add dielectric bead example (#6)

examples/field-behind-dielectric.py

@@ -0,0 +1,94 @@
+#!/usr/bin/env python
+# -*- coding: UTF-8 -*-
+#
+#    Copyright (C) 2009-2015 Ovidio Peña Rodríguez <ovidio@bytesfall.com>
+#    Copyright (C) 2013-2015 Konstantin Ladutenko <kostyfisik@gmail.com>
+#
+#    This file is part of scattnlay
+#
+#    This program is free software: you can redistribute it and/or modify
+#    it under the terms of the GNU General Public License as published by
+#    the Free Software Foundation, either version 3 of the License, or
+#    (at your option) any later version.
+#
+#    This program is distributed in the hope that it will be useful,
+#    but WITHOUT ANY WARRANTY; without even the implied warranty of
+#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+#    GNU General Public License for more details.
+#
+#    The only additional remark is that we expect that all publications
+#    describing work using this software, or all commercial products
+#    using it, cite the following reference:
+#    [1] O. Pena and U. Pal, "Scattering of electromagnetic radiation by
+#        a multilayered sphere," Computer Physics Communications,
+#        vol. 180, Nov. 2009, pp. 2348-2354.
+#
+#    You should have received a copy of the GNU General Public License
+#    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+# This test case calculates the phase retardation that is introduced
+# by a weak dielectric sphere to an incident plane wave. Only the
+# x-polarized light is considered.
+
+# Note: This example computes the phase behind the sphere. In microscopy,
+# the focal plane during imaging is close to the center of the sphere.
+# To compute the phase image that corresponds to that imaged with a focal
+# plane at the center of the bead, numerical refocusing of the computed
+# field `Ex` would be required (e.g. python package nrefocus).
+
+import numpy as np
+import scattnlay
+import matplotlib.pylab as plt
+
+# weak dielectric sphere, e.g. a PMMA gel bead
+n1 = 1.335
+# refractive index of the surrounding medium (water)
+nm = 1.333
+# radius of the sphere in wavelengths
+radius = 0.3
+# extent of the simulation size in wavelengths
+extent = 2.0
+# distance where we want to have the measured field behind the sphere
+# in wavelengths measured from the center of the sphere
+distance = 0.5
+# pixels per wavelength in the output image
+resolution = 20.0 
+
+# size parameters need to be multiplied by (2 PI nm) for the computation
+twopi = 2*np.pi*nm
+
+# There is only one sphere, no layers
+x = np.ones((1, 1), dtype = np.float64)
+x[0, 0] = radius*twopi
+
+# Set the refractive index of the sphere, normalized to that of the medium
+m = np.ones((1, 1), dtype = np.complex128)
+m[0, 0] = n1/nm
+
+nptsx = extent*resolution
+nptsy = extent*resolution
+
+scanx = np.linspace(-extent/2, extent/2, nptsx, endpoint=True)*twopi
+scany = np.linspace(-extent/2, extent/2, nptsy, endpoint=True)*twopi
+
+coordX, coordY = np.meshgrid(scanx, scany)
+coordX.resize(nptsx*nptsy)
+coordY.resize(nptsx*nptsy)
+coordZ = np.ones(nptsx*nptsy, dtype=np.float64)*distance*twopi
+
+coord = np.vstack((coordX, coordY, coordZ)).transpose()
+
+terms, E, H = scattnlay.fieldnlay(x, m, coord)
+
+# take the x-component of the electric field
+Ex = E[:,:,0].reshape(nptsx, nptsy)
+
+# normalize by the background field (free space propagation)
+Ex /= np.exp(1j*2*np.pi*distance*nm)
+
+# plot the phase (np.angle) of the x-component of the electric field
+ax = plt.subplot(111)
+mapper = plt.imshow(np.angle(Ex))
+plt.colorbar(mapper, ax=ax, label="phase [rad]")
+plt.title("phase retardation introduced by a dielectric sphere")
+plt.show()