## Improved regularized solution of the inverse problem in turbidimetric measurements

Applied Optics, Vol. 49, Issue 24, pp. 4591-4603 (2010)

http://dx.doi.org/10.1364/AO.49.004591

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### Abstract

We present results of simulation research on the constrained regularized least-squares (RLS) solution of the ill-conditioned inverse problem in turbidimetric measurements. The problem is formulated in terms of the discretized Fredholm integral equation of the first kind. The inverse problem in turbidimetric measurements consists in determining particle size distribution (PSD) function of particulate system on the basis of turbidimetric measurements. The desired PSD should satisfy two constraints: non negativity of PSD values and normalization of PSD to unity when integrated over the whole range of particle size. Incorporating the constraints into the RLS method leads to the constrained regularized least-squares (CRLS) method, which is realized by means of an active set algorithm of quadratic programming. Results of simulation research prove that the CRLS method performs considerably better with reconstruction of PSD than the RLS method in terms of better fidelity and smaller uncertainty.

© 2010 Optical Society of America

**OCIS Codes**

(290.3200) Scattering : Inverse scattering

(290.4020) Scattering : Mie theory

(290.5820) Scattering : Scattering measurements

(290.5850) Scattering : Scattering, particles

(290.7050) Scattering : Turbid media

(290.2558) Scattering : Forward scattering

**ToC Category:**

Scattering

**History**

Original Manuscript: February 23, 2010

Revised Manuscript: June 4, 2010

Manuscript Accepted: July 7, 2010

Published: August 16, 2010

**Virtual Issues**

Vol. 5, Iss. 13 *Virtual Journal for Biomedical Optics*

**Citation**

Janusz Mroczka and Damian Szczuczyński, "Improved regularized solution of the inverse problem in turbidimetric measurements," Appl. Opt. **49**, 4591-4603 (2010)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-49-24-4591

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