Diffraction, Part 2

If you have ever looked at a streetlight through an umbrella’s fabric and seen a neat array of tiny bright spots; noticed thin streaks of light emanating from images of small, bright lights in photographs; or wondered how the metallic mesh in a microwave oven door allows visible light but not microwaves to pass, then you have encountered diffraction. Many physics experiments, from spectroscopy to measurements of the wavelength of laser light, employ diffraction. Diffraction is the signature phenomena of wave motion.[1]

In Part 1 of this series on diffraction,[2] we met Huygens’ principle and applied it to the interference produced by two slits, modeled as point sources that coherently radiate equal-amplitude and equal-wavelength harmonic waves. The corresponding experiment, first done by Thomas Young in 1801, demonstrated that light is a wave, or, as we would say today, that light behaves as a wave in this situation. In our analysis of the Young experiment we observe waves sufficiently far from their source to make the wave-front curvature negligible across an aperture. Diffraction with such plane waves is called “Fraunhofer diffraction.”

Working within the Fraunhofer paradigm, here we extend Young’s experiment to multiple point sources. We will go to the limit of an infinite number of contiguous infinitesimal point sources to derive the diffraction patterns produced by a single slit as well as its complement, an opaque ribbon. That will put us in the position to consider double slits of finite width as a better model of Young’s apparatus. The result illustrates the array theorem, which says that the image produced by an array of N identical apertures equals the diffraction pattern of one aperture times the interference pattern of N point sources. We will also consider diffraction from all four edges of a rectangular aperture and from a circular aperture.

Before leaving plane waves we will discuss what it means to say that the image on the screen is the Fourier transform of the aperture. For Fraunhofer diffraction, Fourier transforms provide the link between waves, aperture, and image.

See the full article here .