## Algorithm to calculate limiting cumulative particle size distribution functions from turbidimetric data |

Applied Optics, Vol. 53, Issue 2, pp. 301-305 (2014)

http://dx.doi.org/10.1364/AO.53.000301

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### Abstract

An algorithm is offered for finding the range within which cumulative particle size distribution functions can be located in consistency with experimental turbidimetric data at a number of wavelengths. It is based on linear programming and minimization techniques. Several tests were performed. The lower right-hand branch of the corridor was found to locate near the initial distribution function.

© 2014 Optical Society of America

**OCIS Codes**

(100.3190) Image processing : Inverse problems

(290.4020) Scattering : Mie theory

(290.7050) Scattering : Turbid media

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: October 15, 2013

Revised Manuscript: November 28, 2013

Manuscript Accepted: December 6, 2013

Published: January 10, 2014

**Virtual Issues**

Vol. 9, Iss. 3 *Virtual Journal for Biomedical Optics*

**Citation**

Sergei L. Shmakov, "Algorithm to calculate limiting cumulative particle size distribution functions from turbidimetric data," Appl. Opt. **53**, 301-305 (2014)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=ao-53-2-301

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### References

- S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Dover, 1977).
- S. Y. Shchyogolev, “Inverse problems of spectroturbidimetry of biological disperse systems: an overview,” J. Biomed. Opt. 4, 490–503 (1999). [CrossRef]
- T. Kourti, “Turbidimetry in particle size analysis,” in Encyclopedia of Analytical Chemistry: Instrumentation and Applications, R. A. Meyers, ed. (Wiley, 2000), pp. 5549–5580.
- H. Tang and S.-Y. Ding, “Inversion of particle size distribution with unknown refractive index from specific turbidimetry,” in 2010 International Conference on Computer, Mechatronics, Control and Electronic Engineering, Vol. 3 (IEEE, 2010), pp. 116–119.
- G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 330, 377–445 (1908). [CrossRef]
- B. Sedláček, “Light scattering. XVI. Particle size determination by the turbidity ratio method,” Collection of Czechoslovak Chemical Communications (1929-1939, 1947-) 32, 1374–1389 (1967). [CrossRef]
- B. Sedláček and K. Zimmerman, “Integral and differential turbidity ratio method applied to the analysis of changes in the size and number of scatterers,” Polymer Bulletin 7, 531–538 (1982).
- T. Kourti, J. F. MacGregor, and A. E. Hamielec, “Turbidimetric techniques. Capability to provide the full particle size distribution,” in Particle Size Distribution II, T. Provder, ed. (ACS, 1991), pp. 2–19.
- G. B. Dantzig and M. N. Thapa, Linear Programming, 1: Introduction (Springer, 1997).
- O. Platz and R. G. Gordon, “Rigorous bounds for time-dependent correlation functions,” Phys. Rev. Lett. 30, 264–267 (1973). [CrossRef]
- R. McGraw, “Sparse aerosol models beyond the quadrature method of moments,” AIP Conf. Proc. 1527, 651–654 (2013).
- B. D. Bunday, Basic Optimization Methods (Edward Arnold, 1984).
- R. L. Zollars, “Turbidimetric method for on-line determination of latex particle number and particle size distribution,” J. Colloid Interface Sci. 74, 163–172 (1980). [CrossRef]
- G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (Dover, 1961).
- W. Heller, H. L. Bhatnagar, and M. Nakagaki, “Theoretical investigations on the light scattering of spheres. XIII. The “wavelength exponent” of differential turbidity spectra,” J. Chem. Phys. 36, 1163–1170 (1962). [CrossRef]
- D. H. Melik and H. S. Fogler, “Turbidimetric determination of particle size distributions of colloidal systems,” J. Colloid Interface Sci. 92, 161–180 (1983). [CrossRef]
- W. Heller and W. J. Pangonis, “Theoretical investigations on the light scattering of colloidal spheres. I. The specific turbidity,” J. Chem. Phys. 26, 498–506 (1957). [CrossRef]
- P. Rosin and E. Rammler, “The laws governing the fineness of powdered coal,” J. Inst. Fuel 7, 29–36 (1933).
- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, 1983).

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