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Measuring lens extension for reversed enlarger lens
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AndrewC



Joined: 14 Feb 2008
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Location: Belgium

PostPosted: Sun May 10, 2009 1:06 am    Post subject: Measuring lens extension for reversed enlarger lens Reply with quote

Basic question but ...

So lens extension is the distance from the film/sensor to the lens plane divided by focal length.

Using say a 50mm reversed enlarger lens - where is the lens plane ?

Andrew
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JGVilla



Joined: 27 Dec 2007
Posts: 62
Location: Netherlands

PostPosted: Sun May 10, 2009 3:41 am    Post subject: Reply with quote

Now this can easily become a BIG discussion . . .
Something for people with their heart set at mathematics Smile

For each lens in question you need some basic data,
like entrance pupil, exit pupil, internodal distance, etc., etc.
For a lot of lenses this information is not released by the manufacturer.
As you specifically refer to the El Nikkor 50mm f/2.8 here is a diagram I found on the internet (sorry I lost the reference):



When you start calculating realize that the formal focal length of this lens is 52.1 mm (for normal mount, for reverse mount it is apparently about 1 mm less).

From a practical point of view it might be much easier to set up your rig so that you get an exact 1:1 reproduction on the film plane.
Then carefully measure the distance between focal plane to the object (FD = focal distance) and
measure the distance between filter tread and object (WD = working distance). Basic "extension" for 1:1 is FD - WD.
You can do the same for a 2:1 setup and see how much additional extension you need.
Basic 1:1 "extension" minus addtional extension for 2:1 is position of lens plane.
Now with the known focal length of the lens (≈ 52.1 mm) you have a good starting point to calculate the effects of extension on magnification.

Actually in testing my new macro setup I'm on the verge of starting these measurements myself.
But first (next two weeks) I have to attend to some urgent family business,
but I will let you know my results when I get them.
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JGVilla



Joined: 27 Dec 2007
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PostPosted: Sun May 10, 2009 6:23 am    Post subject: Reply with quote

I did a "quick and dirty" initial check:
Total length El Nikkor 50mm N = 39 mm
Total length Nikon BR2a + 40.5-52mm reversal ring = 8.3 mm
Nikon sensor to lens flange = 46.5mm
So total length = 93.8 mm

With this setup I took a picture of a flat stainless steel ruler (camera D2X):
Ruler on picture read about 35.1 mm
Magnification = 23.54 / 35.1 = 0,67 (on DX sensor)
Working distance ≈115 mm (estimated)
This is the "minimum" magnification obtainable on my system.

So next to figure out the extra extension needed to get exactly 1:1
(EXT - FL) / FL = M, wherein
EXT = extension,
FL = focal length, and
M = magnifaction.

With the above data doing some iterations the focal length of the reversed 50mm El Nikkor N is ≈ 51.5 mm.
Further calculations reveal:
(0.67 x 51.5) + 51.5 = 86.0 (is required extension for 0.67 magnification).
Total length was 93.8. so the "lens plane" should be at 7.9 mm from the end of the lens.

Based on all the "figure shuffling" above, I estimate that I need about 16 mm more extension to arrive at 1:1 magnification in my setup.

Note: Edited to delete incorrect information about entrance and exit pupil. BBcode does not allow to strike out text so incorrect text was just deleted.
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Last edited by JGVilla on Sun May 10, 2009 1:04 pm; edited 3 times in total
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rjlittlefield
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PostPosted: Sun May 10, 2009 7:42 am    Post subject: Re: Measuring lens extension for reversed enlarger lens Reply with quote

AndrewC wrote:
Basic question but ...

So lens extension is the distance from the film/sensor to the lens plane divided by focal length.

Using say a 50mm reversed enlarger lens - where is the lens plane ?

Why are you asking the question? That is, how are you going to use the answer?

