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Inverse Scattering and Aperture Synthesis in OCT

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Optical Coherence Tomography

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Abstract

Inverse scattering and aperture synthesis are closely related: In both cases sample structure is computationally derived from data collected outside the sample. This chapter treats with inverse scattering techniques in optical diffraction tomography, and with optical aperture synthesis as a basis in OCT techniques. The techniques described here are based on linearized inverse scattering. In a mathematical linear imaging system there is an object function and an image function; both are elements of the same or of different Euklidian spaces. Usually, the object function is the sample source strength S(r), the image function is the scattered wave spectrum Û (S) (K). A linear mapping is assumed which associates the two functions: Û (S) (K) = O · S(r). In the first section the basic optical diffraction tomography theorem, formulated by E. Wolf, is presented together with its variations and basic properties. The second section demonstrates the large flexibility of inverse scattering based on the ODT theorem.

In the third section aperture synthesis (AS) based inverse scattering is discussed. AS in imaging means to synthesize a large aperture by a series of smaller and more easily accessible apertures. Techniques like B‐scan based AS connect the acquired OCT A‐scan signal with the three-dimensional object structure. Microscopy usually requires high NA optics. Hence, Ralston et al. [68] have resolved the inverse scattering problem analytically relying on a scalar wave model without resorting to the paraxial approximation. Spatially invariant resolution has been confirmed. Interferometric synthetic aperture microscopy (ISAM) has been shown to resolve features in the tissue that are not decipherable from the unprocessed data observed in human breast tumour tissue. Furthermore, Adie et al. [70] have demonstrated that ISAM, with computational adaptive optics correction of aberrations, yields high‐resolution reconstructions of highly scattering rabbit muscle tissue: Astigmatism correction in ISAM not only provides high-resolution reconstruction of tissue structures but, additionally, a significant increase in signal-to-noise ratio of point-like scatterers.

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Acknowledgment

The author thanks primarily his colleagues at the former Institute of Medical Physics at the Medical University of Vienna, in particular W. Drexler, C. K. Hitzenberger, M. Pircher, and B. Grajciar as well as M. Wojtkowski and R. Zawadzki (then) from the University of Torun/Poland.

The author is furthermore indebted to Tyler Ralston, Steven G. Adie, and Stephen A. Boppart from the University of Illinois at Urbana-Champaign, USA, for permission to reproduce Figs. 4.7 and 4.8.

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  1. Medical University Vienna, Vienna, Austria

    Adolf F. Fercher

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Correspondence to Adolf F. Fercher .

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  1. Center for Medical Physics and Biomedical Engineering, Medical University Vienna, General Hospital Vienna, Vienna, Austria

    Wolfgang Drexler

  2. Department of Electrical Engineering and Computer Science and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA

    James G. Fujimoto

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Fercher, A.F. (2015). Inverse Scattering and Aperture Synthesis in OCT. In: Drexler, W., Fujimoto, J. (eds) Optical Coherence Tomography. Springer, Cham. https://doi.org/10.1007/978-3-319-06419-2_5

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