How to get as shallow as possible DoF @3x?

[ggael]

I'm new to this forum, so first of all I'd like to give a big thanks to all members of this forum from which I already gathered a lot of information.

In short, I'm looking for some advices in lens/objective choices to design a setup at about x3 of magnification with:
- very sharp images free of CA on the largest part of the sensor (that's a pretty standard request)
- a reasonable working distance (>30mm)
- and an as shallow as possible DoF with a soft bokeh (that's less standard!)

From the thick lens model, it is well known that in order to reduce the DoF I should favor a large aperture (which is also good for sharpness), but we can also gain other insights:
- for a constant effective pixel size, better increase both sensor pixel size and magnification (this is good as I own a 20MP EOS 5D with rather large pixels of 6.5µm).
- the pupil ratio should be as large as possible.

That's the theory, but it's less clear to me which lens/objective/tubes/etc. combination will best follow those recipes. In particular, I'm not 100% sure how to estimate the working aperture of a up/downgraded infinite microscope lenses. Same for stacked lenses. (I found contradicting resources)

Here are some options I'm considering:

- Mitutoyo APO x5, NA 0.14, @3x
- Mitutoyo APO x2, NA 0.055, @3x
- Stacking, e.g.: the Canon 100mm f/2.8 (I already have it) + reversed 28mm or 35mm lens
- Scanner-Nikkor ED 14 elements (f/2.6 ?)
- Minolta-Scanner 5400 (f/4 ?)

It seems to me that no finite microscope lense option can beat any of the above options. A CFI super fluor x4 NA 0.2 would likely beat the Mitutoyo options, but this one is too expensive, even on used market. The last two scanner options look promising but are hard to find in Europe.

Any ideas?

thank you for reading.

[rjlittlefield]

Welcome aboard!

First, let me simplify your thinking.

For a fixed size subject field, the one thing you really need to think about is the angle of the entrance cone -- the parameter that is called "NA" in microscopy.

Other parameters like pupil ratio and sensor size may appear in some formulas, but in the end they won't actually matter except to the extent that they affect the angle of the entrance cone. So, I think it is simpler to just "skip the middlemen" and concentrate on the entrance cone.

Here are two other relationships that are useful to know:

1. NA = 1/(2*feff_subject), where feff_subject is the effective f-number on the subject side. Similarly, feff_subject = 1/(2*NA).

2. feff_subject = feff_sensor / magnification .

Finally, for stacked lenses where the rear lens is focused at infinity, the front lens is reversed, and the limiting aperture is in the front lens, then feff_subject = nominal f-number of the front lens. (When the rear lens is not focused at infinity, things get much more complicated.)

By the same principle, the NA of an infinite objective is not changed when you use longer or shorter tube lenses to change the magnification.

So then, looking at the options that you've listed...

- The Mitutoyo 5X NA 0.14 will still be NA 0.14 when pushed down to 3X. However, it probably won't cover your full-frame sensor when used this way.

- The Mitutoyo 2X NA 0.055 will still be only NA 0.055 when pushed up to 3X. Sensor coverage will be no problem, but it won't have the shallow DOF and bokeh that you want.

- Stacked lenses will have less DOF than NA 0.14 if the front lens is set to an aperture that is wider than 1/(2*0.14) = f/3.57 . You could beat NA 0.055 with f/9 or wider. These should cover your sensor with no trouble.

- Finite conjugate setups like your last two bullets will have less DOF than the stacked lens approach only when the finite conjugate lens aperture is wider by a factor of 1+1/m, so for example f/3 for the finite conjugate versus f/4 on the front of a stacked pair, both at 3X. In this case both will have effective aperture f/12 back at the sensor, and f/4 from the standpoint of the subject.

Given your goals and constraints, I suggest pursuing the stacked lens approach. There's a good chance you can improve performance by setting both lenses wide open and placing a Waterhouse stop between them to be the limiting aperture for the whole system. With the rear lens set on infinity, the effective f-number of the front lens will be equal to its own FL divided by the stop diameter.

--Rik

[ray_parkhurst]

I'm curious why you are specifically looking for a narrow DOF. Can you share your application?

I tend to agree with Rik (indeed on most things) that the stacked lens approach is probably a good path for you, but I have personally have had little luck with it. I too have been searching for solutions at 3-3.5x, and so far none of my stacked lens options have worked as well as a $50 Lomo finite objective. Perhaps you will have more luck. For sure you should review the various threads relating to stacking, as there is a wealth of info that may save you time and $.

