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Appl. Sci. 2018, 8(9), 1649; https://doi.org/10.3390/app8091649

A New Method to Retrieve the Three-Dimensional Refractive Index and Specimen Size Using the Transport Intensity Equation, Taking Diffraction into Account

1
Laboratoire d’Instrumentation d’Image et Spectroscopie, Institut National Polytechnique Félix Houphouët-Boigny (INPH-B), BP 1093 Yamoussoukro, Cote D’Ivoire
2
Laboratoire de Physique de la Matière Condensée et Technologie, UFR SSMT, Université Félix Houphouët-Boigny, 22 BP 582 Abidjan 22, Cote D’Ivoire
*
Author to whom correspondence should be addressed.
Received: 3 September 2018 / Revised: 12 September 2018 / Accepted: 12 September 2018 / Published: 13 September 2018
(This article belongs to the Section Optics and Lasers)
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Abstract

Refractive index retrieval is possible using the transport intensity equation (TIE), which presents advantages over interferometric techniques. The TIE method is valid only for paraxial ray assumptions. However, diffraction can nullify these TIE model assumptions. Therefore, the refractive index is problematic for reconstruction in three-dimensions (3D) using a set of defocused images, as diffraction effects become prominent. We propose a method to recover the 3D refractive index by combining TIE and deconvolution. A brightfield (BF) microscope was then constructed to apply the proposed technique. A microsphere was used as a sample with well-known properties. The deconvolution of the BF-images of the sample using the microscope’s 3D point spread function led to significantly reduced diffraction effects. TIE was then applied for each set of three images. Applying TIE without taking into account diffraction failed to reconstruct the 3D refractive index. Taking diffraction into account, the refractive index of the sample was clearly recovered, and the sectioning effect of the microsphere was highlighted, leading to a determination of its size. This work is of great significance in improving the 3D reconstruction of the refractive index using the TIE method. View Full-Text
Keywords: tomography; refractive index; size determination; point spread function; transport intensity equation; diffraction tomography; refractive index; size determination; point spread function; transport intensity equation; diffraction
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Agnero, M.A.; Konan, K.; Kossonou, A.T.; Bagui, O.K.; Zoueu, J.T. A New Method to Retrieve the Three-Dimensional Refractive Index and Specimen Size Using the Transport Intensity Equation, Taking Diffraction into Account. Appl. Sci. 2018, 8, 1649.

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