@article{95befacb-7f3d-442a-a612-82d47ea20d73,
  abstract     = {{<p>X-ray-scattering tensor tomography requires dark-field measurements in the projection domain that are both unbiased and rotation equivariant. We show that, in the context of circular-grating-based tensor tomography, the commonly used cell-based chord retrieval (CCR) cannot satisfy either requirement. From the two-dimensional convolution model of circular gratings, we derive a closed-form expression demonstrating that CCR introduces an illumination-coupling term that directly contaminates the measured dark-field amplitude. This illumination-dependent contribution is fixed in the grating frame and therefore does not co-rotate with the sample, producing orientation-dependent errors and breaking rotation equivariance. In contrast, global two-dimensional Fourier transform retrieval cancels illumination through the convolution theorem and is inherently rotation equivariant. Experiments with a laboratory circular-grating-based tensor tomography system confirm both effects. Illumination coupling is thus an intrinsic limitation of CCR and prevents it from achieving rotation-faithful quantitative anisotropic dark-field imaging.</p>}},
  author       = {{Liu, Ruifeng and Deng, Runtao and Song, Peixuan and Kagias, Matias and Zhang, Li and Wang, Zhentian}},
  issn         = {{2331-7019}},
  language     = {{eng}},
  month        = {{07}},
  number       = {{1}},
  publisher    = {{American Physical Society}},
  series       = {{Physical Review Applied}},
  title        = {{Illumination-coupling bias breaks rotation equivariance in x-ray-scattering tensor tomography with a circular grating}},
  url          = {{http://dx.doi.org/10.1103/tsy5-6mvq}},
  doi          = {{10.1103/tsy5-6mvq}},
  volume       = {{26}},
  year         = {{2026}},
}