Normal stresses play a key role in polymer processing, yet accurate measurements are still challenging. Simultaneous rheo-optical measurements are conducted on a poly (vinyl methyl ether) homopolymer melt over a wide range of temperatures and oscillatory shear frequencies, in an effort to measure the normal stresses, by using quantitative flow birefringence measurements. The stress optical rule holds well for this polymer as expected, with the value of the stress optic coefficient of (6.38 +/- 0.19)x10(-11) cm(2)/dyn at 30 degrees C. The first and third normal stress difference coefficients Psi(*)(1), Psi(*)(3), calculated using a single memory constitutive equation applied to the stress and birefringence data, are in excellent agreement. The ratio of the measured third and first normal stress difference coefficients, (1-beta)=0.71 +/- 0.05, agrees well with the result of the Doi-Edwards model with independent alignment approximation (beta=0.28). The measurement of normal stress difference coefficients with such small deviations proves the robust nature of the improved rheo-optical instrument and its ability to measure complete stress tensor.