Mie Simulator GUI Running Application - VirtualPhotonics/MieSimulatorGUI GitHub Wiki

This document describes the inputs, outputs, and execution of the Mie Simulator GUI. As illustrated below, the interface consists of a single input selection panel and five distinct output panels: number density, scattering (µ_s), phase function, reduced scattering (µ_s') and anisotropy (Scattering Asymmetry).

This panel allows users to define the physical properties of particles and the medium for Mie simulations. It supports both Monodisperse (uniform) and Polydisperse (variable) particle distributions across single wavelengths or spectral ranges.

Users must first select the type of particle distribution:

• Monodisperse: All spheres share the same diameter and refractive index.
• Polydisperse: Spheres vary in size and/or attributes. This mode supports three models:
  1. Log-normal: Defined by mean diameter and standard deviation for skew-normal distribution (It is common distribution in particle systems).
  2. Gaussian: Defined by mean diameter and standard deviation for symmetric, "bell-curve" distributions.
  3. Custom: Allows for user-defined distributions via an external file. This is the only mode that supports varying refractive indices for different spheres within the same simulation.

These parameters define the size and density of the particles in the simulation volume.

• Diameter ($d$):
  • Range: $0.1\text{ nm}$ to $300\text{ µm}$. Inputs must be entered in micrometers (µm).
• Sphere Concentration (Conc): Enter the number of spheres per cubic millimeter ($\text{spheres/mm}^3$).
• Volume Fraction (Vol Frac): Represents the ratio of the volume occupied by particles to the total solution volume. for polydisperse systems, this is the sum of the volumes of all individual spheres per unit volume. The upper limit of the volume fraction is $\frac{\pi}{3\sqrt{2}}$ (~0.74). This ensures the volume fraction does not exceed the maximum packing factor for monodisperse spheres (hexagonal close-packed cubic).

Note on Accuracy: MieSimulatorGUI uses the Independent Scattering Approximation. This framework assumes particles are far enough apart to ignore coherent interactions. Accuracy decreases in concentrated regimes. Starting with v2.0, the tool will trigger a warning if a user inputs exceed the physical limits of this approximation (See Scattering Regime Analysis).

The tool uses the relative refractive index computed from the sphere and its surrounding medium.

• Medium Refractive Index (n_med): The refractive index of the surrounding medium.
• Sphere Refractive Index (m_sphere): The refractive index of the sphere can be a real or complex number. A non-zero m_imag indicates the sphere absorbs light. Following the Van de Hulst (1957) sign convention, m_sphere is given by:
  m_sphere = m_real – j m_imag
• Custom Inputs: In Custom polydisperse mode, users can assign unique refractive indices to different spheres using the formats found in the CustomDataSamples folder.

Define the spectral range for the simulation. The tool supports the primary biomedical and atmospheric windows.

• Range: $50\text{ nm}$ to $3000\text{ nm}$ ($3\text{ µm}$).
• Single Wavelength: Set the Start and End values to the same number.
• Spectral Sweep: Define a Start, End, and Step size to see how scattering properties evolve across a spectrum.

• ±5 Margin Slider: After a simulation, use this to make minor adjustments to concentration or volume fraction to observe real-time changes in results without re-entering data.
• Plot Scale Y-Axis: Switch to Log10 scale to better visualize high-dynamic-range data on the vertical axis..
• Show Distribution: (Polydisperse only) Displays the number density distribution ($1\text{ mm}^3$ volume) based on your mean and standard deviation inputs.

• Run Simulation: Computes the Mie scattering results based on current inputs.
• Display Data: Opens a text window showing the raw numerical results.
• Save Data: Exports selected simulation results to a text file.
• Close: Exits the application.

This panel characterizes the physical distribution and scaling of the spheres used in the Mie simulation.

• Number Density ($N_s$): Graphically presents the concentration of spheres in units of [ # / mm³ ].
• Size Parameter ($x$): Located in the subsequent tab, this dimensionless value relates the particle size to the wavelength of light. It is defined as: x = (2π R n_med) / λ_vacuum. where R is particle radius, n_med is refractive index of the surrounding medium and λ_vacuum is wavelength in vacuum [µm].

TIP: When using a Log-normal distribution, select the Log radio button for the x-axis (located below the plot) to properly visualize the distribution spread.

