Include an estimate of the theoretical polarization error

[claudiavr]

Sugiro utilizarmos a expressao do erro teorico da polarizacao do link abaixo. Ela inclui o ruido de Poisson das contagens da fonte e ceu, ruido de leitura e ganho. Essa expressao deve ser adaptada para uso em medidas do seguinte modo:

N* t_exp: valor medio das contagens somando os feixes ordinario e extraordinario por posicao da lamina
N_s* t_exp: valor medio das contagens do ceu por pixel por posicao da lamina  (sugiro usarmos o valor medio do ceu ord. e extraord.)

http://www.inpe.br/etc/docs/calculo_erro_polarizacao.pdf

[juliotux]

@claudiavr , please check if this equation is correct.

$SNR{total} = \sqrt{\sum{(\frac{Zi}{\sigma{Zi}})^2}}$ $\sigma{theor} = 100\% \cdot K \cdot \frac{1}{SNR{total}}$

In principle, I think the $Zi$ terms carry the photometry SNR and, summing $N{WP}$ terms with same SNR we get $SNR{total} = \sqrt{N_{WP}} \cdot SNR$.

[claudiavr]

The sigma_theor expression seems correct for me.

The sum expression for the SNR_total is correct, but I think the "i" parcels are not correct, if Z_i = (f_ord - f_ext)/(f_ord + f_ext), where:

f_ord is the flux of the ordinary beam (already subtracted from the sky) in the "i" image; f_ext is the flux of the extraordinary beam (already subtracted from the sky) in the "i" image.

Each parcel should be:

parcel_i = (f_ord + f_ext)/{f_ord + f_ext+ 2 npix[f_sky_ord + f_sky_ext + 2 B N_R^2 + 4(0.289* G)^2]},

where

f_sky_x is the sky counts per pixel in the "i" image in ord or ext beams.

[juliotux]

Reopening to fix the expression.