In studies of propagation through random media, an equation was developed that governs the propagation of the fourth-order coherence function. Here, we use this equation, without the scattering term, to investigate the propagation of the fourth-order coherence function in free space. Irradiance fluctuations are studied as a special case for infinite and finite beams. For a finite beam, the ... [Show full abstract] normalized on-axis irradiance fluctuations that result from a weak phase screen reach a maximum value before decaying to zero as the propagation distance becomes very large. In agreement with earlier results, the infinite beam is found to approach a constant value.