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Does tuble lens focal length change NA and DOF ??

 
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nathanm



Joined: 02 Jun 2016
Posts: 222
Location: Bellevue, WA

PostPosted: Fri Feb 03, 2017 1:41 pm    Post subject: Does tuble lens focal length change NA and DOF ?? Reply with quote

I have managed to confuse myself with the following issue - if you use a tube lens with a focal length different than the manufacturer, does this change NA ?

NA is a function of the objective focal length and entrance pupil diameter. We tend to think of it as a property of the objective. If the tube lens is the same focal length as the manufacturer intended that is fine.

Many of us on the forum use infinity objectives with a tube lens that is a different focal length than the manufacturer intended.

Mitutoyo assumes 200mm tube lens. Right now I am using 170mm. So a 10X objective is 8.5X in terms of magnification.

I want to calculate DOF so I can determine step size for stacking. Is the DOF the same for my set up at 8.5X as it would be for 10X?

If you assume that the NA is totally a property of the objective then it is the same, and DOF would be the same because it depends on the wavelength and NA as Rik explains here http://janrik.net/MiscSubj/2014/DefocusAnalysis201405/WhatIsTheDOF_DiffractionLimitedLens_v01.pdf.

However, I am not sure that the NA is unaffected.

Rik has a nice discussion of entrance pupil here http://www.janrik.net/PanoPostings/NoParallaxPoint/TheoryOfTheNoParallaxPoint.pdf and the principles are the same.

If the entrance pupil is determined by a physical aperture in the objective, then it won't change, but it could be determined by a physical aperture in the tube lens.

Of course this is all complicated by the fact that these objectives are not really thin lenses, so some of the simplistic formulas are unlikely to work.

In a previous thread on this forum, Rik determined the entrance pupil location for a Mitutoyo 10X, is 73.5mm behind the front of the objective, which places it well BEHIND the objective itself. This lends support to the idea that the tube lens might in fact help determine the size of the entrance pupil.

In addition, I found that I get better results putting the tube lens almost touching the back of the objective. That would put the entrance pupil somewhere inside the tube lens. Put that way it seems pretty obvious that it could have an impact.

Another analogy is what happens (effectively) on a camera lens when you put a teleconverter on it. The aperture of the lens is the same, but the magnification and the effective f-number increases. As a consequence, the DOF changes.

In my case the shorter tube lens decreases magnification, so it is more like taking the teleconverter off, but the idea is the same. This analogy might not hold, but it is suggestive.

If the tube lens affects NA, it should affect the resolution of the objective, which is interesting, but it should also affect DOF, which I need to know for doing optimal stacking.

Of course the DOF and step size for 10X would presumably be smaller than for 8.5X so if I used the 10X figures I wouldn't be caught short, I would just take more shots for a stack than I might optimally require.

But there have been many posts on the forum about people using tube lenses that are longer than 200 mm (the 240 mm and 300 mm apo gerenons have been mentioned). Those people would presumably need to take more steps.
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Pau
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Joined: 20 Jan 2010
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PostPosted: Fri Feb 03, 2017 4:00 pm    Post subject: Reply with quote

Rik and others will provide much more consistent responses, but AFAIK NA is not affected so in principle DOF will be the same.
This will be true if the sensor doesn't limit resolution. If sensor limits it, resolution (on subject size of course) can be lower with shorter tube lenses so actual DOF resolvable by the camera will be longer and you can stack with longer steps.
Does it agree with your experience?
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rjlittlefield
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Joined: 01 Aug 2006
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PostPosted: Fri Feb 03, 2017 6:07 pm    Post subject: Reply with quote

Pau's summary is good. Adding some detail...

There are only two things that can affect the NA of a microscope objective:
1. Blocking some of the image-forming light rays.
2. Moving the entrance pupil farther away from the subject.

Changing the tube lens normally does not do either of those things, which explains why changing the tube lens does not change the subject-side NA.

The camera-side NA definitely is changed, however, in exactly the same way that effective f-number is changed. Using a Nikon 10X NA 0.25 objective at rated magnification gives NA 0.25 and effective f/20. Using a short tube lens and pushing it down to 5X still gives NA 0.25, but effective f/10. This relationship is captured in the usual formula that camera-side effective f# can be computed as actual_magnification/(2*NA).

When the usable image resolution is limited by diffraction and not by sensor, display, or viewer, then DOF depends only on the subject-side NA and thus is not changed by a different tube lens. If you push the magnification low enough that one of those other things limits the resolution, then DOF will increase.

You wrote
Quote:
If the entrance pupil is determined by a physical aperture in the objective, then it won't change, but it could be determined by a physical aperture in the tube lens.

True, and if it is, then the NA will be changed in proportion to the diameter of the restriction. This is the reason why putting an iris just behind the objective lets you adjust the NA.

However, it's generally a bad idea to use a tube lens that restricts the light path. In that case the restriction is typically so far away from the objective lens that it causes significant corner darkening before it adds much central DOF. In other words, it vignettes.

Quote:
In a previous thread on this forum, Rik determined the entrance pupil location for a Mitutoyo 10X, is 73.5mm behind the front of the objective, which places it well BEHIND the objective itself. This lends support to the idea that the tube lens might in fact help determine the size of the entrance pupil.

I assume that you're referring to my post at http://www.photomacrography.net/forum/viewtopic.php?p=195714#195714. I could quibble that you've misread the post; the position I measured is 73.5 mm IN FRONT of the objective. But even if the position of the entrance pupil were behind the objective, inside the tube lens, then still the tube lens could not affect the entrance pupil unless it further restricted the light path. In that case the position of the entrance pupil would change, in addition to its diameter. The same thing happens when you add an iris. The Mitutoyo M Plan Apo 5X is almost telecentric when used by itself, but if you stop it down with an added iris, then the combo is not.

Quote:
Another analogy is what happens (effectively) on a camera lens when you put a teleconverter on it. The aperture of the lens is the same, but the magnification and the effective f-number increases. As a consequence, the DOF changes.

This case illustrates how the situation can determine the result. In fact, adding a teleconverter does not necessarily change the DOF. If the lens is wide enough that you are sensor limited without the teleconverter, then adding the teleconverter does increase DOF. But if the lens is narrow enough that diffraction is your limit to begin with, then DOF is not increased. To take an example with APS-C, suppose you are at f/45 to start with, and then add a 2X teleconverter to make it f/90. In the first case you will have an obviously blurred image, because the Airy disk is big enough to span many pixels. In the second case, the image will be twice as large, and so will the blurs, so there's no effect in terms of resolution and DOF on subject. All the teleconverter has done is to make the image bigger, and in both cases the sensor was good enough to capture all the detail that was in it.

--Rik
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mjkzz



Joined: 01 Jul 2015
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PostPosted: Fri Feb 03, 2017 8:21 pm    Post subject: Reply with quote

Quote:
When the usable image resolution is limited by diffraction and not by sensor, display, or viewer, then DOF depends only on the subject-side NA and thus is not changed by a different tube lens.


I am not around till last year, so I do not know exact definition of terms, but is this DOF referring to depth of field or depth of focus? I gather it is depth of field as it does not change regardless of tube lens.

On the other hand, nathanm was curious about optimal stacking, so I think it will affect step size as the effective aperture changes [added] as well as magnification[/added]
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