Analysis of the interference fringes in a cross-grating interferometer

The on-axis interference pattern of a cross-grating interferometer was analyzed.1 In different cases, the localized fringes can be formed with either an extended white-light source or an extended monochromatic source. If a structured source is used, the contrast of the interference fringes in a 4-beam cross-grating interferometer is similar to that in the 4-pinhole Young’s experiment with different planes along the optical axis corresponding to different pinhole separations. With a cross-gratinglike illuminating source, the fringes are localized in discrete planes. When proper spatial filterings are done, multiple images can be formed at off-axis positions with light from an extended monochromatic source. By suitably choosing 4 beams to interfere, the fringes can be formed with white light. Fringes can also be formed further downstream with different transfer functions. When many cross gratings are used in the cross-grating interferometer, the fringes are formed in a similar way. The three-cross-grating interferometer is particularly interesting because it can be either an in-line interferometer or an off-axis interferometer.