def plot_light_spectrum(n_wavelengths=100):
lambdas, omegas = generate_wavelengths(n_wavelengths)
colors_XYZ = np.zeros((n_wavelengths, 3))
for i, lambd in enumerate(np.linspace(400E-9, 700E-9, n_wavelengths)):
print(i)
# spectrum = generate_gaussian_spectrum(lambdas=lambdas, mu=lambd, sigma=30E-9)
spectrum = generate_mono_spectrum(lambdas=lambdas, color=lambd)
colors_XYZ[i, :] = -ct.from_spectrum_to_xyz(
lambdas, spectrum, normalize=False)
#normalize colors
# colors_xyz = colors_XYZ/np.max(np.sum(colors_XYZ, axis=1))
colors_xyz = colors_XYZ / np.max(colors_XYZ[:, 1])
colors_rgb = ct.from_xyz_to_rgb(colors_xyz.reshape((1, n_wavelengths, 3)),
normalize=False)
colors_rgb /= np.max(colors_rgb, axis=(1, 2))[:, None, None]
# plt.figure(figsize=(2*3.45, 2*2.5))
plt.figure(figsize=(3.45, 2.5))
plt.imshow(colors_rgb, extent=(400E-9, 700E-9, 0, 1), aspect=(300E-9) / 7)
plt.gca().set_yticks([])
plt.gca().set_xticks(np.linspace(400E-9, 700E-9, 4))
plt.gca().set_xticklabels(np.linspace(400, 700, 4).astype(int))
plt.gca().set_xlabel('Wavelength (nm)')
plt.savefig(fig_path + 'spectrum_light.pdf')
def compute_rgb(self, sqrt=False):
if self.rgb_colors is None:
if self.xyz_colors is None:
self.compute_xyz(sqrt)
self.rgb_colors = ct.from_xyz_to_rgb(self.xyz_colors)
return self.rgb_colors
def color_shift_2_figs(n_wavelengths=100, N=10):
rhos = color_shift_cube(wavelengths=np.linspace(400E-9, 700E-9,
n_wavelengths),
rhos=np.linspace(-1, 1, N),
thetas=np.array([0]),
return_XYZ=True)
thetas = color_shift_cube(wavelengths=np.linspace(400E-9, 700E-9,
n_wavelengths),
rhos=np.array([1]),
thetas=np.linspace(0, np.pi, N),
return_XYZ=True)
rhos = rhos.reshape((N, n_wavelengths, 3))
thetas = thetas.reshape((N, n_wavelengths, 3))
max_rhos = np.max(rhos[:, :, 1])
rhos /= max_rhos
thetas /= max_rhos
rhos = ct.from_xyz_to_rgb(rhos, normalize=False)
thetas = ct.from_xyz_to_rgb(thetas, normalize=False)
f, (ax1, ax2) = plt.subplots(2,
figsize=(1.3 * 3.45, 1.3 * 3.45),
sharex=True)
ax1.imshow(rhos, extent=(400E-9, 700E-9, 0, 1), aspect='auto')
ax1.set_yticks(np.linspace(0, 1, 3))
ax1.set_yticklabels(np.linspace(1, -1, 3))
ax1.set_ylabel(r'$\rho$', rotation=0)
ax1.set_title(r'(a) Color rendition with respect to $\rho$')
ax2.imshow(thetas, extent=(400E-9, 700E-9, 0, 1), aspect='auto')
ax2.set_yticks(np.linspace(0, 1, 3))
ax2.set_yticklabels(['$\pi$', '$\pi/2$', '$0$'])
ax2.set_ylabel(r'$\theta$', rotation=0)
ax2.set_title(r'(b) Color rendition with respect to $\theta$')
ax2.set_xticks(np.linspace(400E-9, 700E-9, 4))
plt.gca().set_xticklabels(np.linspace(400, 700, 4).astype(int))
ax2.set_xlabel('Wavelength (nm)')
plt.savefig(fig_path + 'color_shift_2_figs.pdf')
