mieshah 1.0.0

A Python package for calculating light scattering properties/parameters of spheres using Mie theory.

mieshah

This Python package calculates light scattering properties/parameters of spheres by using Mie theory.

Initial version was developed from a mie theory program originally written in FORTRAN and published in the paper: Ghanshyam A. Shah, "Numerical Methods for Mie Theory of Scattering by a Sphere",Kodaikanal Obs. Bull. Soc.(1977) 2, 42-63. In this major updated version has been updated with modern numerical calculation to provide better accuracy in the result.

• Developed by Dwaipayan Deb (2026)

Why this project?

While standard Mie scattering packages like PyMieScatt or miepython are excellent for scattering calculations, mieshah is designed to simplify, automate, and speed up calculations for both monodisperse (single particle) and polydisperse (particle size distribution) scenarios.

• Identical, Validated Results: mieshah implements the standard Mie scattering equations (using Wiscombe's recurrence criteria), yielding results that are numerically identical to other established packages like PyMieScatt and miepython.
• Built-in Symbolic Size Distribution (Polydisperse): Instead of writing complex loops to manually discretize and integrate size distributions, you can pass any arbitrary frequency distribution function as a simple symbolic string (e.g., f="x**-2"). The package automatically handles discretization and integration.
• Physically Accurate Polydisperse Averages: Automatically applies the correct physical weighting (e.g., ratio-of-averages for bulk albedo and scattering cross-section weighting for the phase function and intensities), preventing incorrect flat arithmetic averaging of bulk optical properties.
• Streamlined Single-Particle Analysis (Monodisperse): For single-particle calculations, a single initialization automatically computes all efficiency factors ($Q_{\text{ext}}$, $Q_{\text{sca}}$, $Q_{\text{abs}}$, $Q_{\text{pr}}$, $Q_{\text{bak}}$), the asymmetry parameter, polarization, and angular phase function simultaneously, retrieving all relevant properties in one step.
• Angular Windowing (theta): For both single-particle and polydisperse cases, you can specify an angular window (e.g., theta=[10, 45]) to compute scattering parameters only in the region of interest, significantly reducing computation time and output file size.
• Automated Structured Output: Automatically logs bulk averages (mie1.out) and angular profiles (mie2.csv) to files for easy plotting or post-processing, avoiding the need to write custom CSV exporters in your scripts.

Cite the code (APA style):

Deb, D. (2026). mieshah: Calculate light scattering properties/parameters of spheres by using Mie theory (Version 1.0.0) [Software]. Zenodo. https://doi.org/10.5281/zenodo.15380219

Install command:

pip install mieshah

Use example:

import mieshah as ms
from matplotlib import pyplot as plt

# reff-> effective particle radius (microns), wl-> wavelength (microns), m-> complex refractive index (real, imaginary), 
# f-> size distribution function, incr-> increment for size distribution function
mymie = ms.miescatter(reff=[0.1,1], wl=6.283185307,m=(1.5,0),f="x**-2",incr=0.01)  # With size distribution function
#mymie = ms.miescatter(reff=100, wl=6.283185307,m=(1.5,0.0)) # Without size distribution function (single particle)

print(mymie.reff)
print(mymie.wl)
print(mymie.m)
print(mymie.f)
print(mymie.X) # Size parameter
print(mymie.ALBED) # Albedo
print(mymie.QSCA) # Scattering efficiency
print(mymie.QEXT) # Extinction efficiency
print(mymie.QBAK) # Backscattering efficiency
print(mymie.QABS) # Absorption efficiency
print(mymie.QPR) # Radiation pressure efficiency
print(mymie.I_perp) # Intensity perpendicular to the plane of incidence
print(mymie.I_parl) # Intensity parallel to the plane of incidence
print(mymie.Polar) # Degree of linear polarization
print(mymie.p_theta) # Phase function
print(mymie.theta) # Scattering angle in degrees

plt.plot(mymie.theta[::2], mymie.Polar[::2])
plt.xlabel('Theta (degrees)')
plt.ylabel('Polarization')
plt.title('Degree of Linear Polarization')
plt.show()
plt.plot(mymie.theta[::2], mymie.p_theta[::2])
plt.yscale('log')    
plt.xlabel('Theta (degrees)')
plt.ylabel('Phase Function')
plt.title('Phase Function')
plt.show()

New feature: theta input argument in v0.0.3

The miescatter class now supports an optional theta argument in the constructor, which sets the angular computation window for phase function outputs.

