Relative Illumination (RI) and Chief Ray Angle (CRA)

Relative illumination (RI) is commonly the irradiance at an image-field point divided by the center or maximum irradiance, expressed as a percentage. Edge falloff can come from mechanical vignetting at barrels or stops, the natural cos⁴θ law, lens transmission, and sensor angular response. The cos⁴θ rule is one idealized approximation, not a complete prediction of a real system’s RI curve.

“Maximum-image RI > 30%” is not a universal requirement for every lens or sensor. If used as a project acceptance target, specify maximum image height or sensor corner, aperture, wavelength, flat-field method, whether correction is applied, and whether RI is relative to center or the full-frame maximum. Thirty percent means raw irradiance there is about 0.3× the reference. Gain can raise displayed brightness but also amplifies read noise and reduces dynamic range. Set limits against low-light performance, corner SNR, uniformity correction, and algorithm tolerance.

The chief ray passes through the center of the aperture stop from an object-field point. Image-side CRA is its angle at the image plane relative to the sensor normal. Wide-field, short-focal-length, or compact lenses can have large edge CRA. Color filters, metal layers, and microlens arrays in CMOS sensors have angular response; excessive or mismatched CRA can reduce corner response and create color shading or vignetting.

Obtain the sensor vendor’s CRA response, microlens-offset design, and recommended lens conditions. Ask the lens supplier for image-side CRA versus field and RI curves. Check matching across the full sensor and measure corner illumination, color, SNR, and residuals after flat-field correction. Decenter, tilt, cover-glass thickness, and back focal distance also affect edge behavior, so validate the final module rather than the lens alone.