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343 lines
13 KiB
Python
343 lines
13 KiB
Python
import torch as t
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from matplotlib import pyplot as plt
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import numpy as np
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import matplotlib.pyplot as plt
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from matplotlib.colors import hsv_to_rgb
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from matplotlib.widgets import Slider
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from matplotlib import ticker, patheffects
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from CDTools.tools.polarization import polarization
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all = ['visualize_components_amplitudes',
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'visualize_attenuations',
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'visualize_fast_axes',
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'visualize_global_axes',
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'visualize_phase_ret',
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'visualize_probe']
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def iterator(a, b):
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'''
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A helper function we can use to facilitate to process of iterating over 2D arrays
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'''
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x, y = t.arange(a), t.arange(b)
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x, y = t.meshgrid(x, y)
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x, y = t.ravel(x), t.ravel(y)
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return (x, y)
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def plot_probe_ellipse(a=1, b=1, phase_ret=0, scale=1, x0=4, y0=5):
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'''
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Given a probe vector at a point (x0, y0), visualizes ellipticity
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of its polarization
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Parameters:
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-----------
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a : 1D np.array
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An amplitude of the horizontal component of the probe vector
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b : 1D np.array
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An amplitude of the vertical component of the probe vector
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phase_ret : 1D np.array
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A phase difference in radians bettween the phases of the y and x components
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scale : int
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A scaling factor
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x0, y0: 1D np.array or float
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Defines the location of the vector to be plotted
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Returns:
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--------
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x, y set of points to plot a single ellipse
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'''
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theta = np.linspace(0, 2*np.pi, 20)
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x = x0 + scale * a * np.real(np.exp(1j * theta))
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y = y0 + scale * b * np.real(np.exp(1j * (theta + phase_ret)))
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return x, y
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def plot_attenuations(atten_slow=1, atten_fast=1, fast_ax_angle=0, scale=1, x0=4, y0=4):
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'''
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Plots attenuations along the fast and slow axes
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Parameters:
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-----------
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atten_slow: 1D np.array
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Attenuation along the slow axis
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atten_fast: 1D np.array
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Attenuation along the fast axis
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fast_ax_angle: 1D np.array
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An angle between the fast horizontal and fast axes
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phase_ret: 1D np.array
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A difference in phases gained by the slow and the fast components
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The most clockwise axis is always considered to be the fast one
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scale: 1D np.array
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A scaling factor
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x0, y0: 1D np.array or float
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Defines the location to be plotted at
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Returns:
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--------
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x, y set of points to plot a single Jones matrix of the object
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'''
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angle = fast_ax_angle
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theta = np.linspace(0, 2*np.pi, 20)
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# collection of points to plot a fast axis
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print('angle', np.rad2deg(angle))
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x = x0 + scale * atten_fast * np.real(np.exp(1j * theta))
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x_f = x0 + (x - x0) * np.cos(angle)
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y_f = y0 + (x - x0) * np.sin(angle)
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# collection of point to plot a slow axis
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y = y0 + scale * atten_slow * np.real(np.exp(1j * theta))
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x_s = x0 - (y - y0) * np.sin(angle)
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y_s = y0 + (y - y0) * np.cos(angle)
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return x_f, y_f, x_s, y_s
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def plot_fast_axis(fast_ax_angle=0, scale=1, x0=4, y0=4):
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'''
