  In this two-part article series we provide a generalized description of the
scattering geometry of Bragg coherent diffraction imaging (BCDI) experiments,
the shear distortion effects inherent to the resulting three-dimensional (3D)
image from current phase retrieval methods and strategies to mitigate this
distortion. In this Part I, we derive in general terms the real-space
coordinate transformation to correct this shear, which originates in the more
fundamental relationship between the representations of mutually conjugate 3D
spaces. Such a transformation, applied as a final post-processing step
following phase retrieval, is crucial for arriving at an un-distorted and
physically meaningful image of the 3D scatterer. As the relevance of BCDI grows
in the field of materials characterization, we take this opportunity to
generalize the available sparse literature that addresses the geometric theory
of BCDI and the subsequent analysis methods. This aspect, specific to coherent
Bragg diffraction and absent in two-dimensional transmission CDI experiments,
gains particular importance concerning spatially-resolved characterization of
3D crystalline materials in a realiable, non-destructive manner. These articles
describe this theory, from the diffraction in Bragg geometry, to the
corrections needed to obtain a properly rendered digital image of the 3D
scatterer. Part I provides the experimental BCDI communitcy with the
theoretical underpinnings of the 3D real-space distortions in the
phase-retrieved object, along with the necessary post-retrieval correction
method. Part II builds upon the geometric theory developed in Part I with the
formalism to correct the shear distortions directly on an orthogonal grid
within the phase retrieval algorithm itself, allowing more physically realistic
constraints to be applied.
