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There are those who claim that it can be mathematically proven that Konica M-Hexanon lenses are somehow designed around a different register distance.  The math actually says that they are not - and that the Hexar reaches the same register distance slightly differently.  This means that incompatibilities people are finding are more likely the product of sample variance in bodies and lenses.
Hands off my flange!

One got shot with a 7mm rifle, the other with a .284 rifle. Which is which?!
(thanks to Robert Capa and Jeffery)

1. Depth of field and depth of focus: watch your Ps and Qs
2. The 0.05mm solution of the Hexar RF
3. Keppler's puzzling test
4. The 75 Summilux urban legend

1. Depth of field and depth of focus: watch your Ps and Qs.

It is very, very surprising how many people confuse depth of field with depth of focus. These leads to a lot of speculation (wrong) about what a particular lens and body do not work together properly. Here are a couple of (hopefully) easy definitions. Don't worry about the formulae; I will do all the computations necessary for this article. In fact, you don't have to read the formulae at all.

Depth of field refers to a lens's ability to focus light rays from a set of 3 dimensional objects (the real world) on a flat surface (the emulsion of your film). Fundamentally, it is the mapping of light rays from a three-dimensional universe into a two-dimensional plane. So imagine slapping a stack of overhead transparencies on a copy machine. Depth of field is the ability of the copy machine to combine all of the writing on all of the transparencies onto one side of a piece of copier paper. As is well known, increasing aperture decreases depth of field and decreasing it increases depth of field.

The formula for depth of field (near and far limits is)

Dn = (hs/(h+(s-f)) [the nearest distance subject in focus]

Df = (hs/(h-(s-f)) [the farthest distance subject in focus]

Depth of field (mm) = (hs/(h-(s-f)) - (hs/(h+(s-f))

Where h is the hyperfocal distance at that aperture, f is the focal length, and s is the subject distance.

You get hyperfocal length h = f2 / ac where f is the focal length, a is the numerical aperture and c is the circle of confusion. Use 0.03mm for a typical Circle of Confusion and make sure all of your units are in millimeters.

You can play around with this formular as much as you want, but essentially what it will tell you is that the depth of field increases with any of the following: (a) subject distance; (b) smaller apertures; and/or (c) shorter lens focal lengths.

Depth of focus is just the opposite, the ability to map light rays from a two-dimensional plane (subject) into a three dimensional universe (the space around where the film is in the camera). When the film emulsion falls somewhere within the depth of focus, you get sharp pictures. How do you visualize this? You take a transparency with a big letter "A" on it. You make 100 photocopies onto transparency paper and stack them up. You now have a three-dimensional A from a two-dimensional one. So think of a single piece of colored paper touching the top or bottom of the stack, or somewhere in the middle. Then you have a sharp picture. Inside your camera, there is an aerial image that is similar to that stack, i.e., three dimensional. When the film emulsion intersects that image, you get correct on-film focus.

The formula for depth of focus is

Depth of focus (mm) = 2ca(m+1)

With c as the circle of confusion required, a is the aperture and m is the image magnification. For a subject at infinity with any lens, m (look it up here) can be set to zero (objects at infinity are infinitely small, and accordingly, the limit of magnification as distance approaches infinity is zero). This formula takes into account the fact that as magnification increases, lens extension increases, and with it, effective aperture number is higher. aeff = a*(m+1).

This formula demonstrates many things:

(1) as magnification approaches 1:1 (think: macro), the depth of focus doubles.

(2) telephotos, which at any given distance (other than infinity) have higher magnification, also have greater depth of focus at any given aperture. A 75mm lens at 0.7m has a magnification of 0.12x. At 8 feet, it has a magnification of 0.032.

(3) wide-angles, which at any given distance (other than infinity) have lower magnification, have less depth of focus. A 21mm lens at 0.7m has a magnification of 0.03x. At 8 feet, a 21mm lens has a magnification of 0.009x.

(4) the smaller the aperture, the greater the depth of focus.

(5) a 50mm lens focused at 8 feet has a magnification of 0.021x. Put this number in your pocket for part 3.

