Raman Scattering

A Python module for calculating Raman scattering coefficients, backscattering coefficients, and related optical properties for pure water and seawater.

Overview

Raman scattering is an inelastic scattering process where incident light excites water molecules to a virtual energy state, which then decays to a vibrational level above the ground state. The emitted light has a longer wavelength (lower energy) than the incident light, with a characteristic wavenumber shift of ~3400 cm^-1 corresponding to the O-H stretching mode of water.

This module implements the formulations from:

Bartlett et al. (1998) — Raman scattering coefficient measurements and wavelength dependence
Walrafen (1967) — Wavenumber distribution function (emission spectrum shape)
Ge et al. (1993) — Depolarization ratio and phase function
Mobley (1994) — Light and Water textbook formulations
Sathyendranath & Platt (1998) — Ocean-colour model incorporating transspectral processes (Raman contribution to Rrs)

The module is organized into two parts:

Low-level functions (bing.rt.raman):: Core Raman scattering coefficients, phase functions, emission spectra, and wavelength redistribution.
Rrs functions (bing.rt.rrs):: Higher-level functions for calculating Raman contribution to remote sensing reflectance, including first-order and second-order terms.

Quick Start

import numpy as np
from bing.rt.raman import (
    raman_scattering_coeff,
    raman_backscattering_coeff,
    excitation_to_emission_wavelength,
    summary_at_wavelength
)

# Raman scattering coefficient at 488 nm
b_R = raman_scattering_coeff(488)
print(f"b_R(488 nm) = {b_R:.2e} m⁻¹")  # 2.60e-04 m⁻¹

# Backscattering coefficient
b_bR = raman_backscattering_coeff(488)
print(f"b_bR(488 nm) = {b_bR:.2e} m⁻¹")  # 1.30e-04 m⁻¹

# Emission wavelength for 488 nm excitation
lambda_em = excitation_to_emission_wavelength(488)
print(f"Emission center: {lambda_em:.1f} nm")  # ~585 nm

# Full summary
summary = summary_at_wavelength(488)

Module Contents

Constants

Constant	Value	Description
`B_RAMAN_488_BARTLETT`	2.7×10^-4 m^-1	Bartlett et al. (1998) measurement
`B_RAMAN_488_DESIDERIO`	2.4×10^-4 m^-1	Desiderio (2000) measurement
`B_RAMAN_488_HYDROLIGHT`	2.6×10^-4 m^-1	HydroLight default value
`DEPOLARIZATION_RATIO`	0.17	For water at ~3400 cm^-1
`WAVENUMBER_SHIFT_CENTER`	3400 cm^-1	Center of O-H stretch band

Functions

Scattering Coefficients

raman_scattering_coeff

raman_scattering_coeff(wavelength_excitation, reference_value=2.6e-4, units='energy')

Calculate the total Raman scattering coefficient b_R(λ’).

Parameters:

wavelength_excitation (float or ndarray) – Excitation wavelength(s) λ’ in nm
reference_value (float) – Reference value at 488 nm in m^-1
units (str) – 'energy' (exponent -5.5) or 'photon' (exponent -5.3)

Returns:

b_R in m^-1

Return type:

float or ndarray

Example:

# Single wavelength
b_R = raman_scattering_coeff(400)  # 7.76e-04 m⁻¹

# Array of wavelengths
wavelengths = np.array([400, 450, 500, 550])
b_R = raman_scattering_coeff(wavelengths)

raman_backscattering_coeff

raman_backscattering_coeff(wavelength_excitation, reference_value=2.6e-4, units='energy')

Calculate the Raman backscattering coefficient b_bR(λ’).

The backscattering coefficient is the integral of the volume scattering function over the backward hemisphere (scattering angles from 90° to 180°).

Parameters:

wavelength_excitation (float or ndarray) – Excitation wavelength(s) λ’ in nm
reference_value (float) – Reference value at 488 nm in m^-1
units (str) – 'energy' or 'photon'

Returns:

b_bR in m^-1

Return type:

float or ndarray

Note

For the Raman phase function, the backscattering ratio b_bR/b_R = 0.5 exactly.

