  Intensity minima and maxima of speckle patterns obtained behind a diffuser
are experimentally interchanged by applying a spiral phase delay of charge $\pm
1$ to the impinging coherent beam. This transform arises from the intuitive
expectation that a tightly focused beam is so-changed into a vortex beam and
vice-versa. The statistics of extrema locations and the intensity distribution
of the so-generated "complementary" patterns are characterized by numerical
simulations. It is demonstrated experimentally that the incoherent
superposition of the three "complementary speckle patterns" yield a synthetic
speckle grain size enlarged by a factor $\sqrt{3}$. A cyclic permutation of
optical vortices and maxima is unexpectedly observed and discussed.
