8.5. Arago point
Here, we analyze how Arago point (also called Poisson spot) is generated using in XY and XYZ framework.
More information: https://www.lighttrans.com/use-cases/application-use-cases/observation-of-the-poisson-spot.html
8.5.1. XY
[1]:
from diffractio import np, plt, um, mm, nm, degrees
from diffractio.scalar_masks_XY import Scalar_mask_XY
from diffractio.scalar_sources_XY import Scalar_source_XY
[2]:
x0 = np.linspace(-200 * um, 200 * um, 512)
y0 = np.linspace(-200 * um, 200 * um, 1024)
wavelength = 532 * nm
[3]:
u0 = Scalar_source_XY(x0, y0, wavelength)
u0.gauss_beam(r0=(0 * um, 0 * um), w0=130 * um, z0=0, A=1, theta=0.0)
[4]:
obstacle = Scalar_mask_XY(x0, y0, wavelength)
obstacle.circle(r0=(0 * um, 0 * um), radius=50 * um)
obstacle.inverse_amplitude()
u1 = u0 * obstacle
u1.draw()
[5]:
arago_point = u1.RS(z=2 * mm)
[6]:
arago_point.draw(logarithm=True)
[7]:
arago_point.draw_profile([-150, 0], [150, 0], npixels=2048, order=2)
8.5.2. XYZ
[8]:
from diffractio import np, plt, um, mm, nm, degrees
from diffractio.scalar_fields_XYZ import Scalar_field_XYZ
from diffractio.scalar_sources_XY import Scalar_source_XY
from diffractio.scalar_masks_XY import Scalar_mask_XY
[9]:
import pyvista as pv
pv.set_jupyter_backend("static")
[10]:
x0 = np.linspace(-200 * um, 200 * um, 512)
y0 = np.linspace(-200 * um, 200 * um, 256)
z0 = np.linspace(1 * mm, 2 * mm, 32)
wavelength = 532 * nm
[11]:
u0 = Scalar_source_XY(x0, y0, wavelength)
u0.gauss_beam(r0=(0 * um, 0 * um), w0=130 * um, z0=0, A=1, theta=0.0)
[12]:
obstacle = Scalar_mask_XY(x0, y0, wavelength)
obstacle.circle(r0=(0 * um, 0 * um), radius=50 * um)
obstacle.inverse_amplitude()
u1 = u0 * obstacle
[13]:
u_xyz = Scalar_field_XYZ(x0, y0, z0, wavelength)
[14]:
u_xyz.incident_field(u1)
[15]:
u_xyz.RS(num_processors=1)
time in RS= 2.5367414951324463. num proc= 1
[16]:
u_xyz.draw_XZ(y0=0)
fig = plt.gcf()
fig.set_size_inches(8, 3)
<Figure size 480x360 with 0 Axes>
8.5.3. XZ
Warning: The XZ results are not valid since, as it is an interferential process, radial symmetry is required.
[17]:
from diffractio.scalar_masks_XZ import Scalar_mask_XZ
from diffractio.scalar_masks_X import Scalar_mask_X
from diffractio.scalar_sources_X import Scalar_source_X
[18]:
x0 = np.linspace(-200 * um, 200 * um, 1024)
z0 = np.linspace(1 * mm, 2 * mm, 512)
wavelength = 532 * nm
[19]:
source_x = Scalar_source_X(x0, wavelength)
source_x.gauss_beam(x0=0, w0=130 * um, z0=0, A=1, theta=0.0)
[20]:
mask_x = Scalar_mask_X(x0, wavelength)
mask_x.slit(x0=0, size=100 * um)
mask_x.u = 1 - mask_x.u
[21]:
u1 = source_x * mask_x
[22]:
arago_xz = Scalar_mask_XZ(x0, z0, wavelength)
arago_xz.incident_field(u1)
[23]:
arago_xz.RS()
[24]:
arago_xz.draw()
fig = plt.gcf()
fig.set_size_inches(8, 3)