def lambdas_to_rgb(lambdas):
colors_XYZ = np.zeros((len(lambdas), 3))
for i, lambd in enumerate(lambdas):
spectrum = generate_mono_spectrum(lambdas=lambdas, color=lambd)
colors_XYZ[i, :] = -ct.from_spectrum_to_xyz(
lambdas, spectrum, normalize=False)
#normalize colors
colors_xyz = colors_XYZ / np.max(colors_XYZ[:, 1])
colors_rgb = ct.from_xyz_to_rgb(colors_xyz.reshape((-1, 1, 3)),
normalize=False).reshape((-1, 3))
colors_rgb /= np.max(colors_rgb)
return colors_rgb
def show_spectrum(lambdas,
spectrum,
ax=None,
visible=False,
true_spectrum=True,
vmax=None,
show_background=False,
lw=1,
nolabel=False,
short_display=False,
label=''):
if visible:
spectrum = spectrum[(lambdas <= 700E-9) & (lambdas >= 400E-9)]
lambdas = lambdas[(lambdas <= 700E-9) & (lambdas >= 400E-9)]
lam = lambdas * 1E9
if ax is None:
plt.figure()
ax = plt.gca()
L = len(lam)
if true_spectrum:
cs = [wavelength_to_rgb(wavelength) for wavelength in lam]
# cs = lambdas_to_rgb(lambdas)
else:
colors = plt.cm.Spectral_r(np.linspace(0, 1, L))
cs = [colors[i] for i in range(L)]
# ax.scatter(lam, spectrum, color=cs, s=10)
# ax.plot(lam, spectrum, '--k', linewidth=0.5, zorder=-1, alpha=0.5, dashes=(2,2))
fda.plot_gradient_line(lam, spectrum, ax=ax, zorder=-1, lw=lw, cs=cs)
ax.set_xlim([np.min(lam), np.max(lam)])
if vmax is None:
vmax = 1.1 * np.max(spectrum)
ax.set_ylim(0, vmax)
ax.set_yticks([])
if not nolabel and not short_display:
ax.set_xticks([400, 500, 600, 700])
ax.set_xlabel('Wavelength ($nm$)')
if not nolabel and short_display:
ax.set_xticks([400, 550, 700])
ax.set_xticklabels([400, '$\lambda$ ($nm$)', 700])
ax.set_xlabel(label)
if show_background:
col = ct.from_xyz_to_rgb(
ct.from_spectrum_to_xyz(lambdas, spectrum).reshape(
(1, 1, -1))).flatten()
ax.add_patch(
patches.Rectangle((lam[0], 0.95 * vmax),
lam[-1] - lam[0],
1.05 * vmax,
facecolor=col,
edgecolor='none',
zorder=-10))
def color_shift(n_wavelengths=100, ax=None):
lambdas, omegas = generate_wavelengths(500) #3000
depths = generate_depths(max_depth=7E-6)
rs = [-1, 0.7 * np.exp(1j * np.deg2rad(-148)), 0.2, 1]
r_names = ['$r=-1$', 'Hg', 'Air', '$r=1$']
rs = [0.7 * np.exp(1j * np.deg2rad(148)), 0.2]
r_names = ['Hg', 'Air']
colors_XYZ = np.zeros((len(rs) + 1, n_wavelengths, 3))
modulation = np.linspace(1, 0.2, len(lambdas))
# modulation = 0.5+np.random.rand(len(lambdas))
# modulation = generate_gaussian_spectrum(lambdas, mu=450E-9, sigma=300E-9)
# modulation = generate_gaussian_spectrum(lambdas, mu=450E-9, sigma=150E-9)
# modulation = (np.exp(np.linspace(0,1,len(lambdas)))-1 )/(np.exp(1)-1)
for i, lambd in enumerate(np.linspace(400E-9, 700E-9, n_wavelengths)):
print(i)
