, that $\boldsymbol{\mathcal W}$ satisfies the relation $$\boldsymbol{\mathcal W}(v_1;v_3)= \boldsymbol{\mathcal W}(v_1;v_2) \cdot \boldsymbol{\mathcal W}(v_2;v_3) .$$ Hence, the general solution of the Sachs equation in a Swiss-cheese universe can be obtained by multiplying Wronski matrices, according to $$\begin{gathered}
\label{e.chain}
  \boldsymbol{\mathcal W}(v_{\rm source};0) = \boldsymbol{\mathcal W}_{\rm FL}(v_{\rm source};v_{\rm in}^{(1)})\cdot \boldsymbol{\mathcal W}_{\rm K}(v_{\rm in}^{(1)};v_{\rm out}^{(1)}) \\
 \cdot \boldsymbol{\mathcal W}_{\rm FL}(v_{\rm out}^{(1)};v_{\rm in}^{(2)})\cdots \boldsymbol{\mathcal W}_{\rm FL}(v_{\rm out}^{(N)};0)\end{gathered}$$ where $ \boldsymbol{\mathcal W}_{\rm FL}$ and $\boldsymbol{\mathcal W}_{\rm K}$ are the Wronski matrices computed respectively in the FL region and in the Kottler holes; $v_{\rm in}^{(i)}$ and $v_{\rm out}^{(i)}$ are the values of the affine parameter respectively at the entrance and the exit of the $i$th hole.

Integration of the geodesic and Sachs equations {#sec:resolution}
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Consider an observer lying within a FL region, who receives a photon after the latter has crossed a hole. In this section, we determine the light path from entrance to observation by solving the geodesic equation, and we calculate the Wronski matrix for the Sachs equation.

![A light ray propagates alternatively in FL and Kottler regions. The main geometrical quantities defined and used in Sec. \[sec:resolution\] are depicted in this simplified view of a single hole.[]{data-label="figgeo"}](strategy_one_hole.pdf)

The main geometrical quantities are 