Wavelength Functions

excitation_to_emission_wavelength

excitation_to_emission_wavelength(lambda_ex, delta_nu=3400)

Convert excitation wavelength to emission wavelength.

Parameters:

lambda_ex (float or ndarray) – Excitation wavelength(s) in nm
delta_nu (float) – Wavenumber shift in cm^-1

Returns:

Emission wavelength(s) in nm

Return type:

float or ndarray

Example:

excitation_to_emission_wavelength(488)   # → 585.1 nm
excitation_to_emission_wavelength(400)   # → 463.0 nm
excitation_to_emission_wavelength(550)   # → 676.5 nm

emission_to_excitation_wavelength

emission_to_excitation_wavelength(lambda_em, delta_nu=3400)

Inverse conversion from emission to excitation wavelength.

Parameters:

lambda_em (float or ndarray) – Emission wavelength(s) in nm
delta_nu (float) – Wavenumber shift in cm^-1

Returns:

Excitation wavelength(s) in nm

Return type:

float or ndarray

wavelength_redistribution

wavelength_redistribution(lambda_ex, lambda_em)

Calculate the wavelength redistribution function f_R(λ’, λ) in nm^-1.

This gives the probability density that light at excitation wavelength λ’, if Raman scattered, will be emitted at wavelength λ.

Parameters:

lambda_ex (float) – Excitation wavelength λ’ in nm
lambda_em (float or ndarray) – Emission wavelength(s) λ in nm

Returns:

f_R in nm^-1

Return type:

float or ndarray

Example:

# Emission spectrum for 488 nm excitation
lambda_em = np.linspace(550, 620, 100)
f_R = wavelength_redistribution(488, lambda_em)

Phase Function

raman_phase_function

raman_phase_function(psi, rho=0.17, normalize=True)

Calculate the Raman phase function β_R(ψ) in sr^-1.

Parameters:

psi (float or ndarray) – Scattering angle(s) in radians
rho (float) – Depolarization ratio
normalize (bool) – If True, normalize so ∫β sin(ψ) dψ = 1/(2π)

Returns:

Phase function in sr^-1

Return type:

float or ndarray

The phase function has the form:

\[\beta_R(\psi) = \frac{1 + \delta \cos^2\psi}{4\pi \times \text{normalization}}\]

where δ = (1 - ρ)/(1 + ρ) ≈ 0.71 for ρ = 0.17.

raman_phase_function_simple

raman_phase_function_simple(psi)

Simplified form from the Ocean Optics Web Book:

\[\beta_R(\psi) = \frac{1 + 0.53 \cos^2\psi}{4\pi \times 1.177}\]

Parameters:: psi (float or ndarray) – Scattering angle(s) in radians
Returns:: Phase function in sr^-1
Return type:: float or ndarray

Volume Scattering Function

raman_vsf

raman_vsf(wavelength_excitation, wavelength_emission, psi, reference_value=2.6e-4, units='energy')

Calculate the full Raman volume scattering function β_R(λ’, λ, ψ) in m^-1 sr^-1 nm^-1.

This combines all three components:

\[\beta_R(\lambda', \lambda, \psi) = b_R(\lambda') \times f_R(\lambda', \lambda) \times \tilde{\beta}_R(\psi)\]

Parameters:

wavelength_excitation (float) – Excitation wavelength λ’ in nm
wavelength_emission (float) – Emission wavelength λ in nm
psi (float or ndarray) – Scattering angle(s) in radians
reference_value (float) – Reference value at 488 nm in m^-1
units (str) – 'energy' or 'photon'

Returns:

Volume scattering function in m^-1 sr^-1 nm^-1

Return type:

float or ndarray

Convenience Functions

get_emission_spectrum

get_emission_spectrum(wavelength_excitation, wavelength_emission_range=None, n_points=100)

Get the Raman emission spectrum for a given excitation wavelength.

