  This paper addresses three-dimensional signal distortion and image
reconstruction issues in x-ray Bragg coherent diffraction imaging (BCDI) in the
event of a general non-orthogonal orientation of the area detector with respect
to the diffracted beam. Growing interest in novel BCDI adaptations at
fourth-generation synchrotron light sources has necessitated improvisations in
the experimental configuration and the subsequent data analysis. One such
possibly unavoidable improvisation that is envisioned in this paper is a
photon-counting area detector whose face is tilted away from the perpendicular
to the Bragg-diffracted beam during acquisition of the coherent diffraction
signal. We describe a likely circumstance in which one would require such a
detector configuration, along with experimental precedent at third generation
synchrotrons. Using physically accurate diffraction simulations from synthetic
scatterers in the presence of such tilted detectors, we analyze the general
nature of the observed signal distortion qualitatively and quantitatively, and
provide a prescription to correct for it during image reconstruction. Our
simulations and reconstructions are based on an adaptation of the known theory
of BCDI sampling geometry as well as recently developed projection-based
methods of wavefield propagation. Such configurational modifications and their
numerical remedies are potentially valuable in realizing unconventional
coherent diffraction measurement geometries and eventually paving the way for
the integration of BCDI into new materials characterization experiments at
next-generation light sources.
