Fig. 1. Modification of spatial interpolation algorithm; left: origin, right: after modification. (a) PS after 5 iterations of interpolation for Δr = 0.3125 mm and r₀ = 0.1 m (64π initial phase has been added in the red box area). (b) Ratio between the mean SF D^ϕ (ρ)_r at each sampling point of 10⁴ PSs and the theoretical value.

Fig. 2. Schematic illustration of spatial interpolation. {m′, n′} are grid coordinates, and Δr is the grid spacing. (The solid circles are from the initial PS, the shaded circles are interpolated first, and then the dotted circles are interpolated.)

Fig. 3. Bases and coefficients of time-evolving PSs. (a) Complete orthogonal bases U_i of the 8 × 8 grid. (b) Temporal PSDs of different coefficients. (c) Time sequence of different coefficients for the 32 × 32 grid, V = 5 m/s, r₀ = 0.1 m, and Δr = 0.01 m.

Fig. 4. Spatial characteristics of PSs. (a) Spatial interpolation process of the PS: (a1) initial PS, (a2)–(a5) 1 iteration, 2 iterations, 3 iterations, and 4 iterations. (b), (c) Ratio between the mean SF D_ϕ (ρ)_r of 10⁴ PSs and theoretical value for r₀ = 0.1 m. (b1)–(b3) Different grids, 16 × 16, 32 × 32, 64 × 64, and L = NΔr = 0.08 m; (c1)–(c3) different iterations of interpolation, 1 iteration, 5 iterations, and 9 iterations. (d), (e) Fluctuations of the ratio of the statistical value to the theoretical value of the SF across all distances in PSs. The error bar represents one standard deviation. (d) Different numbers of 16 × 16 PSs; (e) 10⁴ PSs after different iterations of interpolation.

Fig. 5. Temporal characteristics of PSs, V = 5 m/s, r₀ = 0.1 m. (a1)–(a6) Time-evolving PS before temporal interpolation, Δt = 2 ms. (b1)–(b6) Time-evolving PS after temporal interpolation, Δt = 0.5 ms. (c)–(e) Mean temporal PSDs of 10³ sets of interpolated time-evolving PS sequences. (c) Different iterations of spatial interpolation. (d) Different iterations of temporal interpolation. (e) Simultaneous temporal and spatial interpolation. I_s and I_t are the iterations of spatial and temporal interpolation, respectively.

Fig. 6. The comparison between our method and existing methods. (a) The comparison of deviations from SF theoretical value. (b) The comparison of the temporal PSD when the crosswind is 5 m/s.

Fig. 7. The AoA temporal power spectrum in the 460 m atmospheric turbulence channel with r₀ = 3.7 cm. (a) The field-test results^[47]. (b) Our simulation results.