  Quantitative predictions from synthetic radiation diagnostics often have to
consider all accelerated particles. For particle-in-cell (PIC) codes, this not
only means including all macro-particles but also taking into account the
discrete electron distribution associated with them. This paper presents a
general form factor formalism that allows to determine the radiation from this
discrete electron distribution in order to compute the coherent and incoherent
radiation self-consistently. Furthermore, we discuss a memory-efficient
implementation that allows PIC simulations with billions of macro-particles.
The impact on the radiation spectra is demonstrated on a large scale LWFA
simulation.
