What Is Sharpness?

Here’s a diptych of  two faces. It's called “Angry Man/Neutral Woman,” and was created and copyrighted by Aude Oliva of M.I.T and Philippe G. Schyns of the University of Glasgow, in 1997. It is used here with permission.

If you have relatively normal vision (corrected is okay), and are viewing this on a typical computer monitor screen or a printout, you should see an angry-looking man on the left and a calm or neutral-looking woman on the right. If you back away from your computer screen or printout, however, at a certain point you should see the faces switch places. The angry man will be on the right and the neutral woman on the left.

There’s more to this phenomenon than mere optical illusion. It has to do with the way contrast affects sharpness and the manner in which the human eye and brain perceive the world around us. There's a lesson here in how to evaluate cameras, lenses and other equipment.

Manufacturers of such gear often provide some sort of specification qualifying image resolution. It might be the number of megapixels (millions of picture elements), a count of lines (e.g., 1080), dots per inch or line-pairs per millimeter. These are all useful measures of resolution. Unfortunately (or fortunately, depending on your point of view), we’re humans, and humans tend to perceive sharpness rather than resolution.

They are most definitely not the same thing. There are some disagreements on exactly what constitutes sharpness, but the most common answer is that it is proportional to the square of the area under a curve that plots contrast ratio against resolution; the second most common is that it is proportional to the area, not its square. Either way, contrast plays a major role.

Here’s another image. This one is called a contrast-sensitivity grating. Fineness of resolution increases from left to right. Contrast ratio increases from bottom to top.

Contrast Sensitivity
If you have relatively normal vision, you can probably see some sort of bowl-like curve along the bottom of the grating. There is, however, no curve there. It’s being perceived by your visual system. As you move back and forth from your screen or printout, you’ll probably see the curve shift, especially on the right.
It’s that curve shift that’s causing the faces to change. Each face is a composite of two images. The version with the angry man on the left and the neutral woman on the right has maximum contrast at a higher visual resolution than the other. How high? You might be surprised.
On the 20/20 line of an eye chart, each part of the letter E covers one arcminute of retinal resolution. An arcminute is one-sixtieth of a degree. The top horizontal black bar of the 20/20-line E, when viewed at the appropriate distance, covers 1/60th of a degree of the vertical angle of the image on the viewer’s retina. So does the white space beneath it. A black bar and a white bar can be considered two halves of a cycle covering 1/30th of a degree. Put another way, 20/20 vision represents 30 cycles per degree (cpd).
In the composite image, the higher-resolution version is most prominent when it is viewed at about 6 cpd or higher. The lower-resolution version is most prominent when it is viewed at 2 cpd or lower. So the transition occurs at roughly 4 cpd – between 1/7 and 1/8 of the resolution visible with 20/20 vision, clearly showing the importance of contrast in vision.
Contrast is affected by many factors, including aperture, lens quality and image-sensor size. The greater the contrast ratio available at any resolution, the greater the sharpness will be. By extrapolation and all else being equal (which it never is), you could say that when you're searching for a lens and camera system, look for a system that gives you as much contrast and range of tonality as you can find. The resulting images will most likely look sharper.

Manufacturers once routinely offered modulation-transfer function (MTF) graphs (how much contrast gets through a product at different resolutions) with their products. Today, it's a lot harder to find out about MTF, but it's worth trying. Remember: resolution numbers don't tell the whole story of sharpness, and the way in which specs are reported are subjective, at best.

(Editor's note: If you have any questions or comments for Mark Schubin about the relationship between sharpness and contrast, arcminutes, retinal resolution or cycles per degree, please use the Comments section below so we may hear from you.)