7. Quality factor
In RS propagation, the algorithm provides information about the quality in the simulation, as described in F. Shen and A. Wang, “Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula,” Appl. Opt., vol. 45, no. 6, pp. 1102–1110, 2006.
[1]:
%load_ext autoreload
%autoreload 2
7.1. XY Scheme
[2]:
from diffractio import sp, nm, plt, np, mm, degrees, um
from diffractio.scalar_fields_XY import Scalar_field_XY
from diffractio.scalar_sources_XY import Scalar_source_XY
from diffractio.scalar_masks_XY import Scalar_mask_XY
from diffractio.scalar_fields_XY import get_RS_minimum_z, quality_factor
[3]:
wavelength = 0.5 * um
num_x = 512
num_y = 512
range_x=1*mm
range_y=1*mm
x0 = np.linspace(-range_x / 2, range_x / 2, num_x)
y0 = np.linspace(-range_y / 2, range_y / 2, num_y)
To check the minimum z distance where the quality is good we have the get_RS_minimum_z function.
[4]:
z_min = get_RS_minimum_z(range_x,
range_y,
num_x,
num_y,
wavelength,
n=1,
quality=1,
verbose=True)
z min = 3845.47
[5]:
quality = quality_factor(range_x,
range_y,
num_x,
num_y,
z_min,
wavelength,
n=1,
verbose=True)
Quality factor = 1.05
Let us check that the simulation is OK
[6]:
t0 = Scalar_mask_XY(x=x0, y=y0, wavelength=wavelength, info='t0')
t0.square(r0=(0,0), size=range_x)
u2 = t0.RS(z=z_min, new_field=True, verbose=True)
u2.draw(has_colorbar='vertical')
plt.clim(vmin=0)
Good result: factor 1.00
Function get_RS_minimum_z is also available inside the class:
[7]:
z_min = t0.get_RS_minimum_z(verbose=True)
z min = 3.85 mm
Now, let us reduce the distance, to see if the simulation si working worse.
[8]:
t0 = Scalar_mask_XY(x=x0, y=y0, wavelength=wavelength, info='t0')
t0.square(r0=(0, 0), size=range_x)
u2 = t0.RS(z=0.9*z_min, new_field=True, verbose=True)
u2.draw(has_colorbar='vertical')
plt.clim(vmin=0)
- Needs denser sampling: factor 0.90
The quality factor is computed considering the total area. When the mask is smaller that the whole area, good results can be obtained even with quality<1.
[9]:
t0 = Scalar_mask_XY(x=x0, y=y0, wavelength=wavelength, info='t0')
t0.square(r0=(0, 0), size=range_x/2)
u2 = t0.RS(z=0.75 * z_min, new_field=True, verbose=True)
u2.draw(has_colorbar='vertical')
plt.clim(vmin=0)
- Needs denser sampling: factor 0.76
But eventually, it starts to work badly:
[10]:
t0 = Scalar_mask_XY(x=x0, y=y0, wavelength=wavelength, info='t0')
t0.square(r0=(0, 0), size=range_x / 2)
u2 = t0.RS(z=0.66 * z_min, new_field=True, verbose=True)
u2.draw(has_colorbar='vertical')
plt.clim(vmin=0)
- Needs denser sampling: factor 0.67
7.1.1. Distance in terms of the number of data
[11]:
wavelength = 0.5 * um
range_x=1*mm
range_y=1*mm
num_data=np.linspace(32,3000)
zs = np.zeros_like(num_data)
[12]:
for i, data in enumerate(num_data):
z_min = get_RS_minimum_z(range_x,
range_y,
data,
data,
wavelength,
n=1,
quality=1,
verbose=False)
zs[i]=z_min
[13]:
plt.semilogy(num_data, zs)
7.2. X Scheme
The quality factor is also implemented in the X scheme
[14]:
from diffractio import sp, nm, plt, np, mm, degrees, um
from diffractio.scalar_fields_X import Scalar_field_X
from diffractio.scalar_sources_X import Scalar_source_X
from diffractio.scalar_masks_X import Scalar_mask_X
from diffractio.scalar_fields_X import get_RS_minimum_z, quality_factor
[15]:
wavelength = .5 * um
num_x = 512
range_x = 1 * mm
x0 = np.linspace(-range_x / 2, range_x / 2, num_x)
[16]:
z_min = get_RS_minimum_z(range_x,
num_x,
wavelength,
n=1,
quality=1,
verbose=True)
z min = 3779.77
[17]:
t0 = Scalar_mask_X(x=x0, wavelength=wavelength, info='t0')
t0.slit(x0=0, size=0.85*mm)
[18]:
z_min = t0.get_RS_minimum_z()
z min = 3.78 mm
[19]:
u2 = t0.RS(z=z_min, new_field=True, verbose=True)
u2.draw()
- Needs denser sampling: factor 0.97
[20]:
u2 = t0.RS(z=0.9*z_min, new_field=True, verbose=True)
u2.draw()
- Needs denser sampling: factor 0.88
