Stability and locality of amplitude and phase contrast tomographies

Timur E. Gureyev; Glenn R. Myers; Yakov I. Nesterets; David M. Paganin; Konstantin M. Pavlov; Stephen W. Wilkins

doi:10.1117/12.680185

7 September 2006 Stability and locality of amplitude and phase contrast tomographies

Timur E. Gureyev, Glenn R. Myers, Yakov I. Nesterets, David M. Paganin, Konstantin M. Pavlov, Stephen W. Wilkins

Proceedings Volume 6318, Developments in X-Ray Tomography V; 63180V (2006) https://doi.org/10.1117/12.680185
Event: SPIE Optics + Photonics, 2006, San Diego, California, United States

Abstract

We perform a theoretical analysis of the mathematical stability and locality of several modes of amplitude and phase contrast computed tomography (CT) suitable for reconstruction of the 3D distribution of complex refractive index in samples displaying weak absorption contrast. We present a general formalism for CT reconstruction in linear shift-invariant optical systems. Examples of such systems include propagation-based and analyser-based CT. We obtain general formulae for CT reconstruction from analyser-based projection data. We also propose a new tomographic algorithm for the reconstruction of the 3D distribution of complex refractive index in a sample from a single propagation-based projection image per view angle, where the images display both absorption and phase contrast. The method assumes that the real and imaginary parts of the refractive index are proportional to each other. Using singular-value decompositions of the relevant operators we show that, in contrast to conventional amplitude-contrast CT, phase-contrast (diffraction) tomography is mathematically well-posed. The presented results are pertinent to biomedical imaging and non-destructive testing of samples exhibiting weak absorption contrast.

Citation Download Citation

Timur E. Gureyev, Glenn R. Myers, Yakov I. Nesterets, David M. Paganin, Konstantin M. Pavlov, and Stephen W. Wilkins "Stability and locality of amplitude and phase contrast tomographies", Proc. SPIE 6318, Developments in X-Ray Tomography V, 63180V (7 September 2006); https://doi.org/10.1117/12.680185

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