Embodiments of the invention provide a simple and robust system that allows non-resonant background to be removed from anti-Stokes signals generated during coherent anti-Stokes Raman spectroscopy (CARS) even when using cheaper laser systems, which do not have transform limited pulses. In particular, resonant CARS signals have a real and imaginary component. The imaginary component is directly related to the spontaneous Raman spectrum, for which there are already large spectral databases to allow chemical identification. The NRB signal, on the other hand, only has a real component. Within embodiments of the invention we recover the imaginary component of the entire CARS signal by simultaneously generating two CARS signals at orthogonal polarisations: one has the imaginary components destructively interfering with (i.e. subtracted from) the real components, the other has them constructively interfering. Measuring these two polarisations and subtracting them therefore cancels out the real part of the signal, leaving only the imaginary components.