  We develop a general method for customizing the intensity statistics of
speckle patterns on a target plane. By judiciously modulating the phase-front
of a monochromatic laser beam, we experimentally generate speckle patterns with
arbitrarily-tailored intensity probability-density functions. Relative to
Rayleigh speckles, our customized speckles exhibit radically different
topologies yet maintain the same spatial correlation length. The customized
speckles are fully developed, ergodic, and stationary: with circular
non-Gaussian statistics for the complex field. Propagating away from the target
plane, the customized speckles revert back to Rayleigh speckles. This work
provides a versatile framework for tailoring speckle patterns with varied
applications in microscopy, imaging and optical manipulation.
