The Basics of Rangefinder Design
To start off with we will explore the basic rotating mirror design. This type of rangefinder has two pieces, one front surface mirror, or prism, and one beamsplitter ( either a plate or a prism).
They also have two defining values, the base length, and the minimum focusing distance. Depending on the value of these, we can calculate the angle of displacement of the mirror.
Let E be the focusing distance
b the base length
α the focusing angle
θ the angle of displacement
Let’s imagine a rangefinder of base length b = 50mm, with a minimum focusing distance of 1m, the focusing angle will be of α ≈ 2.862 degrees, and θ ≈ 1.431 degrees. It becomes obvious that this design was slowly phased out in camera manufacturing, it requires high tolerances and could quite easily be knocked out of alignment.
There is however two ways to combat the potential inaccuracy of the design, the first is making the base length longer, as that will make θ. The second is the effective base length , this is the value of the base length times the magnification of the eyepiece in front of it. Placing a galilean viewfinder with it’s magnifiying power being m < 1 will reduce the effective base length, putting a galilean telescope (just a viewfinder being looked through the other way) will increase the base length by 1/m times. This what I did in the original Holmium design, adding a 1.5x telescope in front of the beam splitter.
Below you see a chart plotting the effective base length against focal length, the curves show various apertures. For each point where a focal length intersects an aperture curve, the corresponding base length is the smallest for which error is within the DoF and reliable focus can be achieved.
On the chart are some rangefinders, as you can see, a Contax IIa could accurately focus a 80mm f/1 lens if it existed. The 0.72x magnification Leicas are pushing their limit with the 75mm f/1.25 Noctilux, while the M3 wouldn’t have much trouble. The Holmium v2 with it’s effective 31.25mm base length could focus a 50mm f/1 without much of an issue, so its 50mm f/2.8 should be no problem at all.