# spectrum = generate_gaussian_spectrum(lambdas=lambdas, mu=lambd, sigma=30E-9)
spectrum = generate_mono_spectrum(lambdas=lambdas, color=lambd)
colors_XYZ[0, i, :] = -ct.from_spectrum_to_xyz(
lambdas, spectrum, normalize=False)
# spectrum *= modulation
for j, r in enumerate(rs):
window = erfc(np.linspace(0, 3, len(depths)))
lippmann = lippmann_transform(lambdas, spectrum, depths,
r=r)[0] * window
spectrum_replayed = inverse_lippmann(lippmann, lambdas, depths)
colors_XYZ[j + 1, i, :] = -ct.from_spectrum_to_xyz(
lambdas, spectrum_replayed, normalize=False)
#normalize colors
colors_xyz = colors_XYZ / np.max(np.sum(colors_XYZ, axis=2),
axis=1)[:, None, None]
# colors_xyz = colors_XYZ/np.max(colors_XYZ[:,:,1], axis=1)[:,None, None]
colors_rgb = ct.from_xyz_to_rgb(colors_xyz, normalize=False)
colors_rgb /= np.max(colors_rgb, axis=(1, 2))[:, None, None]
# colors_xyz = colors_XYZ/np.max(colors_XYZ[:,:,1])
# colors_rgb = ct.from_xyz_to_rgb(colors_xyz, normalize=False)
# colors_rgb /= np.max(colors_rgb)
if ax is None:
plt.figure(figsize=(3.45, 2.5))
ax = plt.gca()
ax.imshow(colors_rgb, extent=(400E-9, 700E-9, 0, 1), aspect='auto')
L = len(rs) + 1
ax.set_yticks(np.linspace(1 / (2 * L), 1 - 1 / (2 * L), L))
ax.set_yticklabels((['Original'] + r_names)[::-1])
ax.set_xticks(np.linspace(400E-9, 700E-9, 4))
plt.gca().set_xticklabels(np.linspace(400, 700, 4).astype(int))
ax.set_xlabel('Wavelength (nm)')
plt.savefig(fig_path + 'color_shift_PNAS_erfc3_.pdf')
def plot_color_shift_cube(n_wavelengths=100, N=10):
xz = color_shift_cube(wavelengths=np.linspace(400E-9, 700E-9,
n_wavelengths),
rhos=np.linspace(-1, 1, N),
thetas=np.array([0]),
return_XYZ=True)
xy = color_shift_cube(wavelengths=np.linspace(400E-9, 700E-9,
n_wavelengths),
rhos=np.array([1]),
thetas=np.linspace(0, np.pi, N),
return_XYZ=True)
yz = color_shift_cube(wavelengths=np.array([700E-9]),
rhos=np.linspace(-1, 1, N),
thetas=np.linspace(0, np.pi, N),
return_XYZ=True)
max_XZ = np.max(xz[:, :, :, 1])
xz /= max_XZ
xy /= max_XZ
yz /= max_XZ
xz = ct.from_xyz_to_rgb(xz, normalize=False)
xy = ct.from_xyz_to_rgb(xy, normalize=False)
yz = ct.from_xyz_to_rgb(yz, normalize=False)
canvas = figure(figsize=(3.45, 2.5))
axes = Axes3D(canvas)
quads = cube(width=1,
height=1,
depth=1,
width_segments=n_wavelengths,
height_segments=N,
depth_segments=N)
# You can replace the following line by whatever suits you. Here, we compute
# each quad colour by averaging its vertices positions.
RGB = np.average(quads, axis=-2)
RGB[np.average(quads, axis=-2)[:, 0] == 1] = yz.transpose(
(2, 1, 0, 3)).reshape((-1, 3))
RGB[np.average(quads, axis=-2)[:, 2] == 1] = xy.transpose(
(2, 1, 0, 3)).reshape((-1, 3))
RGB[np.average(quads, axis=-2)[:, 1] == 0] = xz.transpose(
(2, 1, 0, 3)).reshape((-1, 3))
