The noise is supposedly Poissonian (in electrons, not in counts).
Hence it is easier to transform counts to electrons to compute the sigma of the noise.
Naming convention:
Ip means image in pixel space, i.e. where the values are in counts;
Ie instead is the corresponding image where values are in electrons.
Remember simple formula:
if y = k * x then var(y) = k2 * var(x)
Single image I:
Poisson => var(Ie) = Ie = g * Ip
Hence:
Ip = Ie / g
and
var(Ip) = var(Ie) / g2 = Ip / g
Eff. Gain := g
Coadded images T = sum( Ii ):
Poisson => var(Te) = Te = sum( Iei ) = g * sum( Ipi ) = g * Tp
hence: =>
Tp = Te / g
var(Tp) = var(Te) / g2 = Te / g2 = Tp / g
Eff. Gain := g
Averaged image M = sum( Ii ) / N :
Here though the poissonian statistics cannot be applied to sum( Iei ) / N !
In fact, the poissonian statistics applies to the total number of electrons.
Poisson => var(Te) = Te = sum( Iei ) = g * sum( Ipi ) = g * N * Mp
T = N * M
Poisson => var(Te) = Te
Hence
var(N * Me) = N * Me
N2 * var(Me) = N * Me
(1) var(Me) = Me / N
and since
(2) Me = Mp * g
(3) var(Me) = var(Mp) * g2
given 1,2,3:
Me / N = Mp * g / N = var(Mp) * g2
var(Mp) = Mp / ( N * g )
Eff. Gain := N * g
|
(Subscribe to new public observations)
