Telecentric lenses simplify non contact metrology

When you use a conventional lens to inspect 3-D parts, an inherent distortion of the image results. The change in magnification with distance in a conventional imaging system is so fundamental that people generally take it for granted. After all, our eyes are a typical conventional imaging system. We accept that an object placed farther away appears smaller than the same object close at hand. The image of the chessboard in Figure 1a illustrates this effect, called perspective. 

We know the squares in a chessboard all have the same size. Yet, in the image, the squares farther away appear smaller than those closer to the observer. This perspective gives the image the appearance of depth. But if you weren’t familiar with a chessboard, you wouldn’t be able to determine from the image whether the smaller squares are farther away or are, in fact, actually smaller. Likewise, conventional optical systems cannot accurately measure dimensions on 3-D objects.

The image in Figure 1b was taken using a telephoto lens—a lens with a long focal length— placed much further away from the chessboard. The longer distance minimizes, but doesn’t eliminate, the perspective differences between the front and rear squares on the board. The image in Figure 1b approaches a telecentric perspective, in which no difference would appear in the sizes of the front and the back squares in the image. A true telecentric lens produces images in which the foreground and background images have the same magnification. If they have the same physical dimensions, they will maintain those dimensions in the image. By eliminating the perspective distortion, telecentric lenses let inspect ion and machine vision systems make accurate metrology measurements. 

Yet, you cannot use these lenses in all applications. Lens manufacturers can make telecentric lenses that produce virtually distortion-free images only over a defined depth, called the telecentric depth. It would prove difficult, if not impossible, to design a lens with a telecentric depth that could cover the entire depth of a chessboard. Manufacturers can produce lenses with telecentric depths of up to 1 in. (2.54 cm). ( Telecentric lenses are available as stock items from various optical manufacturers.) If your vision system needs to measure a connector’s pin lengths, positions, and straightness, a telecentric lens may provide the necessary accuracy. 

^{Fig. 1 — a) The side view of a chessboard through a conventional wide-angle lens shows the effect of perspective.
b) The same chessboard viewed through a telephoto lens shows less of a perspective effect. Telecentric lenses produce similar results.} 

The side view of a lens in Figure 2 shows a simplified representation of a conventional machine-vision lens. 
All imaging lenses have an aperture stop, a physical device that limits the amount of light energy that can pass through the lens, or a group of lenses. In a conventional lens, the opening or closing of the aperture stop changes the overall brightness of the image across the entire image, without affecting the size of the image. In your eye, the iris forms the aperture stop. 

In addition, all lenses contain pupils. Specifically, every lens has both an entrance and exit pupil. The entrance pupil is the image of the aperture stop in object space, and the exit pupil is the image of the aperture stop in image space. That is, the entrance pupil is the image of the aperture-stop image as you would see it viewed from the object side of the lens. The exit pupil is the aperture-stop image as you would see it if viewed from the image side of the lens. 

A lens diagram such as the one shown in Figure 2 typically includes three rays drawn from any point on the object through the lens to the image. The chief, or principal, ray passes obliquely through the center of the aperture stop. The two remaining rays, called marginal or paraxial rays, are drawn to coincide or come close to the edges of the aperture. They represent the outside limits of the “bundle” of light rays that pass through an optical system of one or more lenses. 

The diagram in Figure 2 shows the paths of three light rays that start at a real object—in this case, the tip of an arrow. The three rays trace light paths through the lens to finally produce a corresponding point on the image. When all the rays that pass through a lens converge in a plane, they produce an image. 

In most conventional lenses the aperture stop is located within the lens assembly. The images of the aperture stop, that is, the entrance or exit pupils, are made up of converging light rays. In a telecentric lens, the aperture stop is located at the focal point of the lens. Due to this unique posit ion of the aperture stop, the light rays that form the images of the aperture stop travel parallel to the optical axis and are considered to be located at infinity. 

If you were to look through a telecentric lens from the object side, for example, you would see the entrance 
pupil of the lens. The same is true with a conventional lens. On first observation the pupils may look the same. For the telecentric lens. Your eye focuses at infinity, and the entrance pupil of the lens remains in focus with no further refocusing of your eye as you move the lens closer or farther. On the other hand, with a conventional lens, your eye would need to refocus on the image of the entrance pupil as you move the lens closer or farther away. The fact that the entrance or exit pupil is located at infinity means that the principal ray is parallel to the optical axis of the lens. This characteristic is what defines a telecentric lens. 
 

