Scattering Module Methods & Types

This page groups the most commonly used APIs in a practical order.

Theory Mapping (Quick)

Reference: Sanghavi (2014).

• compute_aerosol_optical_properties (NAI2): Eq. (1) + Fourier framework around Eq. (17)

• compute_aerosol_optical_properties (PCW): Eq. (22) -> Eq. (24)

• reconstruct_phase: Greek/Fourier reconstruction around Eq. (17)

• phase_function, compute_aerosol_XS, compute_ref_aerosol_extinction: Eq. (1)-based cross-sections

For the expanded mapping table and implementation notes, see the Scattering overview.

High-level Workflow

1) Define model inputs

Use make_mie_model to combine aerosol microphysics, wavelength, polarization, truncation, and quadrature settings into a MieModel.

2) Compute optical properties

Use compute_aerosol_optical_properties to produce RT-facing aerosol optical properties: Fourier/Greek coefficients, single-scattering albedo, extinction, and truncation information.

For analytic test or parameterized aerosols, use HenyeyGreensteinPhaseFunction or SyntheticPolarizedHenyeyGreensteinPhaseFunction with analytic_aerosol_optics. This produces the same AerosolOptics container as the Mie path and therefore feeds the normal CoreRT and StandaloneSS layer optics.

3) Reconstruct phase matrix elements

vSmartMOM.Scattering.reconstruct_phase Function

reconstruct_phase(greek_coefs, μ; returnLeg = false)

Reconstruct angle-space scattering-matrix elements from Greek coefficients.

Reference: Sanghavi (2014), Fourier/Greek framework around Eq. (17).

f₁₁ represents the scalar phase function and is normalized as:

Using Legendre basis matrices computed at μ, this function evaluates:

Arguments

• greek_coefs: GreekCoefs coefficients.

• μ: cosine of scattering angles where the matrix should be reconstructed.

• returnLeg: if true, also return (P, P²).

Returns

• ScatteringMatrix when returnLeg=false.

• (ScatteringMatrix, P, P²) when returnLeg=true.

source

$(FUNCTIONNAME)(greek_coefs, μ; returnLeg = false)

Returns the reconstructed elements of the 4x4 scattering matrix at positions f₁₁, f₁₂, f₂₂, f₃₃, f₃₄, f₄₄ from the greek coefficients

f₁₁ represents the phase function p for the Intensity (first Stokes Vector element) and is normalized as follows:

• greek_coefs greek coefficients (Domke Type)

• returnLeg if false (default), just return f₁₁, f₁₂, f₂₂, f₃₃, f₃₄, f₄₄, if true,

• return f₁₁, f₁₂, f₂₂, f₃₃, f₃₄, f₄₄, P, P² (i.e. also the two legendre polynomials as matrices)

source

Convenience Computations

These are useful if you need cross-sections or scalar phase-function outputs without running the full RT-facing workflow.

vSmartMOM.Scattering.phase_function Function

phase_function(aerosol::Aerosol, λ, r_max, nquad_radius)
    -> (μ, w_μ, p11, C_ext, C_sca, g)

Compute scalar phase-function output for a size-distributed aerosol.

The returned p11(μ) is normalized by the bulk scattering cross-section and satisfies:

Asymmetry factor:

Reference: Sanghavi (2014), Mie-amplitude/cross-section setup from Eq. (1), with NAI-style angular integration discussed in Secs. 3-4.

source

phase_function(r::FT, λ::FT, nᵣ::FT, nᵢ::FT) where {FT<:AbstractFloat}
    -> (μ, w_μ, p11, C_ext, C_sca, g)

Monodisperse version of phase_function, for a single radius r. Returns the same tuple as the size-distribution overload.

source

vSmartMOM.Scattering.compute_aerosol_XS Function

compute_aerosol_XS(aerosol::Aerosol, λ, r_max, nquad_radius)
    -> (XS_ext, XS_sca, Cext_eff, Csca_eff)

Compute bulk extinction/scattering cross-sections for a size-distributed aerosol without reconstructing phase matrices.

Returns

• XS_ext: bulk extinction cross-section

• XS_sca: bulk scattering cross-section

• Cext_eff: area-normalized extinction

• Csca_eff: area-normalized scattering

with

Reference: Sanghavi (2014), Eq. (1) for particle-level C_ext/C_sca.

source

vSmartMOM.Scattering.compute_ref_aerosol_extinction Function

compute_ref_aerosol_extinction(model::MieModel{<:NAI2}, FT2::Type=Float64) -> Real

Compute only the bulk extinction cross-section for the aerosol model:

where is evaluated from the Mie series and is represented with quadrature over [0, r_max].

This helper avoids phase-function and Greek-coefficient reconstruction.

