  The applications of vortex beam in biomedical field are always hindered by
light scattering of biological tissues. Recently wavefront shaping technology
has shown the potential in focusing a structured light field through scattering
media. Herein we have proposed a novel theory to describe the field
transformation property of the opaque lens. This theory makes it possible to
generate foci with specified amplitude and phase profiles by well-designing the
incident field. We verify the validity of this theory by experimentally
generating doughnut-shaped foci with various topological charges, and the foci
match well with the theoretical predictions. Meanwhile, we have also analyzed
the limitations of our approach, and it reveals that there is a trade-off
between the thickness of the medium and the acceptance spatial bandwidth of the
incident field. Our approach will inspire new research ideas for the
deep-tissue applications of vortex beam in optics and dynamics, which is
significant to numerous potential bio-photonics technologies.
