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# focal ratio

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### #1 zoltrix

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Posted 07 May 2021 - 04:25 PM

hello

it is well known that in astrophotograpy of deep sky,focal ratio plays a key role
the lower the better
Take a newtonian 200/1000 f5 and a sct 8'' F10
same exposure time
the scopes collect the same amount of photons but the sct spread the image over a larger area of the sensor, thus each pixel gets a lower number of photons from the
target
What about the S/N ?
Assume it is the same in both cases
You could make a linear stretching of the Sct image to obtain the same result as the newtonian even with higher resolution
is it correct ?

### #2 BQ Octantis

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Posted 07 May 2021 - 05:10 PM

If all apertures are equal, the S/N for a fixed integration time and pixel size goes as the inverse square of the focal ratio, i.e., (D/f )2. This is because the captured photon flux goes as the area of the aperture, so ~D 2 . And that flux gets spread across the two dimensions of an image (or pixel) with scaling, so 1/f  2.  So an f/5 aperture gives 4Ã— the SNR of an f/10 aperture.

If by stretching, you mean histogram stretching, you can indeed make the images have roughly the same brightness and contrast through histogram manipulation. But S/N will follow the inverse square of the focal ratio.

If by linear stretching, you mean scaling the image, the S/N goes as the square of the scaling. As you already noted, spreading the photons across more pixels yields more noise. But downscaling the image is akin to binningâ€”creating larger pixels that collect more of the flux.

So for two images of equivalent integration time from the same sensor on two 8-in apertures, one at f/5 and one at f/10â€”down scaling the f/10 image by 50% would yield an image with roughly the same SNR as that of the f/5.

But if you want the SNR of the full scale f/10 image to be the same as the full scale f/5 image, you have to collect photons for 4Ã— as long.

For spatial sampling, using a 2Ã— Barlow on the f/5 Newt would turn it into an f/10 aperture. Then the image scale, FOV, and S/N between the two scopes would be the same.

But not all apertures are equalâ€¦

BQ

Edited by BQ Octantis, 07 May 2021 - 05:46 PM.

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### #3 photoracer18

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Posted 07 May 2021 - 05:15 PM

You are working on some misconceptions. Focal ratio determines how long the exposure needs to be to get the same amount of light, just like a camera lens. So since the 8" F5 Newt has 1/2 the f-ratio as the SCT its exposure only needs to be 1/4 as long (102 vs 52 so 100 vs. 25 = 1/4).  So a 2 minute exposure in the SCT equals a 30 second exposure in the Newt. However actual AP is not as simple as regular photography although the science is the same. AP deals a lot more with noise and other factors. All the size of the sensor tells you is the FOV covered by that scope combo. And you often want to adjust the size of your FOV to make a given object fit better in your sensor coverage (or crop).

### #4 zoltrix

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Posted 08 May 2021 - 02:42 AM

it is what I said
with the newtonian the pixels of the sensors get 4 times the number of photons of the signal (S) in the same period of time
What about the number of photons per pixel coming from the polluted sky i.e the noise (N)?
it is also 4 times higher ?
If so,the image of the sct 8'' is larger and darker but with the same signal to noise ratio (S/N)
You can therefore apply to the image a linear stretching, via software, to obtain the same results with even higher resolution

### #5 BQ Octantis

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Posted 08 May 2021 - 03:07 AM

it is what I said SORT OF
with the newtonian the pixels of the sensors get 4 times the number of photons of the signal (S) in the same period of time YES
What about the number of photons per pixel coming from the polluted sky i.e the noise (N)? LIGHT POLLUTION IS SIGNAL, NOT NOISE
it is also 4 times higher ? YES
If so,the image of the sct 8'' is larger and darker but with the same signal to noise ratio (S/N) NO
You can therefore apply to the image a linear stretching, via software, to obtain the same results with even higher resolution DEFINITELY NOT

Your interpretation is only relevant to sensor noise. But light pollution is signal, not noise. The statistics of the target signal and the light pollution come into playâ€”particularly shot noise. With a slower aperture, the shot noise is worse on both the target signal and the light pollution signal. While the signal-to-signal ratio should be the same, regardless of aperture, the shot noise in each signal will depend on the flux from each (target + aperture) and the integration time. So the resultant S/N will not be the same at all between the apertures.

