Propagation and amplification law of undetermined stray light and influence of signal-to-noise ratio in a multipass amplifier system

•Modulation of non-deterministic stray light due to different components and optical path defects in a multiple amplification system is investigated.•A Mie scattering model for scattering due to multiple cracks and defects is developed.•The temporal and spatial distribution of stray light is analysed and experimentally verified using ray-tracing simulations.•The energy amplification formula for non-deterministic stray light and the signal-to-noise ratio formula for pre-pulse are established.