Diffraction PSF Viewer
Visualize the Airy diffraction pattern from a circular aperture and see how it maps onto a pixel grid to understand energy collection efficiency.
Diffraction PSF Viewer
Interactive Airy pattern viewer with pixel grid overlay. Explore how f-number, wavelength, and pixel pitch affect the diffraction-limited PSF.
Physics
A circular aperture produces the Airy pattern as its point spread function (PSF):
PSF(x) = [2 J₁(x) / x]²
where x = pi D r / (lambda f) , D is the aperture diameter, f is the focal length, and J₁ is the first-order Bessel function.
Key Quantities
- Airy disk radius = 1.22 lambda F/# — the first dark ring of the diffraction pattern. This sets the fundamental resolution limit.
- Encircled energy — the fraction of total energy within a given radius. About 84% falls within the first Airy ring.
- Pixel collection efficiency — when the pixel grid is overlaid on the PSF, the fraction captured by the central pixel depends on the ratio of pixel pitch to Airy disk diameter.
Design Trade-offs
| F/# | Airy radius (550 nm) | Relative to 1.0 um pixel |
|---|---|---|
| 1.4 | 0.94 um | ~1x pixel pitch |
| 2.0 | 1.34 um | ~1.3x pixel pitch |
| 2.8 | 1.88 um | ~1.9x pixel pitch |
As F/# increases, the PSF spreads across more pixels, reducing per-pixel collection efficiency and increasing optical crosstalk.
INFO
This model assumes an ideal circular aperture. Real camera lenses have aberrations that broaden the PSF beyond the diffraction limit, especially at wide apertures.