I recommend you pick up Charles Bracken's Deep Sky Imaging Primer. He goes through the specifics of read noise, bias noise, thermal noise, target signal noise, and light pollution signal noiseâ€”all at the pixel level. And he has plenty of sample problems to work through to help you noodle through the specifics.

You keep using the term resolution. I am purposely using the term scale to refer to the changes in flux caused by changes in spatial sampling and image scaling. Spatial sampling is just the angle subtended by each sensor pixel. It is changed by changing the effective focal length of the setup (by adding a Barlow or focal reducer to the optical train) or by using larger or smaller pixels (or binning). It can be synthetically changed in stacking space with drizzle (sub-pixel alignment and interpolation from dithering). But in image space, it is the image scale that is changed with with bilinear or bicubic interpolation.

Resolution is the detail limit of the aperture caused by the point spread and edge spread functions of the circular aperture. It has nothing to do with noise. While undersampling or oversampling can change the detectable details in the image, it is the aperture alone that sets the image resolution. Upscaling an image with bilinear or bicubic interpolation may fool the eye, but it cannot produce detail that was never sampled. Only dithering or a Barlow can do this.

BQ

Edited by BQ Octantis, 08 May 2021 - 04:56 AM.

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### #6 zoltrix

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Posted 08 May 2021 - 01:22 PM

so , if I understood well

you can distinguish:

a) photons from the target (ex galaxy ), the signal
b) photons from the sky which I called noise but it is also a signal

however also the "Shot noise" must be taken into account which can prevail over the above signals
the shot noise depends upon the flux of the photons per pixel
the higher the flux the lower the shot noise the higher the S/N, assuming the same exposure time

Edited by zoltrix, 08 May 2021 - 01:22 PM.

### #7 ks__observer

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Posted 08 May 2021 - 02:18 PM

you can distinguish:

a) photons from the target (ex galaxy ), the signal
b) photons from the sky which I called noise but it is also a signal

No.

All you have is a pixel value -- the computer reports a number.

You have no idea how many photons are sky versus target.

Noise = sqrt(photons)

More photons = more noise.

But signal grows linearly, and noise by a sqrt.

So more photons = higher SNR

Edited by ks__observer, 08 May 2021 - 02:18 PM.

### #8 BQ Octantis

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Posted 08 May 2021 - 05:35 PM

On a per-pixel basis, the sky glow will just raise the average value of the pixel. The flux from light pollution is quite high, so its shot noise should average out pretty quickly. On an image basis, without clouds the complexity of the sky glow should be very low frequency. I find that for narrow fields of view, a simple linear gradient makes for a good approximation. Sometimes monochrome works. Sometimes it's per channel. As the FOV gets wider, the glow becomes more radial. Eventually, it becomes blobular with no reasonable shape to approximate it.

What we have to do for AP is exploit the tiniest of differences between adjacent pixels to form the structure of the target. The shot noise results in differencesâ€”holes in the dataâ€”that introduce structure that isn't there. That is what noise is. But after a while (how long depends on target brightness, focal ratio, sensor pixel pitch, etc.), it gets outcompeted by residual sensor noiseâ€”thermal noise, hot pixels, amp glow, etc. So we dither to average that out. And for wide open swaths of nothing, we can just use some simple noise reduction.

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### #9 ks__observer

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Posted 08 May 2021 - 06:24 PM

We dither to shmear out fixed pattern noise.

### #10 BQ Octantis

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Posted 08 May 2021 - 06:31 PM

I dither to eliminate walking noise.

### #11 ks__observer

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Posted 08 May 2021 - 06:32 PM

That is fixed pattern noise.

### #12 BQ Octantis

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Posted 08 May 2021 - 06:57 PM

Nope. To split hairs, my walking noise is from residual dark current noise due to the temperature of my darks not matching the temperature of my lights on my stock Canon DSLR. This gets walked in the RA direction from shooting unguided. And my randomly flickering hot pixels leave dotted paths instead of streaks. With dithering, Sigma-reject stacking eliminates both.

I would classify my Canon banding as my fixed pattern noise. Dithering doesn't do anything for it. I use Horizontal Banding Noise Reduction in AstronomyTools v1.6 for that.

