rangefinder accuracy

[ho_co]

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Q: How do rangefinder accuracy, focal length and aperture interrelate?

 

Here is a chart from LFI, dating to before the introduction of the digital M cameras; I don't have the issue or page number immediately at hand. Rotate the PDF in your viewer to avoid stiff neck.

 

The title of the vertical axis is clipped; it should be Suchervergrößerung (viewfinder magnification). Dashed lines represent (from the bottom) the 0.58x, 0.72x and 0.85x finder magnifications of the M6. The M8 and M9 both have a finder magnification of 0.68x.

 

The horizontal axis Brennweite f (focal length) presents a range of focal lengths from 0 to 150 mm.

 

Listed in the upper right corner are the standard assumptions for the M camera:

Angular resolution 1 arc min

Circle of confusion 0.030 mm

Physical base length 69.25 mm

 

Curves are plotted for full aperture values from f/1.0 through f/5.6.

 

The part of the curve lying below a given intersection of aperture and focal length indicates that a lens of that aperture and focal length is within the tolerances of the rangefinder.

 

The part of the curve lying above a given intersection of aperture and focal length indicates that a lens of that aperture and focal length is beyond the ability of the rangefinder mechanism to focus accurately.

 

Remember to consider any external magnification, either from "goggles" on the 135 Elmarit or from the addition of a viewfinder magnifier.

 

The table is calculated on the traditional rangefinder computational values, which with digital sensors, high-resolution lenses and the modern tendency toward great enlargements, are out of date.

 

Nonetheless, the graph clearly why Leica recommends that 135mm lenses other than the Elmarit should be stopped down from full aperture or used with an external magnifier for best results.

 

An improved version of this explanation and chart (along with the formulas involved) might be considered for inclusion in the Leica FAQ list.

 

The chart is here: rfdr accuracy.pdf

 

 

Although the chart is copied from LFI, the formulas on which it is based are in the public domain and I think publishing it is legal under "fair use" rules if nothing else. Moderators, please delete the thread if it is inappropriate or illegal.

 

And someone would do me a great favor if he would publish an Excel worksheet that would duplicate this chart, since I've got no idea how to do it.

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[ho_co]

Here's a lower-resolution version of what's linked above as PDF:

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[Guest #12]

...

And someone would do me a great favor if he would publish an Excel worksheet that would duplicate this chart, since I've got no idea how to do it.

 

Good graph and great explanation. This is the same as a plot of effective base length vs. focal length.

 

Apparently they used a different value for angular resolution/circle of confusion than stated. Here is the graph with a dotted line for 0.68 magnification.

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[ho_co]

... Apparently they used a different value for angular resolution/circle of confusion than stated....

That's interesting. I've noticed that occasionally what is said in the text is different from what the graphic shows, but didn't know that was the case here.

 

 

... This is the same as a plot of effective base length vs. focal length....

Could you post a link to that formula? I think you mentioned it before.

[Guest #12]

That's interesting. I've noticed that occasionally what is said in the text is different from what the graphic shows, but didn't know that was the case here.

 

 

 

Could you post a link to that formula? I think you mentioned it before.

 

I don't have a link, but the derivation goes like this: Equate the expression for rangefinder accuracy to the expression for depth of field, and solve for the magnification. You should get

 

m = a f^2 / (b n c)

 

where m is magnification, "a" is angular resolution, f is focal length, b is baselength, n is aperture, and c is circle of confusion. Anyway, that is something you can put in your spreadsheet, and it's a standard formula.

 

What you put for angular resolution and circle of confusion is really a wild guess; I used something like 6 minutes of arc to make my graph match Leica's. Of course, none of this makes any accounting of the calibration or miscalibration of the equipment.

[ho_co]

... Equate the expression for rangefinder accuracy to the expression for depth of field...

 

Could you post a link to "the expression for rangefinder accuracy" and "the expression for depth of field"?

 

Sorry to be obtuse, just trying to make sense of generating the chart.

 

Thanks!

 

 

 

 

Edit: Thanks, Jaap, for saying you're as buffaloed as I.

[jaapv]

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I don't have a link, but the derivation goes like this: Equate the expression for rangefinder accuracy to the expression for depth of field, and solve for the magnification. You should get

 

m = a f^2 / (b n c)

 

where m is magnification, "a" is angular resolution, f is focal length, b is baselength, n is aperture, and c is circle of confusion. Anyway, that is something you can put in your spreadsheet, and it's a standard formula.

 

What you put for angular resolution and circle of confusion is really a wild guess; I used something like 6 minutes of arc to make my graph match Leica's. Of course, none of this makes any accounting of the calibration or miscalibration of the equipment.

Sorry, you've lost me completely here.

