Focal ratio intuition help please!!!???

[Costas Soler]

Hi!

Very basic question...

I understand that (not how/why!) a faster focal ratio on a telescope/lense allows us to take a photo in a shorter amount of time than a telescope with a larger focal ratio. Is there an intuitive explanation for this? Does something about the geometry of a short focal ratio collect more light per unit time? Sorry if this is a silly question! Just a bit curious. Thanks!

[orion25]

For a given object, a faster scope will give you a brighter image (and larger field) resulting in less time needed for the exposure. The same object in a larger focal ratio (or slower) scope will yield a more magnified but dimmer image, requiring a longer exposure time. I hope this helps.

[Costas Soler]

Thanks very much! I understand how a faster scope gives a wider field. The field is basically the angular area enclosed by the cone projected from the objective lens out into space. That cone's slope, so to speak, is the focal ratio. That's why a scope of  focal ratio f/4 has a wider field than one of f/11 - because the slope of 4 gives a wider cone...  But the part I don't quite understand is how a shorter focal ratio gives you more light. Could you explain why exactly the faster scope gives a brighter image? Thanks again!

[orion25]

Think of it this way: Say you want to take a picture of a globular cluster. If you use a fast scope, say f/4, you'll get the image in a wide field. But if you try to take a picture of the same cluster through a slow scope, say f/8, the image will be more diffuse, i.e., the light is more spread out, yielding a dimmer image and requiring more exposure time to get the image as bright as the one through the fast scope. It's not really more light : the light is more compressed (convergence) in the fast scope appearing brighter, and more diffuse in the slow scope (divergence), appearing dimmer.

[Stu]

Olly's post here may be of assistance.

 

[Riemann]

For a given aperture, the longer the focal length, the less of the sky you see through the eyepiece, so the less light you see through the eyepiece, so the image is dimmer.    So focal length is a good way of comparing the brightness of different scopes of the same aperture but different focal lengths.

For a given focal length, the more aperture you have the brighter the image.   I think that is very intuitive.

The focal ratio is focal length / aperture and lets you take account of both factors at once.

[Mike Hawtin]

This is an example of the inverse-square law.  Any scope/camera combination of a given diameter and pixel size will put more photons into each pixel with a shorter focal length consequently filling each photosite faster, see this for a clearer explanation:

https://en.wikipedia.org/wiki/Inverse-square_law

Mike

 

 

[ollypenrice]

3 hours ago, Costas Soler said:

Hi!

Very basic question...

I understand that (not how/why!) a faster focal ratio on a telescope/lense allows us to take a photo in a shorter amount of time than a telescope with a larger focal ratio. Is there an intuitive explanation for this? Does something about the geometry of a short focal ratio collect more light per unit time? Sorry if this is a silly question! Just a bit curious. Thanks!

Yes. It is incredibly easy to see why a fast scope is fast (when it is fast, but unfornately it is not always fast.) Let's do the easy bit first:

The light gathering area of the scope on the left is 4x that of the scope on the right. It's easy to see why 4x the light makes the capture 4x shorter. The entire explanation is contained in this information. I'll stick my neck out and say that any aternative to this explanation must be either misleading or wrong. (I don't mean 'alternatie to my version of the explanation,' I maen to the underlying argument.)

OK, that was the easy bit. Easy because we have not changed the focal length in this explanation, just as daytime photographers do not change the focal length when they change what they like to call the F stop. What they change is the aperture (by stopping it down with a diaphragm.) What they are doing is, in effect, changing their lens from the one on the left above to the one on the right above and vice-versa. In this situation the F ratio rule applies. Double the aperture = quadruple the light gathering area = reduce exposure times to a quarter.

But .... alas astronomers sometimes change their focal ratio not by changing the aperture but by changing the focal length. When you do this you get no new photons from the original object so you get no increase in speed other than by putting the light onto fewer pixels. You can do that by downsampling the unreduced image. The F ratio rule does not apply to small objects which can be captured at the same aperture and longer focal length.

All good fun!

Olly

[ollypenrice]

1 hour ago, Mike Hawtin said:

This is an example of the inverse-square law.  Any scope/camera combination of a given diameter and pixel size will put more photons into each pixel with a shorter focal length consequently filling each photosite faster, see this for a clearer explanation:

https://en.wikipedia.org/wiki/Inverse-square_law

Mike

 

 

Mike, I believe this is misleading because it fails to consider the number of photosites we are filling. (What you are saying is not wrong but it is not the problem.) Our problem should not be defined in terms of filling photosites, it should be defined in terms of collecting light from dstant objects. If we think in terms of filling photosites then we will persuade ourselves that using a focal reducer will save us time according to the F ratio rule. But it obviously won't. Using a reducer at a fixed aperture will fill photosites faster and this may have an advantage in getting signal above read noise, but it absolutely does not follow the F ratio rule for discrete objects. Downsample the image on the left to the size of that on the right and the difference will be trivial and certainly not in accordance with the F ratio rule.

An astrophotographer should think in terms of the object so 1) decide on the focal length needed to image it 2) understand that, to save time on that target, he or she needs one thing only: more aperture. £££££££.

lly

[ngwillym]

And of course - (in an ideal world or if you chose your camera/scope combination to achieve such ) stars are point sources and therefore would only ever occupy one pixel each - regardless of f-ratio - and then exposure is directly relatede to aperture and is not affected by the f-ratio at all - this would apply to star open star clusters & globulars, but not extened objects like nebulae and galaxies

[Mike Hawtin]

Olly, I don't dispute what you say about downsampling but doing so costs you (in your example) half of your camera's resolution, as an example my C6Hyperstar/Atiik 428 combination gives me 3.2 arcsec/pixel and an image 1930 pixels wide, using the same camera on my 6" F/4 gives me 1.6 arcsec/pixel which downsampled to the Hyperstars image scale reduces my display to 965 pixels wide.  In the real world the only practical way to match the overall performance of an F/2 system with an F/4 is to use a camera with a chip twice the size and bin it 2x2.  So perhaps it would be fairer to say that fast focal ratio imaging is cheaper, but all this is by the by as far as the OP's question is concerned.

Mike

[Costas Soler]

Thanks so much!!! That's extremely helpful, I appreciate it a lot!!

[dph1nm]

The important thing to remember is that although a shorter f-ratio will give a wider field in the same time, it will not normally get you deeper in the same time.

NigelM

[dph1nm]

11 hours ago, ngwillym said:

And of course - (in an ideal world or if you chose your camera/scope combination to achieve such ) stars are point sources and therefore would only ever occupy one pixel each - regardless of f-ratio - and then exposure is directly relatede to aperture and is not affected by the f-ratio at all - this would apply to star open star clusters & globulars, but not extened objects like nebulae and galaxies

Actually, if your star occupies one pixel then a shorter f-ratio will actually require a longer exposure to get the same signal-to-noise, due to the increase in sky signal in each pixel.

NigelM