### #13 Prudentis

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Posted 08 May 2021 - 09:30 PM

it is well known that in astrophotograpy of deep sky, focal ratio plays a key role
the lower the better

Which is one of THE biggest misconceptions that still exists in this hobby.

Almost all aspects of what f-ratio is and what it does, are brought in from daylight photography and keep being misinterpreted and brought into astrophotography. This has gone so far, that all telescope producers, shops, journals and blogs keep repeating it like a mantra. "f/ratio means shorter exposures" as if you could magically increase your image quality by going faster and faster without concerning yourself with aperture or sensor size. This really annoys me.

Take a newtonian 200/1000 f5 and a sct 8'' F10
same exposure time
the scopes collect the same amount of photons but the sct spread the image over a larger area of the sensor, thus each pixel gets a lower number of photons

Correct. This also means, that paired with the SCT the sensor will resolve fainter details inside your object of interest. Fewer pixels for a given object = worse resolution. In theory, only aperture determines the resolution. In real life, it's the aperture and the number of pixels on the sensor for a given image circle.

What about the S/N Assume it is the same in both cases?

Shot noise is the key here (as described by BQ Octantis) This is the ONLY benefit of using faster systems. You increase S/N by sacrificing spatial sampling.

It's up to you, which one you prefer but keep in mind: S/N can be increased by increasing total exposure time, spatial sampling cannot be improved by ANY means other than increasing aperture and changing the pixel size. So for me this is a clear cut case. I do not buy an expensive 10" scope to then not use it's aperture optimally and downsampling it's potential resolution.

Of course, if reduce your scope just to get a wider FOV, because you want to capture a bigger object, this is a perfectly sound approach. Going faster while capturing a small galaxy, only because you want to cut down on your exposure time, is a big waste of the scope's potential.

Edited by Prudentis, 09 May 2021 - 01:03 PM.

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### #14 TxStars

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Posted 09 May 2021 - 01:22 AM

Don't forget you also have to deal with your sky conditions.

If your seeing averages 3--4" then a long focal length scope may not be the best thing for you.

But a 14" f/2 will shove some photons into that imaging chip real good..

Edited by TxStars, 09 May 2021 - 01:24 AM.

### #15 ks__observer

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Posted 09 May 2021 - 04:56 AM

Don't forget you also have to deal with your sky conditions.

If your seeing averages 3--4" then a long focal length scope may not be the best thing for you.

You can still get great pics at 4 arc sec seeing.

You won't get as much detail as 2 arc sec, but you can still take great pictures.

You can bin in post processing to recover SNR from oversampling.

Edited by ks__observer, 09 May 2021 - 04:57 AM.

### #16 zoltrix

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Posted 09 May 2021 - 06:09 AM

No.
All you have is a pixel value -- the computer reports a number.
You have no idea how many photons are sky versus target.
Noise = sqrt(photons)
More photons = more noise.
But signal grows linearly, and noise by a sqrt.
So more photons = higher SNR

ok I did not mean that you (or the sensor) can somehow distiguish the two type of photons
I meant the the total number of photons is the sum of the photons coming from the target and the ones from the sky
however

noise = sqrt(photons)

I assume that for photons you mean the total number regardless of the source
if so a bright target under a dark sky could generate the same noise as a faint target under and heavily polluted sky having the same number of photons ?

### #17 zoltrix

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Posted 09 May 2021 - 06:36 AM

Shot noise is the key here (as described by BQ Octantis) This is the ONLY benefit of using faster systems. You increase S/N by sacrificing resolution.

this is actually what I wanted to know from my first post, the shot noise being confusing for me
I try to explain myself
the lower the focal ratio the higher the flux i.e the number of photons per pixel per second
However even though you can not distinguish the photons coming from the target and the ones from the polluted sky, their proportion should not depend upon the intensity of the flux
Why should you get an higher S/N, all other things being equal ?

besides that :

a) what about the S/N with one only exposure of 60 minutes and 60 stacked frames of 1 minute ?, same tele of course

b) what about the S/N with same focal ratio and same exposure time but different focal lenght / aperture ?

