NOISE: Eq. 9 and observed standard deviation

Equation 9 (from Markus's work notes) and the observed standard deviation are compared

EQUATION 9 is: s_noise (flux) =4*.0.721* [1 + 0.00168 flux + 0.00271 flux^2]^{1/2} =[s_const^2 + s_photon^2 + s_spikes^2]^{1/2}

where flux=average(data195A(420:720,500:800,*),3) quiet region only

OBSERVED STANDARD DEVIATION are calculated for each pixel by calculating the standard deviation of the time series

s_observed(x,y)=sigma(data195A(x,y,*))

first a SIMULATION:

IDL program of the simulation

the simulation takes a data cube (200,200,22) with constant value and adds poisson noise to it.

for these data set we know sigma_noise: sigma_noise = sqrt(flux)

then the simultions calculate sigma_observed as described above.

the theoretical sigma and the observed sigma for the simulation give the following plots:

now Eq. 9 (all terms): s_noise (flux)=[s_const^2 + s_photon^2 + s_spikes^2]^{1/2}

the calculated noise is too large!

photon noise & constant term: s_noise (flux)==[s_const^2 + s_photon^2]^0.5

looks much better, still the calculated values are a little bit too large.