Now, I know you're saying, that's counter-intuitive. It's only counterintuitive if you are conditioned to think that in all circumstance, wide-angles are more forgiving than telephotos. Wrong. It all depends on whose ox is being gored, or more precisely, which end of the lens you are looking through.

Note: all lenses (wide, normal tele) at infinity have the same depth of focus. It's just that normals and teles increase in depth of focus faster as you get closer. Wideangles are thus very sensitive to mechanical tolerances in the lens. This article assumes that your lens is perfect. After all, from Leica, you should be able to expect as much, right? Get your Passport warranty ready.

2. The 0.05mm solution of the Hexar RF

"Guess I won't be seeing you in Leica heaven." Oh well. People wonder why you can never detect a difference between Leica lenses used on a Hexar RF and those used on a Leica body. I had some discussions with Konica USA about flange-film distance issues. And I think I have finally figured it out. As set forth below, there are mathematical reasons why you would never see any difference between using a Leica lens on a Leica and using a Leica lens used on a Hexar. These are also reasons why you might want your camera zeroed to Hexar RF spec but never changed to "Leica spec."

What's the distance, Kenneth? Lots of people have compared this distance and that distance. Perhaps the most egregious example are statements the register distance of a Leica is 27.80 and that of a Hexar is 28.00mm. Who can tell me what measurement on a Leica body is 27.80mm? None. These are the distances. The pressure plate rail specs are from the manufacturers. The film channel measurements are thanks to Erwin Puts.

Leica M body
Hexar RF body
Distance from front flange to pressure plate rails (manufacturer's specification) (both my Leica and my Konica bodies measured to exactly these figures this month) (a)
27.95mm +/- 0.01mm
28.00mm +/- 0.03mm
Film channel depth (measured) (b)
Distance from front flange to inner film rails (subtracting b from a).

Leica lenses are aligned using a special apparatus to a point 27.80mm from the rear of the lens mount. They are not aligned on actual bodies. The 27.80mm figure is where Leica estimates the film emulsion to be, and it corresponds to no physical measurement on an M body. (Erwin Puts) The key distance for the M body is the pressure plate rails. Body focus is defined by the 27.95mm pressure plate rails.

Konica uses the pressure plate as the reference point for body focus (Konica USA). Although Konica says that the 28.00mm figure is used to collimate the M-Hexanon lenses, I have done computations on depth of focus that demonstrate that this is not the case (more on the M-Hexanon lenses in the upcoming Part II). It looks like these lenses are collimated to a first-surface mirror somewhere closer than 28.00mm. I am attempting to obtain a service manual to discover just how the lenses are aligned. I strongly suspect that there is some kind of fixture for this, too. It is very difficult to get information from Konica USA on testing procedures, and I didn't get as far as the shape of the first-surface mirror on this call. I was just happy to hear that my camera was exactly 28.00mm and how they reached that figure...!

Why 28.00mm and not 27.95mm to the pressure plate? The one part I couldn't figure out is why you might choose 28.00mm over 27.95 for the pressure plate rail distance. You might conclude that it is intentional incompatibility. But then reading about Zeiss experiments in film flatness and buckling, I figured it out. The Hexar RF must be wound before every shot. After 30 seconds the film will begin moving forward (Zeiss says 0.04mm in 30 minutes; some people say the film is much of the way there in as little as 30 seconds).

It is more likely than not that in a Hexar, the film will have been wound well in advance of any given exposure. If you then had to choose between replicating a Leica 27.95mm and some other figure for this application, you would probably want to make sure that after some wait, the film would be in the right place.

Konica has long been aware of this, and the Koni-Omega 6x7 rangefinder cameras were actually calibrated to focus at a point 0.2mm ahead of the pressure plate, due to the behavior of 120 film.

With, say, an M3, you can wind anytime you want before shooting. The M3, with its 0.20mm film channel, is both capable of keeping the film a little more under control and of being wound in such a way to minimize postwinding buckling. The Hexar probably has a larger channel depth due to its motor drive (or 0.24mm may be the JIS or other industry norm - so Cosina/Voigtlander users note).

