  Double-pass polarimetry measures the polarization properties of a sample over
a range of polar angles and all azimuths. Here, we present a tolerance analysis
of all the optical elements in both the calibration and measurement procedures
to predict the sensitivities of the double-pass polarimeter. The calibration
procedure is described by a Mueller matrix based on the eigenvalue calibration
method (ECM). Our numerical results from the calibration and measurement in the
Mueller matrix description with tolerances limited by systematic and stochastic
noise from specifications of commercially available hardware components are in
good agreement with previous experimental observations. Furthermore, by using
the orientation Zernike polynomials (OZP) which are an extension of the Jones
matrix formalism, similar to the Zernike polynomials wavefront expansion, the
pupil distribution of the polarization properties of non-depolarizing samples
under test are expanded. Using polar angles ranging up to 25$^{\circ}$, we
predict a sensitivity of 0.5% for diattenuation and 0.3$^{\circ}$ for
retardance using the root mean square (RMS) of the corresponding OZP
coefficients as a measure of the error. This numerical tool provides an
approach for further improving the sensitivities of polarimeters via error
budgeting and replacing sensitive components with those having better
precision.
