In this thread, I want to pull together and fill in some of the finer details that have been discussed in recent months.
Here are the major points I want to make:
- Limits to telecentricity
- Many setups are completely telecentric only in some central part of the image field, then become progressively less telecentric toward the edges and corners.
- The completely telecentric part of the field is also the part where there is no vignetting.
- The diameter of this part can be estimated from lens diameter and working f-number. A smaller aperture (larger f-number) will produce a larger telecentric field, up to a limit that is imposed by lens diameter.
- Limits to measurement
- The alignment algorithm in Zerene Stacker can measure scale changes of a few parts per million in careful tests. Details about this aspect are provided in a separate thread, "On the sensitivity of Zerene Stacker scale measurements".
- At such high precision, confounding effects such as sensor heating can mimic or mask small levels of non-telecentricity. This is also covered in the sensitivity thread.
- To get an accurate measurement of telecentricity, you have to crop away any vignetted portions of the image. Otherwise the measurement will be corrupted by averaging across telecentric and non-telecentric parts of the field.
First, to briefly recap basic aspects…
You make optics telecentric on the object side by positioning the limiting aperture so that it appears to be at infinity, as viewed through the refracting elements in front of it. This can be done either by adding an aperture behind an existing lens or by adding a lens in front of an existing aperture. Either way, the effect is to select the light rays that form the image such that the “chief rays” (the central rays of each bundle) are all oriented parallel to the optical axis, on the object side of the lens. Since those chief rays also pass through the center of the physical aperture, this also means that the aperture is at the focal point of whatever refracting elements are in front of it, and that’s why the aperture appears to be at infinity when you look through the front of the optics.
Consider the following diagrams, which show only the chief rays.
Setup 1. Here is a theoretical thin lens with aperture at lens. This is not at all telecentric.
Setup 2. By moving the aperture backward, we can reduce the angles and move the lens toward telecentric. Note that moving the aperture changes the angles of the rays, but does not change the magnification or distances from lens to subject and sensor.
Setup 3. Here we have made the optics telecentric by moving aperture backward to the right place:
Setup 4. Alternatively, we can make the optics telecentric by adding another carefully selected lens in front of setup 2. Note that this reduces the effective focal length of the optics, so we also must reduce the lens-to-subject and lens-to-sensor distances in order to maintain the same magnification.
OK, so that’s the basic idea behind telecentricity: make the chief rays be parallel to the optical axis by positioning the limiting aperture at the focal point of all the refracting elements in front of it.
However, there’s a catch. The above diagrams implicitly assume that the chief rays all pass through the center of the nominal aperture. That assumption is valid as long as each bundle of rays completely fills the nominal aperture. But beyond a certain distance away from the optical axis, the outer side of the ray bundles will start to be cut off by the edge of the lens, not by the edge of the nominal aperture. When that happens, the nominal aperture is not completely filled with light, the chief ray does not pass through the center of the nominal aperture, and as a result, the optics are no longer telecentric for that point in the subject field.
Here's the way I diagrammed that situation at http://www.photomacrography.net/forum/v ... 337#238337 :
You can estimate the maximum telecentric field by simply subtracting the cone diameter from the lens diameter. Outside the resulting circle, the optics must vignette, resulting in some darkening and loss of telecentricity.
Perhaps a direct illustration of the effect will help to nail it down.
For the following demo, I’ve configured a telecentric system that consists of an Olympus 135 mm f/4.5 bellows macro lens, reversed in front of a Canon 100 mm f/2.8 L IS USM lens. This combo, with the adapters that I’ve used, becomes telecentric when the Canon 100 mm is focused just a little short of infinity, giving a combined magnification 0.804X.
Based on lens and aperture dimensions, I’ve calculated the maximum telecentric field to be about 19.8 mm in diameter.
Here is an image of the full frame. Green circle marks the edge of the telecentric field; red outline marks the area I'm going to animate below. You can see obvious vignetting in the corners.
Now I’m going to zoom in on the corner, and show an animation of two frames that are slightly in front and behind perfect focus (about 0.7 mm).
If the lens were telecentric completely across the field, clear into the corners, then none of the dots on the target would move. But what actually happens, because of the vignetting, is that the field is not telecentric outside the green circle. For these points, image scale changes as focus changes, so in the front/back animation, the dots outside the green circle move radially.
The central portion of this image field is extremely telecentric. When restricted to a crop region of 2100 pixels square or smaller, entirely within the green circle, Zerene Stacker reports a scale change of less than 0.000015 (1 part in 65,000) between the two images. Across the 2000 pixels width of this central area, this change in scale amounts to a misalignment of less than 0.02 pixels on each edge of the image.
However, the edges and corners of the whole frame are not even close to telecentric. For points in the extreme upper left and right corners, the change in scale amounts to 12 pixels in the 4752 pixels across the width of the whole frame. If the entire frame were that far off telecentric, then Zerene Stacker would report a scale difference of about 0.002525 (1 part in 400). However, because the scale change is much smaller than that over most of the frame, the computation reports a sort of average value, only about 0.000642 (1 part in 1600).
If you’re going by the numbers, then there’s some opportunity for trouble when the non-telecentric area is small relative to the whole frame. That’s because the aggregate number may look pretty telecentric but the corners really aren’t. This particular setup shows the problem when the images are cropped to 3600 pixels in width, slightly more than the diameter of the green circle. With that crop done, Zerene Stacker reports less than 0.0002 difference in scale (1 part in 5000). That overall number looks OK, but the corners of the crop are far worse: offset by a full 3 pixels between frames.
Bottom line: avoid the vignettes. The optics will not be telecentric wherever the corners are darkening.
I hope this is helpful.