Zeiss formula

The Carl Zeiss 40mm Triotar lens referred to in Jacobson's lens tutorial.^[1] The dots represent DOF limits for f/8 and f/16; the dots indicate that the lens is focused at approximately the hyperfocal distance for f/16, about 13 feet. Jacobson's inferred circle of confusion diameter, using $c = f\,^2 / (N H)$, was about 0.025 mm.

In photographic optics, the Zeiss formula is a supposed formula for computing a circle of confusion (CoC) criterion for depth of field (DoF) calculations. The formula is $c = d/1730$, where $d$ is the diagonal measure of a camera format, film, sensor, or print, and $c$ the maximum acceptable diameter of the circle of confusion.

The Zeiss formula is apocryphal, in the sense that it has grown to be a well-known named concept by propagation through the internet, even though it has no official origin, little connection to Carl Zeiss Company, and no recognition or usage in the photographic industry outside the web community.

The number 1/1730 derives from a circle of confusion diameter of 0.025 mm on a full-frame 35 mm film format, with diagonal size about 43.25 mm (43.25/0.025 is 1730). The CoC size of 0.025 mm for this format appears in Jacobson's Photographic Lenses Tutorial,^[1] and the 1730 in his 1996 Photographic Lenses FAQ.^[2] Jacobson derived the 0.025 mm CoC number from analysis of the Zeiss Triotar lens DoF markings on the Rollei B35 (see photo). The manual for the Rollei B35 also states 0.025 mm CoC for its tabulated DoF distances, though it also includes an example DoF reading that implies a larger CoC.^[3]

By 2001, the term "Zeiss formula" had appeared, in the manual for the on-line DoF calculator f/calc.^[4]

On the other hand, Zeiss gives the values d/1000 as the traditional standard and d/1500 as the modern standard.^[5]

See also

• Circle of confusion
• Depth of field
• Hyperfocal distance

References

1. David Jacobson (1996). "Photographic Lenses Tutorial". rec-photo. Retrieved 2006. Although there is no one diameter that marks the boundary between fuzzy and clear, .03 mm is generally used in 35mm work as the diameter of the acceptable circle of confusion. (I arrived at this by observing the depth of field scales or charts on/with a number of lenses from Nikon, Pentax, Sigma, and Zeiss. All but the Zeiss lens came out around .03mm. The Zeiss lens appeared to be based on .025 mm.)
2. David Jacobson (1997). "Photographic Lenses FAQ". rec-photo. Retrieved 2006. There is no one circle 'small enough' for all circumstances, but rather it depends on how much the image will be enlarged, the quality of the rest of the system, and even the subject. Nevertheless, for 35mm work c=.03mm is generally agreed on as the diameter of the acceptable circle of confusion. Another rule of thumb is c=1/1730 of the diagonal of the frame, which comes to .025mm for 35mm film. (Zeiss and Sinar are known to be consistent with this rule.)
3. "Rollei B35 / C35". On-line camera manual library of Mike Butkus. Rollei-Werke. Retrieved 2006.
4. Warren Young. "Chapter 14. What Is the “Circle of Confusion”?". ƒ/Calc Manual. Retrieved 2006. ƒ/Calc calculates the CoC using the Zeiss formula: d/1730, where d is the diagonal measure of the imaging area, in millimeters.
5. "Depth of Field – An Insider’s Look" (PDF). Camera Lens News #1. Carl Zeiss AG. 1997. Archived from the original (PDF) on March 7, 2012. Retrieved 2013. A certain amount of blur is supposed to be tolerable. According to international standards the degree of blur tolerable is defined as 1/1000 of the camera format diagonal, as the normally satisfactory value. With 35mm format and its 43 mm diagonal only 1/1500 is deemed tolerable, resulting in 43 mm/1500 ≈ 0.030 mm.