Compare numerical Born orders

Compare finite-sample effective scattering coefficients through order three. The numerical ensemble retains amplitude interference and sampling errors. Integrated coefficients describe finite samples rather than an infinite medium. Error bars describe realization sampling, not discretization error. Field-term diagnostics alone do not certify convergence.

from bornsim.medium.random_medium import GaussianMedium

import sys

import matplotlib.pyplot as plt

from bornsim import EnsembleSampling, Grid, Solver, Source
from bornsim.units import ureg

grid = Grid(
    shape=(8, 8, 8),
    spacing=50 * ureg.nanometer,
)

medium = GaussianMedium(
    background_refractive_index=1.33,
    refractive_index_std=0.01,
    correlation_length=100 * ureg.nanometer,
)

source_configuration_1 = Source(wavelength=633 * ureg.nanometer)

ensemble_solver = Solver(
    source=source_configuration_1,
    order=3,
)

ensemble_sampling_configuration_1 = EnsembleSampling(
    realizations=4,
    seed=42,
)

result = ensemble_solver.ensemble(
    medium=medium,
    grid=grid,
    ensemble_sampling=ensemble_sampling_configuration_1,
)

for index, coefficient in enumerate(result.mu_s.to("1 / meter").magnitude, start=1):
    print(f"Through order {index}: effective μs = {coefficient:.5g} m⁻¹")

result.plot()

plt.show()

Through order 1: effective μs = 1030.3 m⁻¹
Through order 2: effective μs = 1031.8 m⁻¹
Through order 3: effective μs = 1031.5 m⁻¹

Field-term diagnostics

Compare field terms separately from the scattering curves. Decreasing terms alone do not certify convergence of the Born series.

result.plot_field_norms()

plt.show()

Inspect one ensemble realization in 3D

This is the first realization (seed 42) on the calculation grid, not an ensemble average or an infinite-medium material boundary. Drag to rotate and scroll to zoom in the embedded browser view. Regions with higher refractive index are more opaque; opacity is not absorption.

preview_volume = medium.to_volume(
    grid=grid,
    seed=42,
)

medium_figure = preview_volume.plot_3d(
    mode="volume",
    field="refractive_index",
    opacity_scale="increasing",
)

if "--no-browser" not in sys.argv:
    medium_figure.show(renderer="browser")