Parameters:

wavelength_excitation (float) – Excitation wavelength in nm
wavelength_emission_range (tuple or None) – (min, max) emission wavelength range in nm
n_points (int) – Number of points in the spectrum

Returns:

(wavelength_emission, intensity) arrays

Return type:

tuple of ndarray

Example:

lambda_em, intensity = get_emission_spectrum(488)
plt.plot(lambda_em, intensity)

summary_at_wavelength

summary_at_wavelength(wavelength, units='energy')

Get a dictionary of all Raman parameters at a given excitation wavelength.

Parameters:

wavelength (float) – Excitation wavelength in nm
units (str) – 'energy' or 'photon'

Returns:

Dictionary of Raman parameters

Return type:

dict

Example:

>>> summary_at_wavelength(488)
{
    'excitation_wavelength_nm': 488,
    'emission_center_nm': 585.08,
    'wavelength_shift_nm': 97.08,
    'wavenumber_shift_cm-1': 3400.0,
    'scattering_coeff_m-1': 2.6e-04,
    'backscattering_coeff_m-1': 1.3e-04,
    'backscattering_ratio': 0.5,
    'depolarization_ratio': 0.17,
    'units': 'energy'
}

Raman Rrs Functions (bing.rt.rrs)

These functions calculate the contribution of Raman scattering to remote sensing reflectance (Rrs), implementing the Sathyendranath & Platt (1998) formulation.

calc_Rrs_with_raman(a_em, bb_em, a_ex, bb_ex, bb_R, Ed_ratio=1.0, in_G1=None, in_G2=None, mu_d=0.9, mu_u=0.4, mu_R=0.5, include_second_order=True)

Calculate remote sensing reflectance (Rrs) including Raman correction.

This function computes Rrs using the Gordon model for elastic scattering and adds the Raman contribution from Sathyendranath & Platt (1998).

Parameters:

a_em (float or ndarray) – Total absorption coefficient at emission wavelength λ [m^-1]
bb_em (float or ndarray) – Total backscattering coefficient at emission wavelength λ [m^-1]
a_ex (float or ndarray) – Total absorption coefficient at excitation wavelength λ’ [m^-1]
bb_ex (float or ndarray) – Total backscattering coefficient at excitation wavelength λ’ [m^-1]
bb_R (float or ndarray) – Raman backscattering coefficient at λ’ [m^-1]. Can be computed using bing.rt.raman.raman_backscattering_coeff()
Ed_ratio (float or ndarray) – Ratio Ed(λ’)/Ed(λ). Default is 1.0
in_G2 (in_G1,) – Gordon coefficients. If None, use defaults (0.0949, 0.0794)
mu_d (float) – Mean cosine for downwelling irradiance
mu_u (float) – Mean cosine for upwelling irradiance
mu_R (float) – Mean cosine for Raman-scattered light
include_second_order (bool) – If True, include second-order Raman terms. Default is True

Returns:

Remote sensing reflectance Rrs [sr^-1]

Return type:

float or ndarray

Example:

from bing.rt import raman
from bing.rt.rrs import calc_Rrs_with_raman

# At 520 nm emission with 443 nm excitation
a_520, bb_520 = 0.05, 0.002
a_443, bb_443 = 0.03, 0.003
bb_R = raman.raman_backscattering_coeff(443)
Rrs = calc_Rrs_with_raman(a_520, bb_520, a_443, bb_443, bb_R)

calc_R_raman_first_order(a_em, bb_em, a_ex, bb_ex, bb_R, Ed_ratio=1.0, mu_d=0.9, mu_R=0.5)

Calculate first-order Raman reflectance (Term 1).

This is Eq. (11) from Sathyendranath & Platt (1998).

