## Feature #90

closed### Implement bulge-to-total ratio measurement and uncertainties in SExtractor

#### Updated by Emmanuel Bertin over 8 years ago

**% Done**changed from*20*to*50*

The flux ratio for component $c$ is

$$\rho_c = \frac{f_c}{F}$$

with $F = \sum_i f_i$. Hence

$$\frac{\partial \rho_c}{\partial f_i} = \frac{\delta_{ci}\sum_i f_i - f_c}{\left( \sum_i f_i \right)^2} = \frac{\delta_{ci} - \rho_c}{F}$$

where $\delta_{ci}$ is the Kronecker delta. The square uncertainty on $\rho_c$ is therefore:

$$ \sigma^2_{\rho_c} = \sum_i \sum_j \frac{\partial \rho_c}{\partial f_i}\frac{\partial \rho_c}{\partial f_j}V_{ij} = \frac{1}{F^2}\sum_i \sum_j (\delta_{ci} - \rho_c)(\delta_{cj} - \rho_c) V_{ij} = \frac{1}{F^2}\left(\sigma^2_{f_c} + \rho^2_c \sigma^2_F - 2 \rho_c\sum_i V_{ci}\right) $$

where $\rm{V}$ is the flux covariance matrix.

#### Updated by Emmanuel Bertin over 8 years ago

**Status**changed from*New*to*Resolved***% Done**changed from*50*to*100*

Revision r312 (version 2.19.0) adds a series of new parameters:`FLUXRATIO_POINTSOURCE`

: Point-source flux-to-total ratio from fitting,`FLUXRATIOERR_POINTSOURCE`

: Uncertainty on point-source flux-to-total ratio,`FLUXRATIO_SPHEROID`

: Spheroid flux-to-total ratio from fitting,`FLUXRATIOERR_SPHEROID`

: Uncertainty on spheroid flux-to-total ratio,`FLUXRATIO_DISK`

: Disk flux-to-total ratio from fitting, and`FLUXRATIOERR_DISK`

: Uncertainty on disk flux-to-total ratio.

#### Updated by Emmanuel Bertin over 8 years ago

**Status**changed from*Resolved*to*Closed*