• Black Airy Disk physics hoodie, pixel-art Airy diffraction pattern design, worn by a model, front close-up
  • Black Airy Disk physics hoodie, pixel-art Airy diffraction pattern design, worn by a model, back close-up
  • Black Airy Disk physics hoodie, pixel-art Airy diffraction pattern design, front view
  • Black Airy Disk physics hoodie, pixel-art Airy diffraction pattern design, back view
  • Black Airy Disk physics hoodie, pixel-art Airy diffraction pattern design, turning on a model
  • Black Airy Disk physics hoodie, ΨP Pixelated Physics neck label
1 6

Airy Disk HoodieEVEN A PERFECT LENS BLURS | Pixelated Physics

Airy Disk Hoodie – EVEN A PERFECT LENS BLURS | Pixelated Physics

$54.99 USD
$54.99 USD
Sale Sold out
Shipping calculated at checkout. Free US shipping · $10 flat shipping outside the US.
Color
Black
Size
S–5XL
Made
To order · shipping times

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.

Color
Size

Size guideS–5XL · inches

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.

ShippingFree US

Free US shipping. $10 flat shipping outside the US.

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

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
View full details

Field notes

View all
1 3
View all