I.Concept
Shading comprises luminance shading and color shading.

• Luminance shading refers to the uneven distribution of brightness from the center to the edges of an image (Figure 1).
• Color shading refers to the inconsistent color reproduction from the center to the edges of an image (Figure 2).

Figure 1. Schematic diagram of luminance shading	Figure 2. Schematic diagram of color shading

（1）Luminance Shading
Considering the lens system as an aperture, the luminous flux at the center is inherently greater than at the periphery. This disparity results in a higher illuminance at the center of the image sensor.

Figure 3. Illuminance falloff according to the cosine-fourth law.

As shown in Figure 3, assuming the emitting object is a Lambertian (cosinusoidal) radiator, light propagates through the lens system to the sensor plane. From the center to the periphery, the chief ray angle (CRA), denoted as $\theta$, relative to the optic axis,increases. Both the solid angle of the lens system entrance pupil relative to the emitting point and the projected area of the aperture decrease as $\theta$ increases, a phenomenon fundamentally governed by the cosine-fourth law ($\cos^4\theta$ law). Consequently, the luminous flux at the center exceeds that at the edges, causing the sensor's central illuminance to be greater than its peripheral illuminance.

（2）Color Shading
Chief Ray Angle (CRA) Mismatch: When the lens CRA exceeds the acceptance CRA of the image sensor, the incident light misaligns with the sensor's on-chip microlenses and color filter arrays (CFA). This causes light to leak or refract into adjacent pixels, resulting in optical cross-talk and severe spatial crosstalk.

Figure 4. Schematic diagram of optical crosstalk causing color shading

Thin-Film Interference in IR Cut-off Filters: Thin-film interference-based infrared (IR) cut-off filters exhibit a spectral transmittance curve shift toward shorter wavelengths (blue-shift) due to variations in the chief ray angle, resulting in color shading.

Figure 5. Spectral blue-shift of an IR cut-off filter at an increased incident angle