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Airy Disk Hoodie

EVEN A PERFECT LENS BLURS | Pixelated Physics

\[I(x) = I_0\left(\frac{2J_1(x)}{x}\right)^2,\qquad x = \frac{\pi D\sin\theta}{\lambda}\]
$54.99 USD
$54.99 USD
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Size

Size guide S–5XL · inches

Even a flawless lens cannot focus light to a point. The Airy pattern of a circular aperture, I = I₀(2J₁(x)/x)², on a log scale. The first dark ring sits at sin θ = 1.22 λ/D. Pixel-art unisex hoodie in black; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in 2–5 business days

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 circular aperture can't focus light to a point; diffraction turns a point of light into a bright central disk with faint rings. The disk's angular size, 1.22 λ/D, sets the sharpest detail any telescope or eye of diameter D can resolve.

Even a flawless lens cannot focus light to a point.

A circular aperture diffracts the light that passes through it. The image of a star becomes a bright central disk wrapped in faint rings, with intensity (2J₁(x)/x)². George Biddell Airy worked it out in 1835.

The first dark ring falls at sin θ = 1.22 λ/D. That sets the resolution limit of every telescope, camera and eye: two points closer than about this angle blur into one.

The rings are very faint, the first only 1.75% of the peak, so the art steps the intensity on a log scale to show them at all.

The sharpest possible dot has rings.

Equations

\[I(x) = I_0\left(\frac{2J_1(x)}{x}\right)^2,\qquad x = \frac{\pi D\sin\theta}{\lambda}\]
\[\sin\theta_1 = 1.22\,\frac{\lambda}{D}\]
SymbolMeaningUnit
\(I(x)\) intensity in the focal plane \(\mathrm{W/m^2}\)
\(I_0\) peak intensity \(\mathrm{W/m^2}\)
\(J_1\) Bessel function of the first kind, order 1 \(\mathrm{1}\)
\(D\) aperture diameter \(\mathrm{m}\)
\(\lambda\) wavelength \(\mathrm{m}\)
\(\theta\) angle from the optical axis \(\mathrm{rad}\)
\(\theta_1\) angle of the first dark ring \(\mathrm{rad}\)

Sources

  1. Airy (1835) On the Diffraction of an Object-glass with Circular Aperture, Trans. Cambridge Phil. Soc. 5, 283
  2. Born & Wolf, Principles of Optics, 7th ed., Sec. 8.5.2
  3. Hecht, Optics, 5th ed., Sec. 10.2.5

Source Airy, G. B. (1835). On the Diffraction of an Object-glass with Circular Aperture. Transactions of the Cambridge Philosophical Society, 5, 283–291.

Field notes

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