Rangefinder focussing accuracy: rule of thumb

[Lindolfi]

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Rangefinder Accuracy of the M8 and M9

 

There are several publications on the accuracy of the Leica M rangefinder camera. For instance in the Leica Compendium by Erwin Puts. Since the M8 and M9 came on the market, there was an increased need for re-adjustment of lenses and camera bodies and it has been indicated that this has to do with the high resolution of the camera's and pixel peeping on a computer screen. And so the question arises if the inherent accuracy of the rangefinder mechanism is sufficient for the lenses offered and how this depends on the (light level dependent) eyesight of the photographer.

 

To answer this question, I have done some experiments, some measurements and some calculations that I would like to share with you, since it offers a simple rule of thumb (see the end of this posting if you want to skip the theory)

 

First of all, it should be indicated that the reasoning of the rangefinder mechanism can be centered around the focal length of 50 mm. The rangefinder mechanism has been constructed around the displacement of a lens with a focal length of 50 mm. The motion of the small wheel in the camera body forward (lens focussed close by) and backward (lens focussed at infinity) is 4.2 mm (D) for a focus distance from 0.7 meter to infinity for a lens of 50 mm focal length.

 

The motion of that small wheel moves the split image inside the rangefinder over a distance that is equivalent to an angle of 5.7 degrees (M). You can establish that by putting a lens on your camera, put a ruler on the wall at an angle of 3 meter for instance and turn the focus ring from 0.7 meter to infinity and measure the displacement of a fixed line on the wall along the ruler seen in the non moving part of the viewfinder and calculate this linear displacement into an angular displacement.

 

Now the accuracy of the human eye is about 1/60 of a degree ( R ), which is an important number in finding the accuracy of aligning the two images in the rangefinder window. A last item we need is the magnification of the rangefinder window, which is 0.68 (V) times in the M8 and M9.

 

That means that the accuracy (A) with which the 50 mm lens can be focussed is

 

A(50) = R/M*D/V=0.018 mm

 

Since the travel of the wheel of the rangefinder mechanism is scaled with focal length by the mechanism in the lens, we can extend this formula with the focal length relative to 50 mm.

 

A = R/M*D/V*F/50=0.00036.F mm

 

So now we know how accurate we can place any lens relative to the focal plane at various focal lengths.

 

The next question is how accurate it is necessary. This depends on the depth of field (range in the object space in which something is considered to be in focus), which is directly related to the depth of focus (range in the image space in which something is considered to be in focus).

 

To establish the depth of field, we need to know the resolution the sensor has and that of the human eye again. The resolution of the human eye, being 1/60 of a degree, is able to use about 350 pixels per inch at reading distance (250 mm), in practical experiments, I found 300 pixels per inch. If you extend the resolution of the M9 sensor, you get a print of 441 mm long at reading distance. From this I calculated the focus depth of several focal lengths and apertures and from the focus depth the tolerance of the position of the lens relative to the focal plane, which is in the last column of the table below (the higher the percentage the larger the tolerance for error during focussing, 100% is on the verge of focussability).

 

focallength aperture distance (m) Focus Depth (mm) Accuracy (mm) Percentage (%)

21 2.8 0.7 0.041 0.008 542

50 0.95 1 0.014 0.018 78

50 1 1 0.015 0.018 83

50 1.4 1 0.021 0.018 117

50 1.4 0.7 0.022 0.018 122

75 1.4 0.7 0.023 0.027 85

90 2 1.0 0.034 0.032 105

135 3.4 1.5 0.053 0.049 109

135 2.8 1.5 0.045 0.049 93

 

From the focussing accuracy percentage, we can see that the following lenses and apertures can not be focussed reliably with the rangefinder mechanism of the M9, using the maximum resolution possible with the M9 (or M8 printed smaller) and the optimum eyesight of 1/60 of a degree.

