Depth of Field -- Part II

Article and Photography by Ron Bigelow

www.ronbigelow.com

Hyperfocal Distance

When it comes to maximizing the DOF, the hyperfocal distance is a very important concept. Simply stated, the hyperfocal distance is the shortest distance from the camera such that everything from approximately half that distance to infinity will appear sharp. Focusing the camera at the hyperfocal distance results in the greatest DOF possible for a given combination of aperture and focal length.

Figure 1 illustrates a more technical view of hyperfocal distance. When the camera is focused at the hyperfocal distance (i.e., at distance = S), Sf becomes infinity, and Sn becomes about half the hyperfocal distance. Thus, the image will appear sharp from about half the hyperfocal distance to infinity.

Figure 1: Hyperfocal Distance
What this means is that anytime a photographer wants a maximum DOF that extends to infinity, she should focus at the hyperfocal distance. That sounds simple enough. However, there is one problem. When a photographer is out in the field, how can she determine the hyperfocal distance, Sn, and Sf?

A Bit of Math

Before deciding how to use the hyperfocal distance, Sn, and Sf in the field, it is good to know how they are determined. Determining these values is rather straight forward through the use of some basic equations as follows:

Hyperfocal Distance = H = (f2/ac)+f

Nearest distance from the lens that will appear sharp = Sn = S(H-f)/(H+S-2f)

Farthest distance from the lens that will appear sharp = Sf = S(H-f)/(H-S)

Where:

f = Focal length of the lens.

S = The distance at which the camera is focused.

a = Aperture.

c = Circle of Confusion.

In the Field

Figure 2: Depth of Field Scales

There are a number of options available to photographers for determining DOF.

DOF Scales: In years past, many lenses came with DOF scales on the lens (see Figure 2). To set the hyperfocal distance, one simply had to align the infinity symbol with the color coded DOF lines. For example, in Figure 2, the infinity symbol is aligned with the red line that corresponds to the f11 aperture. The distance scale shows that the camera is focused at about 25 ft. The red line on the right side of the lens shows that the nearest distance that will appear sharp, Sn, is about 12 ft.

If a photographer chooses to focus at some distance other than the hyperfocal distance, the DOF lines corresponding with the selected aperture will indicate the nearest and farthest distances that will appear sharp.

Unfortunately, most modern lenses no longer have DOF scales. For photographers that do not have DOF scales on their lenses, other methods must be used.

DOF Tables: Another approach is to use DOF tables. Figure 3 shows a DOF table for a full-frame camera with a 50mm lens. As an example, this table shows that the hyperfocal distance for an aperture of f8 is 31.2ft. If a photographer focuses at this distance, the image will appear sharp from somewhere between 15.30ft and 17.53ft (at the closest distance to the camera) all the way to infinity (at the farthest distance). If the photographer switches to f11 and focuses at 9.0ft, the image will appear sharp from 6.47ft to 14.78ft.

The main drawback to DOF tables is that they are specific to a particular CoC and focal length. For instance, the table in Figure 3 is only good for a CoC of .033 (35mm film or a full-frame sensor) and a 50mm lens. The fact that a DOF table works for only one CoC isn't a big issue for many photographers. When out in the field, many photographers tend to use one camera most of the time. If this is the case, the CoC will not change as long as the camera is not changed to one with a different sized sensor. On the other hand, photographers often use multiple lenses in the field. One solution is to print a DOF table for each focal length that will be used. The tables can be laminated and placed in the photographer's camera bag.

Figure 3: DOF Table for a Full-Frame Camera and 50mm Lens

For Other Sensors

For other sensors, the CoC can be determined by the following formula:

CoC = Diagonal of the sensor/1,301mm

Usually, the sensor diagonals have to be calculated from the length and width of the sensors:

Sensor Diagonal = Square Root (L2 + W2)

Where L = Length of the sensor. W = Width of the sensor.

For your convenience, I have created an Excel based DOF Table that you can download by clicking DOF Table. To utilize the DOF table, you will need to enter the CoC of the camera (in mm) and the focal length of the lens (in mm).

As a general rule of thumb, the following CoCs can be used:

CoC, 35mm/full-frame: 0.033mm.

CoC, Sub-full-frame, 1.6 multiplier: 0.021mm.

CoC, Sub-full-frame, 1.5 multiplier: 0.022mm.

CoC, Sub-full-frame, 1.3 multiplier: 0.026mm.

For other sensors, see the box to the right.

Calculators: Programmable calculators and PDA type devices provide another easy method of determining DOF. I prefer to carry a small programmable calculator in my backpack. The formulas for the hyperfocal distance, Sn, and Sf have been programmed into the calculator. To determine the hyperfocal distance, all I Have to do is enter the CoC of the camera and the focal length of the lens. The hyperfocal distance and Sn will be calculated. If I intend to focus at a distance other than the hyperfocal distance, I must also enter the focus distance; then, the calculator will determine Sf, and Sn.

Being on the Safe Side

It must be remembered that these DOF tools assume that a photographer is going to produce a print of a specific size (usually 8" x 10"). Most of us end up printing larger than this at some point. Therefore, many photographers determine the aperture that the DOF tool indicates will produce the desired DOF. Then, they stop down the lens one stop to add a bit of a safety margin.

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Depth of Field -- Part I