Lens design requires correcting aberrations that may otherwise reduce resolution. A lens designer must also consider the angle a cone of rays makes with the object and/or image. A common way to approximate this angle is the Chief Ray Angle (CRA). The chief ray is the axis of the cone. In optical design, light cones are not necessarily symmetric, but they are close enough to make this definition a reasonable approximation.
We’ll go into more detail below, but a special case is when the CRA is normally incident on every pixel of the image sensor; a lens that creates this condition is called “telecentric”. Telecentricity is desirable for many applications; it results in less variation in magnification with focus and more uniform illumination across the image sensor. For inspection applications, lenses are often designed to be telecentric in the vicinity of the object being measured (object space). This makes it possible to accurately measure dimensions on the object even though they are slightly out of focus. For the remainder of this page, the chief concern will be the CRA in the vicinity of the image (image space).
The chief ray in an optical system is defined as a ray that can be traced from any off-axis point on the object, through the center of the aperture stop, and to a point on the image, as seen in Figure 1 below. It is normally at the center of the cone of rays that illuminate a pixel. This figure shows three cones of rays (red, green and blue) with the chief ray and the upper and lower rays that form the boundary of the cone. For the cone that illuminates the central pixel, the boundary rays are called “marginal rays”. The CRA can be defined at any surface in the lens but usually refers to the angle from the surface normal at which the chief ray intersects the image plane. The CRA is typically different for each pixel of the image sensor.
Figure 1: Chief Ray and Chief Ray Angle
There are an infinite number of chief rays that can be traced through a lens. This is because for every point on the object there is a ray that meets the above definition of a chief ray. Figure 2 below shows the same lens, but with only three chief rays drawn. As can be seen, for this lens the CRA is different for each chief ray.
Figure 2: Chief Rays in a standard Double Gauss Lens
Lenses can be designed to control the CRA so that the chief rays become parallel to the optical axis after refraction from the last lens surface. The lens in Figure 3 has been redesigned so that the CRA for all chief rays are very nearly 0°. When this is the case, the lens is called telecentric in image space. Next, we’ll discuss why image space telecentricity is important.
Figure 3: Chief Rays in a Telecentric Lens
Image sensors can be categorized into “Front-Side Illuminated (FSI)” and “Back-Side Illuminated (BSI)”. In FSI image sensors, the photodiode is deeper into the sensor structure, which results in a narrow acceptance angle (see Figure 4). For the newer BSI image sensors, the photodiode is closer to the front of the image sensor allowing rays at a wider angle of incidence to reach the photodiode. Figure 4 shows the vast improvement in acceptance angle from Sony’s older Pregius FSI sensors to the newer Pregius S BSI sensors.
Figure 4: Angular Acceptance of Front-Side Illuminated vs. Back-Side Illuminated Sensors
Even though newer BSI sensors have larger acceptance angles, telecentricity can still be a very important property. This is especially true when lenses are designed for high-resolution and therefore low F/# (fast lenses). Fast lenses have large marginal ray angles, so these lenses are often made telecentric to avoid losing light in the corners of the image. For example, if we have an F/1.4 lens the marginal ray angle will be about 21° from the chief ray, so the angle of incidence will be the CRA +21°. To minimize light loss in the corners of the image, the chief rays will have to be nearly telecentric.
*Figure 4 pixel structure from: https://scientificimaging.com/knowledge-base/front-side-illuminated-and-back-side-illuminated-imagers/
*Figure 4 plot from: Sony Pregius® S Global Shutter CMOS | Teledyne Vision Solutions
It is very important to control telecentricity when using an FSI sensor or when a BSI sensor will be used with a fast lens. Other applications for lenses telecentric in image space are when there is a filter between the lens and the image sensor (to provide uniform filtering) and when the lens is used in a projector.
At Eckhardt Optics, we routinely design telecentric lenses as well as lenses that match the ideal CRA of different image sensors. Feel free to contact us if you have any additional questions on this topic.