RE: [Leica] 75'lux focusing

["Simon Pulman-Jones" <spulmanjones@lbs.ac.uk>]

Here is the text of Erwin's post about rangefinder focusing accuracy, for
those of you who didn't save it at the time.  It seems to cover just about
every conceivable theoretical aspect of Leica M focusing accuracy - apart,
that is, from the effects of manufacturing tolerances and consistency.

Simon.


From:  Erwin Puts
Subject: Rangefinder accuracy revised (long but it is Xmas)

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