1. Definition
The Chief Ray Angle (CRA) refers to the angle between the chief ray and the normal to the image plane.

• Chief Ray: The ray originating from an object point and directed towards the center of the aperture stop is called the chief ray.
• Marginal Ray: The ray originating from an on-axis object point and passing through the edge of the aperture stop is called the marginal ray.
• Optical Axis: The geometric axis of symmetry of the optical system. For on-axis field points, the chief ray usually coincides with the optical axis; for off-axis field points, the chief ray deviates from the optical axis.
  
• Key distinction: The incident angle is used to describe the angle between any arbitrary ray and the normal to the corresponding surface; whereas the Chief Ray Angle (CRA) specifically refers to the incident angle of the chief ray at the image plane interface.

2. CRA Matching
Lens CRA:
The chief ray exit angle determined by the lens structure, which increases continuously with image height; the single value specified in the datasheet generally refers to the chief ray angle at the sensor's maximum image height.

Sensor CRA:
The designed angular characteristic for matching the lens chief-ray angle (datasheets typically specify the value at the maximum image height as a selection limit), realized by microlens shift and pixel structure, so that the incident beam is refracted onto the target pixel's photodiode active area.

Matching Relationship and Imaging Impact
(1) Ideal Matching (Lens CRA ≈ Sensor CRA)
The tilt angle of the light projected by the lens onto the sensor surface perfectly matches the preset deflection angle of the microlenses. After refraction, the light is converged onto the center of the photodiode’s active area, optimizing the quantum efficiency (QE) of each pixel. The image brightness and color remain uniform across the entire field of view,delivering the best signal-to-noise ratio (SNR).

(2) Lens CRA < Sensor CRA (Lens exit light tilt angle is too small)
Because the preset shift of the microlenses fails to match the actual light rays, some incident rays fall outside the active area of the photodiode after refraction. This leads to insufficient light reception at the edges, causing vignetting, where the four corners of the image appear dark (as shown in the figure below).

(3) Lens CRA > Sensor CRA (Lens exit light tilt angle is too large)
The degree of light tilt exceeds the compensation capability of the microlenses. The light beam is blocked by the pixel metal wiring or undergoes optical crosstalk. This not only reduces light collection efficiency but also causes color crosstalk (as shown in the figure below) and color shading. This defect is difficult to fully correct through backend ISP algorithms.

3. CRA and Microlens Shift
This section focuses on front-side illuminated (FSI) CMOS sensors.

Modern CMOS image sensors integrate a microlens array above the pixel array. The microlenses focus and direct incoming light toward the photodiodes (PDs), thereby improving the light-collection efficiency of the pixels.

The chief ray angle (CRA), measured relative to the optical axis, generally increases toward the edge of the image field. If the microlens of every pixel were centered over its photodiode, highly oblique rays near the edge of the sensor could be blocked by the pixel’s metal interconnect layers, preventing them from reaching the active area of the photodiode. This can cause severe edge shading and brightness nonuniformity.

To address this issue, the microlenses of pixels near the edge can be physically offset relative to the photodiodes, with the offset oriented to match the local chief ray angle. The offset generally increases toward the edge of the image field as the CRA increases. This helps direct oblique light toward the active area of the photodiode, improving pixel-level light-collection efficiency and reducing edge shading.

See Also
Entrance Pupil、Shading