Polarization contrast between a target and its background

How distinct a target's polarization is from its background, for a polarization-sensitive viewer. Each polarization state is mapped to its normalised linear-polarization (Stokes) coordinates $$q = DoP\cos 2\psi, \qquad u = DoP\sin 2\psi,$$ where $\psi$ is the angle of polarization; the polarization distance is the Euclidean separation in this plane, $$\Delta P = \sqrt{(q_t - q_b)^2 + (u_t - u_b)^2}.$$ The factor of two in the angle correctly handles the 180-degree periodicity of polarization orientation, so orthogonal e-vectors (90 degrees apart) at equal degree of polarization give the maximal angular contrast. This is the geometric core of How & Marshall's (2014) polarization-distance model.

Usage

polarization_contrast(target_dop, target_aop, background_dop, background_aop)

Arguments

target_dop, target_aop: Degree of polarization (0-1) and angle of polarization (degrees) of the target. Vectorised.
background_dop, background_aop: Degree and angle of polarization of the background. Vectorised. Scalars are broadcast; implicit partial recycling is rejected.

Value

A data frame with columns delta_dop (absolute difference in degree of polarization), delta_aop (axial angular difference in degrees, [0, 90]), and distance (the polarization distance $\Delta P$).

References

How MJ, Marshall NJ (2014) Polarization distance: a framework for modelling object detection by polarization vision systems. Proceedings of the Royal Society B 281:20131632.

Examples

# A horizontally polarized target against a weakly polarized background:
polarization_contrast(target_dop = 0.5, target_aop = 0,
                      background_dop = 0.1, background_aop = 45)
#>   delta_dop delta_aop distance
#> 1       0.4        45 0.509902