Mixing it up. The interesting thing is when you start mixing bodies and lenses. When you put a Leica lens (27.80mm) on a Hexar RF body, using 0.2mm film (using the Pan F example -- 0.125mm film base; 0.085 emulsion Erwin Puts provided in one of his newsletters), the point of focus (let’s assume one infinitely thin plane of focus) should be at 27.80mm from the body flange (28.00mm – 0.2mm film). After the film the film is wound, it begins buckling forward, and by half an hour later the plane of focus is now midway through the 0.085mm emulsion.

Note: most 35mm film bases are approximately 0.13mm. The emulsion thickness will depend on the type of film. The example above is Ilford Pan F, a 50 ASA film.

With the Leica, the narrower film channel would smash the film flat against the 27.75mm front rail of the film channel, and with the lens set up for 27.80mm, the plane of focus cuts through a level 0.05mm into the emulsion. If there is buckling on the Leica (I don’t think there could be much), the focused plane may actually cut into the base layer (since it is only 0.03mm from the film base to begin with).

Does it match? Assume we are using a Leica lens on a Hexar RF and that the film has just wound (so the pressure plate is contacting the film, and no frontward buckling has occurred). With a Circle of Confusion (CoC) of 0.01mm (very conservative; in fact this what Mr. Puts says is necessary to realize the benefits of Leica glass), with an f/1.0 lens at infinity (possibly the worst combination possible), you would still have a depth of focus (DoFocus) of 0.02mm. This means that if the Hexar RF body is to perfect spec, and Leica lens is to perfect spec, the zone of focus is centered around the front film surface. If the combined error (body plus lens) is +0.02 or –0.02mm, then there might be a problem. With an f/1.4 lens (like, say, a Summilux), DoFocus is 0.028mm, and with an f/2 lens, the figure jumps to 0.04mm, or almost the entire difference in film plane differences between the Hexar and the Leica M. Also, as you come closer than infinity (i.e., raising the magnification), the DoFocus increases. Here is the table at infinity (the magnification of any lens focused at infinity is effectively zero — remember limits from calculus class?):

f/stop COC Mag DoFocus Near Far
1 0.01 0 0.02 27.79 27.81
1.4 0.01 0 0.028 27.786 27.814
2 0.01 0 0.04 27.78 27.82
2.8 0.01 0 0.056 27.772 27.828
3.5 0.01 0 0.07 27.765 27.835
4 0.01 0 0.08 27.76 27.84
5.6 0.01 0 0.112 27.744 27.856
8 0.01 0 0.16 27.72 27.88
11 0.01 0 0.22 27.69 27.91
16 0.01 0 0.32 27.64 27.96
22 0.01 0 0.44 27.58 28.02

If the film bows out 0.04mm toward the lens with the passage of some time, center of the focused plane will move about halfway into the emulsion, making the chance of a hit at f/1 even greater.

The fallacy with using an f/1 lens at infinity is that most people don't use them at that distance. Worse, f/1 lenses may have resolution such that the limiting factor is not the film-plane focusing accuracy, but he lens performance itself.

Let's go back to the recently-wound film. Now if you take into account a +/- 0.03mm manufacturing tolerance for the pressure plate position (this tolerance may or may not be actually used — like I said, mine was 28.00 on the nose), and you still wanted to maintain a 0.01 CoC, you would need to limit your lenses to f/2.8, where the DoFocus is 0.056mm. This might explain the speed of the 90/2.8 M-Hexanon and the 28/2.8 M-Hexanon: perhaps they are designed to work with bodies that have body focus varying over a 0.06mm range. But I have seen no evidence regarding how much Konica bodies actually vary (as I said before, mine measured exactly to spec).

