  Structured light concerns the control of light in its spatial degrees of
freedom (amplitude, phase and polarization), and has proven instrumental in
many applications. The creation of structured light usually involves the
conversion of a Gaussian mode to a desired structure in a single step, while
the detection is often the reverse process, both fundamentally lossy or
imperfect. Here we show how to ideally reshape structured light in a lossless
manner in a simple two-step process. We outline the core theoretical arguments,
and demonstrate reshaping of arbitrary structured light patterns, in the
process highlighting when the technique is applicable and when not, and how
best to implement it. This work will be a useful addition to the structured
light toolkit, and particularly relevant to those wishing to use the spatial
modes of light as a basis in classical and quantum communication.
