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Applied Optics

Applied Optics


  • Vol. 38, Iss. 21 — Jul. 20, 1999
  • pp: 4671–4680

Influence of correlated errors on the estimation of the relaxation time spectrum in dynamic light scattering

Dieter Maier, Michael Marth, Josef Honerkamp, and Jürgen Weese  »View Author Affiliations

Applied Optics, Vol. 38, Issue 21, pp. 4671-4680 (1999)

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An important step in analyzing data from dynamic light scattering is estimating the relaxation time spectrum from the correlation time function. This estimation is frequently done by regularization methods. To obtain good results with this step, the statistical errors of the correlation time function must be taken into account [J. Phys. A 6, 1897 (1973)]. So far error models assuming independent statistical errors have been used in the estimation. We show that results for the relaxation time spectrum are better if correlation between statistical errors is taken into account. There are two possible ways to obtain the error sizes and their correlations. On the one hand, they can be calculated from the correlation time function by use of a model derived by Schätzel. On the other hand, they can be computed directly from the time series of the scattered light. Simulations demonstrate that the best results are obtained with the latter method. This method requires, however, storing the time series of the scattered light during the experiment. Therefore a modified experimental setup is needed. Nevertheless the simulations also show improvement in the resulting relaxation time spectra if the error model of Schätzel is used. This improvement is confirmed when a lattice with a bimodal sphere size distribution is applied to experimental data.

© 1999 Optical Society of America

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(030.5260) Coherence and statistical optics : Photon counting
(290.0290) Scattering : Scattering
(290.5840) Scattering : Scattering, molecules

Original Manuscript: December 15, 1998
Revised Manuscript: March 18, 1999
Published: July 20, 1999

Dieter Maier, Michael Marth, Josef Honerkamp, and Jürgen Weese, "Influence of correlated errors on the estimation of the relaxation time spectrum in dynamic light scattering," Appl. Opt. 38, 4671-4680 (1999)

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  1. K. Schätzel, E. O. Schulz-Du Bois, “Improvements of photon correlation techniques,” Infrared Phys. 32, 409–416 (1991). [CrossRef]
  2. K. Schätzel, “Correlation techniques in dynamic light scattering,” Appl. Phys. B 42, 193–213 (1987). [CrossRef]
  3. K. Schätzel, “New concepts in correlator design,” Inst. Phys. Conf. B 77, 175–184 (1985).
  4. K. Schätzel, R. Peters, “Noise on multiple-τ photon correlation data,” Photon Corr. Spectrosc. Multicomponent Syst. 1430, 109–115 (1991). [CrossRef]
  5. B. J. Berne, R. Pecora, Dynamic Light Scattering (Wiley, New York, 1976).
  6. D. E. Koppel, “Analysis of macromolecular polydispersity in intensity correlation spectroscopy: the method of cumulants,” J. Chem. Phys. 57, 4814–4820 (1972). [CrossRef]
  7. I. D. Morrison, E. F. Grabowski, C. A. Herb, “Improved analysis for particle size determination by quasi-elastic light scattering,” Langmuir 4, 496–501 (1985). [CrossRef]
  8. R. Finsey, P. de Groen, L. Deriemaker, M. Van Laethem, “Singular value analysis and reconstruction of photon correlation data equidistant in time,” J. Chem. Phys. 91, 7374–7383 (1989). [CrossRef]
  9. J. Honerkamp, D. Maier, J. Weese, “A nonlinear regularization method for the analysis of photon correlation spectroscopic data,” J. Chem. Phys. 98, 865–872 (1993). [CrossRef]
  10. 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]
  11. S. W. Provencher, “contin: a general purpose constrained regularization program for inverting noisy linear algebraic and integral equations,” Comput. Phys. Commun. 27, 229–242 (1982). [CrossRef]
  12. V. A. Morozov, Methods for Solving Incorrectly Posed Problems (Springer-Verlag, Berlin, 1984). [CrossRef]
  13. K. Schätzel, R. Drewel, S. Stimac, “Photon correlation measurements at large lag times: improving statistical accuracy,” J. Mod. Opt. 35, 711–718 (1988). [CrossRef]
  14. K. Schätzel, “Noise on photon correlation data: I. Autocorrelation functions,” Quantum Opt. 2, 287–305 (1990). [CrossRef]
  15. C. W. Groetsch, The Theory of Tikhonov Regularization for Fredholm Equations of the First Kind (Pitman, London, 1984).
  16. J. Weese, “A regularization method for nonlinear ill-posed problems,” Comput. Phys. Commun. 77, 429–440 (1993). [CrossRef]
  17. J. Honerkamp, J. Weese, “Tikhonov’s regularization method for ill-posed problems,” Continuum Mech. Thermodyn. 2, 17–30 (1990). [CrossRef]
  18. J. Honerkamp, Stochastic Dynamical Systems (VCH, New York, 1993).
  19. A. Einstein, “Theorie der Opaleszenz von homogenen Flüssigkeiten und Flüssigkeitsgemischen in der Nähe des kritischen Zustandes,” Ann. Phys. 13, 1275–1298 (1910). [CrossRef]
  20. E. Jakeman, “Theory of optical spectroscopy by digital autocorrelation of photon-counting fluctuations,” J. Phys. Gen. Phys. 3, 201–215 (1970). [CrossRef]
  21. M. Kerker, The Scattering of Light and Other Electromagnetic Radiation (Academic, New York, 1969).
  22. Keithley Instruments GmbH, Germering, Germany.

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