# Poisson stats: signal to noise

#### StephenPrivitera

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:

#### Sonty

Last edited by a moderator:

#### arcnets

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.

#### StephenPrivitera

Re: Re: Poisson stats: signal to noise

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.

### The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving