In this letter, we introduce a polarization optimization concept to maximize the sensitivity of the synthetic aperture radar (SAR) backscatter measurements to a biophysical parameter. An iterative method based on Lagrangian multipliers is introduced for optimization. Using a priori information, the optimization identifies the polarization most sensitive (or least sensitive) to the quantity of interest, with best predictive characteristics. The methodology is tested for estimating forest aboveground biomass using polarimetric SAR data acquired by DLR's E-SAR airborne sensor at L- and P-band frequencies over a boreal forest test site in Krycklan Catchment, Sweden. The results show an improvement of sensitivity to forest biomass using the optimized polarization compared to canonical polarizations. Via polarization basis transformation, the correlation of biomass to backscatter is shown to improve by up to 0.23 and 0.59 at L- and P-bands, respectively.