But if you used the standard 0.03mm CoC for 35mm film, you could use even an f/1.0 lens with no problem, despite actual location of the pressure plate being at 27.97 or 28.03mm. Here is the same table recomputed for a 0.03mm (normal) CoC:

f/stop COC Mag DoFocus Near Far
1 0.03 0 0.06 27.77 27.83
1.4 0.03 0 0.084 27.758 27.842
2 0.03 0 0.12 27.74 27.86
2.8 0.03 0 0.168 27.716 27.884
3.5 0.03 0 0.21 27.695 27.905
4 0.03 0 0.24 27.68 27.92
5.6 0.03 0 0.336 27.632 27.968
8 0.03 0 0.48 27.56 28.04
11 0.03 0 0.66 27.47 28.13
16 0.03 0 0.96 27.32 28.28
22 0.03 0 1.32 27.14 28.46

What does this mean in practical terms? First, and perhaps most important is making sure that for very critical use, your Hexar is exactly to the 28.00mm spec and that your Leica lens is exactly to the 27.80mm spec. For most uses, it will probably not matter much where within their respective production tolerances the Hexar RF body and Leica lens fall.

Second, because the 27.80mm figure is not a measurement found on real Leica bodies, you will not be able to adjust any part of a Hexar body to match it. You may be able to move to pressure plate to 27.95mm, but by doing so you may be moving the focused plane into the film base (bad).

Finally, you should try to avoid having Konica USA adjust your body to any particular Leica lens, because it is not clear what they are using to establish where the lens should be focusing.

3. Keppler's puzzling test

The following letter appears on Andrew Nemeth's website. What does it mean? You make the call.

April 30, 2002

Dear Mr. Kuester:

No doubt you probably decided that you would never hear from us concerning the variation in back focus between the Leica M series cameras, and the Hexar RF.

Recently we finally got down to doing a test using a 50mm f/2 Summicron lens on the Voigtländer M body, the Leica M3 and the Hexar RF at 8 feet and f/2. We also had the back focus measured very carefully by a testing laboratory. We found that the back focus of the Hexar RF was 28.7 mm that of the Leica M 3 27.6 mm, and the Voigtländer 27.01 mm.

In examining the lines per millimetre resolution of the Kodak T-Max 100 film with the lens set precisely at 8 feet, we were able to produce 57 lines per millimetre at the center with the Leica M3, and the Voigtländer camera, but only 22 lines per millimetre with the Hexar. We therefore concluded that the Hexar lenses and cameras are not interchangeable whatsoever with the Leica M3 and the Voigtländer cameras. While it is possible that wide-angle Hexar lenses may indeed be useable, they certainly would not be our first choice, and certainly should be avoided for use on Leica or Voigtländer for normal focal length lenses or longer, and for large apertures. Hope
this is the final word on the situation.

Best wishes,
Herbert Keppler

Laying aside the fact that Americans don't spell the world millimeter as "millimetre," this letter makes absolutely no sense.

First, this purports to be a test of a Leica lens with a Leica, a Cosina and a Konica body. Why does it then conclude that "wide angle Hexar" lenses may be usable? They were not tested. Moreover, as we learned above in part 2, a wide-angle lens is no more likely to focus correctly at infinity than a telephoto of the same aperture.

Second, take a hard look at the "back focus" measurements of the bodies. "Back focus" is an attribute of a lens. The attribute of a camera is "body focus." Now take a look at the figures that someone "measured." The back focus of a Leica lens is 27.80mm (spec). The physical measurements of a Leica body are 27.75mm and 27.95mm (spec). Likewise, the physical measurements of a Hexar should be 27.76 and 28.00mm. So what physical attribute of the body are they possibly measuring to come up with these oddball numbers? Last time I checked, the back of the Leica's shutter curtain was not a proper point of focus.

Third, the letter says that they focused the lens at "exactly 8 feet." How? If they did it on a groundglass, there would be no difference in resolution (if they did it consistently). If they did it using the rangefinder, they are introducing a potential source of error. When a person with less than perfect eyesight looks through a 0.6x rangefinder, things get dicey.

