Poisson stats: signal to noise

In summary, The apparent magnitude of a star was measured to be m=16 with a signal-to-noise ratio of 10 integrated over a minute. The uncertainty in the measurement can be found using the equation S/N=sqrt(fAt) and solving for fA. By setting K=0, the value of fA was determined to be 3.98 e-7 J/s. The uncertainty is then calculated to be 6.3 e-4. This can also be solved using error propagation by substituting dI=I/10 into the equation m + dm = -2.5log(I + dI) + K. However, this may be more complicated if RMS noise is considered.
  • #1
StephenPrivitera
363
0
A star was measured to have an apparent magnitude m=16 with S/N=10 integrated over a minute. What is the uncertainty in the measurement?
signal=flux*area*time
noise=sqrt(signal)=sqrt(fAt)
So, S/N=sqrt(fAt)
How can I find fA?
m=-2.5logfAt+K
16=-2.5log(fAt)+K
Hoping that K is arbitrary (please verify this), I choose K=0
Then 16=-2.5log(fAt)
So fA=3.98 e-7 J/s (units inconsequential)
So, uncertainty =6.3 e-4
??
HELP!
edit:
Or, I can get N=uncertainty=sqrt(S/10)=sqrtS <--- something VERY wrong here
 
Last edited:
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  • #3
I think this is an exercise in error propagation.
m=-2.5logfAt+K

You could also write m=-2.5log(I)+K
You have m, and I/dI=10. You want to find dm. (d means differential).

m + dm = -2.5log(I + dI) + K.
You could now substitute dI = I/10, and solve for m. That will work, since I will cancel.

However, I suspect they talk about RMS noise.
Which makes things a bit more complicated.
 
  • #4


Originally posted by arcnets

However, I suspect they talk about RMS noise.
Which makes things a bit more complicated.
No, actually. You're answer if perfect. We went over this today in class. It didn't make sense then, but I think it's finally making sense. I was trying to hard to find S.
 

What is the Poisson distribution?

The Poisson distribution is a probability distribution that is used to model the number of events that occur in a fixed interval of time or space, given that these events occur independently and at a constant rate. It is also known as the discrete exponential distribution.

How is the Poisson distribution used in statistics?

The Poisson distribution is used to calculate the probability of a certain number of events occurring within a given time or space interval. It is commonly used in fields such as biology, economics, and telecommunications to analyze data and make predictions.

What is the signal-to-noise ratio in Poisson statistics?

The signal-to-noise ratio in Poisson statistics refers to the ratio of the expected number of events (signal) to the expected number of random occurrences (noise). It is often used to measure the strength or reliability of a signal in relation to the background noise.

How is the signal-to-noise ratio calculated in Poisson statistics?

The signal-to-noise ratio can be calculated by dividing the mean (λ) by the square root of the mean. This is also known as the signal-to-noise ratio per unit of time. Alternatively, the signal-to-noise ratio can be calculated using the standard deviation.

What are some common applications of Poisson statistics in signal-to-noise analysis?

Poisson statistics and the signal-to-noise ratio are commonly used in fields such as astrophysics, particle physics, and medical imaging to analyze data and detect signals in the presence of noise. They are also used in quality control and reliability analysis to assess the performance of systems and processes.

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