 

The following focal lengths and apertures are in the "unsafe" zone

 

focallength aperture distance (m) Focus Depth (mm) Accuracy (mm) Percentage (%)

50 0.95 1 0.014 0.018 78

50 1 1 0.015 0.018 83

75 1.4 0.7 0.023 0.027 85

135 2.8 1.5 0.045 0.049 93

 

 

While the following focal lengths and apertures are in the "safe" zone

 

focallength aperture distance (m) Focus Depth (mm) Accuracy (mm) Percentage (%)

21 2.8 0.7 0.041 0.008 542

50 1.4 1 0.021 0.018 117

50 1.4 0.7 0.022 0.018 122

90 2 1.0 0.034 0.032 105

135 3.4 1.5 0.053 0.049 109

 

It should be noted that needed rangefinder accuracy is independent of focus distance (including infinity).

 

It should also be noted that if you allow for only 23% more fuzzy images, all lenses can be focussed reliably. On the other hand, if the resolution of the eye is less during focussing, for instance in dim light, more lenses and aperture combinations come into the "unsafe" zone.

 

From the table you can see that the most difficult lens to focus is the 50/0.95 at f/0.95, followed by the 50/1.0 and the 75/1.4. The 135/3.4 is in the safe zone and this is confirmed by my experiments and experience from others on this forum.

 

Since all lenses are known to surpass the resolution of the M8/M9 sensor at full aperture when focussed correctly, that is no factor of importance.

 

Having done repeated measurements with lenses from the above group, confirmed these theoretical considerations. From it a simple rule of thumb emerges, which can easily be memorized:

 

(focal length)/(aperture)<43

 

puts a focal length-aperture combination in the "safe" zone, using good eyesight and very critical demands on the sharpness of the final image.

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[jaapv]

Leica should read this with their " The Apo-Telyt cannot be focussed reliably on the M8/9" :mad:

[SJP]

Now the accuracy of the human eye is about 1/60 of a degree ( R )

Which may on may not be true but rangefinder focusing is based on contrast "snap" not on angular resolution. So although your calculation may be relevant I am not convinced yet.

 

As an aside, is rangefinder about focus accuracy or about rendering of the image? I think the latter. Again feel free to disagree..

[Lindolfi]

Dear Stephen,

 

Contrast snap and angular resolution are related. My experiments with aligning of a line or focus snap on a strong texture does not show a difference. That may vary between persons, but only creates a different constant in the rule of thumb formula, without changing the comparitive relation between focal lengths and apertures.

 

By doing your own focus experiments you can find your personal constant and see if it differs from the average.

 

Rendering of the image depends on focussing, especially in the contrast of the finer details. See "Principles of Optics" by Born and Wolf, Pergamon Press, 5th edition, page 486, figure 9.13 and 9.14 on defect of focus in optical systems.

[lct]

According to the formula b = e*f2/k*z where b is the RF base length, e the visual acuity (0.0003 at approx. 1 arcmin), f the focal length, k the aperture and z the circle of confusion (0.030mm for FF, 0.0226mm for the M8), the safe zones at full aperture are not the same with M8 or M9 due to different CoC values but roughly 50/0.95 are OK with both cameras contrary to 135/3.4 w/o magnification. FWIW.

[pico]

According to the formula b = e*f2/k*z where b is the RF base length, e the visual acuity (0.0003 at approx. 1 arcmin), f the focal length, k the aperture and z the circle of confusion (0.030mm for FF, 0.0226mm for the M8), the safe zones at full aperture are not the same with M8 or M9 due to different CoC values but roughly 50/0.95 are OK with both cameras contrary to 135/3.4 w/o magnification. FWIW.

 

Very good! Now if only a Leica would correct itself to conform when smacked sideways.

 

Nobody has ever criticized my pictures because they were a wee bit OOF. (Possibly because the images are so ignorable.)

 

.

[Guest #12]

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haven't gone through all of this... looks like instead of the usual, you have moved everything to the image space. In the usual, one uses a not-so-great approximation for depth of field to cancel out the object distance. So there is some room for improvement. Can you tell me what version formula you used for the depth of focus?

 

I tried to show in another thread, using measurements from actual lenses, that the error from the equipment calibration may be more important than the error from uncertainty in vision. But what you have done looks really interesting...

[Guest #12]

...

As an aside, is rangefinder about focus accuracy or about rendering of the image? I think the latter. Again feel free to disagree..

 

rangefinder always has to be about the accuracy...lenses have been recalled, brands ruined for not paying attention

[Guest #12]

...

