fPerusing many posts on depth-of-field, I observe facts, data and lore, I now add my 2¢.
A wearisome dialogue on Depth-of-Field:
Before the camera was the camera obsura, in use long before the Common Era. In other words a pinhole can server as a lens. Such a lash-up yields a dim minimal image. However, the pinhole camera is remarkable in the fact that it produces an image that displays infinite depth-of-field. You might not be content with the acuity of this image so you can interchange the pinhole with a lens. The lens gains you image brilliance, and increase sharpness. The downside, now you must address depth-of-field.
So let me start by defining depth-of-field. In geometric optics, a lens is only able to deliver a sharp image for a specified subject distance. However, by observation we pronounce objects before and behind the distance focused upon, to appear sharp. We call this the span depth-of-field. Furthermore, we can, by choice of lens focal length, subject distance, aperture setting, degree of enlargement, viewing distance, and viewing illumination, shrink or swell this span. How do all these factors intertwine?
Fist, the lens images by handing each minuscule point that constitutes the vista individually. Each googolplex of points is projected by the lens onto the surface of film or digital sensor. Each individual point is thus replicated as a circle of light. The size and intensity and color of this circle is a variable. The image is thus comprised of countless illuminated circles. These circles are the smallest fraction of an optical image that conveys intelligence. This circle is juxtaposed with the other circles. Each has a indistinct center with scalloped boundaries. We call this circle the “circle of confusion”. The key point, all optical images consist of countless ill-defined circles. It is the size of these circles that governs depth-of-field.
Now a person with good eyesight can observe a nearby coin as a disk. Suppose a friend recedes with this coin. At what distance will you fail to observe it as a disk? In a sunlit setting, when the coin’s distance is about 3000 diameter away, the average person will observe a point of light, and not a disk of light. Suppose it’s a 3 feet wheel. At 3 x 3000 = 9,000 feet (1.7 miles) the wheel is seen as a point, not a disk. The resolving power of the human will be reduced if the illumination is lower. The 1/3000 standard is too stringent for pictorial photography. The is because we typically view images in subdued light and because the contrast of pictorial images is greatly abridged. For this reason the photo industry has generally adopted 3.4 minutes of arc which works out to a circle of confusion diameter viewed from 1000 times its diameter. Typically 0.5mm viewed from 500mm (20 inches) typical reading distance. If the image being viewed is 1 meter distance (1 yard), the allowable circle size is now 1mm. If it’s a billboard viewed from 100 feet, the circle size can now be 30mm (1.1 inch) in diameter.
How does all this square with the camera and the displayed image? Suppose we mount a 50mm lens on a 35mm full frame. The format size is 24mm height by 36mm length. Our desire is to make an 8X10 inch print for display. Now the 35mm format is tiny and thus we must enlarge the camera image to make an 8x10. The degree of enlargement is 8.5X. If the print is to be viewed from standard reading distance the maximum circle size is 0.5mm. To tolerate the 8.5X enlargement, the circle size at the focal plane of the camera must be 0.05 ÷ 8.5 = 0.0059mm. We have thus discovered the required circle size for this set-up at the focal plane of the camera.
All this rather complicated. Typically, for depth-of-field calculations I adopt a circle size of 1/1000 of the focal length. Thus for a 50mm lens, the circle size allotted is 50 ÷ 1000 = 0.05mm.
This method is convenient plus it allows for typical enlargement based on a “normal” focal length which is the corner to corner measure of the format. To see how this works, consider a compact digital APS-C format size 16mm height 24mm length. Diagonal measure =30mm. Thus the industry assigns 1/1000 of 30mm = 0.03mm as the circle size in camera. To make an 8x10 from this format the degree of enlargement is 12.7. The circle size on the 8x10 will be 12.7 X 0.03 = 0.38mm (within tolerance of 0.5mm.
Let me add that the 1/1000 of the focal length rule-of-thumb is not engraved in stone. Kodak often set this value at 1/1750 and Leica uses 1/1500 for critical work.
How do we calculate depth-of-field?
Hyperlocal distance: Let’s use 1/1000 of the focal length to obtain the hyperlocal distance. We mount a 200mm, 1/1000 of this focal length conveys a circle size of 200 ÷ 1000 = 0.2mm. This day we set the aperture at f/11. We find the working diameter to the 200mm lens set to f/11 = 200 ÷11 = 18.2mm. Now we multiply this value by 1000 = 18.2mm X 1000 = 18,200mm. This value is the hyperlocal distance in millimeters. This value is 18.2 meters or 57.7 feet.
Near point in focus:
P = point focused upon = 10 feet = 3,048mm
NP = near point sharply defined = unknown
FP = far point sharply defined = unknown
D = diameter of circle of confusion = 0.2mm
f-number = 11
F = focal length =200
NP = P/1+PDf/F^2
NP= 2610mm = 2.610 meters = 8 feet 7 inches
FP = P/1-PDf/F^2
FP = 3661mm = 3.661 meters = 12 feet 1 inch
