In conventional interferometry, the intensity of the superposed field is observed to study the phase information of object / sample field. The schemes like Weak measurement scheme, spectral switching observes the intensity of the output field for enhancing the sensitivity of the phase measurements. A scheme to enhance the sensitivity in the measurement of path delays through spectral interferometry by observing the phase accumulated by the superposed field with respect to an additional reference beam is presented. Through the interference with additional reference beam maintained at out-of-phase condition near zero optical path delay with respect to the sample probe beam, it is shown to introduce nonlinearity in phase change measured. In the experimental demonstration, the classic low coherence spectral interferometry is used. The three-beam interference is achieved by a modified Michelson interferometer. According to the setting of initial path delay and amplitude ratio of the interfering fields, the intensity of superposed field shows spectral modulations. Spectral phase is measured from the modulations in the recorded spectral interference using Fourier transform method of fringe analysis. In the Fourier domain, a linear path delay between in the interfering beams gives a linear shift in the position of secondary peak. By filtering the secondary peak from the Fourier domain, and taking the Inverse Fourier transform, the amplitude and phase information of the interfering fields can be obtained. The proposed method maps the linear path delay to highly nonlinear phase accumulation and has the potential to enhance sensitivity of phase measurements.