RDolz, thank you for the careful and detailed work.
I think I can explain some of the more confusing aspects of your observations.
Because the maximum field a telecentric lens can cover is approximately the diameter of its input aperture.
More precisely, the maximum telecentric field is approximately the diameter of the lens input aperture, minus the diameter of the light cone for each part of the subject, at the location of the lens aperture
If the field gets any larger, then in the outer portion of the field, each cone of light gets clipped by the lens aperture on its outside edge. This means that the effective aperture for those points in the field is no longer round. More importantly, the central rays of these modified apertures are no longer parallel to the optical axis.
In that outer part of the field, the system cannot be exactly telecentric, although it will be a lot closer to telecentric than it would be if the added stop were not present.
Notice that in the non-telecentric part of the field, the light cones are smaller than they are in the telecentric area. These areas of the image will get less light, and if they get enough less light, you will perceive them as darker, that is, "vignetted".
There is a simple guideline here: whenever you see vignetting in a system that is supposed to be telecentric, it's a good bet the system is not really telecentric.
To make this more definite, I have used WinLens3D to make a simplified picture of your lens setup. The MD5400 is modeled as a "thin lens" with 36 mm focal length and 13 mm diameter. At the perfect telecentric position 36 mm behind the thin lens I have placed a stop, and I have set the object and image distances to give 2.95X magnification (your HFOV 8 mm).
Then in one case I have set the added stop quite small, only 2 mm diameter, and in another case I have set the added stop to 6.25 mm diameter, as in your test.
Here are the pictures:
In the first case, with the telecentric stop set to 2 mm, the telecentric field diameter works out to be about 10.32 mm, a little more than enough to fully cover the 9.6 mm diagonal that goes with your 8 mm HFOV.
In the second case, with the telecentric stop set to 6.25 mm (your "f4"), the telecentric field diameter is only about 4.63 mm! Outside that small central area, the system will be progressively less telecentric. In the second picture, notice that for the extreme point in the object field, the ray fan is clipped by the edge of the lens so that it does not fill the aperture of the added stop.
A third case, which I have not illustrated, would correspond to your "f8" setting, which according to your table really means an aperture diameter of 3.13 mm. In this case the diameter of the light cone at the lens would be 3.13 * (142.2/(142.2-36) = 4.19 mm, giving a maximum telecentric field of 13 - 4.19 = 8.81 mm, still not quite big enough to cover your whole 9.6 mm diameter.
It's an interesting exercise to think about what this means in terms of image appearance as you move through focus. In the center of the field, where the system is truly telecentric, nothing changes except focus. But in the periphery of the field, where the system is not quite telecentric, the subject changes size along with focus. If your subject consists of a series of small round dots, and you keep the shutter open as you sweep through focus, then in the center of the field the dots will stay round, while in the edges of the field they'll become slightly elongated on the radial axis. It's like a very weak "zoomburst" effect, but restricted to the periphery.
If you then feed a bunch of these images to Zerene Stacker, and ask it to align them, including Scale adjustment, then you can probably imagine that some compromises will be needed. In the center of the field, scale change zero would be perfect, on the edges some other value would be perfect, and in between, other values would be perfect. The final value determined by Zerene Stacker will be some sort of weighted average of all the different scale values.
So, in your table of measured scale changes
, there is not even a single case where the system should be telecentric across the entire field. The one at 8 mm HFOV and "f8" is pretty close, with (in the model) only the corners not being telecentric. I'm thinking that's probably the reason that you got a pretty small value of 0.00434% .
You mentioned that:
There is a point that has puzzled me. Out of curiosity, I calculated the telecentricity in several of the stacks of this image by activating the Scale option in Zerene, ... and it gives me an average of 0,066%!. With the same setup, the first calculations gave me a scale change between each stacking image of 0,041%.
The scale factor computed by Zerene Stacker is only its "best guess", based on comparing pixel values in the two images. The number is quite accurate when two images are identical except for focus, for example when comparing a planar target shot with a flat field lens at two distances that are equally far on both sides of perfect focus. But the number becomes less accurate when the images are not so similar, typical of real subjects that are not even symmetric. With your complicated subject, I am not surprised that the numbers are as different as 0.066% and 0.041%. If anything, I am surprised that the number are so similar!
I think far from 0,02% …. although the stacking + stitching has apparently worked perfectly.
Ah, but remember...
When you turn off scale adjustment in the software, the resulting stacked output will end up having exactly the same overall
geometry that a perfect telecentric lens would give naturally.
In this case the effect of a lens that is not
perfectly telecentric is to cause some radial displacement artifacts in the corners of the images.
But the displacement can only be as bad as the shift from front to rear of each focus step. It does not accumulate, one frame after another.
As a result, when you turn off scale correction in the software, the main difference between a telecentric lens and a non-telecentric lens is how well quality is maintained in the corners of the stacked images.
Lou Jost wrote:
I think that instead of working with the DiMage lens, we should explore the use of longer lenses for this.
Yes, I agree completely. If nothing else, longer lenses have larger diameter apertures, at the same f-number, so they can have proportionally larger telecentric fields.
Finally, RDolz wrote:
it would be good to find a method to correctly measure the telecentricity of a lens.
If the degree of telecentricity is the same everywhere in the field, then I think you will get an accurate number from the method that I described earlier, using a detailed planar subject that is focused equally in front and in back of perfect focus. In this case the aperture can be made smaller without affecting the telecentricity, so stopping down to get more DOF can improve the accuracy of the number.
However, if the degree of telecentricity is not
the same everywhere in the field, as in all of these MD5400 tests, then no single number will suffice to describe the system.