Cycles Per Degree?
February 26, 2010
In reading about visual acuity recently, I noticed that different sources state different figures as the limit of detail that our eyes can resolve.
We’re talking here about the finest line spacings we can see in the center of our vision—the retina’s “fovea”—where our cone cells are most tightly packed. That’s reasonable, since our eyes are constantly scanning across anything we see, noticing significant details, to build up a complete impression.
The acuity unit often mentioned is “cycles per degree.” Each “cycle” is the same as a “line pair”—namely, one black/white pair taken together. You may find human acuity limits quoted as anywhere from 40 to 50 cycles per degree. (But 20/20 vision only corresponds to 30 cycles per degree.)
One reason for this uncertainty is simply that the human contrast sensitivity function means that finer spacings are perceived with much lower clarity. So the limit is not black and white; rather it is literally “in a gray area.”
But if you’re curious, it’s pretty simple to test yourself.
All you really need is a nice long tape measure (50 feet is probably enough).
Draw two heavy lines with a Sharpie, with a gap between them the same width as the lines. Tack the paper to a wall, and hook your tape measure onto a convenient nearby door frame, etc.
Then start walking backwards. At some point you’ll find it becomes very difficult—then impossible—to see the white gap between the lines. Write down your tape-measure distance from the target.
Next, you need to measure the width of your “cycle” (one black line and the white gap). Convert this width into the same units as your tape-measure distance (feet, inches, meters, etc.).
In my case, I’d measured 36 feet on the tape measure; and my “cycle” was 0.0139 feet wide.
Divide the cycle width by the tape-measure distance, and you’ll get some tiny number. Now, to convert this to degrees, you need to take the “inverse tangent” (if you’ve lost your scientific calculator, try the bottom section of this online one).
That gives you the degrees per cycle. To get cycles per degree, divide one by that number.
I didn’t estimate any numbers beforehand; so I was pleasantly surprised that my measured distance translated perfectly into 45 cycles per degree. That was good news both about my eyesight (and my eyeglass prescription), as well as perfectly splitting the range of acuity numbers I’d seen quoted.
But note that I did this test outdoors, on an overcast day. Moderately bright illumination like this gives the maximum visual acuity.
So I did a retest indoors, at an illumination level that might be more relevant to typical print-viewing conditions. Here, the lighting was 7 stops dimmer (1/128th as bright).
Perhaps not surprisingly, it became harder to judge the cut-off point where the white gap disappeared. But it definitely happened at a closer distance—roughly 28 feet.
Crunching those numbers, my indoor acuity dropped to 35 cycles per degree. This illumination level is probably more representative of the conditions used in eye-doctor tests; so being in the ballpark of 30 cycles per degree (20/20 vision) seems pretty plausible.
Now remember from my earlier discussion that detectable detail doesn’t equate very well with subjectively significant detail.
But, sitting typing this, I have unconsciously adjusted my distance from my computer screen so that its height occupies about 32° of my field of vision.
If you think that’s a reasonable distance to view a photo print from, you can do a little math. Even losing some resolution to Bayer demosaicing, a digital camera of 12.5 megapixels would capture all the detail my acuity could discern at all.