Telecentricity and pupil magnification

In a recent thread, commenting on a certain lens, Jerome mentioned that in various of our lenses the exit pupil was substantially forward of its "classical" location, and that this approached a property of a telecentric lens.

A telecentric lens is a type of lens notably used in optical metrology. That is the art of precisely measuring a distance (typically small) on a physical part by observing it through what we can think of as a special kind of view camera. The feature of interest appears, greatly magnified, on the ground glass. We measure the distance on the image (often using a graticule on the ground glass) and then, knowing the magnification, determine the actual distance of interest.

The instrument used is often called an optical comparator, and in many cases what is of interest is not just isolated dimensions by rather the overall profile of some feature on the part. Thus, a template may be provided on the ground glass rather than just a coordinate graticule.

Here we see a typical instrument of this type:



A wrinkle is that, with a conventional optical system, the exact magnification depends on the axial position of the feature on the part, which we cannot always accurately control.

A fully-telecentric lens has its entrance pupil located an infinite distance behind the lens, and the exit pupil an infinite distance in front of the lens. A result (hardly obvious) is that the magnification is independent of the axial location of the feature being observed.


In any case, often in photographic lenses we have an exit pupil that is "forward" of its classical position (which would be at the second principal point of the lens). This may be a byproduct of certain lens design techniques, or it may be arranged as a means of mitigating natural vignetting (the falloff of luminance on the focal plane as we move out from the center of the image).

As I was reviewing this matter, I came upon two technical articles I had almost completed but had not quite. They were at about the "85%-90% finished" state, and had not yet been published.

I brought them both to perhaps "95% finished" and put them on my site so that those of you who might be interested could read them.

The first is entitled "Entrance and Exit Pupils in Photographic Lenses", and is available here:

http://dougkerr.net/Pumpkin/articles/Entrance_Exit_Pupils.pdf

Of particular importance to the topic here is the discussion of the matter of pupil magnification: the fact these two factors are inextricably linked:

• Pupil displacement: the location of the entrance and exist pupils not at the first and second principal points of the lens.

• Pupil magnification: the matter of the relative diameters of the two pupils (they are only equal when there is no pupil displacement).

The second article is entitled "Quasi-Telecentric Lens Design for Digital Cameras", and is available here:

http://dougkerr.net/Pumpkin/articles/Telecentric.pdf

It briefly introduces the concept of the truly telecentric lens, and then discusses why (in the case of a digital camera) we might wish to intentionally give a camera lens a property that approaches that of a truly telecentric lens: an exit pupil that is displaced substantially forward of the first principal point of the lens.

My apologies for any editorial lapses in these early issues of these two articles. As I said, they are nominally (hopefully) at the "95% complete" point.

Best regards,

Doug

True telecentric lenses have many very interesting properties.

Here's one that arises from the fact that, with a true telecentric lens (as used in an optical comparator), the image magnification does not vary with the distance to the object.

Imagine that we have a square hole with parallel sides in a metal block, and we look at it with our telecentric lens along its central axis.

The square boundary at the top surface is imaged with a certain magnification.

Now consider a line around the bore a little way down. It would conceptually be imaged with the same magnification—would have the same size in the image.

And the same would be true of a line drawn around the bore farther down yet.

All these square figures conceptually precisely overlap in the image.

The result is that we do not see the four corner edges of the bore as the familiar "converging" pattern of lines in the image. All we see is the top opening—the four faces and four corner edges seem to go "straight away from us", and can't really be seen.

Now this at first seems contrary to our familiar understanding of perspective in photography. But in fact it is precisely consistent.

The "point of perspective" of a camera—the place where the camera seems to be from the standpoint of perspective—is in fact at the center of the entrance pupil. With a telecentric lens, the entrance pupil is located an infinite distance behind the camera. Thus the lines along the four edges of our square bore arrive at the (infinitely distant) camera perfectly parallel—their projections onto the image are just four dots. We do not see them as lines at all.

Neat stuff!

Best regards,

Doug