# Signal to noise ratio/CCD saturation problem

1. Nov 3, 2009

### s_gunn

1. The problem statement, all variables and given/known data

A 4m telescope has a 16bit controllr with a gain of 1 and must detect faint stars(M>15) without saturating the bright stars(M=8-10).

(i) What is the max no of photo-electrons that can be registered before saturating the CCD?

(ii) The zero point of the system is 16.5mag, what is the longest exposure of a mag 8 star without saturation? (all counts fall on 1 pixel)

(iii) The CCD has read noise of 4 and no dark current. If the SNR is 5 and the background count is 0.1 per second, what is the magnitude of the faintest star that can be detected?

(iv) If the controller is updated to 22bit, what exposure can be used before saturation?

(v) What mag will be the faintest in this case?

2. Relevant equations

(ii) $$m_{zp}-m_{std}=-2.5log(\frac{1 count/sec}{f_{std}})$$

(iii) $$SNR=\frac{Signal}{\sqrt{signal+Background+Dark+Read^{2}}}$$

3. The attempt at a solution

(i) total photo electrons = 2^16 = 65536

(ii) (using equation (ii)) 26.09sec

(iii) (using Equation (iii)) m=16.108

(iv) (using equation (ii)) 1669.71sec

(v) (using equation (iii)) m=20.6

I just wanted to check if I've gone about this the right way if anyone would like something to work through!!