## Mie Light-Scattering Granulometer with Adaptive Numerical Filtering. I. Theory

Applied Optics, Vol. 39, Issue 36, pp. 6897-6917 (2000)

http://dx.doi.org/10.1364/AO.39.006897

Acrobat PDF (348 KB)

### Abstract

A search procedure based on a least-squares method including a regularization scheme constructed from numerical filtering is presented. This method, with the addition of a nephelometer, can be used to determine the particle-size distributions of various scattering media (aerosols, fogs, rocket exhausts, motor plumes) from angular static light-scattering measurements. For retrieval of the distribution function, the experimental data are matched with theoretical patterns derived from Mie theory. The method is numerically investigated with simulated data, and the performance of the inverse procedure is evaluated. The results show that the retrieved distribution function is quite reliable, even for strong levels of noise.

© 2000 Optical Society of America

**OCIS Codes**

(290.3200) Scattering : Inverse scattering

(290.4020) Scattering : Mie theory

**Citation**

Laurent Hespel and André Delfour, "Mie Light-Scattering Granulometer with Adaptive Numerical Filtering. I. Theory," Appl. Opt. **39**, 6897-6917 (2000)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-36-6897

Sort: Year | Journal | Reset

### References

- N. G. Stanley-Woods and R. W. Lines, Particle Size Analysis (Royal Society of Chemistry, London, 1992).
- H. S. Lee, S. K. Chae, and B. Y. H. Liu, “Size characterization of liquid-borne particles by light scattering counters,” Part. Part. Syst. Charact. 6, 93–99 (1989).
- H. Schnablegger and O. Glatter, “Sizing of colloidal particles with light scattering: corrections for beginning multiple scattering,” Appl. Opt. 34, 3489–3501 (1995).
- A. Doicu, J. Köser, T. Wriedt, and K. Bauckhage, “Light scattering simulation and measurement of monodisperse spheroids using a phase Doppler anemometer,” Part. Part. Syst. Charact. 15, 257–262 (1998).
- H. Jiang, J. Pierce, J. Kao, and E. Sevick-Muruca, “Measurement of particle-size distribution and volume fraction in concentrated suspensions with photon migration techniques,” Appl. Opt. 36, 3310–3318 (1997).
- N. De Jaeger, H. Demeyere, R. Finsy, K. Sneyers, J. Van der Beelen, P. Van der Meeren, and M. Van Laethem, “Particle sizing by photon correlation spectroscopy. I. Monodisperse lattices: Influence of scattering angle and concentration of monodisperse material,” Part. Part. Syst. Charact. 8, 179–186 (1991).
- J. Swinthenbank, J. M. Beer, D. S. Taylor, and C. G. McCreath, “A laser diagnostic technique for the measurement of droplets and particle size distribution. Experimental diagnostics in gas phase combustion systems,” Prog. Astronaut. Aeronaut. 53, 421–447 (1977).
- F. Ferri, A. Bassini, and E. Paganini, “Modified version of the Chahine algorithm to invert spectral extinction data for particle sizing,” Appl. Opt. 34, 5829–5839 (1995).
- R. J. Perry, A. J. Hunt, and D. R. Huffman, “Experimental determinations of Mueller scattering matrices for nonspherical particles,” Appl. Opt. 17, 2701–2710 (1978).
- G. Mie, “Beitrage zur Optik trüber Medien speziell kolloidaler Metallösungen,” Ann. Phys. (Leipzig) 25, 377–445 (1908).
- S. Twomey, Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier, New York, 1977).
- C. L. Lawson and R. J. Hanson, Solving Least Squares Problems, Vol. 1 of the Series on Automatic Computation (Prentice-Hall, Englewood Cliffs, N.J., 1974).
- H. Schnablegger and O. Glatter, “Optical sizing of small colloidal particles: an optimized regularization technique,” Appl. Opt. 30, 4889–4896 (1991).
- M. R. Jones, M. Q. Brewster, and Y. Yamada, “Application of a genetic algorithm to the optical characterization of propellant smoke,” J. Thermophys. Heat Transfer 10, 372–377 (1996).
- A. Corana, M. Marchesi, C. Matini, and S. Ridella, “Minimizing multimodal functions of continuous variables with the simulated annealing algorithm,” ACM Trans. Math. Software 13, 262–280 (1987).
