## Improved inversion procedure for particle size distribution determination by photon correlation spectroscopy |

Applied Optics, Vol. 51, Issue 25, pp. 6220-6226 (2012)

http://dx.doi.org/10.1364/AO.51.006220

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### Abstract

We propose a minimum variation of solution method to determine the optimal regularization parameter for singular value decomposition for obtaining the initial distribution for a Chahine iterative algorithm used to determine the particle size distribution from photon correlation spectroscopy data. We impose a nonnegativity constraint to make the initial distribution more realistic. The minimum variation of solution is a single constraint method and we show that a better regularization parameter may be obtained by increasing the discrimination between adjacent values. We developed the S-R curve method as a means of determining the modest iterative solution from the Chahine algorithm. The S-R curve method requires a smoothing operator. We have used simulated data to verify our new method and applied it to real data. Both simulated and experimental data show that the method works well and that the first derivative smoothing operator in the S-R curve gives the best results.

© 2012 Optical Society of America

**OCIS Codes**

(290.3200) Scattering : Inverse scattering

(290.3700) Scattering : Linewidth

(290.5820) Scattering : Scattering measurements

(290.5850) Scattering : Scattering, particles

(300.6170) Spectroscopy : Spectra

**ToC Category:**

Spectroscopy

**History**

Original Manuscript: May 7, 2012

Revised Manuscript: July 20, 2012

Manuscript Accepted: August 3, 2012

Published: August 30, 2012

**Virtual Issues**

Vol. 7, Iss. 11 *Virtual Journal for Biomedical Optics*

**Citation**

Shuai Mao, Jin Shen, John C. Thomas, Xinjun Zhu, Wei Liu, and Xianming Sun, "Improved inversion procedure for particle size distribution determination by photon correlation spectroscopy," Appl. Opt. **51**, 6220-6226 (2012)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-51-25-6220

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