[Guest #12]

maybe this will help--rearrange the formula so it looks like

 

m b = a f^2 / (n c),

 

and that's what would appear in a textbook. The m X b is effective baselength, so you have the effective baselength as a function of the focal length. I would guess the graph is in Osterloh, although I have only glanced at that book. The usual formula for rangefinder accuracy is E = a u^2 / (mb), where u is the distance.

[Guest #12]

Again, I think what's eventually needed is to work out the effect of miscalibration on accuracy, which is probably more important than these other variables. gandolfi did a little of this in an older thread, but I haven't run across anything else.

[ho_co]

Can somebody help?

 

I keep getting ungrounded statements. Does anyone have an idea how the LFI chart was produced?

 

Thanks.

[Guest #12]

...

I keep getting ungrounded statements. Does anyone have an idea how the LFI chart was produced?

 

Thanks.

 

You did not get any ungrounded statements; I gave you the formula the graph is based on, sketched the derivation, and reproduced the graph--you're welcome.

 

Did you check Osterloh? Jaap has the book if you don't. The same information is often given in tabular form; LCT has posted it here for many years and may have a spreadsheet version for all I know, if that's what you want.

[jaapv]

The problem is that these graphs and formulas give a false sense of preciseness. The ability to focus accurately is dependent on many more factors that are disregarded. The subject: amount of light? contrast? low or high frequency? discrete structures? The eye: how high does the individual resolve? vernier vision is usually disregarded (not by Osterloh) And the skill of the photographer. The total upshot is that most experienced RF photographers will be able to focus the Apo Telyt correctly wide open in the vast majority of circumstances that the lens will be used without magnifier. And that is the most accuate statement one can make.

[farnz]

The problem is that these graphs and formulas give a false sense of preciseness. The ability to focus accurately is dependent on many more factors that are disregarded. The subject: amount of light? contrast? low or high frequency? discrete structures? The eye: how high does the individual resolve? vernier vision is usually disregarded (not by Osterloh) And the skill of the photographer. The total upshot is that most experienced RF photographers will be able to focus the Apo Telyt correctly wide open in the vast majority of circumstances that the lens will be used without magnifier. And that is the most accuate statement one can make.

Fair comment, Jaap, but this is about the limits of accuracy of the machine (in this instance the Leica M) so the other variables you mention (light, contrast, ocular resolution etc) need to be excluded at this stage in order to understand the limits of the machine itself.

 

Once the limits of the machine's precision (or asymptotes) are established then the additional variables can be introduced to describe/calculate the ergonomic performance, which will indicate expected tolerances during use.

 

Pete.

[pop]

... The eye: how high does the individual resolve?....

 

Wouldn't that be covered by the variable called "angular resolution"? Is one minute of an arc a reasonable value?

[Guest #12]

...

 

The chart was never about precision--it shows the effect of aperture, focal length, and a magnifier, everything else being equal. It is about the trends, not the actual numbers. There is actually a lot of useful information in the chart.

 

Here is a link for Howard (same formula, different symbols):

 

Epson R-D1: Rangefinder accuracy

 

So is this in Osterloh, or no?

[Xmas]

Hi

 

The title says 'range finder accuracy' it does not say 'system accuracy'

 

e.g.

 

A M8 or M9 with a flat but micro lens surface and a film bowed (varable) and thickness (also variable) will introduce different tolerance band to the system accuracy, as the poor blighters who have upgraded a film M to a digital M may have discovered.

 

etc.

 

I'd suggest sticking at title, cause some of the system things vary in different ways from the rangefinder accuracy.

 

Being snide my mate asked me to look through his Bessa (film) and tell him what was wrong with the rangefinder, nothing I said that is a known feature, he sold it within a week...

 

Noel

[archi4]

Erwin Puts has an article in his book on this subject, as well as in his site.

rangefinder issues

Jaap puts the whole subject into perspective, reality versus the circle of confusion that is theoretically achievable.

 

maurice

[Guest #12]

...Is one minute of an arc a reasonable value?

 

...my mistake, the LFI graph does use 1 min. of arc.

 

I think that's reasonable...some values I've seen are 1.5 for well-lighted line pairs, or 3.4 for average viewing conditions.

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[Guest #12]

Erwin Puts has an article in his book on this subject, as well as in his site.

rangefinder issues

...

 

Thanks for the reference. I found this one amusing because he doesn't even give the equation, much less the source.

 

"I now use a somewhat more complicated equation to reflect the realistic figures."

 

and farther down,

 

"Doing some more calculations, based on equations that are used by Leica ..."

 

If you check his four tables using the formulae above you will find a slight discrepancy...due I think to an approximation that Leica did not make. There are also some typos. It is always interesting which details Leica sweats, and which they don't.

[ho_co]

Erwin Puts has an article in his book on this subject, as well as in his site.

rangefinder issues...

Maurice, see also the next-to-last paragraph of Blog, where he seems to start out dismissive of the LFI article he mentions, but then seems to me to return to the same thing the above chart and its explanation say.