Are long working distance objectives hypercentric?

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cube-tube
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Are long working distance objectives hypercentric?

Post by cube-tube »

Simple question. When the front element of the objective is significantly larger than the area covered by the image (as is the case for most Mitutoyo objectives, or the Nikon 50x SLWD), does that mean that the objective is hypercentric? I imagine the "viewing angle" would be negative, pointing in from the edges of the lens, as opposed to most cameras which have a viewing angle expanding outward, so by that logic it seems like these lenses would be hypercentric.

I have a good understanding of what kinds of images hypercentric and telecentric lenses produce, but I do not totally understand what physical properties of a lens make it hypercentric or telecentric, so I am wondering if my logic is sound.

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Post by rjlittlefield »

When the front element of the objective is significantly larger than the area covered by the image ... does that mean that the objective is hypercentric?
...
I do not totally understand what physical properties of a lens make it hypercentric or telecentric, so I am wondering if my logic is sound.
That particular logic is not sound. What matters is the placement of the limiting aperture, which determines the orientation of the chief rays that run down the centers of all the light cones. When those chief rays are all parallel, you get orthographic projection -- the lens is telecentric. When the chief rays converge toward the lens, you get normal perspective (endocentric); when they diverge toward the lens, you get inverted perspective (hypercentric). It is always the apparent position of the limiting aperture that determines perspective, by selecting which of all the possible rays from each point on the subject becomes the chief ray. The very same refracting elements can produce images that have normal perspective, inverted perspective, or orthographic projection, depending entirely on where the aperture is placed. See http://www.photomacrography.net/forum/v ... 0750#50750 for some discussion.

A carefully drawn ray diagram will show that only a part of the front element is being used for each point on the subject. The difference between endocentric, telecentric, and hypercentric lies in which parts of the front element are being used for each point on the subject, and that's determined by the aperture location.

Strictly speaking, the Mitutoyo M Plan Apos are slightly hypercentric -- if you look into the front of the lens, the limiting aperture appears to be "beyond infinity".

However, as a matter of practice anything at 10X and above has such shallow DOF that the change in scale from front to back of the in-focus slab is negligible. For purposes of focus stacking, standard recommendation is to turn off scale correction in these cases, because it's not needed and actually it is likely to cause problems. See http://www.photomacrography.net/forum/v ... 9878#79878 for discussion. When you turn off scale correction, the stacked image is forced to have overall orthographic projection essentially as if the lens were telecentric, even if it's not.

--Rik

cube-tube
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Post by cube-tube »

@rjlittlefield
Thank you for the information!
I think that it's fascinating that the limiting aperture controls perspective like that. I don't find that very intuitive, to be honest, but it is interesting. Maybe I will look at a ray diagram.
The "position of the limiting aperture" refers to the apparent position within the lens system, not the physical position, correct? So, if an aperture at infinity is closing around parallel rays, then an aperture past infinity is closing around rays converging inward? And an aperture before infinity closes around rays converging outward? Is that correct?

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Post by rjlittlefield »

I agree it is not intuitive that the aperture controls the perspective. Back in 2006, I spent about two weeks of nearly full-time confusion coming to grips with the concept, while struggling to resolve some issues regarding the "no-parallax point" in panorama photography. The paper resulting from that effort is HERE. I suspect that reading it carefully, and more than once, will help with the intuition.

As for the ray diagrams, some good ones (I hope!) will be in the linked paper. Others are at http://www.photomacrography.net/forum/v ... 0750#50750 . But most valuable would be ones that you draw for yourself, using lens systems that you are physically experimenting with.
The "position of the limiting aperture" refers to the apparent position within the lens system, not the physical position, correct?
Correct.
So, if an aperture at infinity is closing around parallel rays, then an aperture past infinity is closing around rays converging inward? And an aperture before infinity closes around rays converging outward? Is that correct?
I'm sure that the words "closing around" correspond to some picture inside your head. But I'm not sure what the picture is, so I am reluctant to say yes or no about the words.

The way I think of it, the aperture selects certain bundles of rays. If the chief rays of all the bundles are parallel at the plane of the subject, then the lens is telecentric. If the chief rays intersect at a point that is behind the subject (on the side away from the lens) then the lens is hypercentric, with inverted perspective. If the chief rays intersect at a point that is in front of the subject (on the same side as the lens), then the lens is endocentric, with normal perspective. So, starting at the subject and moving toward the lens, the chief rays will fan out for hypercentric, be parallel for telecentric, and converge together for endocentric.

--Rik

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