As of ETC version 6.0, the sky background radiance and transmission model is based on the Advanced Cerro Paranal Sky Model.
The web application SkyCalc provides an interface to play with variable sky model parameters independent of specific instruments.
As the sky is an extended source, one has to take in count also of the angle where the plate scale is expressed in arcseconds and depends from the geometry of the actual instrument and corresponds to the effective number of spatial pixels over which the signal is integrated (see section 2) and the slit width is a parameter directly set from the user on the ETC's input interface.