Carrier fringes in the two-aperture common-path interferometer

We present a method to introduce a linear phase into an interference pattern. This phase is introduced when a grating is placed outside of the Fourier plane of a two-aperture common-path interferometer, which is built using a $4f$ optical imaging system. Based on an analysis of near-field diffraction, the introduction of the carrier fringes is mathematically justified. It is important to note that no tilt between the two beams is requested to produce this effect, and it turns out to be simpler, easier, and more versatile than other existing methods. The main attributes and advantages of the setup will be discussed and illustrated in detail with experimental fringe patterns.