plot_transducer_near_fields.py

# -*- coding: utf-8 -*-
"""
Creates a plot of recommended minimum sphere calibration range as a function of transducer beamwidth
and acoustic frequency.

An earlier version of this code (written in Matlab) was used to generate Figure 2.5 in:

Demer, D.A., Berger, L., Bernasconi, M., Boswell, K.M., Chu, D., Domokos, R., Dunford, A.J.,
   Fässler, S.M.M., Gauthier, S., Hufnagle, L.T., Jech, J.M., Bouffant, N., Lebourges-Dhaussy, A.,
   Lurton, X., Macaulay, G.J., Perrot, Y., Ryan, T.E., Parker-Stetter, S., Stienessen, S.,
   Weber, T.C., Williamson, N.J., 2015. Calibration of acoustic instruments (ICES Cooperative
   Research Report 326). https://doi.org/10.17895/ices.pub.5494

and implements equations 2.1b, 2.2, and the factor 3 multiplier mentioned in the caption of
Figure 2.5.

"""

import matplotlib.pyplot as plt
import numpy as np
from labellines import labelLines  # see https://github.com/cphyc/matplotlib-label-lines

c = 1470.  # [m/s] speed of sound in water # pylint: disable=invalid-name
# Calculate the near-field range at these frequencies
freq = np.array([12, 18, 26, 38, 50, 70, 120, 200, 333]) * 1e3  # [Hz]
# The range of transducer 3 dB two-way beamwidths to use
bw = np.linspace(2, 20, 50)  # [deg]

# Force y tick locations as the automatic ones aren't ideal
yticksAt = [1, 1.5, 2, 3, 4, 6, 8, 10, 15, 20]  # [m]

fig, ax = plt.subplots(1)

for f in freq:
    lambda_ = c / f  # [m]
    k = 2 * np.pi * f / c  # [m-1]

    d_t = 3.2 / (k * np.sin(np.deg2rad(bw/2.0)))  # [m]
    r_nf = 3 * np.pi * d_t**2.0 / (4.0 * lambda_)  # [m]

    line = ax.plot(bw, r_nf, color='black', linewidth=2, label=f'{f/1000:.0f} kHz')

labelLines(ax.get_lines(), fontsize=7, xvals=(16, 2))

plt.minorticks_on()
ax.grid(axis='x', which='minor', linewidth=0.5, linestyle=':')
ax.grid(axis='x', which='major')
ax.grid(axis='y', which='major')
ax.set_yscale('log')
ax.set_yticks(yticksAt)
ax.set_yticklabels((str(i) for i in yticksAt))
ax.set_ylim(yticksAt[0], yticksAt[-1])
ax.set_xlim(bw[0], bw[-1])
ax.set_xlabel('Transducer 3 dB beamwidth [°]')
ax.set_ylabel('Minimum sphere range [m]')

plt.savefig('near_field_ranges.png', dpi=300)