When a plane wave incidents upon a periodic diffraction grating, it is noted that the image of the grating is repeated at regular distances away from the grating plane. This distance is called the Talbot length and the periodic images are called Talbot images. It is also noted that at half the length, a self-image occurs which is phase-shifted by half a period and at one-quarter of the Talbot length, the self-image is halved in size. This pattern of the periodic images is what is referred to as a Talbot carpet.
This effect was first observed by Henry Fox Talbot and it was Lord Rayleigh that showed the Talbot effect was a natural consequence of Fresnel diffraction.
Here at MathsOne, one of the Best Maths Tuition Centres in Trivandrum we educate our students in the basics of Mathematics that we often overlook.