### Abstract

It has been shown by Wolf that, if a field amplitude obeys the wave equation, then a derived field quantity (the cross correlation or mutual coherence function), also obeys the wave equation. This result helps clarify the subject of partially coherent light; for example, a Huygens' principle for the propagation of *intensity* is a consequence. A generalization is presented: For that class of linear partial differential equations (p.d.e.'s) in which at least one independent variable, say *t*, does not appear in the coefficients, one can construct from a solution*f*(*P, t*), (*P* representing collectively the other independent variables) a generalized ``cross‐correlation'' function *F*(*P, t; P* _{1}, *t* _{1}, *P* _{2}, *t* _{2} ⋯) satisfying the same p.d.e. as *f*(*P, t*); *F* is an integral over *s* of *f*(*P, t + s*) *g* (*s, P* _{1}, *t* _{1}, *P* _{2}, *t* _{2} ⋯), where (*P* _{1}, *t* _{1}, *P* _{2}, *t* _{2} ⋯) are values of (*P, t*); for particular choices of the highly arbitrary *g, F* can be, for example, (a) the usual cross‐correlation function, used by Wolf, (b) a higher‐order correlation function, (c) the Hilbert transform of *f*(*P, t*), and (d) derivatives of *f*(*P, t*). For linear p.d.e.'s in which two or more independent variables have the above property, higher‐dimensional or vector versions of *F* are obtainable. The existence of this (two‐fold) generalization of Wolf's result suggests the possibility of other physical applications.