Exposure length at different F Stops

[souls33k3r]

Hi All,

I've been scratching my head over how to work it out in the simplest form.

I'm trying to figure out a way to calculate exposure length in seconds at different focal ratio of the same scope (for example when adding a reducer) to get the same amount of data when the F stop changes.

For example: 300s exposure @ F10 (2032 FL). So what will be the exposure length in seconds when the scope is reduce and now @ F7 (1422 FL)

I hope this make sense.

Thanks

[vlaiv]

Depends what you mean by same amount of data.

If you use following setup, then it is pretty easy to understand / calculate:

Aperture mask - you make smaller aperture, then exposure time is proportional to surface of aperture. You need xN amount of time more to capture same number of photons by using N times smaller aperture (by surface). Note though that SNR in longer exposure will not necessarily be the same as with shorter exposure (some noise sources are dependent on time, while others are not).

If you are using focal reductor, then things get a bit awkward - as you need to understand and specify what the same amount of data mean. By using different focal length, you are altering resolution that you are working with. So do you mean same amount of photons per sky surface element (like arc second squared), or do you mean same amount of photons per pixel? Again, in both of these cases SNR will not stay the same - it will change.

[souls33k3r]

I do apologies, i meant same amount of Photons per pixel.

I think i get the idea.

Basically the debate started when someone started quoting random numbers saying For example at F9 if you're taking 180s exposure subs, then when introducing a focal reducer of 0.8x you'll then need 115s @ F7.2.

[vlaiv]

If you want same number of photons per pixel - and this is assuming extended sources (nebulae or galaxies) rather than point sources (like stars) then reasoning goes like this:

Target emits certain number of photons per area per second - you are not changing your aperture so these photons reach sensor surface - it is only matter of how much sky is covered by a pixel. So time ratio is based on ratio of resolutions. If you go from 0.5"/pixel to 1"/pixel - you are increasing "surface" per pixel by factor of 4 (2 in X direction and 2 in Y direction, or just resolution ratio squared since pixels are squares) - then you can decrease your exposure by factor of 4. Mind you - doing so will also alter your SNR - in this particular case you will have slightly higher SNR per exposure - less dark current noise will accumulate in 4 times less exposure (LP will remain the same as it is also surface based - so same amount of LP per pixel).

[catburglar]

Exp time at Fratio 2 = Exp time at F ratio 1 x F ratio 2 squared / Fratio 1 squared 

So for your example changing from F10 to F7

Exp at F7 = 300 x49 / 100= 147 seconds

[alacant]

19 hours ago, souls33k3r said:

So what will be the exposure length in seconds when the scope is reduce and now @ F7 (1422 FL)

The same, surely. You haven't changed the aperture of the telescope, so I don't think it can collect any more or less light and so can't be any brighter or dimmer. If it fitted on the chip at F10, it will simply appear smaller at f7, but you'll need the same exposure length.

15 hours ago, catburglar said:

F7 = 300 x49 / 100= 147 seconds

But that's assuming you are keeping the focal length the same and changing the aperture. The OP isn't.

Don't tell me I still don't understand this!

Cheers.

[vlaiv]

17 minutes ago, alacant said:

The same, surely. You haven't changed the aperture of the telescope, so I don't think it can collect any more or less light and so can't be any brighter or dimmer. If it fitted on the chip at F10, it will simply appear smaller at f7, but you'll need the same exposure length.

But that's assuming you are keeping the focal length the same and changing the aperture. The OP isn't.

Don't tell me I still don't understand this!

Cheers.

As for original OP question, it turns out that who ever quoted "random" figures of going from 180s to 115s when using x0.8 reducer was right if you observe collected photon level per pixel.

If you reduce focal length by x0.8 - you increase arc second per pixel ratio by that figure (or times 1/0.8 = 1.25) - this in turns increases the surface of sky covered by single pixel to x1.5625 (square of 1.25 - since you increased each side by that factor). This in turn lowers acquisition time to reach same ADU level by factor of 1.5625 or in another words 180/1.5625 = 115.2 so 115s is (to a rounding error) correct answer (and not random at all).

What confuses you is that you need the same amount of time in both original FL and reduced FL scope (same aperture, less FL) for matching resolutions (this is important) to obtain same signal - in this case it is aperture per resolution (FL is only implicitly involved via resolution along with pixel size) - so if you match resolution with different focal lengths - by using different pixel sizes - you will have "same speed" system.