Parameters:

a_em (float or ndarray) – Absorption coefficient at emission wavelength λ [m^-1]
bb_em (float or ndarray) – Elastic backscattering coefficient at emission wavelength λ [m^-1]
a_ex (float or ndarray) – Absorption coefficient at excitation wavelength λ’ [m^-1]
bb_ex (float or ndarray) – Elastic backscattering coefficient at excitation wavelength λ’ [m^-1]
bb_R (float or ndarray) – Raman backscattering coefficient at excitation wavelength λ’ [m^-1]
Ed_ratio (float or ndarray) – Ratio of downwelling irradiance Ed(λ’)/Ed(λ). Default is 1.0
mu_d (float) – Mean cosine for downwelling irradiance
mu_R (float) – Mean cosine for Raman-scattered light

Returns:

First-order Raman reflectance R^R(λ, 0)

Return type:

float or ndarray

The first-order term represents direct Raman scattering:

\[R^R(\lambda, 0) = \frac{E_d(\lambda')}{E_d(\lambda)} \times \frac{b_b^R(\lambda')/\mu_d(\lambda')}{K(\lambda') + \kappa^R(\lambda)}\]

calc_R_raman_RE(a_em, bb_em, a_ex, bb_ex, bb_R, Ed_ratio=1.0, s_E=1.0, mu_d=0.9, mu_R=0.5)

Calculate second-order Raman-then-Elastic reflectance (Term 2).

This is Eq. (18) from Sathyendranath & Platt (1998): a downward Raman-scattering event followed by an upward elastic-scattering event.

Parameters:

a_em (float or ndarray) – Absorption coefficient at emission wavelength λ [m^-1]
bb_em (float or ndarray) – Elastic backscattering coefficient at emission wavelength λ [m^-1]
a_ex (float or ndarray) – Absorption coefficient at excitation wavelength λ’ [m^-1]
bb_ex (float or ndarray) – Elastic backscattering coefficient at excitation wavelength λ’ [m^-1]
bb_R (float or ndarray) – Raman backscattering coefficient at λ’ [m^-1]
Ed_ratio (float or ndarray) – Ratio Ed(λ’)/Ed(λ). Default is 1.0
s_E (float) – Shape factor for elastic scattering
mu_d (float) – Mean cosine for downwelling irradiance
mu_R (float) – Mean cosine for Raman-scattered light

Returns:

Second-order Raman-Elastic reflectance R^RE(λ, 0)

Return type:

float or ndarray

Note

This term is typically ~10% of the first-order Raman term.

calc_R_raman_ER(a_em, bb_em, a_ex, bb_ex, bb_R, Ed_ratio=1.0, s_E=1.0, mu_d=0.9, mu_u=0.4, mu_R=0.5)

Calculate second-order Elastic-then-Raman reflectance (Term 3).

This is Eq. (23) from Sathyendranath & Platt (1998): an upward elastic-scattering event followed by an upward Raman-scattering event.

Parameters:

a_em (float or ndarray) – Absorption coefficient at emission wavelength λ [m^-1]
bb_em (float or ndarray) – Elastic backscattering coefficient at emission wavelength λ [m^-1]
a_ex (float or ndarray) – Absorption coefficient at excitation wavelength λ’ [m^-1]
bb_ex (float or ndarray) – Elastic backscattering coefficient at excitation wavelength λ’ [m^-1]
bb_R (float or ndarray) – Raman backscattering coefficient at λ’ [m^-1]
Ed_ratio (float or ndarray) – Ratio Ed(λ’)/Ed(λ). Default is 1.0
s_E (float) – Shape factor for elastic scattering
mu_d (float) – Mean cosine for downwelling irradiance
mu_u (float) – Mean cosine for upwelling irradiance
mu_R (float) – Mean cosine for Raman-scattered light

Returns:

Second-order Elastic-Raman reflectance R^ER(λ, 0)

Return type:

float or ndarray

Note

This term is typically ~10% of the first-order Raman term.

calc_R_raman_total(a_em, bb_em, a_ex, bb_ex, bb_R, Ed_ratio=1.0, s_E=1.0, mu_d=0.9, mu_u=0.4, mu_R=0.5, include_second_order=True)

Calculate total Raman contribution to reflectance at the sea surface.

