Circle of confusion and depth of field – Perceived sharpness extends over more than one plane

You are here: Nature Science Photography – Visual acuity – Image sharpness I

Strictly speaking, a photograph complies with the geometric sharpness criterion according to which a point must be depicted as a point only in one single plane. Nevertheless, most images appear sharp in a larger area than this actual focal plane. Sometimes we even have the impression that the image is sharp „from front to back“. This perception has to do with the resolution tolerance of our visual system, which ensures that a circle of confusion up to a certain diameter still appears to us as a point. For this reason, the range of perceived sharpness extends over a zone that is partly in front of and partially behind the focal point. We call it depth of field (S) and it is a powerful tool in shaping the image. Its size depends directly on the diameter of the circle of confusion. If we set it generously, the depth of field grows; if we start from a low value, it shrinks to a smaller measure. But of course this is not a value we can set arbitrarily. The maximum allowable size of the circle of confusion in the final print depends on the resolving power of the visual system and the viewing distance.

In the previous section („The total resolving power of the visual system“), we determined the resolving power of a human with average visual acuity 20/20 with 1 arcminute. Based on this, we determine that to recognize two points as separate at a viewing distance of 20 cm, they must be at least 0.0582 mm apart. At a viewing distance of 25 cm, this value increases to 0.0727 mm, and at 50 cm it increases to 0.145 mm. The point ceases to be a point and becomes recognizable as a disk only when the circle of confusion exceeds this calculated measure based on visual resolving power. These values apply to the diameter of the circle of confusion in the final print. However, to calculate the depth of field, we require a value for the film plane, which necessitates consideration of the magnification factor. Setting the magnification factor to 8x for the 35 mm format yields a physiologically-based maximum permissible circle of confusion diameter of 0.0073 mm for the negative at a viewing distance of 20 cm.

Calculation 7

However, the photo industry works with a value that deviates from this, which is based on the resolving power of a film from the 1930s and lies in the region of 0.256 mm for the finished print. Assuming 8x magnification, this results in a maximum permissible circle of confusion diameter for the negative of

Calculation 8

The depth-of-field scales of 35 mm lenses, which also assume 8x magnification, are based on values within this range, which is approximately four times larger. For lenses of larger formats, they are modified to the final format of 20×25 cm according to the lower magnification factor to be applied. Table 1 summarizes this.

Format	Standard focal length	Magnification factor to 20×25 cm	Circle of confusion diameter
24 x 36 mm	50 mm	8x	0,032 mm
6 x 6 cm	80 mm	5x	0,055 mm
6 x 7 cm	100 mm	4x	0,064 mm
4 x 5“ (10 x 13 cm)	200 mm	2x	0,128 mm
8 x 10“ (20 x 25 cm)	400 mm	1x	0,25 mm

In addition, the flatness of the film is another factor that is independent of the geometry and influences the diameter of the circle of confusion. Unfortunately, it is also subject to the most imponderables and is the least predictable. From the tests published by Zeiss in (4.) one can take the following hints:

• No film lies really perfectly flat and just.
• In this respect, sheet film behaves more favorably for image sharpness than 35 mm material.
• The film curves by an average of 0.2 mm in 60% of the 35 mm cameras tested.
• The flatness changes with time after the transport process. 35mm film lies more flat after a good 30 minutes, but with medium format the curvature increases with time. It is slight after up to 5 minutes, significant after 15 minutes, and reaches its maximum value after about 2 hours.
• Roll film type 220 offers a flatness better by a factor of 2 than 120 film.
• Zeiss therefore judges for the medium format range as follows: „Use roll film 220 and expose it as fast as you can.“

From this we can learn that film backs that improve flatness by means of vacuum are not mere toys but have a real benefit for image quality. We can calculate the circle of confusion caused by curvature for the focus setting near infinity as follows:

Formula 6
Z_curvature = curvature / f/stop

For the average value of 0.2 mm and aperture 5.6, this results in a circle of confusion of 0.036 mm. This diameter exceeds the pure conservative circle of confusion at the depth of field limit! For this reason, you should always stop down a little more – in the range of one stop – than is actually necessary. Naturally, a lack of flatness in the recording medium does not affect digital cameras. After all, their image sensor is stiff and cannot bulge. This greatly enhances the overall sharpness performance of the shooting system.

The sharp impression itself does not exist!

Now that we have compared the maximum permissible circle of confusion diameter based on a conservative view with its counterpart based on average physiological data, we might assume that the first value and the lens depth-of-field scales based on it basically lead to blurred images. – After all, the first value is roughly three times larger than the second factor. But don’t worry; we already know from practice that this is not the case. The difference between sharp and blurred is more than fluid, and the sharp impression does not exist per se. The physiological value merely represents the limit above which someone with average vision 20/20 can no longer perceive additional geometric sharpness. The conservative value of 0.032 mm, on the other hand, is probably quite close to the lower limit of what is necessary to achieve a sharp impression at all. Between both values lies a „sharpness window“ of practically usable circle of confusion diameters, all of which ensure a visually sharp impression with average vision and without direct comparison with an image based on a smaller circle of confusion diameter. However, a smaller circle of confusion diameter consistently results in a sharper impression within this window!

In practical application, the physiologically based value of 0.0582 mm appears excessively rigid. As we will see in the following sections, this rigidity leads to diffraction limitation starting at medium apertures and a relatively small extension of the depth of field at the optimum aperture. For these reasons, and because it leads to a quite good impression of sharpness, it is more practical to calculate with a value of 0.2 mm for the finished print. At 8x magnification, it leads to a maximum permissible circle of confusion diameter z = 0.025 mm in the negative. We will utilize this as a progressive value in the subsequent steps.

The concept of depth of field explains why some areas of a photograph appear sharp to us and others do not.

Next Geometry and calculation of the depth of field

Main Visual acuity

Previous The focus – true geometric sharpness only exists in one plane

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