### #18 Prudentis

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Posted 09 May 2021 - 09:12 AM

First let me direct you to Robin Glover's talk, since it addresses many of those questions and adds very good context from which you can derive other things you may be interested in. You probably know it, but I watched it ten times already and it is one of the best references on shot exposures so here it goes again: https://www.youtube....h?v=3RH93UvP358

this is actually what I wanted to know from my first post, the shot noise being confusing for me
I try to explain myself
the lower the focal ratio the higher the flux i.e the number of photons per pixel per second
However even though you can not distinguish the photons coming from the target and the ones from the polluted sky, their proportion should not depend upon the intensity of the flux
Why should you get an higher S/N, all other things being equal ?

I have to reiterate some of what wrote yesterday. It was 4:00 AM here and I didn't answer some things correctly (and vented my frustration a bit to much). I didn't mean light poluton but rather shot noise (photon distribution). That is object noise and skyglow noise. (not skyglow itself)

So let's start again and to split the noise types. For this particular discussion we are interested in per/pixel noise changing when more photons hit one pixel. Aperture stays the same, so the total number of incoming photons stays the same and you have the same sensor, so here also, the sensor's own noise will be the same for a given period of time.

What we should look at first is sensor noise and then "sky noise" and determine, how they change with f/ratio.

We have

EDIT: I added point 8, since while it is covered in 6. I think this wasn't clear enough.

1. Hot- and cold pixels
2. Cosmic Rays
3. Bias
5. Thermal noise.
6. Shot noise (photon noise)
7. Sky glow
8. Sky glow noise

Let's tackle them one by one and try to determine, how they affect our pixels with changing only the area, that the sensor covers (changing f/ratio)

1. Dead pixels, irrelevant for this discussion -> irrelevant
2. very limited and not really interesting since they will have a very relevant difference in brightness and can be removed in post-processing effectively as outliers -> irrelevant
3. can be removed very efficiently by bias frames or dark frames - i consider bias irrelevant for this discussion -> irrelevant
4. since read noise it is independent of sub length, it is relevant in this context. The more signal you get in a specific pixel, the lower the read noise's contribution. So faster systems will have a better S/N here due to more signal swamping the read noise faster. This is however relatively minor in modern sensors. A sony IMX 571 for example will have a e-rems of under 1.5 at 100 gain. Still, faster system = beter S/N here => f/5 > f/10 - minor effect
5. obviously temperature based and independent of incoming signal. It builds up linearly, so more signal per pixel, will swamp it faster. This is very relevant for DSLRs and practically negligable in good, cooled astrocameras with low thermal noise cooled to about -10 or -15Â°C, still faster systems will swamp it faster. -> f/5 > f/10 but VERY minor effect (see Robin's talk)
6. now here we arrive at the really interesting noise types and this one is, THE noise type, that we will reduce best by speeding up the system. HOWEVER, this one is also combated easiest with exposure length. -> f/5 > f/10 - most relevant effect
7. This is not really noise but an unwanted type of signal. This is, I think, what you were mainly interested in and this is NOT the noise I was talking about yesterday. This is not "shot noise". You will NOT be able to reduce sky glow by going faster. On the contrary, you will increase sky glow photons by going faster. Both are signal and both will build up proportionally/linear to each other. Increasing exposure or increasing per/pixel signal (faster system) will NOT change the aspect of the two. So if this was your only question, this is a clear no. You CANNOT combat light pollution with faster systems -> irrelevant
8. however the light pollution noise will also, like every other type of shot noise, decrease in relation to the combined signal of SObj and SLp. This is pretty much the same as 6. So along with 6. this noise will be combated with faster systems. -> faster=better

So we have three types of noise, that will benefit from a faster system. The first two are pretty minor and the third one (shot noise) is what I think most astrophotographers think of, when they state "faster system = better". HOWEVER! By going faster you significantly reduce the benefit of a big aperture, that is resolution, by downsampling your object and reducing the spatial sampling. For me this is almost never a good idea, since you can address S/N with total exposure but cannot fix lower sampling by anything other than aperture correctly matched to your sensor. And by best I mean, I would always build the system with the best possible seeing conditions and guiding in mind. The best possible seeing conditions are about 0.4'' and more realistically in normal altitudes somewhere below 1''. I want this to be my reference number and I alwas go below it. I will not be able to fully profit from those on most nights and never reach 0.4 in my garden, but i want to able to get near the maximum on perfect nights. So I build my systems for oversampling up to about 0.5'' in mind since this is my best guiding error. Yes, my stars will be blown out a bit, but this is easiliy corrected in postprocessing. Underslampling can also be addressed (drizzle) but this is added data, not "real" signal. I prefer the other way of adding more signal and then removing imperfections.

