Distalis: Fraunhofer Diffraction
Optics, Waves & Sound arc, page 122 of 193. Back to The Pixelated Physics Universe
Who they are
Distalis has one line, and says it often: “Far field: i only get the fourier transform.”
Distalis is a character of the Optics, Waves & Sound arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
In the Fraunhofer (far-field) regime the diffracted field is the Fourier transform of the aperture.
$$ \begin{gathered} U(x,y) \propto \iint A(\xi,\eta)\, e^{-i\frac{2\pi}{\lambda z}(x\xi + y\eta)}\, d\xi\, d\eta \\ z \gg \frac{a^{2}}{\lambda} \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $U(x,y)$ | far-field amplitude on the screen | — |
| $A(\xi,\eta)$ | aperture transmission | — |
| $\lambda$ | wavelength | m |
| $z$ | aperture-to-screen distance | m |
| $a$ | aperture size | m |
Sources
- M. Born & E. Wolf, Principles of Optics, 7th ed. (Cambridge, 1999), §8.3.3
- J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts, 2005), §4.3
Crossovers
Distalis meets Nickela (Electrons Diffract 1927). Nickela's electrons and Distalis's far-field light obey the same rule: far from the scatterer, the pattern is set by the Fourier transform of the structure. Nickela's structure is a crystal lattice; Distalis's is an aperture.
Distalis meets Arago (Spot of Arago). Arago's spot is a near-field (Fresnel) effect, behind a disc. Distalis lives far away, where the pattern becomes the Fourier transform of the aperture. Same diffraction, different distances.
Distalis meets Waistwyn (Gaussian Beam Rayleigh Range). Waistwyn's Gaussian beam spreads beyond its Rayleigh range, entering Distalis's far field. Tighter waists diverge faster: a smaller aperture gives a wider diffraction pattern.
Wear the lore
- Distalis, the Far-Field Back-Row Watcher Mug
- Related infographic poster: Fraunhofer's Lines – Plate 021 Physics Poster
Concept keywords: Fraunhofer Diffraction, Distalis, Optics, Waves & Sound, physics lore, Pixelated Physics