The Physical Theory of Hyperfocal Distance and its Application to Photography

The Physical Theory of Hyperfocal Distance and its Application to Photography

Ringo Cheung

Oct, 2009

Introduction

Applying the method of producing a long depth of field has long been the practice of experienced photographers, especially for those who are engaged in scene photography. Ansel Adams, who is widely recognized as the master of large format natural scene photography and dark room expert, established the "Group f/64" [1] with some other experts like Edward Weston in the same field. It is known that with a smaller aperture of lens (i.e. larger f-number), a longer (larger) depth of field can be achieved. While this is a widely accepted general knowledge among the professionals and even serious amateurs, the concept and application of Hyperfocal Distance (HFD), which extends the depth of field to a distance of infinity, was largely ignored by modern photographers. This can be seen from the lack of "depth of field" indicator in some modern lenses manufactured today [2].

In this article, important concepts that lead to HFD such as lens maker formula, circle of confusion (COC) and depth of field (DOF) will be explained. It is then followed by an explanation of how the equation of HFD is derived. Finally, its applications to photography will be explained with examples.


Circle of Confusion (COC) and Depth of Field (DOF)

The concept of COC is highly related to depth of field (DOF). Due to the defects of human eyes, we are not able to distinguish a very small circle from a very small spot [3]. When a cone of light rays passes through a lens, it is not perfectly focused even when imaging a point source, instead, an optical spot is resulted. This is the COC, and is used to determine the DOF, the part of the image that is acceptably sharp. Different lens manufacturers have different values of COC. The widely accepted values of COC for 35mm format is 0.03mm, for APS format is 0.02mm and for Four Thirds System is 0.015mm [4].

Hence, DOF can be viewed as the portion of the scene that is acceptably sharp, or appears to be sharp in the image. In some images such as landscape or scene photography, a large DOF is desirable, or appropriate, to depict the fine details of the scene. As a result, scene photographers usually use a very small aperture to achieve a long DOF.

Largest DOF is achieved when focus is set to the so called HFD. The DOF will extend from half the HFD to infinity (as will be proved below). This is the largest DOF possible for a given f-number.

Hyperfocal Distance (HFD)

The following discussion assumes the use of symmetrical thin lenses. For asymmetrical lenses, a factor called "pupil of magnification" must be taken into consideration [5].

Fig.1

Referring to Fig.1 and making use of similar triangles and the thin lens equation [6]

where as usual, O is the object distance, I is the image distance and f the focal length, the near and far limits of DOF is given by [5]:

and

where

s is the subject distance

f is the focal length of the lens

N is the aperture

c is the COC


The HFD formula is derived as follow. According to the definition of HFD, the far limit of DOF, DF is infinity. Hence the denominator vanishes, giving:

where H is the HFD.

On the other hand, the near limit or DN will be H since we are focusing on the HFD. Setting s to H and solving for DN gives [5]:

Hence the depth of field will extend from half of the HFD to infinity.


Examples of Applications of HFD

Recall the formula for HFD is

For a 35mm format camera with typical COC value of 0.03mm, using an f-number of f16 and a lens of focal length 50mm, the HFD is

H = (50)2/ (16 x 0.03) + 50 = 5258.33mm≒5.26m

Hence for this lens using an aperture of f16 and focusing on a distance of 5.26m, the DOF will extend from approximately 5.26÷2 = 2.63m to infinity.

Fig.2

To set the HFD on the camera, first adjust an f-number that will be used, e.g. f16. Then on the lens DOF indicator, set the focus to infinity (fig. 2) [7]. We can see that the DOF indicator gives us the DOF from approx. 5m to infinity. Then turn the focusing ring on the lens until it focuses on the hyperfocal distance of 5m (fig. 3). Now the DOF will be from 2.5m to infinity, meaning that anything within this range will be sharp. In other words, HFD maximizes usable DOF.
With appropriate use of the HFD theory, snap shot on the street (aka street photography) would become easy. By estimating the hyperfocal distance, everything within the range will be sharp. Photographers need only concentrate on framing and motion of the subjects, instead of worrying about the sharpness [7].



References

[1] Biography of Ansel Adams, The Ansel Adams Gallery - http://www.anseladams.com/content/ansel_info/anseladams_biography2.html
[2] DOF, Hyperfocal distance and Calculator, Guides @ nikonians.org - http://www.nikonians.org/html/resources/guides/dof/hyperfocal4.html
[3] 高品質黑白攝影的技法, 蔣載榮, 雄獅圖書股份有限公司, 1996, p.20
[4] Circle of confusion, Wikipedia - http://en.wikipedia.org/wiki/Circle_of_confusion
[5] Depth of field, Wikipedia - http://en.wikipedia.org/wiki/Depth_of_field
[6] How to derive the thin lens equation, Hirophysics.com - http://hirophysics.com/Anime/thinlenseq.html
[7] Using Hyperfocal Distance in Street Photography, Olympus/Zuiko - http://olympuszuiko.wordpress.com/2007/03/20/using-hyperfocal-distance-in-street-photography/