For me the only instances where going faster on a big aperture are a good idea is while shooting nebulae, big glaxies (M31 / M33) and globular clusters. This distincion is hoverer almost never made and this is why I battle this f/ratio misconception so vehemently.

Now to your last two poits:

a) what about the S/N with one only exposure of 60 minutes and 60 stacked frames of 1 minute ?, same tele of course

b) what about the S/N with same focal ratio and same exposure time but different focal lenght / aperture ?

a) with a perfect sensor, this would be 100% equal. The differences come with sensor imperfections and noise. EMCCDs actually come pretty close to this, but they are yet unreachable price-wise for hobby astrophotographers. Of course the real difference for us is tracking/guiding and satellite trails (\$&%\$ you Elon)

The practical limits are, that realistically, in very short exposures, you will not get a significant difference between noise and signal. If during the stacking procedure, the values from neighbouring pixels are too similar, the procedure will not provide adequate results. As you probably know, the algorithms work with average (mean, median) pixel values and remove outliers and the rest are averaged. So if you have very low differences in the pixels, you will either cut off too many relevant pixels or leave in too many "bad" pixels. The second thing is read noise (everything coming from the sensor itself) that builds up slower than shot noise and signal, but here also you need some significant differences between the values, or the algorithms will not be able to distinguish between noise and signal, so you need long enough exposures to swamp the noise in each sub. Only then stacking can do its job.

Even in long exposures, you will have faint detail, that will stay "behind" the noise barrier. There is a signal to sky glow threshold, over which signal "will not pass". So objects, that hide behind the skyglow barrier, cannot be revealed with longer exposures. They have a SNR of < 1. Exposing them longer, will actually decrease their SNR. All othe objects, with SNR > 1 will always benefit from longer exposures or additional stacking. There is a pretty simple method to determine the optimal exposure for your side and it takes into consideration, read noise, skyglow and the noise threshhold you are ready to accept. It's this equasion from Robin's talk: exposure time = C*RÂ²/LPelectronrate where C is a number derived from the % of accepted noise. 1% being 50 2% being 25 and 5% being 10. I shoot with a C of 50 and in my conditions and with my current equipment this means exposure times of about 120s. If my guiding was wors, I'd go for 25 or 10 and accordingly exposures of 60s or 24s.

Of course, as you can deduce, the darker the site and the lower the sky glow, the longer the exposures that actually make sense. You often hear something like "you can get away with shorter exposures in high bortle sites". What this really means is, that in higher Bortle, you rech a point where you don't benefit from longer exposueres and your per-shot SNR reaches the threshold of diminishing returns (C-number). Of course you will get much fainter signals in dark sites (lower P-number) so there is really no substitution for dark skies. I hope this is somewhat clear. I think Robin explains it much better, than I did here

b) I think you can deduce this from my previous responses. Since with f/ratio is staying the same you increase both aperture and FL at the same time, you basically keep the same S/N. The relevant things are: you gain potential resolution (bigger aperture), magnification (higher FL) and move more in the direction of oversampling, which might be good or bad.

Edited by Prudentis, 09 May 2021 - 01:19 PM.

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### #19 ks__observer

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Posted 09 May 2021 - 09:28 AM

if so a bright target under a dark sky could generate the same noise as a faint target under and heavily polluted sky having the same number of photons ?

Yes re noise.

But SNR higher.

### #20 Prudentis

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Posted 09 May 2021 - 12:11 PM

if so a bright target under a dark sky could generate the same noise as a faint target under and heavily polluted sky having the same number of photons ?

Yes, objects will have a better S/N ratio if the signal increases, regardless of the signal source. (photons from the DSO or photons from light pollution)

However this doesn't help us in any way, because faint objects are the ones we are interested in, and in light polluted skies, they will get swamped by light pollution. It doesn't matter, if your S/N is good in a patch of sky, where you would see faint structures, that get swamped by sky glow completely.

You just can't get information out of them, regardless of exposure time since they are burried under a layer of light pollution noise, that you can't possibly remove. There is a point, where the skyfog signal is so strong, that it's noise added to other noice sources completely destroys your object signal => SNRobj = 1.

