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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.

2D PSF (log scale)
Radial Profile
pixel00.511.522.53110⁻¹10⁻²10⁻³10⁻⁴Airy rRadius (um)Intensity
Encircled Energy
84%pixel00.511.522.530%20%40%60%80%100%22.9%Radius (um)EE (%)
Airy radius1.879 um
Airy disk / pixel3.76
Energy in pixel22.9%
Resolution (lp/mm)266

Model scope

Use this browser tool for intuition, relative trends, and design-space exploration. Its local simplified model is not a substitute for RCWA/FDTD sign-off, silicon calibration, or vendor process data.

Learn more

Diffraction · Resolution, MTF, and Pixel Scaling

Physics Notes

Airy Pattern and Pixel Sampling

Plain-English Intuition

Even a perfect lens cannot focus light to a single mathematical point — diffraction smears it into a bright central disk surrounded by faint rings (the Airy pattern). The smaller the aperture or the longer the wavelength, the bigger the smear. When that smear grows larger than one pixel, neighbouring pixels start sharing the same point of light and resolution suffers.

A circular aperture forms an Airy diffraction pattern, which spreads energy across multiple pixels as f-number or wavelength increases.

Assumptions

  • The optical aperture is ideal, circular, aberration-free, and diffraction limited.
  • The PSF is scalar and monochromatic for the selected wavelength; broadband color blur requires spectral integration.
  • Pixel collection is geometric area overlap with the PSF, not a full EM or carrier-transport calculation.

Outputs

  • Airy intensity profile, first dark-ring radius, encircled energy, and pixel-grid overlay.
  • A check of whether diffraction blur is smaller than, comparable to, or larger than the pixel pitch.

Validation Example

  • The first Airy zero should scale linearly with wavelength and f-number: $r_1=1.22\lambda N$.
  • Doubling f-number at fixed wavelength should roughly double the plotted Airy radius.

Core Equations

Airy intensity
$$I(r) = I_0 \left[ \frac{2J_1(\frac{\pi r}{\lambda N})}{\frac{\pi r}{\lambda N}} \right]^2$$
  • \(r\): Radial distance from center
  • \(J_1\): First-order Bessel function
  • \(N\): Lens f-number

J1 is the first-order Bessel function and N is the f-number.

First dark ring
$$r_1 = 1.22 \lambda N$$
  • \(r_1\): Radius of first Airy zero

This gives the common diffraction-limited spot radius estimate.

Encircled energy
$$EE(r) = \int_0^r 2\pi \rho I(\rho) \,d\rho$$
  • \(EE(r)\): Energy inside radius $r$

Pixel collection depends on how much PSF energy falls within the active aperture.

Model Interpretation

  • Diffraction becomes a first-order limit when pixel pitch approaches the wavelength.
  • The PSF viewer assumes an ideal circular aperture and ignores aberrations.
  • For real camera resolution, combine diffraction, pixel aperture MTF, lens aberration, and demosaicing.

Sampling Interpretation

  • Compare $r_1=1.22\lambda N$ with pixel pitch; once the central lobe spans multiple pixels, point detail is shared.
  • Encircled energy is often more useful than peak intensity because a pixel collects finite area, not a point.
  • Longer wavelength and larger f-number both broaden the PSF through the same product $\lambda N$.

Resolution Workflow

  • Use the PSF to judge point spread, then use MTF to judge sinusoidal contrast transfer.
  • Compare the Airy diameter with the pixel pitch and with the Nyquist frequency of the sampling grid.
  • For color sensors, evaluate blue, green, and red separately because $\lambda$ changes the diffraction blur.

Known Missing Physics

  • The ideal Airy PSF omits lens aberration, defocus, cover-glass effects, and microlens aperture truncation.
  • It does not include pixel cross-section geometry, metal shading, or charge diffusion.
  • System resolution also depends on demosaic, sharpening, motion blur, and measurement target processing.

References