This combines the first-order Raman term (Term 1) and optionally the two second-order terms (Terms 2 and 3) from Sathyendranath & Platt (1998).

Parameters:

a_em (float or ndarray) – Absorption coefficient at emission wavelength λ [m^-1]
bb_em (float or ndarray) – Elastic backscattering coefficient at emission wavelength λ [m^-1]
a_ex (float or ndarray) – Absorption coefficient at excitation wavelength λ’ [m^-1]
bb_ex (float or ndarray) – Elastic backscattering coefficient at excitation wavelength λ’ [m^-1]
bb_R (float or ndarray) – Raman backscattering coefficient at λ’ [m^-1]
Ed_ratio (float or ndarray) – Ratio Ed(λ’)/Ed(λ). Default is 1.0
s_E (float) – Shape factor for elastic scattering
mu_d (float) – Mean cosine for downwelling irradiance
mu_u (float) – Mean cosine for upwelling irradiance
mu_R (float) – Mean cosine for Raman-scattered light
include_second_order (bool) – If True, include second-order terms (RE and ER). Default is True

Returns:

Total Raman reflectance contribution

Return type:

float or ndarray

Total Raman reflectance = R^R + R^RE + R^ER

Note

The second-order Raman-Raman terms (Terms 4 and 5) are neglected as they contribute only ~1% of the first-order term (see Section 4.A of the paper).

calc_R_total_with_raman(a_em, bb_em, a_ex, bb_ex, bb_R, Ed_ratio=1.0, s_E=1.0, mu_d=0.9, mu_u=0.4, mu_R=0.5, include_second_order=True)

Calculate total reflectance including elastic and Raman contributions.

This implements Eq. (26) from Sathyendranath & Platt (1998), the simplified model for clear waters.

Parameters:

a_em (float or ndarray) – Absorption coefficient at emission wavelength λ [m^-1]
bb_em (float or ndarray) – Elastic backscattering coefficient at emission wavelength λ [m^-1]
a_ex (float or ndarray) – Absorption coefficient at excitation wavelength λ’ [m^-1]
bb_ex (float or ndarray) – Elastic backscattering coefficient at excitation wavelength λ’ [m^-1]
bb_R (float or ndarray) – Raman backscattering coefficient at λ’ [m^-1]
Ed_ratio (float or ndarray) – Ratio Ed(λ’)/Ed(λ). Default is 1.0
s_E (float) – Shape factor for elastic scattering
mu_d (float) – Mean cosine for downwelling irradiance
mu_u (float) – Mean cosine for upwelling irradiance
mu_R (float) – Mean cosine for Raman-scattered light
include_second_order (bool) – If True, include second-order Raman terms. Default is True

Returns:

Total reflectance R(λ, 0) = R^E(λ) + R^R(λ) + R^RE(λ) + R^ER(λ)

Return type:

float or ndarray

calc_raman_correction_factor(a_em, bb_em, a_ex, bb_ex, bb_R, Ed_ratio=1.0, s_E=1.0, mu_d=0.9, mu_u=0.4, mu_R=0.5, include_second_order=True)

Calculate the multiplicative correction factor for Raman scattering.

This returns the ratio of total reflectance (with Raman) to elastic reflectance, useful for correcting Rrs retrievals.

