Rangefinder Camera Focusing Baseline Length (Effective Base Length / EBL) and Large Aperture Focusing Accuracy Formula

1. The fatal physical problem of rangefinder cameras: the lens aperture and depth of field cannot be directly seen

A single-lens reflex camera (SLR) takes a view directly through the lens, and you can tell how shallow the depth of field is at a glance; while a rangefinder camera measures distance independently through an independent optical window on the top of the fuselage:

1. Geometric triangulation essence of focus accuracy:

• Rangefinder accuracy depends on the width of the base of the "measuring triangle";
• The wider the bottom edge, the greater the parallax angle (Parallax Angle) of light when aiming at the same object, the more obvious the lateral separation displacement of the tiny focus displacement on the macular ghost, and the higher the focus sensitivity;

2. Why do some rangefinder 50mm f/1.4 cameras always lose focus? ：

• Small portable rangefinders (e.g. Olympus 35RC, Minolta Hi-Matic) have ranging windows only 2cm apart;
• When mounting a lens with a very large aperture and an ultra-shallow depth of field, the mechanical and optical measurement resolution of the rangefinder itself is already lower than the allowable circle of confusion error of the physical depth of field of the lens at a large aperture! **
• No matter how sharp the photographer's eye is, the machine itself has physically lost the ability to accurately measure distance.

2. Calculation formula of effective ranging baseline length (EBL - Effective Base Length)

To evaluate whether a rangefinder camera can handle a very large aperture lens, the international optical community has established the only mathematical measurement standard - Effective Baseline Length (EBL):
$$\text{EBL} = \text{PBL (physical baseline length)} \times M \text{ (viewfinder magnification)}$$
Among them:

• PBL (Physical Base Length): the actual physical straight-line distance between the center of the main viewfinder window and the center of the prism of the secondary ranging window (mm mm);
• $M$ (Magnification viewfinder magnification): The ratio of the size of the virtual image in the viewfinder to the size of the real object with the naked eye (such as 0.58x, 0.72x, 0.85x, 0.91x).

Global Classic Rangefinder Camera EBL Performance Ranking:

1. Leica M3 (the king of rangefinder machines):

• PBL = 68.5 mm, viewfinder magnification up to $M = 0.91\text{x}$!
• $\text{EBL} = 68.5 \times 0.91 = \mathbf{62.33 \text{ mm}}$ (The strongest focusing accuracy in history! Designed for 50mm f/1.4 and 90mm f/2 blade focusing).

2. Zeiss Ikon ZM:

• PBL = 75.0 mm (ultra-long physical baseline), $M = 0.74\text{x}$;
• $\text{EBL} = 75.0 \times 0.74 = \mathbf{55.50 \text{ mm}}$.

3. Leica standard Leica M6/MP/M11 (0.72x universal version):

• PBL = 68.5 mm, $M = 0.72\text{x}$;
• $\text{EBL} = 68.5 \times 0.72 = \mathbf{49.32 \text{ mm}}$ (taking into account the golden balance of 28mm wide-angle frame and 50mm focus).

4. Leica wide-angle version Leica M6 0.58x:

• $\text{EBL} = 68.5 \times 0.58 = \mathbf{39.73 \text{ mm}}$ (designed for 21mm/24mm wide-angle, the focus telephoto accuracy is greatly reduced).

5. Voigtlander Bessa R4M (super wide-angle body):

• PBL = 37.0 mm, $M = 0.52\text{x}$;
• $\text{EBL} = 37.0 \times 0.52 = \mathbf{19.24 \text{ mm}}$ (extremely weak accuracy, never usable at a wide aperture of f/1.4!).

3. The theoretical minimum baseline formula and critical red line for lens selection

According to the camera optical physical tolerance formula, a lens with a focal length of $f$, a maximum relative aperture of $A$ (aperture value $N = 1/A$), and an allowable circle of confusion diameter of $c = 0.03\text{mm}$, when shooting at the closest distance of 1 meter, the minimum theoretical limit EBL that the body must have is:
$$\text{EBL}_{\text{Required}} \ge \frac{f^2}{N \times c \times 1000} \times \text{Safety factor}$$
Extreme actual combat matching rules:

• 50mm f/0.95 (Noctilux) / 75mm f/1.25:
• Extremely thin depth of field (just a few millimeters); required EBL baseline is 55mm+!
• Conclusion: Only the Leica M3 (62.3mm) or the M body equipped with a 1.25x/1.4x magnification eyepiece can ensure the close focus rate; when shooting fully open on a 0.58x wide-angle body, the probability of out-of-focus and out-of-focus is as high as 80%!
• 35mm f/1.4 / 50mm f/2.0:
• The required EBL is approximately 25mm ~ 35mm; a regular 0.72x body can be easily controlled with eyes closed.
• 21mm / 28mm wide angle lens:
• The inherent wide-angle depth of field is extremely deep, and there is no risk of out-of-focus even when taking blind shots at hyperfocal distances with the weakest Bessa body or external viewfinder.

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