### #21 zoltrix

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Posted 09 May 2021 - 01:13 PM

]

• This is not really noise but an unwanted type of signal. This is, I think, what you were mainly interested in and this is NOT the noise I was talking about yesterday. This is not "shot noise". You will NOT be able to reduce the impact of sky glow by going faster. Both are signal and both will build up proportionally/linear to each other. Increasing exposure or increasing per/pixel signal (faster system) will NOT change the aspect of the two. So if this was your only question, this is a clear no. You CANNOT combat light pollution with faster systems -> irrelevant
• The light pollution noise will also, like every other type of shot noise, decrease in relation to the combined signal of SObj and SLp. This is pretty much the same as 6. So along with 6. this noise will be combated with faster systems. HOWEVER since especially in darker areas of the sky, the skyglow and it's noise can be so overwhealming that it swamps the SObj above a certain point, there is no real benefit of going faser. (see below)

first of all thanks a lot for your time, I really appreciated it

Probably I misunderstood some things
my understanding was :

a) a pixel receives photons either from the target (signal) and from the skyglow (unwanted signal)
while the signal grows linearly with time the unwanted signal grows with sqrt(time), the unwanted signal being random
Thus by increasing the exposure time and/or by stacking several frames you improve the ratio signal/unwanted signal
on the contrary a fast scope does not produce better results, with the same exposure time, the proportion between signal and unwanted signal being the same

b) Shot noise is due to the fluctuation of the emission of photons
in day time it is not important since you get bilion photons per second but in night time you can receive from the target and from the skay just, for example, 100 photons per seconds on average but
the sequence might be, for example : 120-80-100-110-70 and so on
In this condition the sensor does not work well
By halving the focal ratio you multiply by 4 the flux i.e 400 pixel per second on average buy you smooth also the fluctuation
the benefit is an higher S/N apart of course the other sources of noise

Edited by zoltrix, 09 May 2021 - 01:15 PM.

### #22 ks__observer

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Posted 09 May 2021 - 01:19 PM

It is not exactly that the unwanted signal grows by the sqt, it is that the "noise" grows by sqrt.

T=target photons

S=sky photons

SNR =signal/noise = T/sqrt(T+S)

### #23 Prudentis

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Posted 09 May 2021 - 01:57 PM

first of all thanks a lot for your time, I really appreciated it

You are most welcome   While typing such long responses, I always look up the info I already have to confirm, what I think I know

I guess on the Dunning-Kruger scale I am at the point, where actual knowledge intersects the perceived knowledge for the second time. And I am very aware of the fact, that I have yet very much to learn.

a) a pixel receives photons either from the target (signal) and from the skyglow (unwanted signal)
while the signal grows linearly with time the unwanted signal grows with sqrt(time), the unwanted signal being random

As ks_observer just wrote, the skyglow signal is signal, so it increases linearly, as does the Sobj. The Noise introduced by the skyglow grows by sqrt.

Thus by increasing the exposure time and/or by stacking several frames you improve the ratio signal/unwanted signal

both signals increase linearly, as stated, so the skyglow signal just moves your whole histogram more to the right, so to say. It doesn't add anything, just moves your black-point to the right. By stacking and longer exposures, you improve the SNR due to noise only growing by sqrt.

Think of skyglow (minus skyglow noise) as your new black so it is basically neutral. The bad part about it, is the additional noise. It will swamp your object signal so badly, that it gets under an SNR of 1 and may never be recovered regardless of exposure lenght or stacking.

on the contrary a fast scope does not produce better results, with the same exposure time, the proportion between signal and unwanted signal being the same

Sorry, I see I still didn't make that clear  . You will get better SNR with a faster scope. It comes however at the cost of spatial sampling. So the problem here is, that you can basically achieve the same or very similar results by just downsampling your finished image. Stan Moore has a great article about this: http://www.stanmoore...gFratioMyth.htm

So in short: if you are only interested in a small galaxy, like M106, M101, etc, in the middle of your frame, going faster doesn't really achieve anything useful for you even though the SNR gets better, you use what you are really interested in, details in the object of interest.

