Diffraction from a phase grating that produces a sinusoidal wavefront can result in what is known as a Talbot carpet, discovered experimentally in 1836. The fractal pattern shows repeated images of itself at multiples of a fixed distance (the so-called Talbot distance). The same behavior has been detected in experiments in atomic and quantum physics.

where is the separation between slits in a Ronchi grating, is the wavelength, and is the amplitude; is the Bessel function of order . The series is aproximated with terms and evaluated in step sizes of .

References

[1] M. V. Berry, I. Marzoli, and W. Schleich, "Quantum Carpets, Carpets of Light," Physics World,14(6), 2001 pp. 39–44.

[2] M. V. Berry and E. Bodenschatz, "Caustics, Multiply-Reconstructed by Talbot Interference," Journal of Modern Optics, 46(2), 1999 pp. 349–365.