The New Leica Manual , Morgan & Lester, 1951, states that the average eye, at a viewing distance of 10 inches, can distinguish individual lines when they are no less than about 1/100 inch apart. Thus, in the final print viewed from a distance of 10 inches, "any detail 1/100 inch in size or smaller will be acceptably sharp." This observation forms the basis for the calculation of most depth of field tables.

BUT! A lens focuses at precisely ONE distance. Everything on either side of that distance is out of focus, PERIOD!

• Points more distant than the plane of focus are resolved as points in front of the film, becoming fuzzy circles by the time they reach the film.
• Points closer to the camera would be resolved as points behind the film, so they are also fuzzy circles when they reach the film.

These fuzzy circles are called CIRCLES OF CONFUSION. Unless various degrees of sharpness are used intentionally as part of the image, it is the task of the photographer to make the print appear as if the lens is focused over a wide range from near to far, to make the circles of confusion as small as possible. This "depth of field" can to some degree be controlled.

If the size of the opening is reduced, narrowing the light passage, the size of the CIRCLES OF CONFUSION are reduced on the negative. Thus, "stopping down" or making the aperture smaller gives smaller circles of confusion and extends the range of apparent sharpness. Enlarging the negative enlarges the circles of confusion, hence even smaller apertures are required as the enlargement factor increases. Remember we are striving for 1/100th inch on the print!

BUT - reducing the aperture makes things worse because light has a nasty habit of "bending" around sharp edges at different rates depending on color, and the iris is a circular sharp edge (see Diffraction Limit of Sharpness below).

Factors affecting the depth of field are -

1. focal length of the lens
2. f/stop (aperture) selected
3. size of the acceptable circle of confusion, largely determined by the anticipated viewing distance
4. print enlargement factor
5. the distance focused upon

REMEMBER - ALL calculations shown below MUST be made using the same units, either millimeters OR inches, not both. AND the result will be in the units chosen.

HYPERFOCAL DISTANCE is the distance focused upon which produces the greatest depth of field. It is the nearest point which, when focused upon, will preserve the required circle of confusion at infinity. The near point of acceptable sharpness will be halfway between the hyperfocal distance and the camera. So, if the hyperfocal distance is 40 feet, a range between 20 feet and infinity will be acceptably sharp - FOR THE SELECTED PRINT ENLARGEMENT FACTOR!

If the camera is focused at a point closer to the camera than the hyperfocal distance, infinity will no longer be "in focus" and there will be a FAR point as well as a NEAR point at which the circle of confusion exceeds the desired size. As the point of focus approaches the camera, the distance between the NEAR and FAR limit of sharpness narrows and we say the "depth of field" is reduced.

Since larger format cameras require longer lenses for a "normal" view, smaller apertures are required to achieve a given depth of field. The following table provides a glimpse of the relationship between the focal length, aperture, and print size, using the focal length of a "normal" lens for each of five formats. The f/stop settings shown produce equivalent depths of field. Thus, f/64 with a 324mm lens, and f/3.5 with a Minox, yield the same depth of field! "Group f/64" derived it's name from the need for a very small apertures to achieve sharp images with 8 x 10 cameras. Perhaps we should have a "Group f/3.5".

Note that doubling the linear dimensions of the print also doubles the hyperfocal distance and the point of nearest sharpness. If the camera is focused at infinity, the depth of field would extend only from the hyperfocal distance to infinity - only half as far! To achieve the maximum depth of field, you should, whenever possible, focus on the hyperfocal distance.

Depth of field scales engraved on lenses assume some chosen enlargement factor. For example an 8 x 10 inch print viewed from 10 inches for 35 mm cameras, and 4x5 inch prints for a Minox. It is assumed that larger prints will be viewed from greater distances.

The following tables can be used to assess the depth of field for critical work in which the potential print size is to be greater than the nominal 4 x 5 range for which the depth of field scale on the Minox is calibrated. They are also theoretical in that they ignore the effects of diffraction.

The Minox EC shares the 15 mm lens with its siblings. The lens is stopped down to f/5.6 to increase the depth of field. Focus adjustment is not available. With these design characteristics, the hyperfocal distance, for a 4" x 5" print, is 1.989 meters (6.53 feet). If the lens is permanently focused at 2 meters, the EC table shows the depth of field (range of acceptable sharpness) for the various print sizes.

A conflicting optical phenomenon is the tendency of light to diffract. (change in direction and intensity of a group of waves after passing by an obstacle or through an aperture) . This phenomenon can be witnessed in a stream where ripples deform as they bend around a protruding rock.

The amount of diffraction is dependent on the wavelength, thus varies over the visible spectrum from blue (400 nanometers) to red (700 nanometers). Smaller apertures, and higher frequencies (toward red) increase diffraction and actually decrease resolution and limit the degree of enlargement.

A point of light, composed of various wave-lengths, and greatly magnified, will appear as a circle (Airy disc). Discussions of sharpness or definition generally accept that a circle of 1/200 inch is perceived as "sharp' when viewed from "reading distance".

Leica Manual gives the resolution of a lens as: "...the spacing between two points just resolved is equal to the wavelength of the light used for the measurement, multiplied by the focal length of the lens divided by the diameter." Since the "focal length divided by the diameter" is equal to the f-stop (f-number) tested, the equation is reduced to wavelength * f-number. So, for f/16 and blue light 400 nanometers (blue light) = (400 / 1000000) 0.0004 millimeters, and 0.0004 * 16 (the f/stop) = 0.0064 ( the spacing between two points just resolved), which is (1 / 0.0064) 156.25 lines per millimeter The table at the right shows the resolving power of a lens and the largest enlargement possible at specified f/stops, for both BLUE (400 nanometers) and RED light (700 nanometers), while retaining 100 lines/inch on the print. It is clear that diffraction is NOT the limiting factor to the enlargement of negatives from either the traditional Minox (f/3.5) or the EC (f/5.6).

Note: The table is based on a theoretical calculation of the resolving power of a lens at a specified aperture AND wave length. This is similar to evaluating resolution at maximum contrast, which rarely, if ever, occurs. The values in the table should be at least halved for practical work, and indeed I have seen data to that effect.

Lesson:
Use apertures small enough for the required depth of field, but no smaller!

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