Parameters:

a_em (float or ndarray) – Absorption coefficient at emission wavelength λ [m^-1]
bb_em (float or ndarray) – Elastic backscattering coefficient at emission wavelength λ [m^-1]
a_ex (float or ndarray) – Absorption coefficient at excitation wavelength λ’ [m^-1]
bb_ex (float or ndarray) – Elastic backscattering coefficient at excitation wavelength λ’ [m^-1]
bb_R (float or ndarray) – Raman backscattering coefficient at λ’ [m^-1]
Ed_ratio (float or ndarray) – Ratio Ed(λ’)/Ed(λ). Default is 1.0
s_E (float) – Shape factor for elastic scattering
mu_d (float) – Mean cosine for downwelling irradiance
mu_u (float) – Mean cosine for upwelling irradiance
mu_R (float) – Mean cosine for Raman-scattered light
include_second_order (bool) – If True, include second-order Raman terms. Default is True

Returns:

Correction factor: (R^E + R_raman) / R^E

Return type:

float or ndarray

To remove Raman contribution from measured reflectance:

R_elastic = R_measured / correction_factor

Note

Typical correction factors range from 1.0 to ~1.25, with largest corrections in clear (oligotrophic) waters at longer wavelengths.

calc_R_elastic(a, bb, s=1.0, mu_d=0.9, mu_u=0.4)

Calculate elastic-scattering reflectance at the sea surface.

This is Eq. (5) from Sathyendranath & Platt (1998), the standard elastic scattering term (Term 0 in Table 1).

Parameters:

a (float or ndarray) – Absorption coefficient [m^-1]
bb (float or ndarray) – Backscattering coefficient [m^-1]
s (float) – Shape factor for scattering (s = 1 for isotropic/Rayleigh)
mu_d (float) – Mean cosine for downwelling irradiance
mu_u (float) – Mean cosine for upwelling irradiance

Returns:

Elastic reflectance R^E(λ, 0)

Return type:

float or ndarray

\[R^E(\lambda, 0) = \frac{\mu_u \times s}{\mu_u + \mu_d} \times \frac{b_b}{a + b_b}\]

This is equivalent to the Gordon model when appropriate G factors are used.

calc_attenuation_coeffs(a, bb, mu_d=0.9, mu_u=0.4, mu_R=0.5)

Calculate diffuse attenuation coefficients for elastic and Raman scattering.

Following Sathyendranath & Platt (1998) Eqs. (3) and (4).

Parameters:

a (float or ndarray) – Absorption coefficient [m^-1]
bb (float or ndarray) – Backscattering coefficient [m^-1]
mu_d (float) – Mean cosine for downwelling irradiance
mu_u (float) – Mean cosine for upwelling irradiance
mu_R (float) – Mean cosine for Raman-scattered light (typically 0.5 for isotropic)

Returns:

Dictionary containing attenuation coefficients:

'K': Downwelling attenuation coefficient
'kappa_E': Upwelling attenuation for elastic scatter
'kappa_R': Upwelling attenuation for Raman scatter
'K_R': Downwelling attenuation after Raman scatter

Return type:

dict

Physical Background

Wavelength Dependence

The Raman scattering coefficient follows a strong power-law wavelength dependence:

Units	Excitation Form	Emission Form
Energy	b_R ∝ (λ’)^-5.5	b_R ∝ λ^-4.8
Photon	b_R ∝ (λ’)^-5.3	b_R ∝ λ^-4.6

This strong wavelength dependence means Raman scattering is much more significant at blue wavelengths than at red wavelengths.

Emission Spectrum

The emission spectrum is modeled using the Walrafen (1967) four-Gaussian parameterization:

Component	Weight	Center (cm^-1)	FWHM (cm^-1)
1	0.41	3250	210
2	0.39	3425	175
3	0.10	3530	140
4	0.10	3625	140

This produces the characteristic peak-and-shoulder shape of the water Raman emission band.

Wavelength Shifts

The wavelength shift increases with excitation wavelength due to the fixed wavenumber shift:

λ’ (nm)	λ (nm)	Shift (nm)
350	397	47
400	463	63
450	531	81
488	585	97
500	602	102
550	677	127

Backscattering

The Raman phase function is nearly symmetric about 90°, resulting in a backscattering ratio of exactly 0.5. This is similar to Rayleigh (molecular) scattering and quite different from particle scattering (which is strongly forward-peaked).