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Plots directions of the fast axes only
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'''
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xf, yf, xs, ys = plot_attenuations(fast_ax_angle=fast_ax_angle, atten_fast=1, atten_slow=0, scale=scale, x0=x0, y0=y0)
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return xf, yf
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def plot_figures(shape, num_of_el_along_x=20, num_of_el_along_y=20,
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phases=None, fast_ax_angles=None,
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atten_fast=None, atten_slow=None, scale=5,
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probe=False, attenuations=False, fast_axes=False):
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"""
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All the parameters - np.arrays of shape (shape)
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"""
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x_centers = np.linspace(1, shape[0] - 1, num_of_el_along_x)
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y_centers = np.linspace(1, shape[1] - 1, num_of_el_along_y)
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X, Y = np.meshgrid(x_centers, y_centers)
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X, Y = np.ravel(X), np.ravel(Y)
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xs, ys = np.array([]), np.array([])
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for x, y in zip(X, Y):
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k, m = int(x), int(y)
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if probe:
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xx, yy = plot_probe_ellipse(a=atten_fast[k, m], b=atten_slow[k, m],
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phase_ret=phases[k, m], scale=scale, x0=x, y0=y)
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title = 'Polarized Probe'
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elif attenuations:
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xf, yf, xs, ys = plot_attenuations(atten_slow=atten_slow[k, m], atten_fast=atten_fast[k, m],
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fast_ax_angle=fast_ax_angles[k, m], scale=scale, x0=x, y0=y)
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elif fast_axes:
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xx, yy = plot_fast_axis(fast_ax_angle=fast_ax_angles[k, m], scale=scale, x0=x, y0=y)
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title = 'Fast Axes'
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if attenuations:
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plt.plot(xf, yf, c='b')
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plt.plot(xs, ys, c='b')
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plt.axis('equal')
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plt.title('Attenuations')
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else:
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plt.plot(xx, yy, c='b')
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plt.axis('equal')
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plt.title(title)
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"""
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VISUALIZATION FUNCTIONS (and helper functions)
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"""
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def determine_fast_axis(angle0, angle1):
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# in radians
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w0, w1 = t.as_tensor(angle0, dtype=t.float32), t.as_tensor(angle1, dtype=t.float32)
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diff = (w0 - w1) % (2 * np.pi)
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if t.tensor(0, dtype=t.float32) <= diff and diff <= t.tensor(np.pi, dtype=t.float32):
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fast = 1
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phase_ret = (w0 - w1) % (2 * np.pi)
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gl_phase = w1
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else:
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fast = 0
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phase_ret = (w1 - w0) % (2 * np.pi)
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gl_phase = w0
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if t.allclose((w0 - w1) % (2 * np.pi), phase_ret):
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gl_phase = w1
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fast = 1
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return fast, phase_ret, gl_phase
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def retrieve_obj_info(obj):
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obj_t = obj.transpose(-1, -3).transpose(-2, -4)
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w, v = t.linalg.eig(obj_t)
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b = obj.shape[-1]
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a = obj.shape[-2]
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eigenvectors = t.empty(a, b, 2, dtype=t.cfloat)
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ret_phases = t.empty(a, b, dtype=t.float32)
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global_phases = t.empty(a, b, dtype=t.float32)
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atten_fast = t.empty(a, b, dtype=t.float32)
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atten_slow = t.empty(a, b, dtype=t.float32)
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fast_ax_angles = t.empty(a, b, dtype=t.float32)
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for k, m in zip(*iterator(a, b)):
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angle0, angle1 = t.angle(w[k, m, 0]).to(dtype=t.float32), t.angle(w[k, m, 1]).to(dtype=t.float32)
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fst, phase_ret, gl_phase = determine_fast_axis(angle0, angle1)
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atten0, atten1 = t.abs(w[k, m, 0]), t.abs(w[k, m, 1])
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ret_phases[k, m] = phase_ret
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def fast(b):
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if b == 0:
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eigenvectors[k, m, :] = v[k, m, 0, :]
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atten_fast[k, m] = atten0
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atten_slow[k, m] = atten1
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global_phases[k, m] = angle0
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elif b == 1:
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eigenvectors[k, m, :] = v[k, m, 1, :]
