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Updated: Jul 5, 2026
09:16
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Published on: January 9, 2017
Approximations of the measurable quantity in diffuse optical problems: theoretical analysis of model deviations
Nicolas Ducros1, Anabela da Silva, Jean-Marc Dinten
1Micro Technologies for Biology and Healthcare Division, Commissariat à l'Energie Atomique-Laboratoire d'Electronique de Technologie et d'Instrumentation Micro et Nano Technologies, 17 rue des Martyrs, Grenoble, France. nicolas.ducros@cea.fr
Summary
Photon density better approximates diffuse optical tomography measurements than photon flux. Model deviations depend significantly on optical parameters, impacting accuracy in continuous wave and time domains.
Area of Science:
- Biomedical Optics
- Medical Imaging
- Photon Transport Physics
Background:
- Diffuse optical tomography (DOT) commonly models measurable quantities using photon density or photon flux.
- Actual measurements in DOT detect the radiance accepted by the detection system, not directly photon density or flux.
- Discrepancies arise from using simplified models for measurable quantities in DOT.
Purpose of the Study:
- To theoretically analyze model deviations in diffuse optical tomography.
- To compare the accuracy of photon density versus photon flux as measurable quantities.
- To determine the influence of optical parameters on approximation validity.
Main Methods:
- Utilized the diffusion approximation to the radiative transfer equation.
- Employed extrapolated boundary conditions for analytical solutions.
- Derived an exact analytical expression for the measurable quantity (radiance).
- Assessed model deviations by comparing photon density and flux to the derived analytical expression.
Main Results:
- Photon density provides a better approximation of the measurable quantity than photon flux in semi-infinite geometry.
- This improved approximation holds for both continuous wave and time-domain measurements.
- The accuracy of the photon density approximation is critically dependent on the specific optical parameters of the medium.
Conclusions:
- Photon density is a more suitable surrogate for measurable radiance in DOT models than photon flux.
- Accurate modeling in DOT requires careful consideration of optical properties.
- Future DOT model development should account for these findings to improve measurement accuracy.
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