. Author manuscript; available in PMC: 2022 Jun 17.

Published in final edited form as: IEEE Trans Ultrason Ferroelectr Freq Control. 2022 Mar 30;69(4):1243–1256. doi: 10.1109/TUFFC.2022.3150186

TABLE II.

Pressure Error Parameter Alpha For Membrane Hydrophones

Pressure				Compressional				Rarefactional
Data				Simulation	Simulation	Previous Simulation	Expt	Simulation	Simulation	Previous Simulation	Expt
Method				AF-SC	SB-SC	AF-SC		AF-SC	SB-SC	AF-SC
Linearity	σ_q	σ_m	SI	α_c (RMSD)	α_c (RMSD)	α_c (RMSD)	α_c (RMSD)	α_r (RMSD)	α_r (RMSD)	α_r (RMSD)	α_r (RMSD)
Linear	0	0	0	0.24 (3%)	0.25 (4%)		0.29 (7%)	0.24 (3%)	0.25 (4%)		0.30 (7%)
Nonlinear	0.5	0.4	4%	0.31 (3%)	0.33 (4%)	0.34 (4%)		0.20 (3%)	0.22 (3%)	0.25 (4%)
Nonlinear	1.0	0.8	12%	0.40 (3%)	0.43 (4%)	0.43 (4%)	0.40 (8%)	0.20 (3%)	0.21 (4%)	0.23 (4%)	0.29 (6%)
Nonlinear	2.0	1.6	29%	0.65 (5%)	0.65 (5%)	0.68 (5%)		0.20 (3%)	0.21 (4%)	0.23 (4%)
Nonlinear	3.0	2.2	35%	0.76 (4%)	0.72 (5%)			0.20 (3%)	0.23 (5%)
Nonlinear	4.0	3.1	45%	0.87 (4%)	0.84 (5%)			0.19 (3%)	0.24 (5%)
Nonlinear	5.0	3.9	49%	0.95 (4%)	1.01 (4%)	1.02 (5%)		0.18 (3%)	0.23 (3%)	0.23 (4%)

Exponentially decaying model functions, exp(-αx), were fit to focal pressure magnitude ratios p’/p (where p’ = measured value subjected to spatial averaging and p = true axial value that would be obtained with a hypothetical point hydrophone), where x = d_g / (λ₁F/#). Nonlinearity indexes are σ_q (local distortion parameter), σ_m (nonlinear propagation parameter), and SI (spectral index). RMSD: root-mean-squared difference between data and functional fits. AF-SC: analytic filter spatial convolution. SB-SC: scan-based spatial convolution. Previous simulation data are from Wear et al., IEEE Trans. Ultrason. Ferro., Freq. Control., 67(12), 2674–2691, 2020.