==== Shading ====
**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).

|  {{ yanding:shading-luma.png?380 |}}  |  {{ yanding:shading-color.png?380 |}}  |
|  **Figure 1.** Schematic diagram of luminance shading  |  **Figure 2.** Schematic diagram of color shading  |
   
**II. Causes**\\
**（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.
|  {{ :en:yanding:image_quality_evaluation:image_quality_factors:shading1.png?700 |}}  |
|  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.\\
|  {{ :en:yanding:image_quality_evaluation:image_quality_factors:shading2.png?600 |}}  |
|  **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.\\

|  {{ :en:yanding:image_quality_evaluation:image_quality_factors:shading3.png?400 |}}  |
|  **Figure 5.** Spectral blue-shift of an IR cut-off filter at an increased incident angle  |