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7. Special Lenses
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7.1 Telecentric or "Measurement" Lens
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What does "telecentric" mean?   --   This word indicates that a bundle of rays has its center (crossing point) at infinite distance.
In other words, the rays are parallel. Like often in optics, we can never really reach this ideal. So, "telecentric" most often means that the divergence (or convergence) angle of a bundle is very narrow and we would like it to be zero.

How can a lens become "telecentric"?   --   Very simple indeed, no: in theory.
Place a point source in the focal point and a telecentric bundle will be emanating from the lens, see fig. 7.1a.

fig.7.1a: telecentric bundle (5kByte)

In the real world, no light source can be of zero size and no lens has ideal focusing accuracy; so always some divergence will remain.
And what I described resembles to a search-light more than to a telecentric lens.

But look at the reverted setup (fig. 7.1b).

fig.7.1b:

Here, a telecentric bundle strikes the lens. It is focussed and escapes through a minute aperture, called pinhole, which is placed around the focal point.
This hole serves as a spatial filter: only light from the axial parallel bundle is passed; all other light is rejected.
The smaller the aperture, the better the spatial filtering will work. But we won't carry this effect too far. The lens-dependent blur circle diameter should fit through the aperture. Otherwise the emanating bundle will only be further weakened without positively narrowing the acceptance angle.

What is this funny setup good for?   --   Normally it is used for measurement tasks.
Imagine an object of questionable size shadowing the telecentric bundle. And imagine an exact gauge (e.g. CCD) in the image plane (fig. 7.1c).

fig.7.1c: Imaging with Telecentric Lens (8kByte)

Now you have achieved very good depth of focus at the object side. You may move the object to and fro without disturbing image definition. And, best of all: without any influence on magnification. The object is allowed to have considerable 3D-depth. And all planes, though prone to different object distances, will be imaged to the same scale.

Fine. But if I use backside illumination with a telecentric bundle, then in fact the focal aperture is unneccessary. You see, the bundle   i s   telecentric, so what?

Well, some object features are invisible in back-lit condition. Remember thickness steps on a metal plate. They only shine up in front-lit condition. Here, the focal aperture rejects all slanted rays and even front-lit objects can be imaged (and measured!) telecentrically.

Further on, strictly telecentric illumination is not easily achieved.

Here we have already mentioned one of the two major drawbacks of telcentric lenses: Slanted rays are rejected, fine; but this way, they no more contribute to image luminous incidance! Images, produced by telecentric lenses, are quite obscure. Provided you do not use telecentric backlighting.

For not forgetting it, I'll just add the second drawback:
All rays from the object to the lens must be axial; so, any feature of the object that surpasses the lens entrance pupil size will not be imaged. Telecentric lenses need front lens elements of considerable size, weight, and cost. Or they are suitable for small objects only.

But don't forget the great advantage: As long as you keep the pinhole and image plane in the correct position, the magnification will stay correct. No matter how wrong object distance might be.
  ...   Really NO matter?   --   Well, when selecting a telecentric lens, ask for the residual beam divergence. Given this figure and the allowed tolerance of your measurement, you can easily derive the allowable "depth of focus".

Now there is one last trick with telecentric lenses: You can buy "double sided telecentric" lenses. Even more complicated?   --   Don't worry. First of all it is more convenient to use.

Please recall Fig. 7.1c. There you see that scale (=magnification)   m   is

      m   =   B / G   =   (b - f) / f
where
              B = image size
                  G = object size
                           b = image distance
                               f = focal length

That means: If you cannot define the exact image distance   b ,   then you do not know the exact scale of your object size measurements.

For these cases people add a second lens system behind the focal pinhole, like shown in fig. 7.1d.

fig.7.1d: Imaging with Double Telecentric Lens (11kByte)

Looks a bit like Kepler's telescope (except for the pinhole). But here you can choose nearly any image distance   and scale (= magnification)   m   will always stay

      m   =   f2 / f1

You can buy the complete solution: two lens systems with the correct distance between them and with the pinhole located where the two focal points meet one another. Place object and image sensor anywhere on axis and the magnification is perfect.

Conclusion in short:

Advantage: exact magnification; distance errors nearly don't matter

Drawback:  a) faint   image luminous incidance   and/or expensive illumination
           b) front lens element needs to have at least object diameter.



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Last modified Nov.29th, 2002 00:11