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Diffraction Patterns (Aperture → Light)

The far-field light intensity through slits is the squared magnitude of the aperture's Fourier transform.

I(theta) propto big|mathcal{F}{text{aperture}}big|^{2}

A mind behind this: Joseph Fourier 1768–1830

Formula

\[ I(\theta) \propto \big|\mathcal{F}\{\text{aperture}\}\big|^{2} \]

Diffraction Patterns — Aperture → Far-Field Light

Shine a laser through a slit and the far-field intensity pattern is literally |𝓕(aperture)|². This is how Rosalind Franklin's Photo 51 revealed the DNA double helix in 1952 — she didn't see the molecule directly, she saw its Fourier transform.

Fraunhofer diffraction

\[ I(\theta) \;\propto\; \Big|\,\mathcal{F}\{a(x)\}\,\Big|^{2} \qquad\text{where } a(x) = \text{aperture transmittance} \]

Reference: Wikipedia — Diffraction; Wikipedia — Photo 51. Hecht, E. (2017). Optics, 5th ed., Pearson, Ch. 10. Goodman, J. W. (2017). Introduction to Fourier Optics, 4th ed.

🧪 Try these experiments in order

  1. Set slits = 1, width = 8. You see the famous sinc envelope — the single-slit diffraction pattern.
  2. Set slits = 2. A cosine interference fringe modulates the sinc envelope — this is Young's classic double-slit experiment.
  3. Increase slits to 6, 10. The pattern sharpens into spiky peaks — this is a diffraction grating, how a CD or DVD splits light into colours.
  4. Drop spacing down. The peaks spread apart. The product of slit-spacing × peak-spacing is constant — Fourier's reciprocal relationship.

The aperture (white bars = open, dark = blocked)

Far-field intensity pattern (what you see on the screen behind the aperture)

⚠ Watch out for

  • If spacing × slits exceeds the aperture array length, the slits wrap around — that's numerical aliasing, not real physics.
  • The intensity is |FFT|², so multiplying the aperture amplitude by 2 multiplies the displayed intensity by 4. Don't read brightness as linear in slit width.
✅ Do

Use this principle to figure out crystal & molecule structure (X-ray diffraction, electron microscopy, neutron scattering).

❌ Don't

Confuse the far-field (Fraunhofer) regime shown here with near-field (Fresnel) diffraction — they need different formulas.

Where this matters in industry

X-ray crystallography (every drug development pipeline, DNA structure, protein folding), electron microscopy, astronomical interferometry (Event Horizon Telescope black-hole image, radio astronomy aperture synthesis), CD/DVD/Blu-ray read heads, holography, semiconductor lithography mask design.

🎯 Learning checkpoint

If you halve the slit spacing in the aperture, what happens to the spacing of bright fringes on the screen? (Predict, then check by moving the slider.)

Frequently asked questions

Is it true the diffraction pattern is literally a Fourier transform?

Yes — remarkably, the far-field light pattern through an aperture is the squared magnitude of the aperture's Fourier transform. Nature computes the transform for you, instantly, in light. Narrow the slit here and watch the pattern spread, exactly as the maths predicts.

How did this reveal the structure of DNA?

Rosalind Franklin's famous 'Photo 51' was an X-ray diffraction image of DNA. She never saw the double helix directly — she saw its Fourier transform as a pattern of spots, and the characteristic X-shape in that pattern is the fingerprint of a helix. Crick and Watson read the structure back out of it.

Why do CDs and DVDs make rainbow patterns?

Their surfaces are covered in regularly spaced microscopic tracks — a diffraction grating. White light hitting that grating diffracts each colour to a slightly different angle, spreading the spectrum into a rainbow. The spacing of the tracks sets the angles, just like slit spacing does here.

What is the warning about aliasing in the tool?

If you pack too many slits too far apart, the pattern exceeds what the simulation's grid can represent and you get false, wrapped-around features — aliasing. It is the same effect that makes wagon wheels appear to spin backwards in films, and it is a real limit in any sampled or pixelated system.

Where is diffraction used in technology?

Diffraction gratings split light in spectrometers that identify chemicals and distant stars; the same physics sets the resolution limit of microscopes, telescopes and camera lenses, and underpins X-ray crystallography — the tool that has solved thousands of protein and drug structures.