- F. Ferri, M. Giglio, and U. Perini, “Inversion of light scattering data from fractals by the Chahine iterative algorithm,” Appl. Opt. 28, 3074–3082 (1989).
- D. A. Ligon, T. W. Chen, and J. B. Gillespie, “Determination of aerosol parameters from light scattering data using a inverse Monte Carlo technique,” Appl. Opt. 35, 4297–4303 (1996).
- H. Mellin, “Über die fundamentale Wichtigkeit des Stazes von Cauchy für die Theorien der Gamma und hypergeometrischen Functionem,” Acta Soc. Sci. Fenn. 20, 1–115 (1895).
- J. G. McWhirter and 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).
- G. Viera and M. A. Box, “Information content analysis of aerosol remote sensing experiments using an analytical eingenfunction theory: anomalous diffraction approximation,” Appl. Opt. 24, 4525–4533 (1985).
- M. Bertero, C. De Mol, and E. R. Pike, “Particle sizing by inversion of extinction data,” in Proceedings of an International Symposium on Optical Particle Sizing: Theory and Practice, G. Gouesbet and G. Gréhan, eds. (Plenum, New York, 1988), pp. 55–61.
- M. Bertero, C. De Mol, and E. R. Pike, “Particle size distribution from spectral turbidity: a singular-system analysis,” Inverse Prob. 2, 247–258 (1986).
- G. P. Box, K. M. Sealey, and M. A. Box, “Inversion of Mie extinction measurements using analytic eigenfunction theory,” J. Atmos. Sci. 49, 2074–2081 (1992).
- M. Bertero, C. De Mol, and G. A. Viano, “On the regularization of linear inverse problems in Fourier optics,” in Applied Inverse Problems, by P. C. Sabatier, ed. (Springer-Verlag, Berlin, 1978), pp. 180–199.
- M. Bertero, C. De Mol, and G. A. Viano, “The stability of inverse problems,” in Inverse Scattering Problems in Optics, by H. P. Baltes, ed. (Springer-Verlag, Berlin, 1980), pp. 161–214.
- K. S. Shifrin, “The essential range of scattering angles in measuring particle-size distribution by small-angle method,” Izv. Acad. Sci. USSR Atmos. Oceanic Phys. 2, 559–561 (1966).
- P. L. Butzer and S. Jansche, “A direct approach to the Mellin transform,” Math. Subj. Class. 45A15, 44–02–44–03 (1991).
- M. K. Atakishiyeva and N. M. Atakishiyev, “On the Mellin transforms of hypergeometric polynomials,” J. Phys. A 32, 33–41 (1999).
- J. G. McWhirter, “A stabilized model-fitting approach to the processing of laser anemometry and the other photon correlation data,” Opt. Acta 27, 83–105 (1980).
- H. M. Wadworth, ed., Handbook of Statistical Methods for Engineers and Scientists (McGraw-Hill, New York, 1990).
- C. De Boor, A Practical Guide to Splines (Springer-Verlag, New York, 1978).
- T. N. E. Greville, Theory and Applications of Spline Functions (Academic, New York, 1969).
- A. Ben-David, B. M. Herman, and J. A. Reagan, “Inverse problem and the pseudoempirical orthogonal function method of solution. 1. Theory,” Appl. Opt. 27, 1235–1242 (1988).
- A. Ben-David, B. M. Herman, and J. A. Reagan, “Inverse problem and the pseudoempirical orthogonal function method of solution. 2. Use,” Appl. Opt. 27, 1243–1254 (1988).
- D. Deirmendjian, Electromagnetic Scattering on Spherical Polydispersions (American Elsevier, New York, 1969).
- C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-Interscience, New York, 1983).
- H. C. van de Hulst, Light Scattering by Small Particles, 2nd ed. (Dover, New York, 1981).
- M. E. Essawy and A. Delfour, “Determining size distribution of liquid nitrogen particles flowing in an airstream by scattered light detection,” AIAA J. 18, 665–668 (1980).
- J.-C. Traineau, P. Kuentzmann, M. Prévost, P. Tarrin, and A. Delfour, “Particle size distribution measurements in a subscale motor for the ARANE 5 solid rocket booster,” presented at the AIAA/SAE/ASME/ASEE 28th Joint Propulsion Conference and Exhibit, Nashville, Tenn., 6–8 July 1992.
- J. B. Riley and Y. C. Agrawal, “Sampling and inversion of data in diffraction particle sizing,” Appl. Opt. 30, 4800–4817 (1991).
- E. D. Hirleman, “Optical scaling of the inverse Fraunhofer diffraction particle sizing problem: the linear system produced by quadrature,” J. Part. Charact. 4, 128–133 (1987).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.