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Zone Plate Hoodie

FOCUS BY SUBTRACTION | Pixelated Physics

\[r_n^2 = n\lambda f + \tfrac{n^2\lambda^2}{4}\]
$54.99 USD
$54.99 USD
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Size guide S–5XL · inches

Can rings replace a lens? A Fresnel zone plate can. Each ring, or zone, sits half a wavelength farther from the focus than the last, so neighbouring zones cancel. Block every other zone and the light that is left arrives in step. With four open zones the focus is about 64 times brighter than without the plate. Black pixel-art hoodie; equation, symbols and sources in the physics panel below.

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Details

Size & fitS–5XL

Unisex Heavy Blend hoodie (Gildan 18500), classic fit.

SizeWidthLengthSleeve
S202733.5
M222834.5
L242935.5
XL263036.5
2XL283137.5
3XL303238.5
4XL323339.5
5XL343440.5

Measurements in inches. Width and length ±1 in, sleeve (from center back) ±0.75 in.

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Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

A zone plate focuses light by blocking alternate rings, so that light from every open ring arrives at the focus in step. The ring radii are chosen so that each ring's path to the focus is half a wavelength longer than the one before.

A zone plate focuses light with no glass at all. It is a set of rings, alternately clear and opaque.

The rings are Fresnel zones: each one sits half a wavelength farther from the focus than the last, so r_n² = nλf + n²λ²/4.

Light from neighbouring zones arrives out of step and cancels. Block every other zone and what is left arrives in step, so it adds up at the focus.

On the hoodie the filled rings are the blocked odd zones (the centre disc is zone 1) and the black gaps are the open even zones.

With 8 zones and the odd ones blocked, the on-axis intensity at f is about 64 times that of the unobstructed wave. We checked that by summing the zones numerically.

Equations

\[r_n^2 = n\lambda f + \tfrac{n^2\lambda^2}{4}\]
\[\sqrt{f^2+r_n^2}-f = \tfrac{n\lambda}{2}\]
SymbolMeaningUnit
\(r_n\) outer radius of the n-th zone \(\mathrm{m}\)
\(n\) zone number (1, 2, 3, …) —
\(\lambda\) wavelength of the light \(\mathrm{m}\)
\(f\) primary focal length \(\mathrm{m}\)

Sources

  1. Hecht, E., Optics, 5th ed., Sec. 10.3 (Fresnel diffraction, the zone plate)
  2. Born & Wolf, Principles of Optics, Ch. 8 (Fresnel zones)
  3. Wikipedia, Zone plate

Source Soret, J. L. (1875). Ueber die durch Kreisgitter erzeugten Diffractionsphänomene. Annalen der Physik 232, 99–113.doi.org/10.1002/andp.18752320906

Field notes

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