Reconstruction result

[KaLKMaNLaB]

Dear Paul,

The function fourier_map_2d reconstructs the scattering potential from the measured scattered wavefields. However, when reconstructing this for a real-valued refractive index distribution (in my case a cylinder( the imaginary part is not zero and in fact is about 40% of the real value (hence substantial). According to the theory in your document it should be zero. In your Mie numerical example you just discard the imaginary part.

Please comment on this, is this an error, numerical artifact, or something else?

Thanks,
Jeroen Kalkman

[paulmueller]

Hi Jeroen,

an imaginary part that is non-zero implies absorption. For a purely dielectric cylinder, the imaginary part of the refractive index should be (close to, with numerical errors) zero.

Note that the functions like fourier_map_2d return the scattering potential, not the refractive index distribution. Could this be just a confusion? https://odtbrain.readthedocs.io/en/stable/processing.html#translation-of-object-function-to-refractive-index

[KaLKMaNLaB]

For a pure dielectric scatterer the scattering potential is purely real. But I implemented the code for the Rytov field (Eq. 3.38 of your "The Theory of Diffraction Tomography"), apparently this adds absorption to the case. When I calculate it for the pure Born field everything is fine.

[paulmueller]

Ok, does that mean you used odtbrain.sinogram_as_rytov?

Could you please paste your code and output image? You could use one of the examples as templates for plotting, e.g. https://odtbrain.readthedocs.io/en/stable/ex2d.html#mie-off-center-cylinder