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Mathematical Methods of Optical Coherence Tomography

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Handbook of Mathematical Methods in Imaging

Abstract

In this chapter a general mathematical model of Optical Coherence Tomography (OCT) is presented on the basis of the electromagnetic theory. OCT produces high-resolution images of the inner structure of biological tissues. Images are obtained by measuring the time delay and the intensity of the backscattered light from the sample considering also the coherence properties of light. The scattering problem is considered for a weakly scattering medium located far enough from the detector. The inverse problem is to reconstruct the susceptibility of the medium given the measurements for different positions of the mirror. Different approaches are addressed depending on the different assumptions made about the optical properties of the sample. This procedure is applied to a full field OCT system and an extension to standard (time and frequency domain) OCT is briefly presented.

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Acknowledgements

The authors would like to thank Wolfgang Drexler and Boris Hermann from the Medical University Vienna for their valuable comments and stimulating discussions. This work has been supported by the Austrian Science Fund (FWF) within the national research network Photoacoustic Imaging in Biology and Medicine, projects S10501-N20 and S10505-N20.

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Authors and Affiliations

  1. Computational Science Center, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Vienna, Austria

    Peter Elbau & Leonidas Mindrinos

  2. Computational Science Center, University of Vienna, Vienna, Austria

    Otmar Scherzer

  3. RICAM, Austrian Academy of Sciences, Linz, Austria

    Otmar Scherzer

Authors
  1. Peter Elbau
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  2. Leonidas Mindrinos
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  3. Otmar Scherzer
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Correspondence to Peter Elbau .

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Editors and Affiliations

  1. Computational Science Center, University of Vienna, Vienna, Austria

    Otmar Scherzer

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Elbau, P., Mindrinos, L., Scherzer, O. (2015). Mathematical Methods of Optical Coherence Tomography. In: Scherzer, O. (eds) Handbook of Mathematical Methods in Imaging. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0790-8_44

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