In a conventional coherent anti-Stokes Raman scattering (CARS) microscope system, we generate a local oscillator CARS field and a sample CARS field successively along a single-beam path. A large gradient of relative spectral phase between the two fields is naturally induced by highly dispersive microscope elements. The resulting spectral interferogram is a form of fast varying sinusoidal fringes modulated by the amplitude and phase of the sample CARS field. With the help of the Hilbert transform on the heterodyne part of the interferogram, both real and imaginary quadratures of the sample CARS spectrum are extracted with an improved signal-to-noise ratio.