Mie theory produces three dimensionless efficiency factors: Scattering Efficiency ($Q_{sca}$), Extinction Efficiency ($Q_{ext}$), and Backscattering Efficiency ($Q_{back}$)

By multiplying these efficiency factors by the particle's geometric cross-sectional area ($\pi R^2$), the tool calculates the following cross-sections in units of $[ \text{mm}^2 ]$:

• Scattering Cross-Section: $C_{sca} = Q_{sca} \cdot \pi R^2$
• Extinction Cross-Section: $C_{ext} = Q_{ext} \cdot \pi R^2$
• Backscattering Cross-Section: $C_{back} = Q_{back} \cdot \pi R^2$

• Monodisperse Distributions: The scattering coefficient is calculated simply as the product of the scattering cross-section and the number density: $\mu_s = C_{sca} \times N_s$.
• Polydisperse Distributions: For distributions with varying particle sizes, the software employs a discrete particle model (as detailed by Schmitt and Kumar, 1998), performing a discrete summation of cross-sections across individual particle size bins.

The phase function describes the angular distribution of scattered light. The phase function and complex amplitude scattering matrix elements ($S_1$ and $S_2$) are derived to describe the transformation from the incident electromagnetic field to the far-field scattered field.

• Visualization Options: Users can view the phase function data using both polar and linear plots, and visualize the $S_1/S_2$ matrix elements on either a log or linear scale.
• Resolution Adjustment: Users can refine the detail of their plots by changing the dtheta(dθ) selection. Smaller values will provide higher angular resolution.
• Wavelength Control: Use the "Wavelength Slider" to observe how the behavior of phase function or $S_1/S_2$ matrix elements at specific wavelengths.

This panel analyzes the directional bias of the scattering.

Anisotropy Factor ($g$): The first tab displays the average cosine of the single scattering phase function.

• If $g > 0$, the scattering is predominantly forward-directed.
• If $g < 0$, the scattering is predominantly backward-directed.
• If $g = 0$, the scattering is isotropic (equal in all directions).

Integrated Fractions: The second tab provides specific percentages for total forward (-90° to 90°) and backward (90° to 270°) scattering, allowing for a deeper numerical analysis of the angular distribution.

The Reduced Scattering Panel displays $\mu_s'$, a parameter of high importance in biomedical optics because it characterizes light transport in "thick" or turbid media where multiple scattering events occur.

• Definition: It is computed as the product of the scattering coefficient and the complement of the anisotropy factor:

  μ_s' = μ_s(1 – g)

• µ_s' Power Law Fitting: This tab allows users to compute fitting parameters for the wavelength dependence of $\mu_s'$. This follows the methodology described by Steve L. Jacques (2013), providing a simplified functional form that is often used to non-invasively quantify tissue properties or other turbid materials.

  • Simple Power Law: The simple power law is the most common empirical model used to describe the wavelength dependence of scattering.
  $$\mu_s'(\lambda) = A \left( \frac{\lambda}{\lambda_0} \right)^{-b}$$
  • Complex Power Law: The complex power law model splits the scattering into two distinct physical contributions.
  $$\mu_s'(\lambda) = A \left[ f_{\text{Ray}} \left( \frac{\lambda}{\lambda_0} \right)^{-4} + (1 - f_{\text{Ray}}) \left( \frac{\lambda}{\lambda_0} \right)^{-b_{\text{Mie}}} \right]$$

The reference wavelength ($\lambda_0$) can be selected from the following values: 500 nm, 600 nm, 700 nm, 800 nm, 900 nm, and 1000 nm. The Best Fit button allows users to determine the optimal parameters.

Bohren, C. F., & Huffman, D. R. (1983). Absorption and Scattering of Light by Small Particles. John Wiley; Sons, Inc.

Hulst, H. C. van de. (1957). Light scattering by small particles (p. 470). John Wiley; Sons Inc.

Jacques, S. L. (2013). Optical properties of biological tissues: a review. Phys. Med. Biol., 58(14), 5007–5008. https://doi.org/10.1088/0031-9155/58/14/5007

Mie, G. (1908). Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen. Annalen Der Physik, 330(3), 377–445. https://doi.org/10.1002/andp.19083300302

Schmitt, J. M., & Kumar, G. (1998). Optical scattering properties of soft tissue: a discrete particle model. Applied Optics, 37(13), 2788–2797. https://doi.org/10.1364/AO.37.002788

Wiscombe, Warren J. (1979). Mie Scattering Calculations : Advances in Technique and Fast, Vector-Speed Computer Codes (NCAR TECHNICAL NOTE; pp. 1–98). National Center for Atmospheric Research. https://opensky.ucar.edu/islandora/object/technotes:232

Wiscombe, W. J. (1980). Improved mie scattering algorithms. Appl. Opt., 19(9), 1505–1509. https://doi.org/10.1364/AO.19.001505

Last edited: Feb 6, 2026