A localized approximation approach for the calculation of beam shape coefficients of acoustic and ultrasonic Bessel beams

Topical Issue - Numerical, computational and theoretical acoustics

Open Access

Figure 3

Exact and LA-remodeled field intensities ${| ψ_{i}^{exa} (x, y, 0) |}^{2}$ ${\left|{\psi }_i^{{exa}}(x,y,0)\right|}^2$ and ${| ψ_{i}^{LA} (x, y, 0) |}^{2}$ ${\left|{\psi }_i^{{LA}}(x,y,0)\right|}^2$ , and logarithmic percent errors $\ln [100 | ({| ψ_{i}^{exa} (x, y, 0) |}^{2} - {| ψ_{i}^{LA} (x, y, 0) |}^{2}) / {| ψ_{i}^{exa} (x, y, 0) |}^{2} |]$ $\mathrm{ln}\left[100\left|\left({\left|{\psi }_i^{{exa}}(x,y,0)\right|}^2-{\left|{\psi }_i^{{LA}}(x,y,0)\right|}^2\right)/{\left|{\psi }_i^{{exa}}(x,y,0)\right|}^2\right|\right]$ for the zero-order Bessel beams of Figure 2 with α = 1°, 10° and 50°. (a)–(d) α = 1°. (e)–(h) α = 10°. (i)–(l) α = 50°. The corresponding BSCs are shown in Figure 2(a), (e) and (k), respectively.

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