Hyperfocal distance revisited - using depth of field concepts in photographic composition

Most PSA members are acquainted with the concept of depth of field, i.e., the zone of sharpness extending in front of and behind a point on an object which is exactly focused by the lens. Without question, it is an important consideration in the making of a photograph. Although there are times when a small depth of field is advantageous, this article is concerned with maximizing depth of field as, for example, in landscape photography where it is frequently desired to have both foreground and background in sharp focus. To achieve maximum depth of field, hyperfocal distance focusing is widely recommended. If a lens is focused at its hyperfocal distance, objects from half the hyperfocal distance to infinity will be within the zone of sharpness. In point of fact, focusing on the hyperfocal distance maximizes the depth of field for a given lens at a given aperture. Although this sounds like a good thing, the following analysis suggests that it is anything but. First, however, it is necessary to review a basic principle associated with the depth of field concept.

The Circle of Confusion:

A Depth of Field Principle

Suppose we set up a screen at some distance from a slide projector, making sure that it is exactly perpendicular to the axis of the projector lens. If we focus a point on a slide in projector, it will appear as a point or as close to a point as the resolution of lens, film, and screen will allow. If we now move the screen a small distance farther away, the point appears as a disk of light, and the same holds when we move the screen closer to the projector. These disks of light are known as "circles of confusion" since the larger the disks the more un-sharp the image on the screen will appear to be. If we replace the projector with the camera, the slide with the film, and the screen with the object, the principle remains the same.

The typical human eye cannot distinguish between a disk of light 0.25mm in diameter and a true point. Therefore, if an image is made up of circles of confusion no larger than this value, the image will be satisfactorily sharp. However, since the image on the film must be enlarged, either as a print or as a slide, the circles of confusion must be smaller to maintain the same degree of sharpness, i.e., no larger than 0.25mm divided by M where M is the magnification.

For example, if M is 10 the circle of confusion on the film must be no larger than 0.025mm. This figure is clearly arbitrary since it varies with the particular human eye and with the magnification actually being employed. As a consequence, the "standard" circle of confusion varies with whoever is making the optical calculations. Values used by lens manufacturers when making up depth of field tables are typically in the vicinity of 0.03mm. Nikon's depth of field tables for their 58mm fl.2 Noct-Nikkor lens, for example, utilize a circle of confusion of 0.032mm, while it is 0.031mm for the Nikkor AF 85mm fl.8, and 0.03mm for the Tokina AF 28-70mm f2.8 zoom. (Neither of these firms specified the circle of confusion used; these figures were back-calculated from the depth of field data supplied with these lenses.) Depth of field tables are, like depth of field preview levers and depth of field markings on lenses, fast disappearing ommodities. None of my Sigma lenses, for example, came with depth of field tables.

The circle of confusion, therefore, is a component of the measure of the resolution or sharpness of an image when viewed as a print or a projected slide. At the beginning of this article, depth of field was defined as the zone of sharpness extending in front of and behind a point on an object which is exactly focused by the lens. It can now be defined more exactly as the distance extending in front of and behind the point of focus where a true point is represented by a circle of confusion not exceeding 0.03mm or whatever standard is being employed.

Hyperfocal Distance

If a lens is focused at its hyperfocal distance, a point from half the hyperfocal distance to infinity will be represented by a circle of confusion not exceeding the standard being employed. The hyperfocal distance is dependent upon three things: (1) the focal length of the lens, (2) the aperture set on the lens, and (3) the circle of confusion standard that is used. With regard to focal length, the hyperfocal distance is generally applied only to wide-angle lenses, since the hyperfocal distance of long focal length lenses is usually too great to be of much practical value. The hyperfocal distance of a 24mm lens at f5.6, for example, is (assuming a circle of confusion of 0.03mm) 11.25 feet, where for a 400mm lens it is over 3124 feet or about 6/10ths of a mile. For the latter, the closest "foreground" in focus is 3/10th of a mile away! The hyperfocal distance is inversely proportional to the f-stop, i.e., it increases as the decreases. For example, the hyperfocal distance of a 24mm lens at f4 is 15.75 feet; at f5.6 it is (4/ 5.6)*15.75 or 11.25 feet. Thus maximum benefit when focusing at the hyperfocal distance is achieved with short focal length lenses set at narrow apertures. The hyperfocal distance is also inversely proportional to the assumed circle of confusion, i.e., it increases as the assumed circle of confusion decreases. For example, the hyperfocal distance of a 24mm lens set at f4 with an assumed a circle of confusion of 0.03mm is 15.75 feet; if we assume a circle of confusion of 0.02, the hyperfocal distance is now (0.03/0.02)*15.75 or 23.6 feet.

