PHOTOOG Photography writings by Olivier Giroux

2May/113

Floating Elements Are Required

When I tested the Leica 90mm Summarit-M (review) I experienced what I consider to be severe focus issues. The lens back-focused at long distances (10 meters or more) and front-focused at short distances (less than 1.5 meters). This caused me to suspect my rangefinder, which I confirmed had grown a small error, but the lack of a true solution after a round of tweaks forced me to research the subject of focus a bit more.

Now I understand the overarching principles just well enough to convince myself that the behavior I observed in the 90mm Summarit-M is by design.  It's not because it is desirable behavior, but because correcting it is an expensive affair. This is what ultimately is going to prevent me from recommending the 90mm Summarit-M to all but mirrorless camera users.

Note: this article builds upon this Wikipedia article on focal length.
You might want to read it, or go back to it later.

Analysis

On the chart below are several key quantities that vary with the object distance, i.e. the intended placement of the focal plane.  These quantities must follow set relationships in order for the rangefinder system to function.


All the curves go with the left scale, except for the green curve which goes with the right scale.

The blue line on the chart above describes the distance between the lens and the sensor plane (image distance) for a 50mm lens focused on an object at the distance indicated on the bottom (object distance). This implies a change in position of the lens to achieve focus, and it is the same quantity commonly known as the "extension" of the lens. The camera’s rangefinder mechanism is designed specifically to track this displacement with the sensing arm, by following the back end of the lens as it moves relative to the rest of the system (precisely, a 51.5mm lens' motion is the benchmark for Leica M cameras).

The red line describes the same relation of image distance to object distance for a 90mm lens. At first glance this seems to follow the same trend as the 50mm lens but with some acceleration factor linking the two, and the tracking ratio looks like 1.8 = 90mm/50mm. This faster movement would not work with the camera's sensing arm if connected, so a multiplier is implemented in the lens barrel with a second threaded movement to correct for it. In this case the multiplier slows down the motion by a factor of 1.8 times.

Unfortunately the ratio of 1.8 is only valid when the lens is focused at infinity. The green line (on the right scale) shows how the ratio between the image distances for the two lenses actually varies with object distance. A variable ratio cannot be implemented with simple threads - that would require some sort of cam tracing a high order curve, and that would be more difficult and expensive to machine and assemble.  Alternatively the tracking surface on the lens could be machined carefully to draw a high-order curve, and that is presumably similarly expensive.  (Both costs here are presumed because otherwise I assume they would have been done by Leica.)

A third option is to introduce an additional movement to alter the focal length of the lens as the object distance changes - this is the well-known concept behind floating elements. The effect can be very subtle in the image space and still deliver tremendous improvements to the linearity of the tracking ratio. The orange line shows the change in focal length needed to maintain the tracking ratio of 1.8 throughout the focus range. At the closest point of 0.7m the lens would have a focal length of 85mm instead of the nominal 90mm.

Hence by construction a rangefinder system needs floating elements to maintain consistency of focus for lenses that are far enough away from the 51.5mm ideal to show noticeable focus error. If a long lens like the 90mm Summarit-M does not incorporate floating elements then the best one can do is hedge on the error fraction by making a compromise.


Magnitude of error at varying object distances for two different tracking ratios, f=90mm.

The blue line depicts a naïve calibration for a 90mm lens using the tracking ratio for objects at or near infinity, with a worst-case error of 4% at the closest focus distance. The red line instead uses a tracking ratio that is completely correct at 2 meters and has error bounded to within 2% in the demarcated focus range. The red line depicts the precise behaviour I observed from the Summarit at the moment I took it out of the box from LensRentals – i.e. the lens came out of the Leica factory with this error balanced exactly the way that I expect it would be.

Note that while floating elements show a clear path to improvement, a real-world implementation will probably not be perfect.  The floating elements are also likely to be installed on a threaded carriage which would force a linear relationship to the object distance.  I do not know enough about optics to predict whether this would allow correction of more than first-order terms in the error function (and whether that is enough to reach simple mechanical assembly tolerance).  Realistically residual error will always be part of the system, but in a system with floating elements the magnitude of error should be far less.

Raw Data

The table below has the numeric data for both charts in this article.

S1 S2 (f=50) S2 (f=90) Ratio S2 error (R=1.800) S2 error (R=1.838) f (S2=1.8*S2)
1000m 50.003mm 90.008mm 1.800 0.0% 2.1% 89.996mm
100m 50.025mm 90.081mm 1.801 0.0% 2.1% 89.964mm
10m 50.251mm 90.817mm 1.807 -0.4% 1.7% 89.641mm
2m 51.282mm 94.241mm 1.838 -2.1% 0.0% 88.235mm
1m 52.632mm 98.901mm 1.879 -4.2% -2.2% 86.538mm
0.7m 53.846mm 103.279mm 1.918 -6.2% -4.2% 85.135mm

Conclusion (this is not "focus shift")

When you consider that digital sensors require much more precise focusing that film does/did then it’s hard to recommend using any long lens that doesn’t incorporate floating elements with the M9 camera. It’s clear that short lenses also suffer from this issue, but longer lenses with shallow depth of field are simply merciless when it comes to error in focus.

It's very likely that a large fraction of blurry images have been erroneously accounted as coming from photographer error, or rules of thumb like "this lens is soft at close range".

Watch for a push to floating elements in future lenses from Leica. The rumor is that Leica has stopped production of the 90mm APO Summicron ASPH precisely to add floating elements to it, although it’s hard to know if the rumor source was merely speculation based on Leica performing this exact surgery on the 35mm Summilux-M ASPH.  Looking back to the noise surrounding the Summilux update I think people hastily referred to its problems as "focus shift", an entirely different mechanism related to spherical aberration which the Summilux ASPH does not have.

Hope you found this useful,

Olivier


Comments (3) Trackbacks (4)
  1. Kudo’s for you, Oliver! Impressive you have found this and investigated on it.

    A little addition:
    One of the reasons the ZM Sonnar 85/2.0 is so expensive is that it has exactly the kind of rangefinder cam with the special curves you describe. This is so difficult to make and requires such a precision that Cosina obviously is not able to produce it. Therefore this lens is made in Germany (which adds to the production costs).

    I am not able to tell more about the Summilux 90 ASPH except that I have never ever read anywhere about focusing errors as you describe for the Summarit. I therefore would expect (also seeing the high pricepoint) this lens to have this specially shaped rangefindercam too. I will try to confirm this in the next week or so as I find this a very interesting topic.

    Please continue with these kinds of articles!

    Greetings,

    mpve

  2. I found this article very interesting. I think that you might have found a great insight, although, it shouldn’t matter for causing focusing errors. The way the rangefinder system works, there is a ramp that pushes against a wheel in the camera body. The ramp turns as the lens is focused. Leica could machine any profile on the ramp that they like even a non-linear one. So they could tune the ramp profile to make up any of these differences with or without having floating elements.


Leave a comment