We describe the measurement of low differential group delay and fiber birefringence using a commercial polarization analyzer based on a free-space rotating quarter waveplate polarimeter. Stress-induced birefringence is isolated from the 60-cm fiber under test by placing it in a suitably designed fiber chuck. A referencing scheme is used to eliminate system birefringence. The suitability of this setup for the measurement of low polarization mode dispersion (PMD) is demonstrated. We also report results that demonstrate limitations of the recently proposed Jones matrix exponential expansion for first-order PMD measurement in devices with high second-order PMD.