The slower scope will produce a better result with long enough integration time, since with better spatial sampling, you can get more details. You basically use your big aperture to the fullest whereas with going faster, you decrease saptial sampling. And this once lost, can never be recovered through any means. On the slower system, you can always add more integration time, even after you have processed the picture. You can always go back to the same object and add more integration time. Going fast on small galaxies is for lazy people who want instant results and for posting shots on instagram with its low resolution pictures. If you want a wallpaper out of your astrophotos, you have to use the aperture to its fullest, meaning filling the sensor optimally, up to the best possible spatial samplig taking your pixel size, seeing and guiding into consideration. Let's say you can reach a guiding of 1'' and build your rig for below 1'' sampling. On a bad night, you will haev a seeing of 2'' and not reach the full potential but on a good night, where the sseing is below 1'' you will get the best possible image, that this setup can get.

Now if you add a 0.5 reducer and thus speed up the system 2x, you will only get 2'' sampling, which will really hurt the end result. You could basically print a poster, that is twice the size with the same detail, as if you shoot with the faster system. You will however have to expose the target longer, to get the best possible result SNR wise.

If you are interested in a wide field nebula or a big galaxy or a sensor filling globular cluster, going faster may actually be a very good idea.

b) Shot noise is due to the fluctuation of the emission of photons
in day time it is not important since you get bilion photons per second but in night time you can receive from the target and from the skay just, for example, 100 photons per seconds on average but
the sequence might be, for example : 120-80-100-110-70 and so on
In this condition the sensor does not work well
By halving the focal ratio you multiply by 4 the flux i.e 400 pixel per second on average buy you smooth also the fluctuation
the benefit is an higher S/N apart of course the other sources of noise

Yes, this is exactly how this works. (abstracted of course  ) Have you watched Robn's talk. I think he clarifies this much much better than I can.

The fluactuation will not be as much as 30% like in your example. I think it's more like 5%. The higher the signal, the lower the fluctuation percent wise, of course and vice versa. It is a stochastic distribution so its probability to hit 100 per pixel should look like a bell curve. Most pixels will be very near 100 with fewer and fewer outliers diverging more %-wise.

Edited by Prudentis, 09 May 2021 - 02:00 PM.

### #24 bobzeq25

bobzeq25

ISS

• Posts: 24,653
• Joined: 27 Oct 2014

Posted 14 May 2021 - 11:43 PM

What all the above overlooks.

You can greatly reduce the fixed component of skynoise with gradient reduction in processing.

So what remains is mostly the random component which increases as the square root.  While signal increases linearly.

The bottom line is that lower F ratio operates in similar fashion to total imaging time.   Just as more total imaging time is better, faster optics are better in light pollution.  They reduce total imaging time, for the same snr.  Lowering the F ratio one F stop is equivalent to twice the total imaging time.

I'm in Bortle 7, can do much better in less time with my C8 RASA, F2, than I can with my slower scopes.  Two examples below.  Both used one shot color cameras.  Mono plus filters would be even better, but hard to implement with a RASA (it can be done).

Broadband target, no (not so) magic light pollution filter used.  Look at the dim dust, in Bortle 7, with only 1.8 hours total imaging time.

Emission nebula, duoband pseudo narrowband filter.  This is a dim target, and that's all of 2.0 hours total imaging time.

Better versions than the crummy (required) CN jpgs, here, with acquisition details.

https://www.astrobin.com/t5173s/

https://www.astrobin.com/kis712/

There are two focal ratio "myths".  The first is that it's everything.  The second is that it's unimportant.  Among other things, reducers are very popular for good reasons.  There is some improvement in snr with the higher numerical image scale with faster  scopes, but it's _not_ the only thing that's going on.

This is a more complicated business than many think.  Theoretical analyses on CN all too often simply reflect what factors are left in, and what are omitted.  Why I post actual examples.  The factors are in there.  <smile>  I spent substantial effort on good gradient reduction.

Edited by bobzeq25, 14 May 2021 - 11:58 PM.

### #25 Huangdi

Huangdi

Apollo

• Posts: 1,083
• Joined: 24 Jul 2019

Posted 15 May 2021 - 06:36 AM

Bottom line is a faster setup will almost always make a better image easier to acquire.

It's easy to get fed up with math, but when a single 5min H-Alpha exposure at F2 looks cleaner and more detailed than many finished F6 refractor images I see online, that's when I don't care about math anymore ðŸ¤£
• bobzeq25 likes this

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