Phase object tomography with fractional derivatives

Jesus Jimenez-Garcia; G. Rodriguez-Zurita

doi:10.1117/12.437182

14 August 2001 Phase object tomography with fractional derivatives

Jesus Jimenez-Garcia, G. Rodriguez-Zurita

Proceedings Volume 4419, 4th Iberoamerican Meeting on Optics and 7th Latin American Meeting on Optics, Lasers, and Their Applications; (2001) https://doi.org/10.1117/12.437182
Event: IV Iberoamerican Meeting of Optics and the VII Latin American Meeting of Optics, Lasers and Their Applications, 2001, Tandil, Argentina

Abstract

In this work, fractional-derivative filtering is proposed to be incorporated in the system which detects projections emerging form an object as wave front phase variations only. Because it is well known that the square of the derivative of fractional order q equals ½ is linearly proportional to the first order derivative, a real spatial filter with amplitude transmittance proportional to the square root of the frequency has been prosed in order to obtain irradiance variations linearly related with the derivative of phase for phase object detection. Corresponding analysis is shown, where parallel phase projections are filtered with such a spatial filter prior to backprojection for reconstruction. Instead of performing integration of projections, description of the tomographic imaging process of the resulting space filtered backprojections is carried out and the 2D equivalence of the filter is discussed. Numerical examples are provided.

Citation Download Citation

Jesus Jimenez-Garcia and G. Rodriguez-Zurita "Phase object tomography with fractional derivatives", Proc. SPIE 4419, 4th Iberoamerican Meeting on Optics and 7th Latin American Meeting on Optics, Lasers, and Their Applications, (14 August 2001); https://doi.org/10.1117/12.437182

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