Reference: Sanghavi (2014), Eq. (1) for C_ext(r).

source

Analytic Phase Functions

Analytic phase-function aerosols are lightweight scattering sources for idealized tests, sensitivity experiments, and StandaloneSS validation. They are not a separate RT implementation: each analytic source is projected into GreekCoefs and then consumed by the same CoreRT optical-property machinery as Mie-derived aerosols.

vSmartMOM.Scattering.AbstractAnalyticPhaseFunction Type

AbstractAnalyticPhaseFunction

Analytic phase/scattering matrix source that can be converted to Greek coefficients and then used by the standard MOM optical-property path.

source

vSmartMOM.Scattering.HenyeyGreensteinPhaseFunction Type

HenyeyGreensteinPhaseFunction(g)

Scalar Henyey-Greenstein phase function, (1 - g^2) / (1 + g^2 - 2g cosΘ)^(3/2), normalized so its sphere average is one.

source

vSmartMOM.Scattering.SyntheticPolarizedHenyeyGreensteinPhaseFunction Type

SyntheticPolarizedHenyeyGreensteinPhaseFunction(; g, polarization_fraction)

Diagnostic polarizing Henyey-Greenstein-like scattering matrix. The f11 element is standard Henyey-Greenstein; f12/f11 follows the bounded toy law polarization_fraction * (1 - cosΘ^2) / (1 + cosΘ^2). This is intended for tests and sensitivity experiments, not as a Mie substitute.

source

vSmartMOM.Scattering.greek_coefficients Function

greek_coefficients(phase; l_max=64, nquad=max(2l_max+1, 64))

Project an analytic phase/scattering matrix into Greek coefficients so it can enter the same CoreRT MOM path as Mie-derived aerosol optics.

source

vSmartMOM.Scattering.analytic_aerosol_optics Function

analytic_aerosol_optics(phase; single_scattering_albedo=1, extinction_cross_section=1, l_max=64)

Create an AerosolOptics object from an analytic phase/scattering matrix. The returned object is directly consumable by the existing CoreRT aerosol mixing and Fourier-moment code.

source

vSmartMOM.Scattering.phase_matrix_first_column Function

phase_matrix_first_column(greek, μ₀, μv, Δϕ, Val(N))

Evaluate the first column of the scattering phase matrix for an unpolarized incident beam at one plane-parallel sun-view geometry. μ₀ and μv are positive cosines and Δϕ is the vSmartMOM relative azimuth in radians.

source

phase_matrix_first_column evaluates the single-scatter phase-matrix column needed for an unpolarized direct solar beam at one exact sun-view geometry. It is the shared hook used by StandaloneSS vector paths for the sun-to-atmosphere-to-sensor term.

Wigner Utilities (PCW)

vSmartMOM.Scattering.compute_wigner_values Function

compute_wigner_values(m_max::Integer, n_max::Integer, l_max::Integer)

Compute the Wigner 3j values for all (m, n, l) combinations up to m/n/l max, for (m1, m2, m3) = (-1, 1, 0) (wigner_A) and (-1, -1, 2) (wigner_B)

source

compute_wigner_values(N_max)

Shorthand for compute_wigner_values(2N_max + 1, N_max + 1, 2N_max + 1)

source

vSmartMOM.Scattering.save_wigner_values Function

save_wigner_values(filepath, wigner_A, wigner_B)

Save the Wigner A and Wigner B matrices at the given filepath

source

vSmartMOM.Scattering.load_wigner_values Function

load_wigner_values(filename)

Load the Wigner A and Wigner B matrices from the given filepath

source

Types

Core abstract interfaces

vSmartMOM.Scattering.AbstractAerosolType Type

type AbstractAerosolType

Abstract aerosol type

source

vSmartMOM.Scattering.AbstractFourierDecompositionType Type

type AbstractFourierDecompositionType

Abstract aerosol Fourier Decomposition computation type (NAI2 and PCW)

source

vSmartMOM.Scattering.AbstractPolarizationType Type

type AbstractPolarizationType

Abstract Polarization type

source

vSmartMOM.Scattering.AbstractTruncationType Type

AbstractTruncationType

Abstract supertype for phase-function truncation methods. All concrete methods are dispatched through truncate_phase and supply l_max(t) (the per-band Legendre cutoff that the RT pipeline allocates for). Subtypes:

• NoTruncation — identity. Use when the phase function has no sharp forward peak (canopy, isotropic scattering, smooth Rayleigh).

• δBGE — δ-BGE-fit (Sanghavi & Stephens 2015, JQSRT 159 §3); recommended for hyperspectral retrievals.