 

I think you have replaced accurately measuring the baselength with not-so-accurately measuring the ... whatever you call it (But I did get about 6 degrees).

[Lindolfi]

Thanks for the reactions!

 

lct: The formula you use has a square of the focal length in the formula, because it expresses the critical effective baselength. Focus depth is independent of focal length, but it comes back linearly in my rule of thumb because the necessary motion of the lens for focussing scales linearly with focal length.

 

lct: the CoC for the M8 and M9 can be chosen differently. That is a matter of choice. What I did is use the pixel pitch of the camera's and print to the critical size at reading distance. The print of the M8 will be smaller than that of the M9.

 

#12: The calculations are based on these formula's I derived: click.

 

#12: You are absolutely right about that I measured rangefinder baselength this way, but it is accurate enough when compared with 2*atan(69.25/2/700)*180/pi=5.6636 degrees, and I found 5.7 degrees with the measurement.

[adan]

The 135 f/2.8 lenses come with a built-in 1.5x magnifier (effectively changing the eye resolution to 1/90th of a degree, or otherwise changing the geometry and math). Do these calculations account for that difference?

[Lindolfi]

Thanks Andy, important extra factor. No, I did not include that for the 135/2.8. And of course when you add a 1.25x or 1.4x magnifier to the viewfinder, the percentages can be multiplied with that factor. Also the constant 43 should be multiplied by that factor.

 

Here's a little spreadsheet I made: click

based on the formula's published here: click

 

So that you can check everything. A column for viewfinder magnification is included. You can copy rows to create more examples. The red columns are input, the green one output, the other ones in-between results.

 

The CoC is based on the pixel pitch of the M9. You can play with the rangefinder base, aperture etc.

[lct]

The 135 f/2.8 lenses come with a built-in 1.5x magnifier (effectively changing the eye resolution to 1/90th of a degree, or otherwise changing the geometry and math). Do these calculations account for that difference?

The effective baselength (EBL) formula takes magnification into account (69.25 mm mechanical base length * 0.68x VF mag. * 1.5x goggles mag. = 70.64 mm EBL) but i don't know for the OP's formula.

[Guest #12]

...

 

Thank you for the extra details. I can't access the spreadsheet, so can only comment on the first post. I'm wondering now what's gained compared to the usual method? I was expecting a formula analogous to the one LCT gave.

 

You replaced the usual accuracy formula. For me, the motivation for the old formula is easier to give than the motivation for the new formula. And the old formula has a long history, back to the days of bombing ship masts.

 

The rule of thumb is a good idea, but it's only for a particular camera, and we could get one just as easily from LCT's formula.

[Guest #12]

The effective baselength (EBL) formula takes magnification into account (69.25 mm mechanical base length * 0.68x VF mag. * 1.5x goggles mag. = 70.64 mm EBL) but i don't know for the OP's formula.

 

yes he used "V" for the magnification

[bocaburger]

(focal length)/(aperture)<43

 

puts a focal length-aperture combination in the "safe" zone, using good eyesight and very critical demands on the sharpness of the final image.

 

For me a crucial factor is how tired my eyes happen to be at the moment. Sometimes I can see the images snap into contrast, other times not so well. The same street signs from the same distance I see clearly when I drive to the office in the AM, are often blurry when I'm driving home later in the day.

[Lindolfi]

#12, you posted a formula that is based on equating depth of field to rangefinder accuracy

 

http://www.l-camera-forum.com/leica-forum/customer-forum/181452-rangefinder-accuracy.html#post1702554

 

This formula can also be found on page 246 of Erwin Puts Leica Compendium 2nd edition (2011)

 

This formula produces different results from my derivations, because mine are done in image space. When I use your formula (which should be the same as that of lct), I get

 

focal_length aperture critical_effective_baselength

50 1.4 17.85

50 0.95 26.31

75 1.4 40.18

135 3.4 53.60

 

And since the effective rangefinder base is 69.25*0.68=47.09 mm, the 135/3.4 is "unsafe" while the 50/0.95 is "safe". In my derivation in image space, it is the other way around.

