  This work proposes an innovative approach to improve Bragg coherent
diffraction imaging (BCDI) microscopy applied to time evolving crystals and/or
non-homogeneous crystalline strain fields, identified as two major limitations
of BCDI microscopy. Speckle BCDI (spBCDI), introduced here, rests on the
ability of a strongly non-uniform illumination to induce a convolution of the
three-dimensional (3D) frequency content associated with the finite-size
crystal and a kernel acting perpendicularly to the illumination beam. In the
framework of Bragg diffraction geometry, this convolution is beneficial as it
encodes some 3D information about the sample in a single two-dimensional (2D)
measurement, i.e., in the detector plane. With this approach, we demonstrate
that we can drastically reduce the sampling frequency along the rocking curve
direction and still obtain data sets with enough information to be inverted by
a traditional phase retrieval algorithm.
  Numerical simulations, performed for a highly distorted crystal, show that
spBCDI allows a gain in the sampling ratio ranging between 4 and 20 along the
rocking curve scan, for a speckle illumination with individual speckle size of
50 nm. Furthermore, spBCDI allows working at low intensity levels, leading to
an additional gain for the total scanning time. Reductions of a factor of about
32 were numerically observed. Thus, measurements in the 0.3 s time scale at 4th
generation synchrotrons become feasible, with a remarkable performance for the
imaging of strongly distorted crystals. Practical details on the implementation
of the method are also discussed.
