Observable coherence theory for statistically periodic fields

The framework of cyclostationary random processes is used to develop classical coherence theory for the measurement of statistically periodic stochastic optical fields, such as those produced by pulsed lasers. Cycloergodicity is invoked to show that precise and accurate inferences of the nonstationary process statistics can be made from a single field realization. In particular, many-pulse observations using nonlinear and/or nonstationary techniques, such as spectral shearing interferometry, can be used to fully characterize the standard two-time correlation function of a statistically periodic source. The theory is demonstrated through the simulation of spectral shearing interferometry and frequency-resolved optical gating measurements.