A full Mie scattering subroutine is employed to calculate what we call the linear polarization phase function (LPPF; percent polarization and e-vector orientation of radiation as a function of scattering angle) that results from refraction of the direct solar beam from air into water followed by single scattering by spherical hydrosols. The separate effects of refraction at the air–water interface, hydrosol size, the real and imaginary parts of the hydrosol refractive index, and absorption by the surrounding medium (water) on the LPPF are investigated. All of the above factors are found to alter the LPPF, changing the value of the maximum percent polarization ($P_{\max }$), the location of $P_{\max }$, the number of fluctuations in the LPPF, or the location of the neutral points (points of 0 percent polarization), though absorption by the surrounding medium is found to have only a minimal effect. The character and extent of the influence on the LPPF is found to depend on the scattering regime (Rayleigh, Mie, or geometric optics). We conclude that in calculating underwater polarization, it is important to take into consideration Mie scattering even in relatively clear waters. We also find a coupling between the partial polarization and the e-vector orientation, which suggests that for some polarization-based visual tasks, only one of these would suffice. Other implications for aquatic animal polarization vision are discussed.

© 2012 Optical Society of America

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