Inverse-Adding-Doubling Algorithm: Translating measurements into models

We discussed before how raw reflectance and transmittance spectra provide a story of a photon's journey through a sample material. But turning those spectra into generalizable optical properties can be tricky. Sample preparation and additional input data are needed for this.

In order to convert generalized spectrophotometry measurements into actionable optical properties, such as absorption (μₐ) and reduce scattering (μₛ') coefficients, we use a method called the inverse adding-doubling (IAD) algorithm.

Here, we will explain how we take our spectrophotometry data [link] (i.e., reflectance, transmittance) and use IAD to calculate generalized optical properties. 

Optical Properties Calculation with Inverse Adding-Doubling (IAD) 

Getting from transmittance and reflectance spectra into absorption and scattering spectra requires a bit of math - namely because multiply-scattered light in thick tissue samples makes directly mapping reflectance and transmittance into absorption and scattering tricky.

Turns out the math is pretty complicated. But Scott Prahl figured it all out 30+ years ago and made a simple program to extract generalized absorption and scattering parameters from spectrophotometry measurements, called Inverse-Adding-Doubling (IAD) Algorithm. 

The details of IAD can be found on Scott's website and his lab’s Github. 

TL/DR: Based on a derived radiative photon transport model (accounting for anisotropy and sample geometry), the algorithm brute-force iterates on µ_a and µ _s’ spectra until the estimated reflectance and transmission spectra converge to match the measured data.

The parameters we get from this calculation are:

• Absorption coefficients (μ_a): which tell us how far light travels (on average) in a sample before it is absorbed. 
• Reduced scattering coefficients (µ_s’): which tell us how far light travels (on average) before it is scattered.
  The “reduced” form of scattering coefficient empirically generalizes tissue optical anisotropy - a topic for another day. 

The units for these properties are mm^-1. You can think of this value as the thickness of tissue light can travel through before two-thirds of the light is absorbed or scattered. These reference values let us generalize photon transport in arbitrarily-sized samples, which we can engineer stable, workable material for R&D without compromising real-world optical characteristics. 

When we run the IAD algorithm on our spectrophotometry data from before, with added information for sample anisotropy and geometry, the optical properties we get back are shown in the figure to the right.

With this data in hand, we can now

• Computationally model photon transport to guide device design
• Design new materials to optically mimic tissue with any shape or size. 
• Design and create phantoms to benchmark optical sensing devices with. 

At QUEL Imaging, spectrophotometry and IAD are the main tools we rely on to rigorously measure and optimize material formulations at targeted wavelengths of interest. With these material formulations defined, we can manufacture a variety of shapes and sizes to help accelerate your device development

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Our team helps device development teams understand and manage tissue optics problems in medical device design all of the time. Reach out to learn how we can help accelerate your product development projects with added expertise in tissue optics.