Usage

from miesh2 import miescatter

mies = miescatter(
    reff=[1, 5],
    wl=0.5,
    m=(1.5, 0.01),
    f='x**-2',
    incr=0.1,
    theta=[10, 45]
)

• theta=[min,max] runs the scattering phase calculation from min degrees to max degrees.
• If theta is omitted, default range is [0,180].
• theta must be a list of two values; otherwise the code exits with a message.
• However single int value is allowed e.g. theta=45

Behavior

• With theta=[10,45], the method computes results only for angles 10 through 45 degrees.
• Internally, miecalc() iterates for ITH in range(self.th_min+1,self.th_max+2) and converts each angle to radians for phase calculations.

Output

• mie1.out contains global sphere averaged optical parameters:
  • X, QSCA, QEXT, QABS, ALBED, ASYM, QPR, QBAK.
• mie2.csv contains per-angle data:
  • theta, I_perp, I_para, Polar, p_theta.

Key Improvements in pymieshah (v1.0.0 vs v0.0.3)

pymieshah (v1.0.0) introduces significant performance, accuracy, and code modernization improvements over the older version (v0.0.3). These improvements affect execution speed, physical correctness of size-averaged quantities, and numerical stability:

1. $N \times$ Computational Speedup via Parameter Precalculation

• Old Behavior (v0.0.3): Single-particle parameters (Mie coefficients $a_n, b_n$ and efficiencies) were recalculated inside the angular loop for every angle $\theta$. For $N$ angles and $M$ size bins, the recurrence relations were evaluated $N \times M$ times.
• New Behavior (v1.0.0): Single-particle parameters for all size bins are precalculated and cached exactly once before entering the angular loop. The angular loop now only performs the lightweight sum over Legendre polynomials.
• Impact: For a full sweep of $N$ angles (e.g., $181$ angles from $0^\circ$ to $180^\circ$), this results in a speedup of approximately $180\times$ for polydisperse calculations.

2. Correct Physical Weighting for Size Distributions

• Albedo ($\text{ALBED}$): Corrected to be the ratio of the average scattering efficiency to the average extinction efficiency ($\langle Q_{\text{sca}} \rangle / \langle Q_{\text{ext}} \rangle$) rather than the simple average of individual albedos (average of ratios): $$\text{Albedo}{\text{avg}} = \frac{\sum Q{\text{sca}}(r) f(r) \Delta r}{\sum Q_{\text{ext}}(r) f(r) \Delta r}$$
• Phase Function ($P(\theta)$) and Intensities ($I_{\parallel}, I_{\perp}$): Corrected to be weighted by the scattering cross-section ($C_{\text{sca}}(r) \propto Q_{\text{sca}}(r) \cdot x(r)^2$) rather than a flat arithmetic average over the frequency distribution $f(r)\Delta r$. This ensures that larger or more strongly scattering particles correctly dominate the collective phase function: $$P_{\text{avg}}(\theta) = \frac{\sum P(\theta, r) C_{\text{sca}}(r) f(r) \Delta r}{\sum C_{\text{sca}}(r) f(r) \Delta r}$$

3. Modernized Algorithm & Numerical Stability

• Legacy Code Removal: Replaced the legacy dimpy-based fixed array allocations (e.g., dim(21001)) with native, dynamic NumPy complex arrays (complex128).
• Wiscombe Termination Criterion: The recurrence termination limit is now dynamically computed using Wiscombe's criterion: $$n_{\text{stop}} = x + 4 x^{1/3} + 2$$ This prevents unnecessary iterations, avoids array overflow, and ensures numerical stability for large size parameters.

Dependencies

• numpy
• sympy
• dimpy (or replacement array initialization)

Notes

• If reff is a range and f is supplied, an effective weighted average (frequency distribution) is computed.
• If reff is a single value, f should be omitted.

Zenodo Release

Zenodo project doi:https://doi.org/10.5281/zenodo.15380219