  Linear polarized light has been used to view the solar corona for over 150
years. While the familiar Stokes representation for polarimetry is complete, it
is best matched to a laboratory setting and therefore is not the most
convenient representation either for coronal instrument design or for coronal
data analysis. Over the last 100 years of development of coronagraphs and
heliospheric imagers, various representations have been used both for direct
measurement and analysis. These systems include famous representations such as
the (B, pB) system that is analogous to the Stokes system in solar observing
coordinates, and also internal representations such as in-instrument Stokes
parameters with fixed or variable "vertical" direction, and brightness values
through a particular polarizing optic or set thereof. Many polarimetric
instruments currently use a symmetric three-polarizer measurement and
representation system, which we refer to as "(M, Z, P)", to derive the (B, pB)
or Stokes parameters. We present a symmetric derivation of (B, pB) and Stokes
parameters from (M, Z, P), analyze the noise properties of (M, Z, P) in the
context of instrument design, develop (M, Z, P) as a useful intermediate system
for data analysis including background subtraction, and draw a helpful analogy
between linear polarimetric systems and the large existing body of work on
photometric colorimetry.