 

That is why I posted the results yesterday on top of the need to see what the more critical demands since the digital rangefinder appeared does to the critical boundery with fresh eyes (you are right bocaburger, that is an important issue).

 

Erwin also indicates that more critical values of CoC are required in some instances, and my value based on the sensor of the M9 is in that line (CoC=0.014mm)

 

Now the question is which is the best approximation of the real thing? I can not find any error in my derivation (equating the tolerance of lens movement to that possible with the rangefinder mechanism and a standard visual acuity), nor have I found a derivation of the formula that Erwin, you and lct use.

[thighslapper]

An interesting read.

Well done !

Having a dozen lenses which are almost all less than perfect on my M9 (despite a trip to Solms) I too have been testing, comparing, computing and compiling various tables to see if I am just expecting too much from the equipment itself....

 

When one factors in the tolerances in sensor alignment, rangefinder adjustment and lens calibration it strikes that it is a miracle you can focus accurately at all with any of the more exotic Leica lenses wide open .....

 

One practical point that you have not mentioned is the lens barrel diameter .... I personally find the Noct 0.95 easier and more consistent in focussing than the 50/1.4 as you can make smaller incremental adjustments more accurately with the larger barrelled lens.... but there again I always use a Japan exposures 1.35 mag.... which having variable dioptre adjustment ensures the viewfinder image is perfectly adjusted to your eyes...... and the nature of the reference image used to focus on is also critical ..... a lot of errors with this and similar lenses can be traced back to subjects where there is no sharp or contrasty focus point...

 

This is only scratching the surface of a big complex subject with multiple variables involved..... keep up the good work....

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[lct]

...Erwin also indicates that more critical values of CoC are required in some instances, and my value based on the sensor of the M9 is in that line (CoC=0.014mm)

Now the question is which is the best approximation of the real thing? I can not find any error in my derivation (equating the tolerance of lens movement to that possible with the rangefinder mechanism and a standard visual acuity), nor have I found a derivation of the formula that Erwin, you and lct use.

The best formula is the one which matches best your experience i guess. I'm OK with the classical one personally but if i applied Puts' CoC value to it very few of my lenses could be focused accurately actually. No 90/2.8 on the M9 fo instance...

[Lindolfi]

So let's get through the steps needed.

 

[1] First of all, according to my derivations, depth of focus does not depend on focal length. That is one reason why you can have a depth of focus scale on a view camera that only shows aperture, not focal length. Here my Gandolfi view camera: click

 

[2] The motion of the lens relative to the sensor scales linearly with the focal length at equal motion of the rangefinder cam. (for a 50 mm lens the cam moves the same amount as the lens, for longer lenses it moves more than the cam, for shorter it moves less)

 

[3] The depth of focus scales linearly with aperture number.

 

Checked it all again and found the error!!

 

Assumption [2] is wrong! The lens cell moves with the square of focal length, not linearly at equal movement of the rangefinder cam.

 

So I should use the factor F*F/2500 in stead of F/50 (F is focal length in mm). I've made a new spread sheet, and now the 135/3.4 is more difficult to focus than the 50/0.95.

 

Spreadsheet: click

 

Terribly sorry for the circle of confusion I created. I think we (#12, lct, Erwin and I) agree now.

 

Only problem is that now 50/0.95, 50/1, 75/1.4, 90/2.8, 90/2, 135/3.4 and 135/2.8 all fail to meet the criterium of focussability, and that is because of the more critical CoC used of 0.014.

 

If you relax that again to CoC=0.03 you get that only the 135/3.4 can not be focussed correctly (sorry Jaapv).

 

The order of difficulty of focussing is (with difficulty relative to 50/1.4 in red)

 

focal_length aperture relative_difficulty

135 3.4 2.9

135 2.8 2.4

90 2 2.2

75 1.4 2.2

90 2.8 1.6

50 0.95 1.5

50 1 1.4

50 1.4 1.0

 

To bring it all up to recent standards of the images possible with the M9, the rangefinder base simply (!) has to increase a factor of two in size. For that there is no space. The M house makes it possible to make the base 98 mm long, which should solve part of the deficit. There is a small conflict between the release mechanism under the button and the small range finder window however....