Finally, and most damningly, when you do the calculations for a 50/2 Summicron, you find that Keppler's lab's results are absolutely impossible. Now pull out that magnification number you pocketed in part 1. First, with the lens at f/2, you get this table (with a 0.03mm Coc, and don't forget the correct magnification figure from Section 1):

f/stop COC Mag DoFocus Near Far
2 0.03 0.021 0.12252 27.739 27.861

Now if the lens is focusing at exactly 27.80mm (its spec), on a Leica body with a "back focus" of "27.60mm," and assuming that 27.60mm is the position of the emulsion, the whole plane of focus starts 0.13mm behind the emulsion, or a figure greater than to the entire depth of focus. This would seriously degrade resolution, and you would never see 57lp/mm. But let's give the testing the benefit of the doubt. Now let's put the pressure plate at 27.60mm. That means the emulsion starts (moving toward the front of the body) at 27.47mm from the body flange, again seriously wrong. Now the image the lens is throwing is .26mm behind the emulsion (twice the entire depth of focus), again causing huge degradations.

Do the same thing with the Cosina at "27.1mm." At f/2 and 8 feet, and assuming that 27.1mm is the midpoint of the emulsion, you miss by 5 times the entire depth of focus. Put the pressure plate there, and the emulsion ends up around 26.8mm, again, missing the depth of focus by a figure equal to the depth of focus.

So how are you getting such a any resolution for two bodies, when the body focus is so different (the spread between the two measurements is 0.5mm, or 4x the depth of focus)? You would have to be using a CoC of 0.09mm (three times the norm). With a CoC that big, you can see visible (and big) problems on a 4x6 print, a problem which no Hexar user has thus far reported.

It's not hard to see how a lab could come up with a strange result like this. You are performing the test it in two distinct operations: you are making some kind of body dimensional measurement (inconsistently) and then separately focusing at 8 feet using the camera's rangefinder. So effectively, you destroy the linkage between resolution and body focus by introducing focusing error. This essentially makes the test unreliable as a predictor of compatibility (as if the strange body dimensional measurements and conclusion opposite to the optical norm weren't bad enough).

Only Keppler can tell you how Pop Photo obtained the results it did.

Reality Check: Aric Rothman writes that: "Using a vernier micrometric depth gauge, I measured the Lens Flange to Film (LTF) distances on my Leica M6 (classic) and Hexar RF. In both cases, a section of Fuji Neopan film was placed in position on the film rails and the cameras' backs were closed. Each camera was measured four times, and the results averaged. The depth gauge accuracy was verified using a digital caliper. The LTF of the M6 was 27.98mm. The LTF of the Hexar RF was 27.97mm. What does this mean? I don't know. I do know that I have taken pics using a CV Nokton wide open on my Hexar RF with excellent results. I have also taken pics using M-Hexanon 50mm/2 and 28mm lenses mounted on both my M6 and HRF with excellent results. My test results, admittedly of very small sample size, appear to be at odds with tests showing LTF differences between Leica Ms and Hexar RFs on the order of 1.8mm."

4. The Summilux 75 urban legend

Now let's address one last thing. Every time a Summilux 75 fails to focus at f/1.4 and 0.7m, it is blamed on the camera or the lens (oh, my camera's body focus is not calibrated, oh, my lens is out of adjustment). When a Hexar RF is involved any focus problems are blamed on a "different" body focus. How about facing the truth: that your rangefinder focusing is deficient, your rangefinder is out of alignment, or you can't hold the lens steady?

At that distance and aperture, depth of focus is 0.0948mm, or enough to cover any flange-to-film issue with a Leica or a Hexar, even before the film starts moving. But the depth of field is 5.08mm. Can you hold, focus and shoot a 2.5 pound camera without moving it a quarter inch? It's likely that this is where the human factor starts running the show. Yes, you can blame the lens cam, rangefinder and collimation if it makes you feel better.

So you have it on a tripod? Well then, is your rangefinder perfectly aligned? Even on a good day, a Leica M-type rangefinder becomes more and more inaccurate the closer than a meter you are. Add your eyesight and the parallax error in the rangefinder to the mix, and it still looks like something other than the lens or the body focus. If you really want that short tele Summilux, get the 80/1.4 Summilux-R. At least you can see those focusing errors coming.