The atmospheric Δ_angle (forward exclusion half-angle) lives inside the truncation type that needs it, not as a free parameter on CoreRT.vSmartMOM_Parameters — different methods have different hyper-parameters and NoTruncation has none.

source

Aerosol and model types

vSmartMOM.Scattering.MieModel Type

MieModel{FDT<:AbstractFourierDecompositionType, FT}

Configuration for a Lorenz–Mie scattering computation. Specifies the aerosol (size distribution + refractive index), wavelength, polarization type, truncation strategy, and integration parameters. The computation_type selects between NAI-2 (Siewert) and PCW (Domke) Fourier decomposition algorithms.

Pre-computed Wigner symbol tables (wigner_A, wigner_B) can be supplied for PCW; they default to trivial placeholders when unused.

Fields

• computation_type

• aerosol

• λ

• polarization_type

• truncation_type

• r_max: Maximum radius [μm]

• nquad_radius: Number of quadrature points for integration over size distribution

• wigner_A

• wigner_B

source

Aerosol defines a size distribution and complex refractive index. See the Library for its canonical docstring.

Fourier decomposition types

The supported Fourier decomposition families are NAI2 and PCW.

Polarization types

vSmartMOM.Scattering.Stokes_IQUV Type

struct Stokes_IQUV{FT<:AbstractFloat}

A struct which defines full Stokes Vector ([I,Q,U,V]) RT code

Fields

• n: Number of Stokes components (int)

• D: Vector of length n for ... (see eq in Sanghavi )

• I₀: Incoming Stokes vector for scalar only

source

vSmartMOM.Scattering.Stokes_IQU Type

struct Stokes_IQU{FT<:AbstractFloat}

A struct which defines Stokes Vector ([I,Q,U]) RT code

Fields

• n: Number of Stokes components (int)

• D: Vector of length n for ... (see eq in Sanghavi )

• I₀: Incoming Stokes vector for scalar only

source

vSmartMOM.Scattering.Stokes_IQ Type

struct Stokes_IQ{FT<:AbstractFloat}

A struct which defines Stokes Vector ([I,Q]) RT code.

Fields

• n: Number of Stokes components (int)

• D: Vector of length n for ... (see eq in Sanghavi )

• I₀: Incoming Stokes vector for scalar only

source

vSmartMOM.Scattering.Stokes_I Type

struct Stokes_I{FT<:AbstractFloat}

A struct which define scalar I only RT code

Fields

• n: Number of Stokes components (int)

• D: Vector of length n for ... (see eq in Sanghavi )

• I₀: Incoming Stokes vector for scalar only

source

Truncation type

vSmartMOM.Scattering.NoTruncation Type

NoTruncation(; l_max=typemax(Int))

Identity truncation — phase functions are passed through unchanged.

This is the correct choice for radiative transfer through media whose phase function has no sharp forward peak: canopy bi-Lambertian scattering (the f_tr → 0 limit of Sanghavi & Stephens 2015 Eq. 8 is exactly the identity), isotropic scattering, and smooth Rayleigh. For Mie aerosol or ice-cloud forward peaks use δBGE instead.

source

vSmartMOM.Scattering.δBGE Type

δBGE{FT}(l_max, Δ_angle)

δ-BGE-fit truncation, vector form (Sanghavi & Stephens 2015, JQSRT 159, §3 — extension of Hu et al. 2000 to vector RT). Fits truncated Legendre coefficients outside the forward exclusion cone of half-angle Δ_angle and renormalises by the retained scattering fraction   .

Recommended over plain δ-m for hyperspectral retrievals because δ-m has known DSE and PTE errors near exact backscatter (Sanghavi & Stephens 2015 §2.4).

Fields

• l_max: Truncation length for Legendre terms

• Δ_angle: Exclusion angle for forward peak (in fitting procedure) [degrees]

source

Output types

GreekCoefs stores the Fourier/Greek coefficient representation consumed by the RT kernels, and AerosolOptics groups those coefficients with extinction, single-scattering albedo, and truncation outputs.

Linearized output types

vSmartMOM.Scattering.linGreekCoefs Type

struct GreekCoefs{FT}

A struct which holds all Greek coefficient lists (over l) in one object. See eq 16 in Sanghavi 2014 for details.

Fields

• α̇: Greek matrix coefficient α, is in B[2,2]

• β̇: Greek matrix coefficient β, is in B[1,1] (only important one for scalar!)

• γ̇: Greek matrix coefficient γ, is in B[2,1],B[1,2]

• δ̇: Greek matrix coefficient δ, is in B[4,4]

• ϵ̇: Greek matrix coefficient ϵ, is in B[3,4] and - in B[4,3]

• ζ̇: Greek matrix coefficient ζ, is in B[3,3]

source

vSmartMOM.Scattering.linAerosolOptics Type

struct AerosolOptics

A struct which holds all computed aerosol optics

Fields

• lin_greek_coefs: Greek matrix

• ω̃̇: Single Scattering Albedo

• k̇: Extinction cross-section

• ḟᵗ: Truncation factor

source