<p>Here's a simple start, and I suggest you must include your sensor's noise -- not flat-fielding, but just the accumulated readout noise in a pixel.</p>
<p>You can use the Poisson SNR rule for the incoming light, so optical noise <span class="math-container">$N_o = \sqrt{S_o}$</span>.  Just add the electronics noise, again as a simple model, <span class="math-container">$N_e = C_(readout) + k\tau$</span> where <span class="math-container">$\tau$</span> is the integration time and <span class="math-container">$k$</span> represents leakage current into the pixel well.   <span class="math-container">$S_o$</span> also equals some constant times <span class="math-container">$\tau$</span> , so just combine the two noise terms in an RSS manner, i.e. <span class="math-container">$ N_{tot} = \sqrt{N_o^2 + N_e^2}$</span> .</p>

CC BY-SA 4.0
2020-10-06T22:48:08.140Z
Why are you saying "electronic noise" depends on exposure time? Readout noise is independent of exposure time.
ProfRob
CC BY-SA 4.0
2020-10-07T12:25:14.373Z
@RobJeffries  The noise associated with the readout switches is independent, but the leakage current filling the pixel well **is** time-dependent,   I'll add that.
Carl Witthoft
CC BY-SA 4.0
2020-10-07T13:13:31.643Z
The conventional term is "dark current". It is usually negligible compared to (e.g.) sky noise - which is also proportional to the square root of time.
ProfRob
CC BY-SA 4.0
2020-10-06T18:16:48.827Z
2020-10-07T12:26:13.010Z
2020-10-07T12:26:13.010Z
Carl Witthoft
<p>I need help on how to estimate an exposure time for a desirable <a href="https://en.wikipedia.org/wiki/Signal-to-noise_ratio" rel="nofollow noreferrer">signal to noise ratio (SNR)</a>. For example, given the magnitude and a desired SNR of a star we want to achieve, how long should the exposure time be? We may assume that the noise is only due to counting statistics, and ignore dark and flat noise. Any useful function to make this estimate?</p>

CC BY-SA 4.0
2020-10-05T19:19:12.817Z
This would depend a great deal on the hardware and viewing conditions and weather conditions.  You really need to experiment with your equipment to develop a feel for it's behavior.  It is truly amazing what a difference good image processing techniques make (a great example in [this video about capturing Martian volcanoes on YouTube](https://www.youtube.com/watch?v=a8dPnkN3rwc) ).
StephenG - Help Ukraine
CC BY-SA 4.0
2020-10-05T21:07:26.390Z
I understand, that's why I asked for an equation
user35427
CC BY-SA 4.0
2020-10-06T10:50:47.000Z
It's a good question, but I think you need to add some more information about what kinds of information are given. Should it start with photon flux at the sensor, or a star's magnitude and a telescope's point spread function, or is it an extended object like a planet?
uhoh
CC BY-SA 4.0
2020-10-08T07:21:56.303Z
Still no information about what kind of observations are being done. Is this optical imaging of a point source?
ProfRob
<observational-astronomy><flux>
Determining needed exposure time given SNR
user35427
# Determining needed exposure time given SNR

(Asked by: username_0 on 2020-10-05)

I need help on how to estimate an exposure time for a desirable [signal to noise ratio (SNR)](https://en.wikipedia.org/wiki/Signal-to-noise_ratio). For example, given the magnitude and a desired SNR of a star we want to achieve, how long should the exposure time be? We may assume that the noise is only due to counting statistics, and ignore dark and flat noise. Any useful function to make this estimate?

**Tags:** observational-astronomy, flux

> **Comments:**
> **username_1**: This would depend a great deal on the hardware and viewing conditions and weather conditions.  You really need to experiment with your equipment to develop a feel for it's behavior.  It is truly amazing what a difference good image processing techniques make (a great example in [this video about capturing Martian volcanoes on YouTube](https://www.youtube.com/watch?v=a8dPnkN3rwc) ).  
> **username_0**: I understand, that's why I asked for an equation  
> **username_2**: It's a good question, but I think you need to add some more information about what kinds of information are given. Should it start with photon flux at the sensor, or a star's magnitude and a telescope's point spread function, or is it an extended object like a planet?  
> **username_3**: Still no information about what kind of observations are being done. Is this optical imaging of a point source?  

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## 1 answers

### Answer by username_4 on 2020-10-06. Score: 0 | Accepted answer

Here's a simple start, and I suggest you must include your sensor's noise -- not flat-fielding, but just the accumulated readout noise in a pixel.

You can use the Poisson SNR rule for the incoming light, so optical noise $N\_o = \sqrt{S\_o}$. Just add the electronics noise, again as a simple model, $N\_e = C\_(readout) + k\tau$ where $\tau$ is the integration time and $k$ represents leakage current into the pixel well. $S\_o$ also equals some constant times $\tau$ , so just combine the two noise terms in an RSS manner, i.e. $ N\_{tot} = \sqrt{N\_o^2 + N\_e^2}$ .

> **Comments:**
> **username_3**: Why are you saying "electronic noise" depends on exposure time? Readout noise is independent of exposure time.  
> **username_4**: @RobJeffries  The noise associated with the readout switches is independent, but the leakage current filling the pixel well **is** time-dependent,   I'll add that.  
> **username_3**: The conventional term is "dark current". It is usually negligible compared to (e.g.) sky noise - which is also proportional to the square root of time.  

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