Colorful radial Talbot carpet at the transverse plane

In this work we theoretically and experimentally investigate the diffraction of spatially coherent and collimated white light beam from radial amplitude gratings. Theoretical part of the work is resolved with the Fresnel-Kirchhoff integral. In the experimental part, a collimated wave-front of a white light beam emitting from a halogen lamp is transmitted through a radial amplitude grating. We digitally record the diffraction pattern in various distances from the grating using a CCD camera. The resulted diffraction pattern that we call it "Colorful radial Talbot carpet at the transverse plane" has a shape-invariant form under propagation. The other significant aspects of this pattern are the existence of a quite patternless dark area located around the optical axis and an intense rainbow-like ring in the vicinity of the patternless area. The rainbow color changes radially from the violet in the vicinity of the patternless area to red by increasing the radius in which the purity of the colors in the inner side is dominant. We call this phenomena "diffraction-based rainbow". In addition, the transverse plane Talbot carpet pattern consists colorful self-images of the grating's spokes at the larger radii. The theoretical calculations and experimental results verify each other completely. The introduced diffraction-based rainbow can be utilized in spectrometry.