Methods and instruments are provided for measuring differences in fractional reflectivity changes between transverse electric (TE or s-polarized) and transverse magnetic (TM or p-polarized components of an obliquely incident light with high sensitivity and low noise. Also provided are high sensitivity, low noise methods and instruments for measuring differences in fractional reflectivity changes between R-polarized (right-circularly polarized) and L-polarized (left-circularly polarized) components of a near-normal incident light. The methods take advantage of a nulling step to minimize harmonics of the optical signal derived from a first sample. Determination of odd and even harmonics of the optical signal derived from a second sample allows determination of refractive index and optical absorption coefficient differences between two samples to be determined with high sensitivity and low noise.