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Speckle patterns are ubiquitous in optics and have multiple applications forwhich the control of their spatial correlations is essential. Here, we reporton a method to engineer speckle correlations behind a scattering medium throughthe singular value decomposition of the transmission matrix. We not onlydemonstrate control over the speckle grain size and shape but also realizepatterns with non-local correlations. Moreover, we show that the reach of ourmethod extends also along the axial dimension, allowing volumetric speckleengineering behind scattering layers.

Speckle engineering through singular value decomposition of the transmission matrix