  For partially coherent light fields with random fluctuations, the intensity
distributions and statistics have been proven to be more propagation robust
compared with coherent light. However, its full potential in practical
applications has not been realized due to the lack of four-dimensional optical
field measurement. Here, a general modal decomposition method of partially
coherent light field is proposed and demonstrated. The decomposed random modes
can be used to, but not limited to, reconstruct average intensity, cross
spectral density and orthogonal decomposition properties of the partially
coherent light fields. Due to its versatility and flexibility, this method
provides a powerful tool to further reveal light field invariant or retrieve
embedded information after propagation through complex media. The
Gaussian-shell-model beam and partially coherent Gaussian array are used as
examples to demonstrate the reconstruction and even prediction of second-order
statistical characteristics. This method is expected to pave the way for
applications of partially coherent light in optical imaging, optical encryption
and anti-turblence optical communication.
