dealing with $N$-body gravitational systems in an expanding space. The fact that matter is not continuously distributed can however imprint some observations, in particular regarding the propagation of light with narrow beams, as discussed in detail in Ref. [@cemuu]. It was argued that such beams, as e.g. for supernova observations, probe the spacetime structure on scales much smaller than those accessible in numerical simulations. The importance of quantifying the effects of inhomogeneities on light propagation was first pointed out by Zel’dovich [@zel]. Arguing that photons should mostly propagate in vacuum, he designed an “empty beam” approximation, generalized later by Dyer and Roeder as the “partially filled beam” approach [@DR72]. More generally, the early work of Ref. [@zel] stimulated many studies on this issue [@dash; @Bertotti; @gunn; @refs; @weinberg; @DR81; @fangwu; @Rose:2001qi; @Kibble:2004tm; @Kostov:2009uc; @linder88; @tomita; @Mortsell:2001es; @Bolejko:2010nh; @Takahashi:2011qd].

The propagation of light in an inhomogeneous universe gives rise to both distortion and magnification induced by gravitational lensing. While most images are demagnified, because most lines of sight probe underdense regions, some are amplified because of strong lensing. Lensing can thus discriminate between a diffuse, smooth component, and the one of a gas of macroscopic, massive objects (this property has been 