Fit an isolated-sphere scattering measurement

Recover a sphere diameter from one dimensionless scattering-efficiency measurement. This uses the isolated-particle Mie model. It does not represent multiple scattering, near-field coupling, or positional correlations in dense particle systems.

The fitted diameter is approximately 180 nanometers within the stated bounds. The prediction is a scalar dimensionless efficiency. One noiseless channel with a fixed refractive index demonstrates parameter recovery; it does not establish uniqueness over a wider diameter range.

iteration    1 | objective 0.035303537 | step 0.1
iteration    2 | objective 0.0083962553 | step 0.1
iteration    3 | objective 0.00081984712 | step 0.1
iteration    4 | objective 0.00081984712 | step 0.05
iteration    5 | objective 0.00081984712 | step 0.025
iteration    6 | objective 1.2293524e-05 | step 0.025
iteration    7 | objective 1.2293524e-05 | step 0.0125
iteration    8 | objective 1.2293524e-05 | step 0.00625
iteration    9 | objective 1.2293524e-05 | step 0.00313
iteration   10 | objective 1.9310194e-07 | step 0.00313
iteration   11 | objective 1.9310194e-07 | step 0.00156
iteration   12 | objective 1.9310194e-07 | step 0.000781
iteration   13 | objective 1.9310194e-07 | step 0.000391
iteration   14 | objective 3.0152357e-09 | step 0.000391
iteration   15 | objective 3.0152357e-09 | step 0.000195
iteration   16 | objective 3.0152357e-09 | step 9.77e-05
iteration   17 | objective 3.0152357e-09 | step 4.88e-05
iteration   18 | objective 4.711693e-11 | step 4.88e-05
iteration   19 | objective 4.711693e-11 | step 2.44e-05
iteration   20 | objective 4.711693e-11 | step 1.22e-05
iteration   21 | objective 4.711693e-11 | step 6.1e-06
iteration   22 | objective 7.3619446e-13 | step 6.1e-06
iteration   23 | objective 7.3619446e-13 | step 3.05e-06
iteration   24 | objective 7.3619446e-13 | step 1.53e-06
iteration   25 | objective 7.3619446e-13 | step 7.63e-07
converged after 25 iterations | objective 7.3619446e-13
converged (52 model evaluations)
objective = 0.000000

from PyMieSim import (
    Measure,
    FitParameter, MeasuredData, PlaneWave, PolarizationState, Simulation, Sphere,
    fit_parameters, ureg,
)

source = PlaneWave(
    wavelength=532 * ureg.nanometer,
    polarization=PolarizationState(angle=0 * ureg.degree),
    amplitude=1 * ureg.volt / ureg.meter,
)
target_diameter = 180 * ureg.nanometer
target = Simulation(
    scatterer=Sphere(diameter=target_diameter, material=1.59, medium=1.0),
    source=source,
).get(Measure.QSCA)


def model(parameters):
    sphere = Sphere(diameter=parameters["diameter"], material=1.59, medium=1.0)
    return Simulation(scatterer=sphere, source=source).get(Measure.QSCA)


result = fit_parameters(
    model=model,
    observation=MeasuredData(values=target),
    parameters=[
        FitParameter(
            name="diameter",
            initial=130 * ureg.nanometer,
            bounds=(80 * ureg.nanometer, 260 * ureg.nanometer),
        )
    ],
    max_iterations=250,
    show_progress=True,
)

print(result.summary())