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.

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.

Chief Ray Angle Mismatch

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 

Optical Chief Ray and Marginal Ray

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.

What does CRA mismatch look like Physically and why CRA Mismatch more important at high CRA Angles?


 Low profile lenses (short TTL) typically have very high CRA, as optical design performance does not converge (is not good) if a low CRA requirement is forced on the design.

To aide cell phone manufacturers with system-level image quality, sensor manufacturers adjust the spatial design of microlenses on the sensor to compensate for lens CRA. This microlens adjustment is generally only available to high volume (>10Mpcs/yr) companies, so the rest of us must just do our best to select the right sensor variant and matching lens.
 

Oblique Dependence of Microlenses at 25° CRA (CIL023 2.2mm F/2.2)

Oblique Dependence of Microlenses at 15° CRA (CIL039 3.9mm F/2.8)

Correcting for color shading due to CRA mismatch

CRA mismatch CAN be corrected for in post process, but ONLY in applications with well controlled static illumination such as industrial machine vision for inspection.

When the light sources change, it becomes challenging to compensate. This is due the friendly topic of metamerism. We've seen a major CRA mismatch (20° non-linear mismatch) overcome before in a regular indoor environment, so it is doable to a "good enough" extent. This requires advanced ISP tuning with a calculated pixel-level spectral energy distribution 3DMLUT approach. This in turn will slow down other performance metrics in your camera and/or require more compute, so generally not the best practice to get into this sitatuon.  

Additionally, there are only a handful of leading image quality experts with the requisite knowhow and experience to get to a "good enough" quality with a >15° nonlinear mismatch with a sensor at 33°.  I estimate <50 people in the world and it is near impossible to hire them as they are in high demand at big tech companies. So unless you are fortunate enough to be on a team with one of these experts, we highly advise against venturing down the rabbit hole of thinking you can solve >15° nonlinear CRA mismatch in software: your project will likely have a 6-12 month delay and budget overrun.

Regardless of the approach and expertise there will be more color tuning corner cases that occur with huge CRA mismatch, than when you have a well-matched lens to sensor CRA.

The Take-Away: We suggest Low Linear CRA (~<20°) Lenses/Sensors when Possible.

Otherwise Match 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.

What's Your Application? Our Board Lenses Cover the Spectrum.

Wide-Angle 3.6mm Lens

CIL336-F1.9-M12A650

Wide-Angle 3.6mm Lens

188°@6.6mm IP67 M12 Fisheye

CIL222-F2.0-M12A650

188°@6.6mm IP67 M12 Fisheye

Objectif M12 Fisheye 185°@7.8mm

CIL227-F2.5-M12ANIR

Objectif M12 Fisheye 185°@7.8mm

Faut-il un objectif IP65+ ?

Nous proposons des variantes IP65+ de nombreux objectifs. Celles-ci conviennent aux applications exposées à l'environnement, sans fenêtre.

La robotique mobile ?

Trouvez une lentille à faible F# ou à faible distorsion pour optimiser votre cadence de vision par ordinateur.

Objectif M12 à faible distorsion de 2,2 mm

CIL023-F2.2-M12A650

Objectif M12 à faible distorsion de 2,2 mm

Objectif grand angle 3,5 mm M12

CIL335-F1.8-M12A660

Objectif grand angle 3,5 mm M12

Objectif M12 de moyenne portée 7,6 mm

CIL080-F1.8-M12IR

Objectif M12 de moyenne portée 7,6 mm

Objectif M12 Fisheye 200°@5,7mm IP67

CIL217-F2.7-M12ANIR

Objectif M12 Fisheye 200°@5,7mm IP67

Objectif téléobjectif 35 mm M12

CIL350-F2.4-M12A650

Objectif téléobjectif 35 mm M12

Objectif téléobjectif 26 mm M12

CIL260-F2.0-M12IR

Objectif téléobjectif 26 mm M12

La surveillance ?

Nos objectifs à faible F# et à haute résolution conviennent aux caméras dômes à 180°, aux scènes à faible luminosité et aux scènes à éclairage IR actif.

Consommateur / AR+VR ?

Nos objectifs fisheye haute résolution vous permettront de concevoir des caméras 360° et les objectifs stéréographiques sont équivalents aux objectifs "GoPro".

Objectif M12 Fisheye 226°@3.9mm

CIL212-F2.2-M12A660

Objectif M12 Fisheye 226°@3.9mm

Objectif M12 de 2,6 mm à faible distorsion

CIL028-F2.3-M12A650

Objectif M12 de 2,6 mm à faible distorsion

Objectif GoPro 3.0mm M12

CIL331-F2.5-M12A660

Objectif GoPro 3.0mm M12

Objectif M12 de 1,8 mm à faible distorsion

CIL018-F2.8-M12A650

Objectif M12 de 1,8 mm à faible distorsion

Objectif M12 de 2,6 mm à faible distorsion

CIL028-F2.3-M12A650

Objectif M12 de 2,6 mm à faible distorsion

Objectif M12 3,9 mm sans distorsion

CIL039-F2.8-M12IR

Objectif M12 3,9 mm sans distorsion

Vidéo-conférence ?

Nos objectifs M12 grand angle, à faible distorsion et haute résolution permettent une déformation optimale des objets sans post-traitement.

La robotique aérienne ?

Nos lentilles légères et miniatures sont idéales pour la prévention des collisions, la visualisation à longue distance et la visualisation par le client final.

Petit objectif M12 de 2,1 mm

CIL821-F2.4-M12ANIR

Petit objectif M12 de 2,1 mm

Objectif M12 grand format 3,5 mm

CIL334-F2.2-M12ANIR

Objectif M12 grand format 3,5 mm

Objectif grand angle 3,5 mm M12

CIL335-F1.8-M12A660

Objectif grand angle 3,5 mm M12

La surveillance ?

Nos objectifs à faible F# et à haute résolution conviennent aux caméras dômes à 180°, aux scènes à faible luminosité et aux scènes à éclairage IR actif.

Vidéo-conférence ?

Nos objectifs M12 grand angle, à faible distorsion et haute résolution permettent une déformation optimale des objets sans post-traitement.