Re: [Leica] Rangefinder accuracy revised (long but it is Xmas)

["Marshall C. Hunt Jr" <huntmc2@fuse.net>]

Many thanks to our Sinter Klaus for two Christmas gifts. Of course, as I read them, it means that any focusing inaccuracy is our own fault! Does that mean we should practice focusing, and stop practicing typing?

Erwin Puts wrote:

> Dear Luggers,
>
> A long time ago I gave you some figures about the theoretical accuracy of the Leica rangefinder. These figures have become kind of a standard in discussing the limits and possibilities of the leica RF and are based on a formula used in many optical handbooks. Leica recently gave me a more elaborate equation that is tuned to their needs and mechanical capabilities. (you see: the Lug is an important forum).
> Before discussing the items involved I would ask anyone reading this article or putting it in some archive to respect the issue of copyright. It took me many hours to study and re-evaluate these issues and given the considerable research involved, I would like to protect my investment. Recently I received some emails from persons who directed my attention to some interesting lens reports in the lug-archive, obviously unaware that the reports were written by me and not my brother! This is not a joke!! I am willing to share all info I have on Leica with all of you on the Lug, but the least I can ask is to do some proper referencing.
> Now on to more important matters: range finder accuracy.
> Obviously any measuring instrument has some tolerances, mechanical and optical/visual. The RF of the Leica measures the distance of an object by superimposing two images of that object and noting the degree of coincidence of both images. If both images fully align, the distance measured is correct. As our eye is the critical factor here, the limit of accuracy is dictated by the eye's visual resolution. So any equation that tries to compute the RF accuracy has this limit of visual resolution incorporated. The necessary accuracy is also defined by the blur circle that relates to the depth of field. The eye has a maximum limit of resolution of 0,06 mm at a viewing distance of 25cm, translating to 8 linepairs/mm. Mostly we use a more practical limit of 0,1mm, that translates to 5lp/mm. Even this limit is too fine for most uses and so the industry settled to a more convenient 2 lp/mm as the norm for optical formula. These 2 lp/mm translate to a distance between two adjacent objects
> (points or lines) of 0.25mm (1 mm divided by 4). As we are talking here about the print or transparancy , we need to translate this figure to another one on the negative. Assuming an 8 times enlargement factor we divide the .025 mm by 8 and we get at 0,03mm: the famous diameter of the blur circle. The importance of this blur circle is this: as long as a pont on the negative is smaller than 0.03mm AND we limit our enlarg ment to about 8 times , all points will be visually sharp as perceived by the eye. The depth of field distance is based on this assumption.
> We know that in reality we only have an infinitely small sharpness plane that is 'aritificially' extended into three dimensional space by this DOF mechanism, combined with the resolution limit of the eye.
> The rangefinder in theory measures a point in space at only one exact distance, which is not feasable. There ia always a certain latitude in measuring inaccuracy: the focusing error. Slightly before and slightly behind the real distance the insrument will give identical reasons. So as a bottom line for range finder accuracy we must state that the distance of the focusing error is at least equal or less than the DOF distance. That is the most minimum demand.
> As the range finder is based on triangulation, we do not use in our equations lp/mm but the equivalent angular resolution.
> For the limit of 0.06mm the angular resolution is 1 minute of arc. For the mostly used 2 lp/mm the rangular resolution is 3,4 minutes of arc. The former figure relates to optimum viewing conditions and the latter one to normal conditions.
> We are almost there! The triangulation method obviously is more accurate as the base length is larger. Leica has an effective baselength of 49.86mm for the M2/4/5/6 and 58.863 mm for the HM series. Contrary to most authors I must state that the physical base of ALL Leica bodies from M1 over the M3 to the latest M6 is identical (69,25mm). The only difference is the magnification (0,72 or .95 or .92).
> Any equation that computes the RF accuracy will use at least three variables: Effective base-length, visual resolution in angles and blur circle diameter. These are intimately related.
