The Definition of Lens Chief Ray Angle and the dreaded CRA mismatch
Lens Chief Ray Angle Mismatch and Impact on Image Quality
The chief ray angle (CRA) of a lens and the chief ray of a sensor affect image quality factors such as color shading and vignetting.
The magnitude of impact from CRA mismatch can be approximated using the Difference of Squares. This is dependent on the sensor's pixel architecture, but is a good first order rule of thumb.
Thus, we generally recommend matching CRA within +/-10° if the sensor's CRA is <10°, +/-7° if the sensor's CRA is >10° and <20°, and within +/-4° if the sensor's CRA is >20°. This mismatch tolerance must hold across the entire field of view, so make sure to compare a full plot if the sensor's specification sheet says "non-linear" on it.
Below is an example of problematic CRA mismatch compared to proper mismatch with our CIL340 M12 Lens.
What is the Chief Ray Angle of a Lens?
The chief ray of a lens is the ray that goes through the center of the aperture stop in an optical system.
If you look into a lens from object space, the chief ray is the ray that crosses the optical axis at the entrance pupil.
If you look from image space, this is the ray at the center of the exit pupil.
Hecht's "Optics" Fifth Edition has a great explanation and description on page 185 for a general three element optical imaging system : https://www.pearson.com/en-us/subject-catalog/p/optics/P200000006793/9780137526420
Chief rays exist for every illuminated point in object space. Let's see how this looks for a "Real World" lens; our CIL039.
When people discuss the Chief ray angle, they typically refer to the "Maximum CRA" which corresponds to the widest field of view of a lens combination.
To accurately compare the chief ray of a lens and the chief ray of a sensor, you must consider the CRA across the usable area of the image.
Why Does CRA Matching Matter?
Each pixel bayer filter has an acceptance angle before spectral crosstalk begins. This section is still under construction...
The Take-Away: We suggest always Matching the Lens Chief Ray Angle As Closely to the sensor as possible
Incorrect CRA matching can result in radial red to green color shading from the center of an image to the corner.
This shading is dependent upon illumination conditions, so it makes Image Quality Tuning extremely difficult.
This is a common issue when trying to build a camera using a "Mobile" Sensor with an "Industrial" Lens or vis-versa. We've seen multiple startup projects run into this issue, resulting in extensive cost (>$100k) and schedule (>1yr) overruns.
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Our wide-angle, low distortion, high resolution M12 lenses result in optimal object deformation without post-processing.