Fig. 12.

Time for calculating the exit wave for the zone plate test object as a function of increasing the transverse array size along with the number of nodes, with each node given a transverse grid size of $N_x\times N_y={4096}^2$ (leading to a net array size of ${65536}^2$ for 256 nodes, as indicated just below the top of the plot). For each algorithm, the number of slices $n_C$ was as required for convergence to the error tolerance ${[\overline{A}{\xi }_{\varphi }]}_{\text{zp}}$ of Eq. (28), giving values of $n_C$ that were in all cases within 1 or 2 slices of the values shown in Fig. 9. This “weak scaling” test shows that both the finite difference and tiling-based short-distance Fresnel multislice approaches scale well as the problem size increases with the number of nodes used, consistent with the “strong scaling” test results of Fig. 10. With the full-array Fresnel multislice approach, the time required for data communication between nodes for full-array FFTs means that even with many nodes available large problems require considerably more time to compute.