  To study nanostructures on substrates, surface-sensitive reflection-geometry
scattering techniques such as grazing incident small angle x-ray scattering are
commonly used to yield an averaged statistical structural information of the
surface sample. Grazing incidence geometry can probe the absolute
three-dimensional structural morphology of the sample if a highly coherent beam
is used. Coherent Surface Scattering Imaging (CSSI) is a powerful yet
non-invasive technique similar to Coherent X-ray Diffractive Imaging (CDI) but
performed at small angles and grazing-incidence reflection geometry. A
challenge with CSSI is that conventional CDI reconstruction techniques cannot
be directly applied to CSSI because the Fourier-transform-based forward models
cannot reproduce the dynamical scattering phenomenon near the critical angle of
total external reflection of the substrate-supported samples. To overcome this
challenge, we have developed a multislice forward model which can successfully
simulate the dynamical or multi-beam scattering generated from surface
structures and the underlying substrate. The forward model is also demonstrated
to be able to reconstruct an elongated 3D pattern from a single shot scattering
image in the CSSI geometry through fast-performing CUDA-assisted PyTorch
optimization with automatic differentiation.