[ggael]

Thank you very much for your detailed answer. Your first remark motivated me to re-derive the DoF formulas from scratch, and the different terms make more sens now, and indeed my remark on the pupil ratio was kind of irrelevant.

The stacked option is indeed the most promising to reach high effective aperture, but from what I read so far, and as ray_parkhurst pointed out too, this solution is quite hazardous. Fortunately, we managed to get access to a bunch of lenses for testing, and we just tested the following combo:

EOS 5D + canon 100mm f/2.8 macro focused @ininity + canon 50mm f/1.4 reversed mounted focused @infinity

This gives a 2x magnification. A quick test revealed a very shallow DoF, and a sharp image at the center, but the image only covers a very small fraction of the full-frame sensor, and even an APS-C crop would exhibit very strong vignetting with completely black corners... I guess I have to read more on stacked lenses and we'll do more experiment tomorrow.

We also have access to a high quality tube-lens (ITL200). Even though it's designed for microscope objectives, maybe it could play well with reverse mounted lenses. Time for fun experiments!


@ray_parkhurst: My application is as accurate as possible depth estimation, mostly in the context of cultural heritage. My expertise is rather on the side of the algorithms. Regarding the Lomo, I've seen roberotoole's good reviews of it, but I don't think that's a good choice for targeting super shallow DoF, and for my application a planar corrected lens makes more sens.

[ray_parkhurst]

@ray_parkhurst: My application is as accurate as possible depth estimation, mostly in the context of cultural heritage. My expertise is rather on the side of the algorithms. Regarding the Lomo, I've seen roberotoole's good reviews of it, but I don't think that's a good choice for targeting super shallow DoF, and for my application a planar corrected lens makes more sens.

I suspected that depth measurement was your likely application. Thanks for confirming.

Do you really need full field coverage? Do you plan to make multiple simultaneous measurements across the field? If you could remove the coverage constraint, then your options would open up dramatically, as you have already witnessed.

[ggael]

Sadly, yes. Ultimately we plan to scan artifacts as large as 30cm x 30cm so we cannot afford loosing 75% of the pixels. But this is already good to get stacks and play with the depth from focus part.

[Lou Jost]

Do you care about color? If you can do this in monochrome light, you can get much sharper images and you can use photolithography lenses, which have perfectly flat fields and are usually telecentric and distortion-free to facilitate stitching.

[Chris S.]

Ggael, welcome to the forum!

My application is as accurate as possible depth estimation, mostly in the context of cultural heritage.

. . .we plan to scan artifacts as large as 30cm x 30cm. . . .

I wonder if "Reflected Light DIC Microscopy" would be a better bet for your application than relying on thin depth-of-field as a method of depth measurement? "DIC," in this contect, refers to "differential interference contrast." I'm far from knowledgeable about the technique, but perhaps other members of the forum have used it and could give it a thumbs-up or thumbs-down for your needs.

Some members of our forum use transmitted light DIC, which is a very different thing. It permits wonderful images of transparent or semitransparent subjects such as protists, by enhancing contrast between regions of differing indices of refraction. Reflected light DIC, on the other hand, is far simpler to set up, can be used on opaque subjects, and provides information about the surface topography of the subject.

At one time, I thought I'd try adding reflected DIC to my macro rig. Did some background reading that made it seem quite feasible; purchased a set of Nomarski prisms (necessary for DIC--but where transmitted DIC requires a pair of these prisms for each lens, reflected DIC requires just one). Somewhere after that, this project got back-burnered, and I haven't returned to it since.

A couple of possible references: Microscopy U:Reflected Light DIC Microscopy and Principles of interference microscopy for
the measurement of surface topography by Peter de Groot.

Again, just a thought--I'll emphasize that I'm far from being expert on the subject.

--Chris S.

[ray_parkhurst]

Well, what did you settle upon for your application?

[ggael]

Sadly I 'm still waiting for the shipping of hardware pieces (adaptors, motorized stage, ring light, etc.) so that we can properly test our lenses at disposal.

With a very dirty setup the ITL200 + canon 50mm f/1.4 reversed looked promising but at 4x the field of view is too limited. We'll also try with a Nikkor 85mm f/1.8D. I'll post some pictures once everything can be properly assembled. Hopefully this week.