  Speckle patterns are ubiquitous in optics and have multiple applications for
which the control of their spatial correlations is essential. Here, we report
on a method to engineer speckle correlations behind a scattering medium through
the singular value decomposition of the transmission matrix. We not only
demonstrate control over the speckle grain size and shape but also realize
patterns with non-local correlations. Moreover, we show that the reach of our
method extends also along the axial dimension, allowing volumetric speckle
engineering behind scattering layers.
