Circle of confusion for viewing images on a smartphone

Question

I'm shooting images on my DSLR and wondering what the circle of confusion would be if it were to be viewed only on an iPhone.

As I understand it, the CoC formula can be expressed as: (Acuity * Viewing Distance) / (Display Diagonal / Camera Sensor Diagonal)

So for the classic example of an 8x10 print at 10" using a full frame sensor: (0.001 * 254mm) / (322mm / 43.3mm) = 0.034 mm CoC

I found a study that claimed typical phone viewing distance is around 269mm. The diagonal of my iPhone is 126mm when cropped to 3:2. So for a full frame sensor: (0.001 * 269) / (126 / 43.3) = 0.087 mm CoC.

Does that seem right?

Answer 1

Because the viewing size of the image is ~ 1/3 standard, and the viewing distance is ~ standard; the CoC requirement for the recording medium would be ~ 1/3 as demanding (3x larger)... i.e. .09mm instead of .03mm for a FF camera.

So yes, your result makes sense.

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I edited the question to clarify what you were actually asking

Answer 2

The physics that encompasses circle of confusion size is based on the resolving power of the human eye. As you know, objects appear smaller with distance. If a friend holds a coin 1 inch in diameter and walks away, the apparent size of the coin shrinks. At a distance of 3000 diameters away, the coin now appears only as a point of reflected light, not as a disk. Additionally, a wagon wheel 3 feet in diameter becomes a point at 9000 feet (1 ¾ miles). The 3000 X diameter rule-of-thumb is based on human eyes with 20/20 vision in bright sun. Change any of these parameters and the rules change . Because of the contrast of photos and their typical viewing conditions, the industry uses 1000 X the diameter. That works out to 3.4 minutes of arc, equivalent to 1/100 of an inch viewed from 10 inches (0.25mm or 1/50 of an inch viewed from 20 inches (0.5mm viewed from 500mm).

The diagonal measure comes into play, we tend to view photographs from a distance about equal to their diagonal measure. Consider a print 8x10 inch made from 35mm full frame. We must enlarge the 35mm image 8x to obtain this enlargement. The diagonal measure of an 8x10 is 13 inches. We tend to view this size print from about 13 inches. Given these considerations, depth-of-field tables are likely based on a circle size of ½ millimeter. To accomplish, in the camera, the maximum permissible circle size becomes 0.5mm ÷ 8 = 0.1mm.

The answer to your question is – the subpixels (red – green – blue) glowing dots on the phone should be no larger than 0.5mm, however, smaller is better. Viewed from 10 inches they need to be 1/000 of an inch = 0.25mm.

Let me add – a neat way the industry uses for depth-of-field tables is to express the circle of confusion size as a fraction of the focal length. This method roughly takes into account how much magnification will likely be applied to produce the viewed image. Often the circle size chosen is 1/1000 of the focal length. For critical work Leica uses 1/1500 of the focal length and Kodak used 1/1750 from very critical work.

Answer 3

Circle of Confusion is a term that applies only to capturing images through optical lenses. It doesn't apply to displaying images, so the question is a non sequitur.

If you're trying to determine the optimal viewing distance from your phone's display, that depends on your eyes.