A technique is described for representing the behavior of partially coherent optical systems by using overcomplete basis sets. The scheme is closely related to Gabor function theory. Through singular-value decomposition it is shown that if E is a matrix containing the sampled basis functions, then all of the information needed for optical calculations is contained in S=EE~(dagger) and R=E~(dagger)E. For overcomplete sets, S can be inverted to give a dual basis set, E=S~(-1)E, which can be used to find the correlation matrix elements A of a sampled bimodal expansion of the spatial coherence function. Overcomplete correlation matrices can be scattered easily at optical components. They can be used to determine (i) the natural modes of a field; (ii) the total power in a field, P_(t)=Tr[RA]; (iii) the power coupled between two fields, A and B, that are in different states of coherence, P_(c)=Tr[RARB]; and (iv) the entropy of a field, Q=Tr[ZΣ_(r)(I-Z)~(r)/r], where Z=RA/Tr[RA].
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