The analytical expressions for the average bit error rate and the outage probability of a heterodyne differential phase-shift-keying underwater wireless optical communication (UWOC) system are derived with proper consideration of all of the channel-degrading effects, including absorption, scattering, and turbulence-induced fading. The scintillation index of a spherical wave is evaluated in order to quantify the underwater system performance in a strong turbulence regime. The spherical wave propagating through the strong underwater turbulence environment is modeled as gamma-gamma distribution. Then, the system performance is simulated for various variations of the underwater turbulence, i.e., the rate of dissipation of kinetic energy per unit mass of fluid, the ratio of temperature to salinity contributions to the refractive index spectrum, and the UWOC system link length. The results show that the analytical expressions for describing the system performance are valid.

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A real-time complex amplitude reconstruction method for determining the dynamic beam quality M² factor based on a Mach-Zehnder self-referencing interferometer wavefront sensor is developed. By using the proposed complex amplitude reconstruction method, full characterization of the laser beam, including amplitude (intensity profile) and phase information, can be reconstructed from a single interference pattern with the Fourier fringe pattern analysis method in a one-shot measurement. With the reconstructed complex amplitude, the beam fields at any position z along its propagation direction can be obtained by first utilizing the diffraction integral theory. Then the beam quality M² factor of the dynamic beam is calculated according to the specified method of the Standard ISO11146. The feasibility of the proposed method is demonstrated with the theoretical analysis and experiment, including the static and dynamic beam process. The experimental method is simple, fast, and operates without movable parts and is allowed in order to investigate the laser beam in inaccessible conditions using existing methods.

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