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Lens Shading Simulator ​

Simulate relative illumination across the sensor based on chief ray angle, microlens shift optimization, and cos⁴ fall-off. Visualize per-channel color shading.

Lens Shading Simulator

Simulate relative illumination across the sensor based on CRA, pixel design, and cos⁴ fall-off. Visualize per-channel color shading.

Center RI
100%
Corner RI
38.3%
Edge RI
62.2%
RI Loss (stops)
1.38 EV
2D Shading Map
38%
100%
Radial Profile
30%40%50%60%70%80%90%100%0.00.30.50.81.0Relative Position (r/r_max)RI (%)

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

Signal Chain · Pixel Optical Effects

Physics Notes

Relative Illumination and CRA Shading

Plain-English Intuition

Even with a perfect lens, the corners of every image come out darker than the centre — it is geometry, not a defect. Light arrives at edge pixels at a steep angle while the pixel optics are tuned for straight-on rays, so corner response drops. Modern sensors compensate by shifting microlenses inward at the edges, and image processing fills in the rest.

Lens shading combines optical cos-fourth falloff, chief-ray angle mismatch, microlens offset, and color-channel angular response.

Assumptions

  • Relative illumination combines chief-ray angle, cos-fourth falloff, and compact microlens-shift compensation.
  • The sensor map is radially simplified and does not include lens design ray files, pupil aberrations, or per-pixel measured correction tables.
  • Color shading is represented by channel-dependent angular sensitivity, not a full spectral ISP correction.

Outputs

  • 2D relative-illumination map, radial falloff, corner loss in stops, channel imbalance, and compensation trend.
  • A quick view of whether optical CRA, pixel pitch, or microlens shift is likely to drive corner shading.

Validation Example

  • With zero CRA and no channel imbalance, the map should be nearly flat apart from any intentional falloff term.
  • Increasing maximum CRA should reduce corner relative illumination and can produce stronger color shading.

Core Equations

Cos-fourth falloff
$$RI(\theta) \approx \cos^4(\theta)$$
  • \(RI\): Relative Illumination
  • \(\theta\): Chief Ray Angle (CRA)

This is a classical first-order model for image-plane relative illumination.

Microlens shift
$$\text{shift} \approx h_{\text{stack}} \cdot \tan(CRA_{\text{eff}})$$
  • \(h_{\text{stack}}\): Optical stack height

Refraction in the stack usually makes CRA_eff smaller than the air-side CRA.

Color shading
$$G_c(r) = \frac{S_c(0)}{S_c(r)}$$
  • \(G_c(r)\): Spatial gain correction

Per-channel lens-shading correction equalizes radial response.

Model Interpretation

  • Color shading appears when R/G/B angular responses are not identical.
  • Microlens shift improves edge response but can reduce center tolerance if overdone.
  • Production correction tables combine optical design and factory calibration.

Shading Sources

  • Lens geometry creates classical $\cos^4\theta$ falloff before pixel optics are considered.
  • Pixel stack angular response adds color-dependent rolloff when R/G/B filters respond differently to CRA.
  • Microlens shift corrects lateral focus displacement but must match stack height and refracted CRA.

Correction Workflow

  • Measure flat fields per channel, estimate radial or 2D gain maps $G_c(r)$, and apply correction before color processing.
  • Separate optical shading from illumination nonuniformity and dust by using calibrated fixtures.
  • Validate correction at multiple focus distances and apertures if the lens system changes CRA distribution.

Known Missing Physics

  • The model does not solve full lens chief-ray distribution, pupil aberration, or sensor cover-glass refraction.
  • Correction tables can amplify corner noise because they multiply weak signals.
  • Real products also compensate manufacturing variation, module tilt, and color-temperature dependence.

References