In object space, we think of the real-world lens as a thin lens located at the entrance pupil. The entrance pupil is generally located within the physical lens, but not always. Wherever it is located, light rays in object space proceed in straight lines until they reach the entrance pupil. The effects of any elements in front of this position are taken into account when the entrance pupil position is calculated. In the same way, we think of the real-world lens as a thin lens located at the exit pupil in image space.
For many lenses, the entrance and exit pupils are located near each other and within the physical lens. The exit pupil may be in front of or behind the entrance pupil. For certain special lens types, the pupils are deliberately placed far from their “natural” positions. For example, a telephoto lens has its exit pupil far in front of its entrance pupil (figure 5). In this way, a long-focal-length lens fits into a short package. A telecentric lens has its entrance pupil at infinity, well behind its exit pupil (figure 6).
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Figure 4. Thick-lens model
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Figure 5. Telephoto lens
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Figure 6. Telecentric lens
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Aberrations
If real lenses followed first order theory, lens design would be easy. Unfortunately, it is difficult to make a real lens approximate this behavior. Diffraction sets a lower limit on image spot size. The differences between ideal “diffraction limited” behavior and real-lens behavior are called aberrations.
The job of the lens designer is to choose glasses, curvatures, and thicknesses for the lens’ elements that keep its overall aberrations within acceptable limits. Such a lens is said to be well corrected. It is impossible to design a lens that is well corrected for all conjugates, FOVs, and wavelengths. The lens designer works to correct the lens over the small range of operating conditions at which the lens must function. The smaller the range, the simpler the design can be.
A lens that is corrected for one set of conditions may show significant aberrations when used under a different set of conditions. For example, a surveillance lens with a magnification of 1/10 is corrected for distant objects. By using extension tubes, the image conjugate of the lens can be extended so that the lens forms an image at a magnification of 1. But this image may show significant aberrations, because the lens was not corrected to work at these conjugates.
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Standard Lenses
Commercial lenses, produced in high volume, are by far the best value in terms of performance for the price. Finding a suitable stock lens is the most cost-effective solution to a machine vision problem. Table 1 lists various lens types and their range of operating conditions. Commercial lenses incorporate design and manufacturing techniques that are not available in custom designs. For example, a lens for a 35-mm, single-lens reflex (SLR) camera that costs one hundred dollars at the local camera store would cost ten thousand dollars to design and many thousands of dollars to manufacture in small quantities. It is always best to consider commercial lens options before starting a custom lens design.
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| Lens type |
Magnification |
Image format |
Object FOV |
Focal length |
Working f-number
(object side) |
| Surveillance |
<0.1 |
1¼" CCD format |
large |
2–50 mm |
>20 (adjustable) |
Standard
Machine Vision |
.05–5 |
2/3" CCD |
2–200 mm |
25–75 mm |
>4 (adjustable) |
Telecentric
Machine Vision |
.07–5 |
2/3" CCD |
2–170 mm |
N/A |
>6 (adjustable) |
F-mount
Lenses |
<1 |
45 mm |
large |
35–100 mm |
>4 (adjustable) |
Large/Medium
Format
Photographic |
<1 |
80 mm |
large |
50–250 mm |
>4 (adjustable) |
Photographic
Enlarger |
2–20 |
500 mm |
50 mm |
40–150 mm |
>4 (adjustable) |
| Microscope |
5–100 |
requires additional lens |
<2 mm |
5–40 mm |
0.1–0.95 NA (fixed) |