--Rik
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JGVilla



Joined: 27 Dec 2007
Posts: 62
Location: Netherlands

PostPosted: Sun May 10, 2009 7:44 am    Post subject: Reply with quote

Adding 15.9 mm extra extension gives a "ruler reading" on the picture of 24.2 mm.
23.54 / 24.2 = 0,973 magnifaction. For exact 1:1 magnification total length required would be 111.3 mm, which includes:
Nikon focal plane to lens flange = 46.5 mm
Total length of El Nikkor 50mm N lens = 39.0 mm
Physical extension = 25.8 mm

Each additional extension of 51.5 mm will give an extra 1x magnification, so:
Physical extension 25.8 mm = 1:1
Physical extension 77.3 mm = 2:1
Physical extension 128.8 mm = 3:1
Physical extension 180.3 mm = 4:1
Physical extension 231.8 mm = 5:1

To make life simple, for any (reasonable) magnification use the following formula to calculate needed physical extension:
Physical extension (in mm): EXT = (m x 51.5) - 25.8
where physical extension is length of required extension tubes or bellows extension.
With given physical extension: m = ( EXT - 25.8 ) / 51.5 +1

Edited to add formulae
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Last edited by JGVilla on Sun May 10, 2009 2:00 pm; edited 2 times in total
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AndrewC



Joined: 14 Feb 2008
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PostPosted: Sun May 10, 2009 8:06 am    Post subject: Re: Measuring lens extension for reversed enlarger lens Reply with quote

rjlittlefield wrote:
AndrewC wrote:
Basic question but ...

So lens extension is the distance from the film/sensor to the lens plane divided by focal length.

Using say a 50mm reversed enlarger lens - where is the lens plane ?

Why are you asking the question? That is, how are you going to use the answer?

--Rik


Even parts curiosity and wanting to calculate dof for a given amount of extension. I've been playing with some lens formulae recently and people happily quote magnification as extension / focal_length but don't really define what it means.

Jan's suggestion is good but if someone else had already done the hardwork I'd be prepared to believe them that wheels are best round rather than triangular Smile

rgds,

Andrew
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mgoodm3



Joined: 08 Sep 2008
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PostPosted: Sun May 10, 2009 9:10 am    Post subject: Reply with quote

The point where the focal length is measured from is not the entrance or exit pupil. The points are the "principal planes" of the lens.

Most enlarging lenses are relatively symmetric - the entrance and exit pupils are about the same size. From that you can infer that the principal panes are near the center of the lens - probably several mm's toward the camera side (mounted forward or reverse).
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rjlittlefield
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PostPosted: Sun May 10, 2009 9:18 am    Post subject: Re: Measuring lens extension for reversed enlarger lens Reply with quote

AndrewC wrote:
Even parts curiosity and wanting to calculate dof for a given amount of extension. I've been playing with some lens formulae recently and people happily quote magnification as extension / focal_length but don't really define what it means.

Here's a quick review of the theory.

Ordinary lenses closely follow the "thick lens model", in which all of the refracting power of the lens is concentrated into two imaginary refracting surfaces. For your purposes, the key feature of this model is that it has two "principal planes" from which distances are measured.

An object at infinity produces an image that is sharply focused 1 focal length behind the "rear principal plane". If you know the focal length of the lens, you can use this fact to find the location of the plane -- just set up to focus at infinity, and measure from the image plane 1 focal length toward the lens.

The "front principal plane" can be found by reversing the lens and doing the same test.

Once you know the locations of the principal planes, you can use the usual lens formula 1/f = 1/o + 1/i, just measuring o and i from the corresponding principal planes.

Life gets more challenging if you don't know the focal length to start with. Of course there are procedures to determine the focal length from measurements, but they are fairly elaborate. (One of them is outlined by JGVilla, to determine the amount of additional extension needed to go from magnification m to m+1.) For your purposes, the manufacturer's spec is probably close enough.

