Lens Chief Ray Angle (CRA) and CRA Mismatch

Introduction

In digital camera design – especially for robotics and computer vision – one often overlooked parameter is the Chief Ray Angle (CRA). Simply put, CRA describes the angle at which light from a lens hits the image sensor. For optimal performance, a lens's CRA should closely match what the sensor is designed for. When they don't align (a situation called CRA mismatch), the result can be distorted colors, darkened image corners, and other image quality problems.

This article explains what the chief ray is, why CRA mismatch occurs, how it affects your images, and how to avoid these issues by choosing the right lens – such as the many M12 lenses available – for your camera.

What is the Chief Ray and Chief Ray Angle (CRA)?

The Chief Ray of a Lens

The chief ray of a lens is the ray of light from an off-axis point in the scene that passes through the center of the lens's aperture stop. In other words, if you look at a lens, the chief ray is the principal light ray from a given object point that goes through the middle of the lens (the center of the entrance pupil) and heads toward the image plane. Every point in the object has its own chief ray through the optical system, and these chief rays define how light from different angles travels through the lens.

Chief Ray Angle in Lenses and Sensors

Chief Ray Angle (CRA) is the angle between the chief ray and the optical axis of the lens. For a given lens-sensor setup, we often refer to the maximum chief ray angle at the image sensor (usually occurring at the sensor's corners) as "the CRA" of that system. For example, a lens might be said to have a CRA of 20°, meaning at the edge of the image, the chief ray strikes the sensor at a 20° angle relative to the perpendicular (optical axis).

Image sensors themselves are built to work with a certain CRA range. Modern CMOS image sensors have tiny microlenses over each pixel that help direct incoming light into the photodiode. The sensor's specified CRA (sometimes called pixel chief ray angle) usually refers to the maximum angle those microlenses can effectively gather light.

What is CRA Mismatch (and Why Does It Matter)?

CRA mismatch refers to the situation where the chief ray angle of the lens does not align with the chief ray angle that the sensor is designed to accept. In practice, this means the light from the lens is hitting the sensor's pixels at too steep or too shallow an angle compared to what the sensor's microlenses are optimized for.

Effects of CRA Mismatch

• Reduced light capture: If light arrives at too steep an angle, it might not pass through the pixel's microlens correctly or might hit the metal layers of the sensor, causing a loss of signal. In extreme cases, pixels near the edge of the sensor might receive significantly less light, contributing to vignetting.
• Optical crosstalk: Light hitting at the wrong angle can end up in a neighboring pixel's photodiode. In a color sensor (with a Bayer color filter array), this means light of one color can leak into a pixel meant for another color, causing color information mix-up.
• Color shading: The optical crosstalk and differing light falloff across the image can produce a radial color tint or shading – often red-green tinted – from the center of the image to the corners. Portions of the image might appear to have the wrong color or a gradient of color across them.
• Loss of image quality: Overall, a mismatched CRA can degrade contrast and require higher gains in the camera's image signal processor (to boost dark areas), which in turn introduces noise. The image may look hazy, low in contrast, or have color and brightness inconsistencies.

RGB vs Monochrome: Critical Differences

CRA mismatch primarily affects RGB (color) sensors due to the wavelength-dependent nature of the optical crosstalk. When light hits at the wrong angle in a color sensor with a Bayer filter, it can leak from one color channel to another, creating the characteristic color shading.

Monochrome sensors exhibit significantly reduced sensitivity to CRA mismatch because:

• No color filter array means no color channel crosstalk
• Uniform spectral response reduces differential effects
• Simpler pixel structure with less complex light paths

Multiple CRA Variants: A Critical Selection Factor

Many modern sensors are available in multiple CRA variants. For example, a popular Sony IMX sensor might be offered in:

• 0° CRA variant: For telecentric or specialized optical systems
• 12° CRA variant: For standard industrial lenses
• 28° CRA variant: For mobile or compact camera modules

These variants share the same pixel architecture and electronic specifications but differ in microlens positioning. Selecting the appropriate variant is crucial for system performance and cannot be changed after procurement.

Why Is CRA Mismatch Hard to Fix in Post-Processing?

If you find yourself with a lens-sensor combination that has a CRA mismatch, you might wonder: can't we just correct the color and brightness in software after capturing the image? The answer is that you can attempt to, but it's extremely difficult to get right except in very controlled conditions.

Large sensor companies actually design different versions of sensors with different CRA optimizations. High-volume phone manufacturers work closely with sensor suppliers to fine-tune pixel microlenses for their specific lens designs. They can do this because they know the exact lens that will be used and produce millions of units. For most of us, we have to pick a sensor that's already on the market and then choose a lens to match.

The challenge is that color shading corrections are specific to the lighting and scene. Change the illumination (different spectrum or angle of lighting) and the color shading pattern might change, due to interactions between light color and the microlens/pixel response (a phenomenon related to metamerism).

How to Ensure Your Lens and Sensor CRA are Properly Matched

Best Practices for CRA Matching

• Choose compatible components from the start: Research the sensor's CRA specification and look for lenses advertised with a similar CRA. Many sensor datasheets list a "chief ray angle" or provide a CRA vs. field angle graph.
• Stay within tolerance: As a rule of thumb, try to keep the difference between the lens CRA and sensor CRA within the tolerances shown above. Some experts suggest keeping it within ±3° for best results, especially for sensors with very small pixels.
• Use "low CRA" sensors when available: If your application isn't constrained by a super-small lens, consider using image sensors that have a relatively low CRA requirement (say 0–15°). They pair well with many off-the-shelf machine vision lenses.
• Avoid the mobile-industrial trap: Never pair a high-CRA mobile sensor (20-35°) with an industrial M12 lens not designed for that CRA. This is asking for trouble and is one of the most common mistakes in camera design.
• Consider the entire field of view: Ensure the lens's chief ray angle at the very corner of the image still falls within the sensor's acceptable range. Non-linear CRA profiles require careful analysis across the entire field.
• Don't over-index during qualification: The magnitude of shading is somewhat subjective and application-dependent. Experimental testing with your actual use case is more valuable than theoretical analysis. Build prototypes and test under representative conditions.

Conclusion: Proper CRA Matching for Better Vision

Understanding Chief Ray Angle and its impact on image sensors is crucial for anyone working on camera hardware in robotics or computer vision. It's an aspect of optics that bridges the lens and sensor domains. A well-matched lens and sensor duo will produce cleaner, more accurate images, while a mismatched pair might leave you scratching your head over weird color shifts and dark corners.

The takeaway is clear: pay attention to CRA early, choose the right components, and you won't have to chase fixes later. Remember that RGB sensors are much more sensitive to CRA mismatch than monochrome, and that the subjective nature of shading means experimental validation trumps theoretical analysis.

At Commonlands, we emphasize CRA matching in all our lens recommendations. Our M12 lens collection is curated for embedded vision applications, and we provide detailed specs (focal length, F-number, CRA, etc.) to help you make an informed choice. By selecting a lens with the proper chief ray angle for your sensor, you'll achieve better image quality with less effort spent on calibration.