A method and apparatus for convolving spectroscopic data with certain phase information for practicing phase-compensated sensitivity-enhanced spectroscopy (PCSES). PCSES uses a beam of radiation in a polarization state PSp from a source emitting at a plurality of wavelengths, and places in the beam a compensator capable of altering polarization state PSp by applying a delimited phase shift Δ between two orthogonal polarization axes of the radiation to restrict a finely-vibrating spectrum. A sample disposed in the beam after the compensator generates a response beam by reflection, transmission or even both. A polarization state PSa of the response beam is passed to a detector to determine a spectrum of the response beam. A first spectrum is collected when polarization states PSp, PSa and the compensator are in a first polarization-altering configuration and a second spectrum is collected when polarization states PSp, PSa and the compensator are in a second polarization-altering configuration. A phase-compensated spectrum is then derived from just the first and second spectra thereby allowing the user to undertake optical characterization, including the measurement of film thickness t and complex indices of refraction n, k of the sample with as few as just two polarization-altering configurations.