^{Fig. 2 — A conventional machine vision lens passes light through an aperture stop, through the glass lens itself, and projects an image onto a camera detector (not shown).} 

Three types of telecentric lenses are appropriate for metrology vision systems. In an object-sided telecentric lens (Figure 3), the lens and aperture are configured so the principal ray from the object to the lens runs parallel to the lens’ optical axis. A small change in the distance from the object to the object- sided telecentric lens does not change the magnification of the resulting image. But these small distance changes can occur only within a small region of distances—the telecentric depth. Only within this region does the resulting principal ray from the image run parallel to the optical axis. In a conventional lens, the principal ray is not parallel to the optical axis, so the lens will magnify points on an object based on their distances from the lens. 

The image from an image-sided telecentric lens (Figure 4) is insensitive to small changes in the posit ion of the image plane. In a camera, small differences in the distance between the lens and an image detector do not affect the size of the image. Thus, these small changes do not affect the accuracy of measurements made on the resulting images. A bilateral telecentric lens (Figure 5) combines the advantages of both object- and image-sided telecentric lenses into one form, thus providing the highest degree of measurement accuracy for objects with different heights. 

A bilateral telecentric lens accurately reproduces dimensional relationships within its telecentric depth, and it isn’t susceptible to small differences in the distance between the lens and the camera’s sensor. In general, these lenses provide a means of accurately imaging 3-D objects when critical measurements are necessary.

^{Fig. 4 — An image-sided telecentric lens maintains the dimensional information in an image within the telecentric depth. Thus, slight changes in an image sensor’s position do not affect dimensional accuracy.}

^{Fig. 5 — A bilateral telecentric lens includes elements of object-sided and image-sided telecentric lenses.}

^{Fig. 3 — In an object-sided telecentric lens, the principle ray remains parallel to the optical axis for objects within the telecentric depth.} 

Compare performance parameters

Unfortunately, optical manufacturers do not use a common set of parameters to specify their lenses. Definitions of key terms will help you understand the basic nomenclature and performance criteria you’ll encounter when you select a telecentric lens. The eight most important specifications are described below, and Table 1 lists some typical values for a telecentric lens that will ensure accurate dimensional image quality. 

• Magnificat ion is the ratio of the size of the image to the size of the object. A magnification specification of 1:2 means the lens reduces the object by a factor of 2 when 
• it projects the image onto a camera’s sensor. 
• Numerical aperture specifies the size of the “bundle” of light rays that passes through the lens. The larger the numerical aperture, the more light reaches the image sensor. 
• Image size or sensor format specifies the maximum image size a lens can form. 
• Object size or field of view gives the maximum size object that the lens can image. Due to the way a telecentric lens works, the field of view cannot exceed the diameter of the lens’ front surface. So, in general, telecentric lenses cannot view objects more than an inch or two across. 
• Working distance specifies the distance from the object to the front of the lens housing. A telecentric lens operates properly at only one working distance. 
• Telecentric depth or telecentric range is the total distance above and below an object that remains in focus and at constant magnification. You can place objects you wish to measure anywhere within the telecentric range. But whatever you want to measure must exist entirely within this range. 

Do not confuse telecentric depth with the depth of field specified for a conventional lens; they’re independent lens characteristics. For a conventional lens, depth of field defines the range of distances in which you can locate an object and still have the lens produce a focused image.

• Telecentricity describes the angular deviation of the principal ray from a ray parallel to the optical axis. A lower angular value means a lens will reproduce an image more accurately. 
• Distortion is an absolute deviation, in micrometers (μm), from a theoretical perfect point. It is a function of image height. A smaller value means a more accurate measurement. 

Telecentric lenses do have some limitations. They produce a fairly small image, which generally means you must use them with small CCD arrays such as those used in 2/3-in. C-mount cameras. And a telecentric lens can only view objects within a field equivalent to the front diameter of the lens assembly. Of course, your inspection system can move objects into the field of view as needed. 

Although telecentric lenses won’t fit every machine-vision need, they have important roles to play when you need accurate measurements that do not all take place in the same plane.