Example: Radiative Transfer Source Term

In radiative transfer calculations, Raman scattering appears as a source term. For unpolarized light:

import numpy as np
from raman_seawater import raman_vsf

def raman_source_term(L_excitation, lambda_ex, lambda_em, psi):
    """
    Calculate Raman scattering source term for RT equation.

    Parameters
    ----------
    L_excitation : ndarray
        Radiance at excitation wavelength [W m⁻² sr⁻¹ nm⁻¹]
    lambda_ex : float
        Excitation wavelength [nm]
    lambda_em : float
        Emission wavelength [nm]
    psi : ndarray
        Scattering angles [radians]

    Returns
    -------
    S_raman : ndarray
        Source term contribution [W m⁻³ sr⁻¹ nm⁻¹]
    """
    beta_R = raman_vsf(lambda_ex, lambda_em, psi)
    # Integrate over solid angle (simplified)
    S_raman = beta_R * L_excitation
    return S_raman

Example: Effect on Remote Sensing Reflectance

Raman scattering can contribute significantly to remote sensing reflectance, especially in clear waters at red wavelengths:

import numpy as np
import matplotlib.pyplot as plt
from raman_seawater import raman_scattering_coeff, excitation_to_emission_wavelength

# Wavelengths where Raman contributes to Rrs
emission_wavelengths = np.array([550, 600, 650, 700])

# Find corresponding excitation wavelengths
for lam_em in emission_wavelengths:
    # Light at ~450-500 nm scatters into these wavelengths
    lam_ex = 1e7 / (1e7/lam_em + 3400)  # Approximate
    b_R = raman_scattering_coeff(lam_ex)
    print(f"Light at {lam_ex:.0f} nm → {lam_em} nm, b_R = {b_R:.2e} m⁻¹")

Limitations and Notes

Temperature/Salinity Dependence: The current implementation uses Walrafen (1967) parameters for pure water at 25°C. The emission spectrum shape varies slightly with temperature and salinity (see Artlett & Pask 2017).
Pure Water vs Seawater: Bartlett et al. (1998) found no statistically significant difference between pure water and seawater Raman scattering coefficients.
Polarization: The phase function averages over all polarization states. For polarized radiative transfer, a full Mueller matrix treatment is required.
Energy vs Photon Units: Use units='energy' for radiative transfer codes like HydroLight that work in energy units (W m^-2 nm^-1), and units='photon' for Monte Carlo simulations that track photon numbers.

References

[SathyendranathPlatt1998]

Sathyendranath, S. and Platt, T. (1998). “Ocean-colour model incorporating transspectral processes,” Appl. Opt. 37, 2216-2227.

[Bartlett1998]

Bartlett, J.S., Voss, K.J., Sathyendranath, S., and Vodacek, A. (1998). “Raman scattering by pure water and seawater,” Appl. Opt. 37, 3324-3332.

[Desiderio2000]

Desiderio, R.A. (2000). “Application of the Raman scattering coefficient of water to calculations in marine optics,” Appl. Opt. 39, 1893-1894.

[Ge1993]

Ge, Y., Gordon, H.R., and Voss, K.J. (1993). “Simulation of inelastic-scattering contributions to the irradiance field in the ocean: variation in Fraunhofer line depths,” Appl. Opt. 32, 4028-4036.

[Mobley1994]

Mobley, C.D. (1994). Light and Water: Radiative Transfer in Natural Waters. Academic Press.

[Walrafen1967]

Walrafen, G.E. (1967). “Raman spectral studies of the effects of temperature on water structure,” J. Chem. Phys. 47, 114-126.

[Artlett2017]

Artlett, C.P. and Pask, H.M. (2017). “Optical remote sensing of water temperature using Raman spectroscopy,” Opt. Express 25, 2840-2851.

[OOWB]

Ocean Optics Web Book: https://www.oceanopticsbook.info/view/scattering/level-2/raman-scattering