8.13. Talbot effect

from diffractio import plt, sp, np, um, mm, degrees, num_max_processors
from diffractio.scalar_masks_X import Scalar_mask_X
from diffractio.scalar_masks_XZ import Scalar_mask_XZ
from diffractio.scalar_sources_X import Scalar_source_X
from diffractio.scalar_fields_XZ import Scalar_field_XZ
from diffractio.utils_multiprocessing import execute_multiprocessing

8.13.1. Standard Talbot effect

x = np.linspace(-350 * um, 350 * um, 2048)
z = np.linspace(0 * um, 10 * mm, 512)
wavelength = 0.6238 * um
period = 40 * um
z_talbot = 2 * period**2 / wavelength

u0 = Scalar_source_X(x, wavelength)
u0.plane_wave(A=1)

t = Scalar_mask_X(x, wavelength)
t.ronchi_grating(x0=0 * um, period=40 * um, fill_factor=0.5)

talbot_effect = Scalar_field_XZ(x, z, wavelength)
talbot_effect.incident_field(u0 * t)
talbot_effect.BPM()

talbot_effect.draw(kind="intensity")
plt.ylim(-150 * um, 150 * um)

8.13.2. Gauss illumination: separation of orders

u0 = Scalar_source_X(x, wavelength)
u0.gauss_beam(x0=0 * um, w0=150 * um, z0=0 * um, A=1, theta=0.0)

t = Scalar_mask_X(x, wavelength)
t.ronchi_grating(x0=0 * um, period=15 * um, fill_factor=0.5)

talbot_effect = Scalar_field_XZ(x, z, wavelength)
talbot_effect.incident_field(u0 * t)
talbot_effect.WPM()

talbot_effect.draw(kind="intensity", logarithm=1e2)

8.13.3. Ronchi grating at focal distance of a lens

%%time
x0 = np.linspace(-500 * um, 500 * um, 1024*4)
z0 = np.linspace(0 * um, 2 * mm, 1024*2)
wavelength = 1 * um

u0 = Scalar_source_X(x=x0, wavelength=wavelength)
u0.plane_wave(A=1, theta=0 * degrees)

u1 = Scalar_mask_XZ(x=x0, z=z0, wavelength=wavelength)
u1.incident_field(u0)

focal, _ = u1.lens(
    r0=(0 * um, 500 * um),
    size=800 * um,
    radii=(0.6 * mm, -1.4 * mm),
    thickness=0.25 * mm,
    refractive_index=1.5,
    angle=0 * degrees,
    mask=(50 * um, 3 + 0.05j),
)

refractive_index = 1.5
height_grating = 20 * (refractive_index - 1) * wavelength / 2
u1.ronchi_grating(
    period=25 * um,
    fill_factor=0.5,
    length=2 * mm,
    height=height_grating,
    r0=(0 * um, 100 * um),
    Dx=0 * um,
    refractive_index=refractive_index,
    heigth_substrate=height_grating,
    refractive_index_substrate=refractive_index,
    angle=0 * degrees,
)

u1.surface_detection()
u1.draw_refractive_index()

edge_matrix = u1.borders

u1.smooth_refractive_index(pixels_filtering=8, type_filter=2)

CPU times: user 2.01 s, sys: 759 ms, total: 2.76 s
Wall time: 2.29 s

u1.BPM(verbose=False)
u1.draw(kind="intensity", logarithm=True, draw_borders=True, edge_matrix=edge_matrix)

8.13.3.1. Desplacement of a grating in a double grating system

def __experiment_grating_movement__(dict_params):
    delta_x = dict_params["delta_x"]
    period = dict_params["period"]
    t1 = dict_params["t1"]
    t2 = dict_params["t2"]
    t2.ronchi_grating(period=period, x0=delta_x, fill_factor=0.5)
    u2 = t1 * t2
    return u2

def creation_dictionary(deltas_x, period, t1, t2):
    # create Parameters: for multiprocessing
    dict_Parameters = []
    for i, delta_x in enumerate(deltas_x):
        dict_Parameters.append(dict(delta_x=delta_x, period=period, t1=t1, t2=t2))
    return dict_Parameters

x0 = np.linspace(-400 * um, 400 * um, 1024 * 1)
wavelength = 0.85 * um
period = 50 * um
z_talbot = 2 * period**2 / wavelength
z0 = z_talbot / 2
delay = 0.001

t1 = Scalar_mask_X(x0, wavelength, info="__experiment_grating_movement__")
t1.ronchi_grating(period=period, x0=0 * um, fill_factor=0.5)
t1.RS(z=z0, new_field=False)

t2 = Scalar_mask_X(x0, wavelength, info="__experiment_grating_movement__")
t2.ronchi_grating(period=period, x0=0 * um, fill_factor=0.5)

deltas_x = np.linspace(-60 * um, 60 * um, 256)

dict_Parameters = creation_dictionary(deltas_x=deltas_x, period=period, t1=t1, t2=t2)

u_s, time_proc = execute_multiprocessing(
    __experiment_grating_movement__,
    dict_Parameters,
    1,
    verbose=True,
)

x = u_s[0].x

Good result: factor 4.00
num_proc: 1, time=0.01840353012084961

%matplotlib qt5

fig = plt.figure()
ax1 = fig.add_subplot(211)
ax2 = fig.add_subplot(212)
perfil = np.zeros_like(deltas_x)

(h1,) = ax1.plot(x, np.zeros_like(x), "k", lw=2)
ax1.set_xlim(x[0], x[-1])
ax1.set_ylim(0, 2)
ax1.set_xlabel(r"$x (\mu m)$")

(h2,) = ax2.plot(deltas_x, perfil, "k", lw=2)
ax2.set_xlim(deltas_x[0], deltas_x[-1])
ax2.set_ylim(0, 0.5)
ax2.set_xlabel(r"$\Delta x (\mu m)$")

incr_frames = 1
for i in range(0, len(deltas_x), incr_frames):
    intensidad = abs(u_s[i].u) ** 2  # sacar fuera
    perfil[i] = intensidad.mean()
    plt.suptitle(r"$\delta x={:6.2f}\,\mu m$".format(deltas_x[i]), fontsize=18)
    h1.set_ydata(intensidad)
    h2.set_ydata(perfil)
    plt.draw()
    plt.pause(0.0001)

plt.close()

%matplotlib inline