I normally recommend to measure DOF instead of calculating it, since the calculations are easy to get wrong. But if your heart is set on calculation, then be aware that the standard formulas only work for "symmetrical" lenses, meaning here that the aperture appears to be the same size from front and rear. If the aperture appears to be different sizes from front and rear, then the lens is "asymmetrical" and you have to include a correction factor depending on the magnification and a ratio called the "pupillary magnification factor". See pages 256-258 of Lefkowitz, The Manual of Close-Up Photography.

Unfortunately there is much incorrect information published about the entrance and exit pupils. It is commonly written and diagrammed that the pupils are located in the front and rear principal planes. This is not correct. The actual location of the pupils can be very far away from the principal planes, even pushed to infinity in the case of telecentric lenses. For many purposes -- but far from all of them -- it works nicely to think about an entrance or exit pupil in terms of its projection onto the corresponding principal plane, and this is what's shown in the diagrams.

Hope this helps...

--Rik
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JGVilla



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PostPosted: Sun May 10, 2009 12:02 pm    Post subject: Re: Measuring lens extension for reversed enlarger lens Reply with quote

Checking the theoretical diagrams on internet I presume that the front principal plane is normally denoted as H (or H1) and the rear principal plane as H' (or H2).
In the El Nikkor diagram above, the front principal plane (H) is however drawn to the right side (towards the lens mount).
I think that makes sense as the object in case of a enlarger lens is the "negative" and the image is projected on a light sensitive plate on the enlarger's baseboard.
Using an enlarger lens as a macro lens (at least at magnifications > 1:1) it makes sense to reverse the lens as the object is then still at the "correct" side of the lens.

When using the El Nikkor 50mm as a macro lens all (focal length) measurements should be based on the principal plane indicated by H (not H'). Correct?
This would neatly corresponds with my measurement where I found that the "lens plane" was at 7.9 mm from the lens end.
The principal plane (H) is also exactly at 7.9 mm (20.6 - 13.1 + 0,4) from the "lens end" at the lens mount.

rjlittlefield wrote:
Unfortunately there is much incorrect information published about the entrance and exit pupils.
It is commonly written and diagrammed that the pupils are located in the front and rear principal planes.
This is not correct. ...
I will cross that out in my original posting to avoid further misleading information Embarassed

Edited for clarifcation.
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Last edited by JGVilla on Sun May 10, 2009 1:16 pm; edited 3 times in total
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AndrewC



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PostPosted: Sun May 10, 2009 12:08 pm    Post subject: Re: Measuring lens extension for reversed enlarger lens Reply with quote

rjlittlefield wrote:

....
I normally recommend to measure DOF instead of calculating it, since the calculations are easy to get wrong. But if your heart is set on calculation, ....

Hope this helps...

--Rik


Indeed it does, as always Smile

Actually I'm an engineer, so I can just about calculate 2+2=4, but to be safe I usually allow a margin for error and call it 5. Then do a test run anyway. Luckily I don't build skyscrapers and bridges Smile

Andrew
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mgoodm3



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PostPosted: Sun May 10, 2009 1:30 pm    Post subject: Reply with quote

I don't think that it's possible to have the principal planes reversed (front behind the rear) like it is shown in the diagram and have a (+) focal length lens...
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JGVilla



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PostPosted: Sun May 10, 2009 1:44 pm    Post subject: Reply with quote

mgoodm3 wrote:
I don't think that it's possible to have the principal planes reversed (front behind the rear) like it is shown in the diagram and have a (+) focal length lens...


Unless you define the side of the lens mount as "front" and the side of the filter thread as the "back" of the lens.
The would make sense for a enlarger lens (see previous above) which is something like a lens reverse mounted in its casing.
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rjlittlefield
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PostPosted: Sun May 10, 2009 2:20 pm    Post subject: Reply with quote

JGVilla wrote:
Checking the theoretical diagrams on internet I presume that the front principal plane is normally denoted as H (or H1) and the rear principal plane as H' (or H2).
In the El Nikkor diagram above, the front principal plane (H) is however drawn to the right side (towards the lens mount).
I think that makes sense as the object in case of a enlarger lens is the "negative" and the image is projected on a light sensitive plate on the enlarger's baseboard.
Using an enlarger lens as a macro lens (at least at magnifications > 1:1) it makes sense to reverse the lens as the object is then still at the "correct" side of the lens.

