Revealing and Mitigating Transmittance and Reflectance Errors in Integrating-Sphere Characterization of High-Albedo Scattering Media
Abstract
Accurate optical characterization of high-albedo scattering media is fundamentally limited by integrating-sphere measurement errors. Scattering events spatially redistribute photons, leading to lateral beam spread and angular divergence that bias measured reflectance and transmittance. Here, we investigate these deviations, which are quantified and interpreted by using the point spread function (PSF), guided by the radiative transfer equation. Experiments and Monte Carlo modelling show that the widely used external-mount integrating-sphere configuration introduces systematic, configuration-dependent errors that become pronounced when scattering-induced lateral spreading is substantial. Using a normalised PSF to quantify photon redistribution, we map the characteristic lateral spreading length across a broad (taus,g) parameter space in the high-albedo limit, providing a basis for evaluating errors in specific measurement geometries. We further quantify the influence of measurement geometry and show that, in the pencil-beam limit, maintaining L/Dport≲ 0.01 reduces the discrepancy arising from the finite collection aperture to approximately \qty{1}{\percent}. In addition, we introduce an internal-mount integrating-sphere protocol that suppresses scattering-related losses and yields transmittance and reflectance measurements in good agreement with theoretical predictions. Overall, our work helps users of integrating-sphere measurements identify scattering-related errors and improve the reliability of transmittance and reflectance characterization across a wide range of application areas.
Related
- Fabrication and characterization of multi-shell nested fully annular quasi-ellipsoidal focusing mirrors with m=3 supermirrors for small-angle neutron scattering
- Extending the Similarity Spectrum to the SWIR for quality control of above water reflectance measurements
- Learning-Based Reconstruction of Optical Properties in Bilayered Media from Single-distance Time-Resolved Reflectance Measurements
- Higher-order adaptive behaviors outperform pairwise strategies in mitigating contagion dynamics
- Mitigating Disease Spread by Design in Refugee and IDP Camps
BibTeX
@misc{xu2026revealing,
title = {{Revealing and Mitigating Transmittance and Reflectance Errors in Integrating-Sphere Characterization of High-Albedo Scattering Media}},
author = {Zhijie Xu and Ernesto Pini and Lorenzo Pattelli and Ioannis Papakonstantinou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32403},
eprint = {2610.32403},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32403},
}
RIS
TY - UNPB
TI - Revealing and Mitigating Transmittance and Reflectance Errors in Integrating-Sphere Characterization of High-Albedo Scattering Media
AU - Zhijie Xu
AU - Ernesto Pini
AU - Lorenzo Pattelli
AU - Ioannis Papakonstantinou
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32403
UR - https://arxiv.org/abs/2610.32403
AB - Accurate optical characterization of high-albedo scattering media is fundamentally limited by integrating-sphere measurement errors. Scattering events spatially redistribute photons, leading to lateral beam spread and angular divergence that bias measured reflectance and transmittance. Here, we investigate these deviations, which are quantified and interpreted by using the point spread function (PSF), guided by the radiative transfer equation. Experiments and Monte Carlo modelling show that the widely used external-mount integrating-sphere configuration introduces systematic, configuration-dependent errors that become pronounced when scattering-induced lateral spreading is substantial. Using a normalised PSF to quantify photon redistribution, we map the characteristic lateral spreading length across a broad (taus,g) parameter space in the high-albedo limit, providing a basis for evaluating errors in specific measurement geometries. We further quantify the influence of measurement geometry and show that, in the pencil-beam limit, maintaining L/D_port≲ 0.01 reduces the discrepancy arising from the finite collection aperture to approximately \qty{1}{\percent}. In addition, we introduce an internal-mount integrating-sphere protocol that suppresses scattering-related losses and yields transmittance and reflectance measurements in good agreement with theoretical predictions. Overall, our work helps users of integrating-sphere measurements identify scattering-related errors and improve the reliability of transmittance and reflectance characterization across a wide range of application areas.
ER -