Abstract
Characterization of nanoparticles on surfaces is a challenging inverse problem whose solution has many practical applications. This article proposes a method, suitable for in situ characterization systems, for estimating quantitative features of nanoparticles on surfaces from scattering profiles and their derivatives. Our method enjoys a number of advantages over competing approaches to this inverse problem. One such advantage is that only a partial solution is required for the companion direct problem. For example, estimating the average diameter of nanoparticles to be 53 nm is possible even when a researcher's existing scattering data pertain to nanoparticles whose average diameters are in multiples of 5 nm. Two numerical studies illustrate the implementation and performance of our method for inferring nanoparticle diameters and agglomeration levels respectively.
Original language | English |
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Pages (from-to) | 1369-1382 |
Number of pages | 14 |
Journal | Journal of Quantitative Spectroscopy and Radiative Transfer |
Volume | 112 |
Issue number | 8 |
DOIs | |
State | Published - May 2011 |
Bibliographical note
Funding Information:This material is based upon work supported by the National Science Foundation under Grant No. DMS-0706857 . Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors also thank the three anonymous reviewers for constructive suggestions that improved this material.
Funding
This material is based upon work supported by the National Science Foundation under Grant No. DMS-0706857 . Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The authors also thank the three anonymous reviewers for constructive suggestions that improved this material.
Funders | Funder number |
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National Science Foundation (NSF) |
Keywords
- Characterization
- Compound estimator
- Direct problem
- Evanescent wave
- Inverse problem
- Scattering profile
ASJC Scopus subject areas
- Radiation
- Atomic and Molecular Physics, and Optics
- Spectroscopy