll bin.

Real, real world…. I like imaging big things as fast as I can so chose the fastest camera lens for the job at the correct F/L to fit the thing in. As I go up in F/L, the hole at the front gets bigger.

That in theory should make both camps happy.

Dave.

[Demonperformer]

Don't know if this is of any use?

[Macavity]

http://www.astrometrica.at/papers/PointSources.pdf

Stars, Asteroids, and even the (pseudo-)nuclei of comets, are point-sources of light. In recent times, most observers use CCDs

to observe these objects, so it might be worthwhile to think about some details of detecting and measuring point sources with a

CCD. First, this paper discusses the properties of point-sources, and how they can describe them with a small set of numerical

values, using a Point Spread Function (PSF). Then, the sources of noise in CCD imaging systems are identified. By estimating

the signal to noise ratio (SNR) of a faint point source for some examples, it is possible to investigate how various parameters

(like exposure time, telescope aperture, or pixel size) affect the detection of point sources. Finally, the photometric and

astrometric precision expected when measuring faint point sources is estimated.

Whether it answers the specific question or not, the above (worked examples) helped me a lot - With the basic terminology. Of course, it is for point sources. I'm still looking for an analogous treatment for extended sources - If indeed that is possible. Perhaps therein lies the "wiggle room", or is it to do with (UK) seeing conditions?

There is always room for anecdotal evidence, in any theory though?

[dph1nm]

But, and please forgive my ignorance on the subject, but you are gathering less total photons with a longer focal length unless you increase the size of the detector, right? (just checking).

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

[dph1nm]

I'm still looking for an analogous treatment for extended sources - If indeed that is possible

Just replace the PSF by a broader function (exponential or Sersic profiles are often used for galaxies) and the maths is the same. Galaxies can basically be treated as stars taken in very bad seeing!

NigelM

[dph1nm]

So the f-ratio myth can really be boiled down into one question. Do you think the number of photons per arcsecond (you believe f-ratio is a myth) or the number of photons per pixel (you believe exposure depends on f-ratio) is the overriding factor in determining the final depth of your astronomical image?

NigelM

[RikM]

I can't pretend to understand the maths behind this, but if you had two f/5 scopes, one at 500mm focal length and one at 1000mm focal length, the image of a galaxy on the camera chip would appear twice the size in the long scope so since that scope is also a larger apureture (to achieve f/5) it gathers more photons. The image is more spread out but more photons are captured therefore the galaxy appears at the same brightness for a given exposure time constant between the two scopes.

So I think image brightness depends on f/ratio.