Vector carrier frequency by interfering the kth harmonic of two rulings rotated polarly

• Interferograms consisting of inclined parallel fringes by superposition of kth harmonic of two gratings rotated polarly.
• Modulation of vector carrier frequency in three forms: magnitude only (MM), direction only (DM), and magnitude and direction (MDM).
• Experimental verification in a double-aperture common-path interferometer.

This paper presents a method for introducing carrier fringes inclined at any angle into an interferogram. The setup is built on a 4f optical system consisting of two apertures in the input plane and a Ronchi ruling in the Fourier plane. Additionally, a Ronchi ruling rotated on polar direction is placed at each aperture and two passband filters are placed in the Fourier plane for filtering the kth harmonic of their spectra. We demonstrated that the magnitude and direction of the vector carrier frequency depend on the grating period at the input plane, the polar angles, and the kth harmonic, which gives this method the ability to modulate its magnitude only, or its direction only, or both in a wide range. The theoretical model and experimental results are shown in this paper.