Flatland optics. III. achromatic diffraction

In the previous two sections of “Flatland optics” [J. Opt. Soc. Am. A 17, 1755 (2000); 18, 1056 (2001)] we described the basic principles of two-dimensional (2D) optics and showed that a wavelength λ in threedimensional (3D) space (x, y, z) may appear in Flatland (x, z) as a wave with another wavelength Λ=λ/cos α. The tilt angle α can be modified by a 3D-Spaceland individual, who then is able to influence the 2D optics in a way that must appear to be magical to 2D-Flatland individuals-in the spirit of E. A. Abbott’s science fiction story of 1884 [Flatland, a Romance of Many Dimensions, 6th ed. (Dover, New York, 1952)]. Here we show how the light from a white source can be perceived in Flatland as perfectly monochromatic, so diffraction with white light will be free of color blurring and the contrast of interference fringes can be 100%. The basic considerations for perfectly achromatic diffraction are presented, along with experimental illustration of Talbot self-imaging performed with broadband illumination.