Estimating quantitative features of nanoparticles using multiple derivatives of scattering profiles

Richard Charnigo, Mathieu Francoeur, Patrick Kenkel, M. Pinar Mengüç, Benjamin Hall, Cidambi Srinivasan

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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 languageEnglish
Pages (from-to)1369-1382
Number of pages14
JournalJournal of Quantitative Spectroscopy and Radiative Transfer
Issue number8
StatePublished - 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.


  • Characterization
  • Compound estimator
  • Direct problem
  • Evanescent wave
  • Inverse problem
  • Scattering profile

ASJC Scopus subject areas

  • Radiation
  • Atomic and Molecular Physics, and Optics
  • Spectroscopy


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