Chief ray angle (CRA) explained

Chief ray angle, or CRA, appears on almost every lens and sensor datasheet, yet it is one of the least understood numbers in camera design. A lens and sensor can each be excellent and still produce dark, tinted, soft corners together, simply because their CRAs do not match. This article explains what CRA is, why sensors care about it, and what a mismatch does to the image.

What the chief ray is

Every point in the scene sends a cone of light through the lens. The chief ray is the one ray of that cone that passes through the center of the aperture stop. It marks the center of the light cone, so it tells you the direction from which light arrives at each point on the sensor.

The chief ray angle is the angle between that ray and the optical axis where it reaches the image plane. At the image center the chief ray runs along the axis, so the CRA is 0°. Toward the edge of the image the chief ray tilts more and more, and the CRA grows. A lens therefore does not have one CRA but a CRA curve: CRA versus image height, usually quoted at full image height (the corner) as a single maximum value.

Why compact lenses have large CRA

To a first approximation, CRA ≈ atan(image height / exit-pupil distance), where the exit-pupil distance is measured from the exit pupil to the sensor. Phone lenses must be extremely short, so their exit pupil sits only a few millimeters from the sensor. On a sensor with a 3.2 mm half-diagonal (about 1/2.8″), an exit pupil 5 mm away gives a corner CRA of about 33°; at 20 mm it is about 9°, and at 100 mm under 2°.

That is why phone camera lenses often reach 25–35° at the corner, while larger M12 and C-mount lenses for security and machine vision are often 15° or less. An image-side telecentric lens puts its exit pupil at infinity, so the CRA is close to 0° across the whole image.

Why the sensor cares: microlenses

A pixel is not a flat surface. Light passes through a microlens, a color filter and several microns of dielectric and wiring before it reaches the light-sensitive photodiode. The microlens focuses light into the photodiode, but only if the light arrives from the direction it was designed for.

To handle light arriving at an angle near the image edge, sensor designers shift each microlens (and usually its color filter) slightly toward the image center, by an amount that grows with distance from the center. The sensor datasheet states the CRA this shift was designed for, often as a single value at full image height, sometimes as a full curve. Back-side illuminated (BSI) sensors have a shorter stack than older front-side illuminated (FSI) ones and tolerate angle better, but the microlens shift still has to fit the lens.

What a CRA mismatch does to the image

When the lens CRA differs from the angle the sensor's microlenses expect, the error is zero at the image center and grows toward the edges. That produces four effects, all strongest in the corners:

• Luminance shading. Less light reaches the photodiodes, so the corners darken beyond the lens's own relative illumination. This happens whether the lens CRA is larger or smaller than the sensor's design value.
• Color shading. Light that misses a photodiode under a red filter can land in a neighbor under a green filter, and each color channel loses a different amount of signal. A uniformly lit gray card turns slightly tinted toward the edges, often reddish, magenta or greenish, and the tint can differ between left and right or top and bottom.
• Crosstalk and lower sharpness. Signal leaking into neighboring pixels blurs fine detail and desaturates color in the corners, and can create small differences between the two green channels of a Bayer pattern that show up as fine maze-like artifacts after demosaicing.
• Calibration that never quite fits. Lens shading correction in the image processor can brighten corners and remove most of the tint, but the gain also amplifies corner noise, the tint changes with the color temperature of the light, and crosstalk blur cannot be undone.

Matching lens and sensor

Compare the two CRA curves over the full image height, not just the maximum values. A common rule of thumb is to keep the difference within about 2–3° everywhere on the sensor; some sensors tolerate more, and the sensor maker's application notes are the final word.

Mismatch in the other direction matters too. A near-telecentric machine-vision lens with almost 0° CRA, placed on a phone sensor whose microlenses are shifted for 30°, sends light straight down through microlenses that expect it from an angle. The corners still darken and tint, just the other way around. Sensors meant for telecentric optics are often specified with 0° CRA, meaning no microlens shift.

How to check a pairing

1. Get both curves. The lens datasheet usually lists CRA against image height or field; the sensor datasheet gives its design CRA, sometimes as a curve.
2. Put them on the same axis. Convert both to image height in millimeters. The sensor's full height is half its active diagonal, which you can calculate from resolution and pixel pitch.
3. Compare across the field, not just at the corner. Many lens CRA curves are nonlinear and peak before the corner, while microlens shifts are often linear.
4. Test with a flat field. Image a uniformly lit diffuser or integrating sphere and compare corner-to-center ratios for each color channel, under at least two light sources.

Key points

• CRA is the angle of the chief ray, the ray through the center of the aperture stop, where it reaches the sensor. It is 0° at the center and grows toward the edges.
• Short lenses have their exit pupil close to the sensor and therefore large CRA; telecentric lenses have nearly 0°.
• Sensors shift their microlenses for one design CRA. A lens with a different CRA, larger or smaller, causes dark corners, color tint, crosstalk and softer corners.
• Compare full CRA curves, keep the difference within a few degrees, and verify with a flat-field test.