AstrOmatic software » SExtractor

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.

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.