Application of Singular Systems to Some Data Reduction Problems in Modern Optics

  • M. Bertero
  • C. De Mol
  • E. R. Pike
Conference paper
Part of the Inverse Problems and Theoretical Imaging book series (IPTI)


Many data reduction or “inverse” problems in optics originate from scattering or imaging experiments, where radiation is incident on a sample as a probe of some unknown characteristic of that sample. The scattered radiation is measured after interaction with the sample by means of a detector or a set of detectors. Since, in most problems, the property of interest is not directly accessible to measurement, the output of the detectors has to be processed and interpreted in order to provide as much relevant information as possible about the required structural function characterizing the sample. As usual in optics, we will call this unknown function the object and denote it by f(x), where x represents a one- or multi-dimensional space or time (or both space and time) variable, according to the problem under study. When considering an inverse problem, we shall assume that the direct problem has been solved, i. e. that we have a good mathematical model describing the interaction between the radiation and the sample and associating the corresponding data function g(x), also called the image, to a given object f(x). Moreover, we will restrict ourselves to situations where a linear or linearized model holds true or is good enough in practice, so that the problem of recovering the object f(x) from its image g(x) is a linear inverse problem. In the present paper, we review the basic features of some data reduction problems in which we have been particularly interested during the last few years. They relate to several practical applications, namely various situations in confocal scanning microscopy and various techniques for particle sizing by laser light scattering. More generally, the problems discussed hereafter could be viewed as case studies for many other applied linear inverse problems encountered in optics and other fields.


Inverse Problem Impulse Response Singular System Fredholm Integral Equation Singular Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • M. Bertero
    • 1
    • 2
  • C. De Mol
    • 3
  • E. R. Pike
    • 4
    • 5
  1. 1.Dipartimento di Fisicadell’Università di GenovaGenovaItaly
  2. 2.Istituto Nazionale di Fisica NucleareGenovaItaly
  3. 3.Département de MathématiqueUniversité Libre de BruxellesBruxellesBelgium
  4. 4.Department of PhysicsKing’s CollegeStrandLondonUK
  5. 5.RSREGreat Malvern, WorcesterUK

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