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'Forward and inverse radiative transport using adding-doubling'

Project description

by Scott Prahl

iadpython will be a pure Python module to do forward and inverse multiple light scattering (radiative transport) in layered materials. Calculations are done using van de Hulst’s adding-doubling technique.

The original adding-doubling algorithm was developed by van de Hulst to model light propagation through layered media. I extended it to handle Fresnel reflection at boundaries as well as interactions with integrating spheres.

Finally, the code was further extended to handle lost light using Monte Carlo techniques for inverse calculations.

Version v0.4.0 started the migration to a pure-python implementation. This version includes the ability to do forward calculations of light transport through layered 1D structures.

The long-term goal is rewrite the integrating sphere, inverse algorithm, and lost light calculations in pure python so that one can do inverse calculations (i.e., reflection and transmission measurements to intrinsic absorption and scattering properties).

Both inverse and forward calculations are currently possible using the iadc framework. This is a python interface to the inverse adding-doubling package written in C by Scott Prahl <>. This works now but is a nuisance to install and maintain because of its dependence on compiling and installing a C library.

See <> for full documentation of iadpython.


The following will do a forward calculation:

import iadpython as iad

mu_s = 10  # scattering coefficient [1/mm]
mu_a = 0.1 # absorption coefficient [1/mm]
g = 0.9    # scattering anisotropy
d = 1      # thickness mm

a = mu_s/(mu_a+mu_s)
b = mu_s/(mu_a+mu_s) * d

# air / glass / sample / glass / air
s = iadpython.Sample(a=a, b=b, g=g, n=1.4, n_above=1.5, n_below=1.5)
ur1, ut1, uru, utu = s.rt()

print('Collimated light incident perpendicular to sample')
print('  total reflection = %.5f' % ur1)
print('  total transmission = %.5f' % ut1)

print('Diffuse light incident on sample')
print('  total reflection = %.5f' % uru)
print('  total transmission = %.5f' % utu)


To install:

pip3 install iadpython

If you just want to do forward calculations then you’re done.

If you want to do inverse calculations, then you’ll need to build and install the libiad library:

git clone
cd iad
# edit Makefile as needed
make install-lib


Required Python modules: numpy, matplotlib, ctypes, scipy


iadpython is licensed under the terms of the MIT license.

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