Focusing: Hyperfocal

Distance Versus Infinity

Precisely what happens when you focus at the hyperfocal distance and at infinity? Let's compare them using a 24mm lens set at f4, and calculating the hyperfocal distance using a circle of confusion of 0.030mm. Figure 1 shows the actual circles of confusion achieved at various distances, and Figure 2 is a detail from the left hand side of Figure 1. Table 1 includes the data upon which Figures 1 and 2 are based, but also supplies similar information for a 24mm lens at apertures f8, fl6, and f22.

[TABULAR DATA OMITTED]

Figure 1 shows that focusing at the hyperfocal distance does indeed come through as advertised since at no time within the range H/2 to infinity (where H is the hyperfocal distance) is the circle of confusion greater than 0.03mm. At H/2 and at infinity it is exactly 0.03mm; at H it is zero. However, over most of the distance the circle of confusion is quite close to 0.03mm. On the other hand, over most of the distance for infinity focusing, the circle of confusion is quite close to zero! In Figure 2 we see that from H/2 to 2H, hyperfocal distance focusing is admittedly superior to infinity focusing. At H/2 the circle of confusion for infinity focusing is 0.06mm or twice 0.03mm; at H it is equal to 0.03mm. At 2H the circle of confusion is 0.015mm or 1/2 0.03mm for both focusing methods. Note the simple relationship here, i.e., that the actual circle of confusion at any multiple of hyperfocal distance at infinity focus is merely the circle of confusion assumed for the calculation of the hyperfocal distance divided by that multiple. For example, at 3H the circle of confusion at infinity focus is 0.03/3 or .010mm. This relationship holds for all lenses at all apertures, and is independent of the assumed circle of confusion used for the calculation of the hyperfocal distance focus curves.

What's A Photographer To Do?

Now that we have the facts, what do we conclude from them? The traditional argument for using the hyperfocal distance goes something like this: "When you focus at infinity, you lose the depth of field that lies beyond infinity. Since there is nothing beyond infinity, why waste your depth of field?". Additionally, the comment is often made that you don't lose anything by using the hyperfocal distance. The truth is that when you focus at the hyperfocal distance you are penalizing, in the sense of tolerating a larger circle of confusion, most of the objects in your viewfinder, i.e., these objects will be close to the level of resolution equal to the circle of confusion assumed for the calculation of the hyperfocal distance. The standard for the circle of confusion is arbitrary, and the figures commonly used were set back in the days when neither films nor lenses were capable of great resolution. Improvements have been made, however, and the old standards don't make much sense now. What you obtain in return for this penalty is a modest addition to your depth of field, i.e., the distance between H/2 and 2H; for a 24mm lens at f22, this is a matter of only 4.29 feet. In my view this is hardly a wise tradeoff. Assuming that your back is not against a canyon wall or on the edge of a precipice, if the 4.29 feet is that important, simply back up!

This analysis suggests that the optimal course of action is to focus at infinity and insure that there is nothing in the field of view nearer than twice the hyperfocal distance. This guarantees a circle of confusion equal to or better than that obtained when focusing on the hyperfocal distance. However, unlike the hyperfocal method where the circle of confusion rapidly approaches the nominal value, the infinity focus circle of confusion rapidly approaches zero. Incidentally, it is as easy to determine twice the hyperfocal distance as it is to determine the hyperfocal distance itself. Lacking hyperfocal tables in the field, photographers have traditionally determined the hyperfocal distance by setting the infinity marking on the depth of field scale alongside the aperture being used. The focus indicator then points to the hyperfocal distance. Just double it and make sure that nothing in the field of view lies within this distance. Note that with infinity focus there is no need to go to the next smallest f-stop as many photographers do when focusing on the hyperfocal distance. Since the circle of confusion is inversely proportional to aperture, this practice only decreases the maximum circle of confusion by a factor of the square root of 2 (i.e., approximately 1.4), the ratio of one f-stop to the next. The infinity focus method recommended above decreases the maximum circle of confusion by a factor of 2. Clearly the advantages of focusing at the hyperfocal distance have long been misrepresented to photographers; it is time to change the traditional "wisdom".

Technical Note: The depth of field formulas used for the calculation of the circles of confusion in Table 1 and Figures 1 and 2 (Reference: Focal Encyclopedia of Photography, Focal Press, 1969) used a pupillary magnification factor of 1.0 and did not include modifications for physical factors that also contribute to loss of sharpness such as diffraction, lens aberrations, diffusion in the film, and diffusion in the print or projected image. Pupillary magnification and physical blur corrections to depth of field calculations generally are significant only at close-up distances, not at the distances with which we are concerned here.

COPYRIGHT 1993 Photographic Society of America, Inc.
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