This is origin of famous F/ratio myth - photographers noted that when you have "faster" system - it accumulates light faster. Implicit in this statement is that pixel sized don't change. So everyone started regarding F/8 scopes slower than F/5 scopes. But acquisition time can be the same if they have same aperture and same resolution (thus different pixel sizes matching respective FLs). F/8 scope can even be faster than F/5 scope (again depending on aperture and resolution/pixel size).

[alacant]

1 hour ago, vlaiv said:

f you reduce focal length by x0.8 - you increase arc second

Ahhgghh! I promise to do my homework more thoroughly. Fearing hijacking the thread, would you allow me just one more shout?

If I snap m51 with my 150 f8 and DSLR, I use the same time as with my 150 f5. The main difference is that it's smaller with the latter. What should I be doing? Increasing the time at f8?

21 hours ago, souls33k3r said:

 

16 hours ago, catburglar said:

 

[vlaiv]

25 minutes ago, alacant said:

Ahhgghh! I promise to do my homework more thoroughly. Fearing hijacking the thread, would you allow me just one more shout?

If I snap m51 with my 150 f8 and DSLR, I use the same time as with my 150 f5. The main difference is that it's smaller with the latter. What should I be doing? Increasing the time at f8?

Depends what you want to achieve. If you want to achieve the same SNR per sub - increase sub time. It is almost as above calculation - duration increase should be same as surface per pixel decrease. It will not produce exactly the same SNR, but a bit lower, because more dark noise accumulates in longer exposure. In regular photography, where there is plenty of light one can ignore dark current - hence the "speed" of the lens in photography.

If you want to have final image at the same level of SNR - you can shoot more subs or go for longer subs - but in this case, you must account for read noise as well (if you go for larger number of subs) - since each sub carries one dose of read noise irrespective of sub duration.

This way you will get same SNR but at different resolutions - F/8 will show larger / more detailed image (provided that resolution was limited by sampling rate and not seeing/guiding).

Third option is to bin your F/8 image (even in software). Again this approach will not match SNR exactly due to read noise. But if you had camera with 0 read noise, and you had such F/ratios that you could match resolution by binning - then you could use same exposure time and bin subs on longer focal length and you would get the same SNR.

[ollypenrice]

23 hours ago, souls33k3r said:

Hi All,

I've been scratching my head over how to work it out in the simplest form.

I'm trying to figure out a way to calculate exposure length in seconds at different focal ratio of the same scope (for example when adding a reducer) to get the same amount of data when the F stop changes.

For example: 300s exposure @ F10 (2032 FL). So what will be the exposure length in seconds when the scope is reduce and now @ F7 (1422 FL)

I hope this make sense.

Thanks

As you're seeing from Vlaiv's answer, the 'F stop' hasn't changed because there isn't one. The term F stop comes from camera lenses with diaphragms to 'stop down' the aperture while leaving the focal length and pixel scale unaltered. A focal reducer leaves the aperture unchanged but reduces the focal length, so changing the focal ratio and the pixel scale. This is not playing with words: the two ways of changing the F ratio are not equivalent.

It's also confusing to think in terms of collecting 'the same amount of data' because you are not collecting the same data. You have a wider FOV with the reducer so you collect data with the reducer which you exclude without it. Do you want this extra data? This normally depends on the target. The best use of a focal reducer is to widen the FOV.

Olly

[Stub Mandrel]

Olly - n. Mythical creature summoned by uttering the words 'f-ratio'.

U.E.D.

[catburglar]

5 hours ago, alacant said:

But that's assuming you are keeping the focal length the same and changing the aperture. The OP isn't.

Don't tell me I still don't understand this!

Cheers.

Obviously you’re right, but in terms of SNR (which is a key determinant of the how far you can push the image during processing) the maths works the same way as for changing the aperture.

The element that we lose is image scale because the sampling rate is reduced because of the shorter FL 

[ollypenrice]

The OP won't lose any real resolution with the reducer, though, despite the reduction in image scale. The system is oversampling even with it in place. (0.55"PP unbinned, I make it.) 

The big players will be the guiding and the seeing on the night. I'd make a point of waiting for good seeing to shoot the L. It isn't needed so much for the colour. In NB imaging the experts often use the Ha as luminance as well as putting it in the chosen palette's colour channel. Since the Ha usually contains the finest structural details that would be the one to prioritize when the seeing is good.

Olly

[souls33k3r]

Apologies for the delay in replying .. fasting and holidays means i'm less online and more busy praying.

I'm going to leave this topic alone for a while and might revive it at a later stage after Ramadan.

Thank you all for taking your valuable time out to reply. Rest assured, i will revisit this thread and read all the replies up to a point where i am able to fully and properly understand.