B-fields In STar-forming Region Observations (BISTRO): Technical Foundations for Quantitative 450/850 $μ$m JCMT SCUBA-2/POL-2 Polarimetry

We present five technical validations of SCUBA-2/POL-2 polarimetry on the James Clerk Maxwell Telescope at 450 and 850 $μ$m, using 174 archival fields in 69 molecular cloud regions and subsets appropriate to each test. Extended-source calibration avoids a deterministic shift of $Δβ=-1.05$ in the dust emissivity index $β$ that would result from calibrating extended emission using peak brightness. We modeled Stokes $I$ noise with additive and signal-dependent components. The measured median ratio of surface-brightness noise at 450/850 $μ$m is 25. Independent tests of Stokes $Q,U$ noise support approximately equal additive variances and weak error correlations, providing a basis for propagating polarization uncertainties. Corrections determined for individual fields reduce additive zero-level offsets of order $1$ mJy arcsec$^{-2}$ in the 450 $μ$m Stokes $Q$ and $U$ intensities. The three-step regression leaves a median combined residual amplitude of $0.07$ mJy arcsec$^{-2}$. Independent comparisons with SOFIA/HAWC+ at 154 and 214 $μ$m support the correction in strongly affected fields. We matched the 450 $μ$m maps to the modeled 850 $μ$m beam and the common $12.6''$-$300''$ range of angular scales. We compared three reductions of the same 450 $μ$m observations across 30 sources. Taking the median angular residual relative to the final product for each source, we find that beam matching reduces the median over sources from $6.3^\circ$ to $4.7^\circ$. After matching, 29 of the 30 sources have median residuals below $10^\circ$. We also quantified how residual $Q/U$ offsets propagate in ratios of polarization fractions, differences in spectral indices, and polarization angles. These validations provide procedures and quantitative references for interpreting POL-2 measurements and combining them with polarimetry at other wavelengths.