Skip to main content

Part of the book series: European Consortium for Mathematics in Industry ((XECMI))

  • 37 Accesses

Abstract

Problems such as the determination of the sizes of microparticles by light scattering or the improvement of the images of a confocal scanning laser microscope require the solution of first-kind linear integral equations. In this paper we review our work intended to understand the limits of resolution which may be achieved in these problems. The results obtained are relevant not only for the correct interpretation of the output of commercial instruments but also for the improvement of their design.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bayvel, L.P.; Jones, A.R.: Electromagnetic Scattering and its Applications. Applied Science Publishers (1981).

    Book  Google Scholar 

  2. Bertero, M.; Pike, E.R.: Resolution in diffraction limited imaging, a singular value analysis I. The case of coherent illumination. Optica Acta 29 (1982) 727 - 746.

    Article  MathSciNet  Google Scholar 

  3. Bertero, M.; Boccacci, P.; Pike, E.R.: On the recovery and resolution of exponential relaxation rates from experimental data: a singular-value analysis of the Laplace transform inversion in the presence of noise. Proc. R. Soc. Lond. A383 (1982) 15 - 29.

    Google Scholar 

  4. Bertero, M.; Grünbaum, F. A.: Commuting differential operators for the finite Laplace transform. Inverse Problems 1 (1985) 181 - 192.

    Article  MathSciNet  MATH  Google Scholar 

  5. Bertero, M.; Brianzi, P.; Pike, E.R.: On the recovery and resolution of exponential relaxation rates from experimental data: Laplace transform inversions in weighted spaces. Inverse Problems 1 (1985) 1 - 15.

    Article  MathSciNet  MATH  Google Scholar 

  6. Bertero, M.; Boccacci, P.; Defrise, M.; De Mol, C.; Pike, E.R.: Superresolution in confocal scanning microscopy II. The incoherent case. Inverse Problems 5 (1989) 441 - 461.

    Article  MathSciNet  Google Scholar 

  7. Bertero, M.; Boccacci, P.; Brakenhoff, G.J.; Malfanti, F.; van der Voort, H.T.M.: Three-dimensional image restoration and super-resolution in fluorescence confocal microscopy. J. Microsc. 157 (1989) 3 - 20.

    Article  Google Scholar 

  8. Bertero, M.; Pike, E.R.: Exponential-sampling method for Laplace and other dilationally invariant transforma: I. Singular-system analysis. Inverse Problems 7 (1991) 1-20; II. Examples in photon correlation spectroscopy and Fraunhofer diffraction. Inverse Problems 7 (1991) 21 - 41.

    Google Scholar 

  9. Brakenhoff, G.J.; Blom, P.; Barends, P: Confocal scanning light microscopy with high aperture immersion lenses. J. Microsc. 117 (1979) 219 - 232.

    Google Scholar 

  10. Brakenhoff, G.J.; van der Voort, H.T.M.; van Sprosen, E.A.; Nanninga, N.: Three-dimensional imaging by confocal scanning fluorescence microscopy. Ann. N. Y. Acad. Sci. 483(1986) 405 - 415.

    Article  Google Scholar 

  11. Chowdhury, D.P.; Sorensen, C.M.; Taylor, T.W.; Merklin, J.F.; Lester, T.W.: Application of photon correlation spectroscopy to flowing Brownian motion systems. Appl. Optics 23 (1984) 4149 - 4154.

    Article  Google Scholar 

  12. Cummins, H.Z.; Pike, E.R. (editors): Photon Correlation and Light Beating Spectroscopy. Plenum Press (1977).

    Google Scholar 

  13. Cori, F.; Guattari, G.: Signal restoration for linear systems with weighted impulse. Singular value analysis for two cases of low-pass filtering. Inverse Problems 1 (1985) 67 - 85.

    Article  MathSciNet  Google Scholar 

  14. Jerri, A.J.: The Shannon sampling theorem. Its various extensions and applications: A tutorial review. Proc. IEEE 65 (1977) 1565 - 1596.

    Article  MATH  Google Scholar 

  15. King, G.B.; Sorensen, C.M.; Lester, T.W.; Merklin, J.F.: Photon correlation spectroscopy used as a particle size diagnostic in sooting flames. Appl. Optics 20 (1982) 976 - 978.

    Google Scholar 

  16. Miller, K.: Least squares methods for ill-posed problems with a prescribed bound. SIAM J. Math. Anal. 1 (1970) 52 - 74.

    MATH  Google Scholar 

  17. Ostrowsky, N.; Sornette, D.; Parker, P.; Pike, E.R.: Exponential sampling method for light scattering polydispersity analysis. Optica Acta 28 (1981) 1059 - 1070.

    Article  Google Scholar 

  18. Sheppard, C.J.R.; Choudhury, A.: Image formation in the scanning microscope. Optica Acta 24 (1977) 1051 - 1073.

    Article  Google Scholar 

  19. Titchmarsh, E.C.: Introduction to the Theory of Fourier Integrals. Clarendon Press (1948).

    Google Scholar 

  20. Walker, J.G.; Pike, E.R.; Davies, R.E.; Young, M.R., Brakenhoff, G.J.; Bertero, M.: Superresolving scanning optical microscopy using holographic optical processing. J. Opt. Soc. Am. A10 (1993) 59 - 64.

    Google Scholar 

  21. Young, M.R.; Jiang, S.H.; Davies, R.E.; Walker, J.G.; Pike, E.R.; Bert-ero, M.: Experimental confirmation of superresolution in coherent con-focal scanning microscopy using optical masks. J. Microsc. 165 (1992) 131 - 138.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Fachmedien Wiesbaden

About this chapter

Cite this chapter

Bertero, M., Pike, E.R. (1994). Inverse Problems in Particle Sizing and Confocal Microscopy. In: Engl, H.W., McLaughlin, J. (eds) Proceedings of the Conference Inverse Problems and Optimal Design in Industry. European Consortium for Mathematics in Industry. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-96658-2_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-322-96658-2_1

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-322-96659-9

  • Online ISBN: 978-3-322-96658-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics