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We present and analyze an experiment to characterize the effect of turbidity to pulsed optical time transfer through water. During optical time transfer through water, two modules are each equipped with an atomic clock and timing electronics to keep and compare time independently. One module emits a laser pulse to a remote clock. The departure of the laser pulse from is time stamped with respect to a reference clock. The arrival of the pulse at the remote unit is time stamped with respect to its clock. The discrepancy between clocks is computed by comparing the measured departure time from plus the estimated time of flight of the pulse to the measured time of arrival at the remote unit. The estimated time of flight and the resulting time transfer performance are affected by the pulse propagation channel conditions. To analyze the effects of various channel conditions, we present the clock discrepancy, the measurement noise of an array of time stamps, and the Allan deviation. Allan deviation is a common metric in the time and frequency community to evaluate the stability of a series of events, where lower values are correlated with greater stability. This is an especially effective tool for studying nonstationary processes, where mean and deviation are a function of time, rather than constant. Additionally, insight into the dominant noise contributions of the frequency instability can be drawn by plotting the Allan deviation versus averaging time. In order to evaluate the free-space optical time transfer, Allan Deviation plots are generated for the empty, still water, and turbid water filled tank. Optical time transfer Allan deviation is compared to Allan Deviation generated from simultaneous frequency counter measurements through coaxial cables to differentiate between clock and channel stability.
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