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High-precision underwater 3D cameras are required to automate many of the traditional subsea inspection, maintenance and repair (IMR) operations. In this paper we introduce a novel multi-frequency phase stepping (structured light) method for high-precision 3D estimation even in turbid water. We introduce an adaptive phase-unwrapping procedure which uses the phase-uncertainty to determine the highest frequency that can be reliably unwrapped. Light scattering adversely affects the phase estimate. We propose to remove the effect of forward scatter with an unsharp filter and a model-based method to remove the backscatter effect. Tests in varying turbidity show that the scatter correction removes the adverse effect of scatter on the phase estimates. The adaptive frequency unwrapping with scatter correction results in images with higher accuracy and precision and less phase unwrap errors than the Gray-Code Phase Stepping (GCPS) approach. [ABSTRACT FROM AUTHOR]