  Studying the coherence of an optical field is typically compartmentalized
with respect to its different optical degrees of freedom (DoFs) -- spatial,
temporal, and polarization. Although this traditional approach succeeds when
the DoFs are uncoupled, it fails at capturing key features of the field's
coherence if the DOFs are indeed correlated -- a situation that arises often.
By viewing coherence as a `resource' that can be shared among the DoFs, it
becomes possible to convert the entropy associated with the fluctuations in one
DoF to another DoF that is initially fluctuation-free. Here, we verify
experimentally that coherence can indeed be reversibly exchanged -- without
loss of energy -- between polarization and the spatial DoF of a partially
coherent field. Starting from a linearly polarized spatially incoherent field
-- one that produces no spatial interference fringes -- we obtain a spatially
coherent field that is unpolarized. By reallocating the entropy to
polarization, the field becomes invariant with regards to the action of a
polarization scrambler, thus suggesting a strategy for avoiding the deleterious
effects of a randomizing system on a DoF of the optical field.
