A telescope's image of a star is never a perfect point — it is the star's light diffracted by the shape of the mirror's opening (the aperture). This pattern is the telescope's point spread function (PSF), and in the Fraunhofer (far-field) regime it is exactly the squared magnitude of the 2D Fourier transform of the aperture's transmission function:
PSF(θ) = | F{ A(x,y) } |²
A(x,y) = 1 where a segment is open and clear of struts, 0 elsewhere
The left canvas is a live editor for A(x,y): a 19-segment hexagonal mirror (JWST-style) you can click segment-by-segment, plus struts you toggle and resize. Every change re-samples that mask onto a grid and runs a genuine 2D discrete Fourier transform (a real 1D FFT applied along rows then columns) to render the right canvas — the star's simulated image. Remove a segment or a strut and the spike pattern on the right changes immediately, because it is a real computed Fourier transform of exactly the mask you edited, not a static picture.
Rayleigh resolution: θ_R = 1.22 λ / D
Strut diffraction: θ_sp ≈ λ / w (w = strut width)
- Click segments — turning off a hexagon changes which gap edges are present, which changes which directions the spikes point in.
- 3 vs 4 struts — a tripod mount (JWST) throws 6 large spikes; a 4-strut "+" mount (Hubble-style) throws 8 shorter ones. Removing struts entirely removes their spikes and leaves only the hexagon-gap spikes.
- Strut width — a thinner strut diffracts light through a wider angle (θ ≈ λ/w), so thin struts make long faint spikes and thick struts make short bright ones.
- Mirror diameter — bigger D shrinks the central core (sharper resolution) without changing spike directions.
- Wavelength — every diffraction angle scales with λ, so red light spreads both the core and the spikes further than blue light.
- Core encircled energy — the fraction of the total diffracted light landing inside the Airy-core radius; removing segments or adding struts steals light from the core and throws it into the spikes, so this number drops as the aperture gets smaller or more obstructed.