> In my earlier computations I used an angular resoluton of 1.6 minutes of arc, as an average between the minimum and maximum fgures. The also use a somewhat more complicated equation.
> Let me first present the original figures as a reference. The equation tells us the critical aperture, that is needed for any focal lenght so that the rf accuracy and the dof distance are equal as explained above.
>
> Focal lenght Aperture with 0.72 Aperture with 0.85mm
> 21 0.15 0.13
> 24 0.20 0.16
> 28 0.26 0.22
> 35 0.41 0.33
> 50 0.84 0.71
> 75 1.88 1.6
> 90 2.71 2.3
> 135 6.1 5.16
>
> It is clear that up to 50mm the accuracy is well above any critical demand.So for all the rest of this article we limit ourselves to 50mm and above.
> The revised figures using a more narrow angular resolution and the other equation are as follows.
>
> Focal lenght Aperture with 0.72 Aperture with 0.85mm
> 50 0.34 0.30
> 75 0.79 0.67
> 90 1.13 0.96
> 135 2.55 2.16
>
> This table gives the limits of accuracy when all variables are ideal: high contrast image, the eye at its best etc.
> The difference between the two tables then can be interpreted as follows. The newer one gives the ideal and theoretical values, the former table the worst case situation: low light, low contrast object, tired eye etc.
> It does prove that the mechanical/optical design of the Leica RF is up to the most demanding accuracy. If one has problems with accurate rangefinding (and many recent posts do tell us this) it can be related to the worst case situation as defined in the former table.
>
> There is another approach for the determination of RF accuracy.
> The question now is: given a focal length, a maximum aperture and a defined diameter of blur circle what is the value of the effective base length. When using this approach we need to distinguish between the resolution of the eye when point objects are involved and when lines are involved. The eye is much better at determining when a broken straight line is not aligned that at determining the distance between two object points. The former property is called vernier acuity and is enployed in the leica Rf, explaining its uncanny accuracy.
> Doing some more calculations based on equations that are used by Leica we get this table;
>
> Based on point distance discrimination
> Focal length Aperture Effective base lenth needed
> 50 2.0 12.5 mm
> 50 1,4 17.9 mm
> 50 1,0 25.0 mm
> 75 1,4 40.2 mm
> 90 2,0 40.5 mm
> 90 2.8 28.9 mm
> 135 4,0 45.6 mm
> 135 3,4 53.6 mm
> 135 2,8 65,0 mm
>
> The vernier acuity is 6 times more accurate than the point distance discrimination. In theory! But the tables are based on a conservative blur circle of 0.03mm. If we would like to use the optical quality of leica lenses to the most we need a blur circle diameter that is 2 to 3 times smaller. So the figures presented could be halved again to represent theoretical accuracy. Here I am conservative and would use the table above as reference. But be aware that the accuracy now s good enough for the rendition of extremely fine detail at enlargements of 15 times for critical close view inspection.
>
> Yet another way to get a feeling for RF ccuracy is a tabulation of the focusing erro
> at several distances for point and vernier acuity.
>
> Point acuity.
> Distance Magnification 0.72 Magnification 0.85
> 1 meter 6 mm 5 mm
> 2 meter 24 mm 20 mm
> 3 meter 54 mm 46 mm
> 5 meter 150 mm 127 mm
> 10 meter 600 mm 509 mm
> 50 meter 15042 mm 12741 mm
>
> The figures for 10 and 50 meter are NOT a typing error. It tells you that at a distance of 10 meter the focusing error is 60 cm plus and minus. At a 50 meter distance the eroor is an unbelievable 15 meter. This last figure tells you that long distance focusing is a game of chance.
>
> Enter now the vernier acuity in the Leica RF
>
> Vernier acuity.
> Distance Magnification 0.72 Magnification 0.85
> 1 meter 1 mm 0.8 mm
> 2 meter 4 mm 3.4 mm
> 3 meter 9 mm 7.6 mm
> 5 meter 25 mm 21 mm
> 10 meter 100 mm 85 mm
> 50 meter 2507 mm 2124 mm
>
> This table tells you that when circumstances are ideal even the most accurate range finder at 50 meter could be off for 2,5 meter plus or minus. Note also that at a more realistic distance of 10 meter we can expect accurate measuring within 10 cm plus or minus or a range of 20 cm.
>
> I did some practical measurements and at a distance of 3 meter I arrived at an error of 15mm, above the theoretical figure of 9mm, but still very good.
>
> I hope this discussion will be helpfull in assessing the RF problems we all encounter and to take into account the many variables that are needed to analyse the RF accuracy in a scientific matter.
>
> Erwin Puts
>
> This text copyright Erwin Puts, 1998