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Applied Optics

Applied Optics


  • Vol. 30, Iss. 33 — Nov. 20, 1991
  • pp: 4889–4896

Optical sizing of small colloidal particles: an optimized regularization technique

Heimo Schnablegger and Otto Glatter  »View Author Affiliations

Applied Optics, Vol. 30, Issue 33, pp. 4889-4896 (1991)

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Optical particle sizing in the range of 10 nm up to several micrometers by means of quasi-elastic and elastic light scattering requires sophisticated data inversion techniques. We have developed an optimized regularization technique that can be used for the inversion of such light-scattering data. The technique has been successfully tested for a large number of simulated and measured data. It is easy to handle. Typical problems that arise in practical applications are discussed.

© 1991 Optical Society of America

Original Manuscript: May 21, 1990
Published: November 20, 1991

Heimo Schnablegger and Otto Glatter, "Optical sizing of small colloidal particles: an optimized regularization technique," Appl. Opt. 30, 4889-4896 (1991)

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  1. B. E. Dahneke, Measurement of Suspended Particles by Quasi-Elastic Light Scattering (Wiley, New York, 1983).
  2. S. W. Provencher, “A constrained regularization method for inverting data represented by linear algebraic or integral equations,” Comput. Phys. Commun. 27, 213–227 (1982). [CrossRef]
  3. D. L. Phillips, “A technique for the numerical solution of certain integral equations of the first kind,” J. Assoc. Comput. Mach. 9, 84–97 (1962). [CrossRef]
  4. S. Twomey, “On the numerical solution of Fredholm integral equations of the first kind by inversion of the linear system produced by quadrature,” J. Assoc. Comput. Mach. 10, 97–101 (1963). [CrossRef]
  5. O. Glatter, H. Sieberer, H. Schnablegger, “A comparative study on different scattering techniques and data evaluation methods for sizing of colloidal systems using light scattering,” Part. Part. Syst. Charac. (to be published).
  6. C. de Boor, A Practical Guide to Splines (Springer-Verlag, New York, 1978). [CrossRef]
  7. T. N. E. Greville, Theory and Application of Spline Functions (Academic, New York, 1969).
  8. J. Schelten, F. Hossfeld, “Application of spline functions to the correction of resolution errors in small-angle scattering,” J. Appl. Crystallogr. 4, 210–223 (1971). [CrossRef]
  9. H. Greschonig, O. Glatter, “Determination of equivalence points of sigmoidal potentiometric titration curves,” Microchem. Acta 2, 389–399 (1986).
  10. O. Glatter, M. Hofer, “Interpretation of elastic light scattering data. III. Determination of size distributions of polydisperse systems,” J. Colloid Interface Sci. 122, 496–506 (1988). [CrossRef]
  11. P. W. Barber, S. C. Hill, Computational Light Scattering (World Scientific, Singapore, 1990).
  12. E. D. Hirleman, “Optimal scaling of the inverse Fraunhofer diffraction particle sizing problem: the linear system produced by quadrature,” in Optical Particle SizingTheory and Practice, G. Gouesbet, G. Grehan, eds. (Plenum, New York, 1988).
  13. O. Glatter, “Data evaluation in small angle scattering: Calculation of the radial electron density distribution by means of indirect Fourier transformation,” Acta Phys. Austriaca 47, 83–102 (1977).
  14. O. Glatter, “A new method for the evaluation of small-angle scattering data,” J. Appl. Crystallogr. 10, 415–421 (1977). [CrossRef]
  15. O. Glatter, “Determination of particle-size distribution functions from small-angle scattering data by means of the indirect transformation method,” J. Appl. Crystallogr. 13, 7–11 (1980). [CrossRef]
  16. O. Glatter, “Data treatment,” in Small Angle X-Ray Scattering (Academic, New York, 1982), Chap. 4.
  17. C. L. Lawson, R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N.J., 1974).
  18. J. G. McWhirter, E. R. Pike, “On the numerical inversion of the Laplace transform and similar Fredholm integral equations of the first kind,” J. Phys. A 11, 1729–1745 (1978). [CrossRef]
  19. M. Bertero, P. Boccacci, C. De Mol, E. R. Pike, “Extraction of polydispersity information in photon correlation spectroscopy,” in Optical Particle Sizing, Theory and Practice, G. Gouesbet, G. Grehan, eds. (Plenum, New York, 1988).
  20. K. Müller, O. Glatter, “Practical aspects to the use of indirect Fourier transformation methods,” Makromol. Chem. 183, 465–479 (1982). [CrossRef]
  21. J. L. Shi, J. H. Gao, Z. X. Lin, “Formation of monosized spherical aluminum hydroxide particles by urea method,” Solid State Ionics 32/33, 537–543 (1989). [CrossRef]
  22. R. C. Weast, Handbook of Chemistry and Physics (Chemical Rubber, Cleveland, 1982).

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