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atten_fast[k, m] = atten1
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atten_slow[k, m] = atten0
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global_phases[k, m] = angle1
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if t.allclose(angle0, angle1):
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# then it's a linear polarizer, fast ax - the one for which attenuation is bigger
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if atten0 > atten1:
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fst = 0
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else:
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fst = 1
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fast(fst)
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cos = np.abs(eigenvectors[k, m, 0])
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sin = np.abs(eigenvectors[k, m, 1])
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if t.allclose(cos, t.zeros(1, dtype=t.float32)):
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fast_ax_angles[k, m] = 90
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else:
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fast_ax_angles[k, m] = t.atan(sin/cos)
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fast_ax_angles = np.asarray(fast_ax_angles, dtype=np.float32)
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ret_phases = np.asarray(ret_phases, dtype=np.float32)
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global_phases = np.asarray(global_phases, dtype=np.float32)
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atten_fast = np.asarray(atten_fast, dtype=np.float32)
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atten_slow = np.asarray(atten_slow, dtype=np.float32)
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return fast_ax_angles, ret_phases, global_phases, atten_fast, atten_slow
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def visualize_components_amplitudes(obj, rot_angle=0, logarithmic=False):
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# coord_rot angle is the only angle in degrees here
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def coord_rot(angle):
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angle = t.as_tensor(angle, dtype=t.float32)
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angle = t.deg2rad(angle)
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a = t.stack((t.cos(angle), t.sin(angle)), dim=-1)
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b = t.stack((-t.sin(angle), t.cos(angle)), dim=-1)
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return t.stack((a, b), dim=-2).to(dtype=t.cfloat)
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for k, m in zip(*iterator(obj.shape[-2], obj.shape[-1])):
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obj[:, :, k, m] = t.matmul(coord_rot(rot_angle), obj[:, :, k, m])
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components = [obj[i, j, :, :] for i, j in zip(*iterator(2, 2))]
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if logarithmic:
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components = [np.log(comp)/np.log(10) for comp in components]
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titles = ['Amptlitudes of the a components', 'Amplitudes of the b components',
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'Amplitudes of the c components', 'Amplitudes of the d components']
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for i in range(4):
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amplitude = np.abs(components[i])
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plt.imshow(module)
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plt.colorbar()
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plt.title(titles[i])
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def visualize_phase_ret(obj, logarithmic=False):
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print('DHSBCUYLIWGBCGLWIYV')
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fast_ax_angles, ret_phases, global_phases, atten_fast, atten_slow = retrieve_obj_info(obj)
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if logarithmic:
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ret_phases = np.log(ret_phases)/np.log(10)
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plt.imshow(ret_phases)
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plt.colorbar()
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plt.show()
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def visuallize_global_phases(obj, logarithmic=False):
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fast_ax_angles, ret_phases, global_phases, atten_fast, atten_slow = retrieve_obj_info(obj)
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if logarithmic:
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global_phases = np.log(global_phases)/np.log(10)
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plt.imshow(global_phases)
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plt.colorbar()
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plt.show()
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def visualize_fast_axes(obj, num_of_el_along_x=20, num_of_el_along_y=20, scale=1):
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fast_ax_angles, ret_phases, global_phases, atten_fast, atten_slow = retrieve_obj_info(obj)
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A, B = obj.shape[-2], obj.shape[-1]
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plot_figures((A, B), num_of_el_along_x=num_of_el_along_x, num_of_el_along_y=num_of_el_along_y,
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fast_ax_angles=fast_ax_angles, scale=scale, fast_axes=True)
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def visualize_attenuations(obj, num_of_el_along_x=20, num_of_el_along_y=20, scale=1):
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fast_ax_angles, ret_phases, global_phases, atten_fast, atten_slow = retrieve_obj_info(obj)
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A, B = obj.shape[-2], obj.shape[-1]
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plot_figures((A, B), num_of_el_along_x=num_of_el_along_x, num_of_el_along_y=num_of_el_along_y,
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phases=ret_phases, atten_slow=atten_slow, atten_fast=atten_fast,
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fast_ax_angles=fast_ax_angles, scale=scale, attenuations=True)
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def visualize_probe(probe, scale=1, num_of_el_along_x=20, num_of_el_along_y=20):
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a = np.abs(probe[..., 0, :, :])
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b = np.abs(probe[..., 1, :, :])
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phases = np.angle(probe[..., 1, :, :]) - np.angle(probe[..., 0, :, :])
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A, B = np.asarray(probe.shape[-2]), np.asarray(probe.shape[-1])
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plot_figures((A, B), num_of_el_along_x=num_of_el_along_x, num_of_el_along_y=num_of_el_along_y,
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phases=phases, atten_fast=a, atten_slow=b, scale=scale,
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probe=True)
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#
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# def object_from_components(a, b, c, d):
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# ab = t.stack((a, b), dim=-3)
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# cd = t.stack((c, d), dim=-3)
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# return t.stack((ab, cd), dim=-4)
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#
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# def object_from_quarters(a, b, c, d):
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# ab = t.cat((a, b), dim=-1)
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# cd = t.cat((c, d), dim=-1)
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# return t.cat((ab, cd), dim=-2)
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#
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# def generate_birefringent_obj(shape, func_axes=None, func_ret_phases=None, func_global_phases=None, fast_axes=[0, 0, 90, 90], phases=[0, 18, 40, 18]):
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# ret = [polarization.generate_birefringent_obj(fast_axis=i, phase_ret=j) for i, j in zip(fast_axes, phases)]
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# A = shape[0]
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# B = shape[1]
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# def to_rad(angle):
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# angle = t.as_tensor(angle)
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# return t.deg2rad(angle)
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#
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# if func_axes is None:
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# # 4 sets of components for each quarter
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# components = [[ret[i][j][k].repeat(A//2, B//2) for j, k in zip(*iterator(2, 2))] for i in range(4)]
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# # build the quarters from the components
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# quarters = [object_from_components(*comp) for comp in components]
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# obj = object_from_quarters(*quarters)
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# else:
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# X, Y = t.arange(A), t.arange(B)
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# X, Y = t.meshgrid(X, Y)
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# obj = t.empty(2, 2, A, B, dtype=t.cfloat)
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# for i, j in zip(*iterator(A, B)):
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# x, y = X[i, j], Y[i, j]
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# axis = func_axes(x, y)
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# ret = func_ret_phases(x, y)
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# gl = func_global_phases(x, y)
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# obj[:, :, i, j] = polarization.generate_birefringent_obj(fast_axis=axis, phase_ret=ret, global_phase=gl)
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# w, v = t.linalg.eig(obj[:, :, i, j])
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#
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# # t.tensor of shape (2, 2, A, B)
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# return obj
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#
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# def axes(x, y):
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# # return (x-25)**2 + (y-25)**2
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# return x * 20
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#
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# def phases(x, y):
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# # return ((x - 5) ** 2 + (y - 5) ** 2) * 20
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# return (x) * 10
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#
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# def glob(x, y):
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# return x * 10
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#
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# def amp(x, y):
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# return 1 + 0.05 * (x + y)
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#
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# def build_probe(shape, phase_ret_func=None, amps_func=None):
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# probe = t.empty(2, shape[0], shape[1], dtype=t.cfloat)
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# for x, y in zip(*iterator(probe.shape[-2], probe.shape[-1])):
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# phase = phase_ret_func(x, y)
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# phase = t.deg2rad(phase).to(dtype=t.cfloat)
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# abs = amps_func(x, y).to(dtype=t.cfloat)
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# probe[0, x, y] = abs
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# probe[1, x, y] = abs * t.exp(phase * 1j)
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#
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# return probe
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#
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#
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# obj = generate_birefringent_obj((10, 10), func_axes=axes, func_ret_phases=phases, func_global_phases=glob)
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# probe = build_probe((10, 10), phase_ret_func=phases, amps_func=amp)
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# # visualize_probe(probe, num_of_el_along_x=10, num_of_el_along_y=10, scale=0.1)
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# visualize_fast_axes(obj, num_of_el_along_x=10, num_of_el_along_y=10, scale=0.1)
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# # visualize_phase_ret(obj)
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# # visuallize_global_phases(obj)
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# # visualize_attenuations(obj, num_of_el_along_x=10, num_of_el_along_y=10, scale=0.3)
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# plt.show()
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