What are the meanings for the different terms used for polarizers?

Extinction is described generally as a polarizing filter's ability to absorb polarized light that has an orientation 90° to the polarizer's axis of polarization.

The Extinction Ratio is the ratio of power for plane-polarized light going through a polarizer with its axis oriented parallel to the plane of polarization over the power of plane-polarized light going through that same polarizer with its axis oriented perpendicular to the plane of polarization (for example, 700:1). A more technical definition of Extinction Ratio, follows from the Handbook of Optics (Vol. I, 5-13):

Extinction Ratio = r = T₂/ T₁ » ½ (T^{^} / T|| )

where:

T₁ = maximum transmittance parallel to plane of polarized beam

T₂ = minimum transmittance perpendicular to plane of polarized beam

T|| = maximum transmittance of two polarizers parallel in unpolarized beam

T^{^} = minimum transmittance of two polarizers perpendicular in unpolarized beam

Note: all "T"; values are for monochromatic light.

Example: If using an unpolarized light source, a direct reading of the extinction ratio is not possible but can be estimated. If the unpolarized source has a wavelength of 550nm and the parallel transmission is 27.17% and the crossed transmission is 0.02%, then the extinction ratio at 550nm is approximately 3.7 x 10^-4.

Polarization Efficiency is the percentage of how efficiently one polarizer polarizes incident light over the total amount of polarized light. For example, a linear polarizer with 99% efficiency transmits 99% of the incident light in the intended polarization (p-polarization state) and 1% in the opposite polarization (s-polarization state). Again a more technical definition exists, as based from the Handbook of Optics (Vol. I, 5-13):

Polarization Efficiency = P.E. (%) = [(H₀-H₉₀) / (H₀+H₉₀)]^1/2 x 100

where:

H₀ = average transmittance (unpolarized incident light) of parallel polarizers, over
400-700nm

H₉₀ = average transmittance (unpolarized incident light) of crossed polarizers,
over 400-700nm

Note: "H" values are averages from 400 to 700nm (not the same as "T" values)

Example: If the source is again unpolarized and the average parallel transmission across the visible is 26.53% and the average crossed transmission across the visible is 0.01%, then the polarization efficiency is 99.96%