Table 1.

Signal and noise transfer relations. The term ${\overline{q}}_i$ describes the mean x-ray fluence at stage i, and ${\overline{g}}_i$ describes the mean gain at stage i. The terms u and v refer to 2D spatial coordinates in the detector plane, with Δu_i and Δv_i being the respective sampling intervals at stage i, and f_u and f_v referring to the spatial-frequency counterparts. Similarly, x, y, z refer to 3D spatial coordinates in the reconstruction with Δx_i, Δy_i, and Δz_i being the respective sampling intervals at stage i, and f_x, f_yf_z being the 3D spatial-frequency counterparts.

Stage	Signal	Noise
Gain stage	${\overline{q}}_i(u,v)={\overline{g}}_i{\overline{q}}_{i-1}(u,v)$	$S_i(f_u,f_v)={\overline{g}}_i^2(f_u,f_v)+{\sigma }_{g_i}^2{\overline{q}}_{i-1}+S_{{\mathrm{add}}_i}(f_u,f_v)$
Stochastic spreading stage	${\overline{q}}_i(u,v)={\overline{q}}_{i-1}{(u,v)}_s^{**}{P}_i(u,v)$	$S_i(f_u,f_v)=[S_{i-1}(f_u,f_v)-{\overline{q}}_{i-1}]T_i^2(f_u,f_v)+{\overline{q}}_{i-1}$
Deterministic spreading stage	${\overline{q}}_i(u,v)={\overline{q}}_{i-1}{(u,v)}^{**}{P}_i(u,v)$	$S_i(f_u,f_v)=S_{i-1}(f_u,f_v)T_i^2(f_u,f_v)$
Sampling stage	${\overline{q}}_i(u,v)={\overline{q}}_{i-1}(u,v)\mathit{III}(u∕\Delta u_i,v∕\Delta v_i)$	Si(fu,fv)=Si−1(fu,fv)**ΔuiΔviIII(fuΔui,fvΔvi)