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@PHDTHESIS{Kyrion:709351,
      author       = {Kyrion, Tobias},
      othercontributors = {Frank, Martin and Herty, Michael Matthias},
      title        = {{L}inear and {N}onlinear {I}nverse {P}roblems in {A}erosol
                      {S}pectroscopy},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      reportid     = {RWTH-2017-09884},
      pages        = {1 Online-Ressource (ii, 143 Seiten) : Illustrationen,
                      Diagramme},
      year         = {2017},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University; Dissertation, RWTH Aachen University, 2017},
      abstract     = {In this work we study the evaluation of optical aerosol
                      measurements. Our aim is to reconstruct the size
                      distributions of aerosol particles from optical light
                      extinction measurements in order to obtain a safe
                      measurement technology for potentially harmful aerosols
                      inside a nuclear reactor containment. The first half of this
                      work is devoted to linear inverse problems. In particularwe
                      study the linear integral equation relating aerosol particle
                      size distributions tooptical extinction measurements via Mie
                      theory. We derive reconstruction algorithms which work
                      independently from a human operator and thus do not require
                      any monitoring or further adjustments. Based on statistical
                      observations, we deriveresidual-based methods for finding
                      the appropriate number of discretization points and the
                      regularization parameter for Tikhonov regularization. Since
                      particle size distributions are non negative, we apply non
                      negativity constraints throughout the whole reconstruction
                      process and all results are derived for constrained
                      regression problems. A special emphasis lies on
                      computational efficiency, since we demand that a single
                      inversion must be completed in less than thirty seconds on a
                      regular notebook.We compare our method based on the
                      discrepancy principle with a Monte Carlo inversion method,
                      where we also apply non negativity constraints. Here the
                      regularization parameter is considered as a model variable
                      and retrieved together with the sought-after size
                      distributions. Then the discrepany principle strategy is
                      generalized to the case of two-component aerosols, where the
                      aerosol particle material is a mixture of two pure component
                      materials. In addition to the particle size distribution, we
                      retrieve the unknown mixingratio of the two components. In
                      the second half of this work we study the nonlinear inverse
                      problem of reconstructing the refractive indices of an
                      aerosol material from measurements of monodisperse aerosols.
                      First we investigate this problem for a fixed light
                      wavelength. We take into account all local minima found here
                      and regard them all ascandidate solutions. Then we apply a
                      selection method based on smoothness estimates for
                      refractive index curve sections covering consecutive light
                      wavelengths. The resulting coupled refractive index
                      reconstructions are regularized further using
                      Phillips-Twomey regularization.},
      cin          = {110000 / 115020},
      ddc          = {510},
      cid          = {$I:(DE-82)110000_20140620$ / $I:(DE-82)115020_20140620$},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2017-09884},
      url          = {https://publications.rwth-aachen.de/record/709351},
}