# Adding an alpha value to the colour array.
RGBA = np.hstack((RGB, np.full((RGB.shape[0], 1), 1)))
collection = Poly3DCollection(quads)
collection.set_color(RGBA)
axes.add_collection3d(collection)
plt.gca().set_xticks(np.linspace(0, 1, 4))
plt.gca().set_xticklabels(np.linspace(400, 700, 4))
plt.gca().set_xlabel('Wavelength $\lambda$')
plt.gca().set_yticks([0, 0.5, 1])
plt.gca().set_yticklabels(['0', '$\pi/2$', '\pi'])
plt.gca().set_ylabel(r'$\theta$')
plt.gca().set_zticks([-1, 0, 1])
plt.gca().set_zlabel(r'$\rho$')
return xz, xy, yz
def color_shift_cube(wavelengths=np.linspace(400E-9, 700E-9, 100),
rhos=np.linspace(-1, 1, 10),
thetas=np.linspace(0, np.pi, 10),
return_XYZ=False):
lambdas, omegas = generate_wavelengths(100) #3000
depths = generate_depths(max_depth=5E-6)
colors_XYZ = np.zeros((len(rhos), len(thetas), len(wavelengths), 3))
window = erfc(np.linspace(0, 4, len(depths)))
for n, lambd in enumerate(wavelengths):
print(n)
spectrum = generate_gaussian_spectrum(lambdas=lambdas,
mu=lambd,
sigma=30E-9)
# spectrum = generate_mono_spectrum(lambdas=lambdas, color=lambd)
# colors_XYZ[0, 0, n, :] = -ct.from_spectrum_to_xyz(lambdas, spectrum, normalize=False)
for i, rho in enumerate(rhos):
for j, theta in enumerate(thetas):
r = rho * np.exp(-1j * theta)
lippmann = lippmann_transform(lambdas, spectrum, depths,
r=r)[0] #*window
spectrum_replayed = inverse_lippmann(lippmann, lambdas, depths)
colors_XYZ[i, j, n, :] = -ct.from_spectrum_to_xyz(
lambdas, spectrum_replayed, normalize=False)
#normalize colors
# colors_xyz = colors_XYZ/np.max(np.sum(colors_XYZ, axis=2),axis=1)[:, None,None]
if return_XYZ:
return colors_XYZ
colors_xyz = colors_XYZ / np.max(colors_XYZ[:, :, :, 1])
colors_rgb = ct.from_xyz_to_rgb(colors_xyz, normalize=False)
colors_rgb /= np.max(colors_rgb)
if len(rhos) == 1:
plt.figure(figsize=(3.45, 2.5))
plt.imshow(colors_rgb[0, :, :, :],
extent=(400E-9, 700E-9, 0, 1),
aspect=(300E-9) / 2)
plt.gca().set_yticks(np.linspace(0, 1, 3))
plt.gca().set_yticklabels(['0', '$\pi/2$', '\pi'])
plt.gca().set_ylabel(r'$\theta$')
elif len(thetas) == 1:
plt.figure(figsize=(3.45, 2.5))
plt.imshow(colors_rgb[:, 0, :, :],
extent=(400E-9, 700E-9, 0, 1),
aspect=(300E-9) / 2)
plt.gca().set_yticks(np.linspace(0, 1, 3))
plt.gca().set_yticklabels(np.linspace(1, -1, 3))
plt.gca().set_ylabel(r'$\rho$')
if len(rhos) == 1 or len(thetas) == 1:
plt.gca().set_xticks(np.linspace(400E-9, 700E-9, 4))
plt.gca().set_xticklabels(np.linspace(400, 700, 4).astype(int))
plt.gca().set_xlabel('Wavelength $\lambda$ (nm)')
return colors_rgb
lippmann_hg, _ = lippmann_transform(lambdas, spectrum, depths, r=-0.7)
lippmann_air, _ = lippmann_transform(lambdas, spectrum, depths, r=0.2)
# window = (np.cos(np.linspace(0, np.pi, len(depths)))+1)/2
# window = np.linspace(1,0, len(depths))
# window = np.exp(np.linspace(0, -7, len(depths)))
window = erfc(np.linspace(0, 4, len(depths)))
# window = np.ones(len(depths))
lippmann_hg *= window
lippmann_air *= window
omegas = 2 * np.pi * c / lambdas
spectrum_hg = inverse_lippmann(lippmann_hg, lambdas, depths)
spectrum_air = inverse_lippmann(lippmann_air, lambdas, depths)
c1 = ct.from_xyz_to_rgb(
ct.from_spectrum_to_xyz(lambdas, spectrum).reshape((1, 1, -1)))
c2 = ct.from_xyz_to_rgb(
ct.from_spectrum_to_xyz(lambdas, spectrum_hg).reshape((1, 1, -1)))
c3 = ct.from_xyz_to_rgb(
ct.from_spectrum_to_xyz(lambdas, spectrum_air).reshape((1, 1, -1)))
# plt.close('all')
# plt.figure()
# show_spectrum(lambdas, spectrum, ax=plt.gca(), show_background=False)
# plt.title('original spectrum')
# plt.savefig(fig_path + 'original.pdf')
#
# plt.figure()
# show_lippmann_transform(depths, lippmann_hg, ax=plt.gca())
# plt.title('Lippmann transform Hg')
