La définition de l'angle de rayonnement du chef-lieu de l'objectif et la redoutable inadéquation de l'ARC

Inadéquation de l'angle de rayonnement de la lentille et impact sur la qualité de l'image 

Jan 20, 2023
by Max Henkart
Updated Oct 18, 2024

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.

Below is an example of problematic CRA mismatch compared to proper mismatch with our CIL340 M12 Lens.

Mauvaise rencontre entre le chef Ray et l'angle de vue

What is the Chief Ray Angle of an Image Sensor?

Let's first start with the architecture of a modern Complementary-Metal-Oxide-Semiconductor (CMOS) pixel. Here is a simplified pixel architecture from Sony's website that I've marked up.

In this simplified marketing drawing, you can see the different components of a pixel.

An introductory textbook for diodes that we went through back in the day at UofR is Sze and Lee "Semiconductor Devices, 3rd ed."

CMOS image Sensor CRA Starvis2.webp__PID:6c23d145-7026-4128-82dd-1b8dfe06770c

Qu'est-ce que l'angle de rayonnement principal d'une lentille ?

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 first-order optics diagram and description on page 185 for a general three element optical imaging system: 

Rayon principal optique et rayon marginal

Chief rays exist for every illuminated point in object space.  Let's see how this looks for a "Real World" lens.

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.

A quoi ressemble physiquement le décalage de l'ARC et pourquoi le décalage de l'ARC est-il plus important à des angles d'ARC élevés ?


Les objectifs à profil bas (TTL court) ont généralement un CRA très élevé, car la performance de la conception optique ne converge pas (n'est pas bonne) si une exigence de CRA faible est imposée à la conception.

Pour aider les fabricants de téléphones cellulaires à obtenir une qualité d'image au niveau du système, les fabricants de capteurs ajustent la conception spatiale des microlentilles sur le capteur afin de compenser le CRA de l'objectif. Cet ajustement des microlentilles n'est généralement disponible que pour les entreprises à fort volume (>10Mpcs/an), de sorte que le reste d'entre nous doit simplement faire de son mieux pour sélectionner la bonne variante de capteur et la lentille correspondante.
 

Dépendance oblique des microlentilles à 25° CRA(CIL023 2,2mm F/2,2)

Dépendance oblique des microlentilles à 15° CRA(CIL039 3,9mm F/2,8)

Correction de l'ombrage des couleurs dû à la non-concordance de l'ARC

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 

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°.

However, it really depends on the pixel architecture and your application.

Jon Stern from GoPro's optics team provided his opinion publicly during a talk at the Embedded Vision Summit in 2020: View Slide 22 Here.

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.

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.

Quelle est votre application ? Nos lentilles couvrent tout le spectre.

Objectif fisheye M12 215°@6,8mm

CIL220-F2.3-M12B650

Objectif fisheye M12 215°@6,8mm

Objectif M12 de 2,2 mm à faible distorsion

CIL023-F2.2-M12A650

Objectif M12 de 2,2 mm à faible distorsion

La robotique mobile ?

Trouvez une lentille à faible F# ou à faible distorsion pour optimiser votre vision sur ordinateur.

Vision industrielle ?

Nos objectifs compacts et économiques à monture C sont conçus pour les capteurs à obturateur global de format allant jusqu'à 1,1" ~ 1,2".

Objectif Fisheye 180°@14,2mm à monture C

CIL505-F2.2-CMANIR

Objectif Fisheye 180°@14,2mm à monture C

Objectif 8 mm à monture C 1,1" 12MP

CIL508-F2.4-CMANIR

Objectif 8 mm à monture C 1,1" 12MP

Objectif 3,2 mm sans distorsion

CIL034-F2.3-M12A660

Objectif 3,2 mm sans distorsion

Objectif M12 de 2,7 mm à faible distorsion

CIL027-F2.8-M12A650

Objectif M12 de 2,7 mm à faible distorsion

Intelligent Everywhere ?

Nos objectifs à faible distorsion avec plusieurs F# peuvent être utilisés pour optimiser la profondeur de champ.

La surveillance ?

Nos objectifs fisheye et à correction IR conviennent aux caméras de sonnette et aux scènes éclairées par des infrarouges actifs.

190°@5,7mm Objectif Fisheye M12

CIL290-F2.2-M12A660

190°@5,7mm Objectif Fisheye M12

IR Corrected 4.4mm M12 Lens CIL046

CIL046-F2.0-M12A650

IR Corrected 4.4mm M12 Lens CIL046

200°@4.5mm Objectif MiniFisheye M12

CIL914-F2.4-M12B650

200°@4.5mm Objectif MiniFisheye M12

Objectif Fisheye 195°@5,2mm

CIL818-F2.0-M12A660

Objectif Fisheye 195°@5,2mm

Faut-il se salir ?

Nos lentilles IP67 et IP69K conviennent aux applications exposées à l'environnement.

La robotique aérienne ?

Nos minuscules lentilles sont idéales pour éviter les collisions et reconnaître les objets.

Objectif Fisheye 195°@5,2mm

CIL818-F2.0-M12A660

Objectif Fisheye 195°@5,2mm

Petit objectif M12 de 2,1 mm

CIL821-F2.4-M12ANIR

Petit objectif M12 de 2,1 mm