But I think in this case the principal planes should not be reversed.
When using the El Nikkor 50mm as a macro lens all (focal length) measurements should be based on the principal plane indicated by H (not H'). Correct?
This would neatly corresponds with my measurement where I found that the "lens plane" was at 7.9 mm from the lens end.
The principal plane (H) is also exactly at 7.9 mm (20.6 - 13.1 + 0,4) from the "lens end" at the lens mount.

I would not trust the labeling of H versus H'. But we should be able to figure it out.

Taking your measurement of 52.1 mm focal length, the "film-side" principal plane should be 52.1 mm away from the back focus point. In the diagram on right, it says that the back focus is 31.4. The point 52.1 away from there is labeled H'. The front focus is listed as 23.2, and going 52.1 mm away from there is the point labeled H. In other words, the "film-side" principal plane lies farther away from the film than the other principal plane does. I think this is what you are calling "reversed".

In the diagram on left, I can't tell which point is labeled H and which is labeled H'. However, the relationship appears to be the same, although the planes are much closer together in that case.

Using the lens diagrammed on right, reversed, I think the sensor-to-principal-plane measurement should go to H, not H'.

Does this agree with your measurements? I do not have that lens, so I cannot confirm it myself.

--Rik
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mgoodm3



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PostPosted: Sun May 10, 2009 3:08 pm    Post subject: Reply with quote

rjlittlefield wrote:

Taking your measurement of 52.1 mm focal length, the "film-side" principal plane should be 52.1 mm away from the back focus point. In the diagram on right, it says that the back focus is 31.4. The point 52.1 away from there is labeled H'. The front focus is listed as 23.2, and going 52.1 mm away from there is the point labeled H. In other words, the "film-side" principal plane lies farther away from the film than the other principal plane does. I think this is what you are calling "reversed".


--Rik


That is what I was referring to by reversed. It doesn't make any sense for me. I have never seen this situation pop up in WinLens and these are pretty normal lens designs. That's why I question the diagrams. It's kinda like a thick lens with a (-) thickness.
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JGVilla



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PostPosted: Sun May 10, 2009 4:18 pm    Post subject: Reply with quote

rjlittlefield wrote:
Taking your measurement of 52.1 mm focal length . . .

The focal length of 52.1 mm is actually taken from the user manual:

I read somewhere that the focal length of this lens - when reverse mounted - was slightly less than 52.1mm which seems to be confirmed by my calculations/measurements (51.5mm)

rjlittlefield wrote:

. . . the "film-side" principal plane should be 52.1 mm away from the back focus point.
In the diagram on right, it says that the back focus is 31.4. The point 52.1 away from there is labeled H'.
The front focus is listed as 23.2, and going 52.1 mm away from there is the point labeled H.
In other words, the "film-side" principal plane lies farther away from the film than the other principal plane does.
I think this is what you are calling "reversed".

I fully agree. I also think that when I talked about "reverse" principal planes, this really contributed to confusion (excuses to mgoodm3). Confused

rjlittlefield wrote:
Using the lens diagrammed on right, reversed, I think the sensor-to-principal-plane measurement should go to H, not H'.
Does this agree with your measurements?

Now here is the answer to the question I should have posed in the first place.Very Happy
Based on your short refresher course and information I checked on the internet,
what I really wanted to know was on which principal plane should I base my calculations with this lens reverse mounted?
And yes, based on my measurements, I also came to the conclusion that the calculations should be based on principal plane H.

Thanks for helping me out.
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