arim.scat.sdh_2d_scat#

arim.scat.sdh_2d_scat(inc_theta, out_theta, frequency, radius, longitudinal_vel, transverse_vel, min_terms=10, term_factor=4, to_compute=frozenset({'LL', 'LT', 'TL', 'TT'}))[source]#

Scattering coefficients for a side-drilled hole in 2D

The scattered field is given by:

u_scat(r, theta) = u0 * sqrt(1 / r) * exp(-i k r + i omega i ray) *
                   (sqrt(lambda_L) A(theta) e_r +
                    sqrt(lambda_T) B(theta) e_theta)

where A(theta) and B(theta) are the scattering coefficients for respectively L and T scattered waves and where e_r and e_theta are the two vectors of the cylindrical coordinate system.

The coefficient for LL, LT, TL and TT are obtained from Lopez-Sanchez’s paper, equations 33, 34, 39, 40. See also Brind’s paper.

Another difference with these papers is the definition of theta. We use the NDT convention where pulse-echo corresponds to theta=0. For Brind, Lopez-Sanchez et al. pulse-echo corresponds to theta=pi.

The number of factor in the sum is:

maxn = max(min_terms, ceil(term_factor * alpha), ceil(term_factor * beta))

Parameters:

inc_theta (ndarray) – Angle in radians. Pulse echo case corresponds to inc_theta = out_theta
out_theta (ndarray) – Angle in radians.
frequency (float)
radius (float)
longitudinal_vel (float)
transverse_vel (float)
min_terms (int)
term_factor (int)
to_compute (set) – See SCAT_KEYS

Returns:

result – Keys corresponds to ‘to_compute’ argument. Values have the shape of theta.

Return type:

dict

References

[Lopez-Sanchez] Lopez-Sanchez, Ana L., Hak-Joon Kim, Lester W. Schmerr, and Alexander Sedov. 2005. ‘Measurement Models and Scattering Models for Predicting the Ultrasonic Pulse-Echo Response From Side-Drilled Holes’. Journal of Nondestructive Evaluation 24 3): 83–96. doi:10.1007/s10921-005-7658-4.

[Brind] Brind, R. J., J. D. Achenbach, and J. E. Gubernatis. 1984. ‘High-Frequency Scattering of Elastic Waves from Cylindrical Cavities’. Wave Motion 6 (1): 41–60. doi:10.1016/0165-2125(84)90022-2.

[Zhang] Zhang, Jie, B.W. Drinkwater, and P.D. Wilcox. 2008. ‘Defect Characterization Using an Ultrasonic Array to Measure the Scattering Coefficient Matrix’. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 55 (10): 2254–65. doi:10.1109/TUFFC.924.

arim.scat.sdh_2d_scat#

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