Wednesday, December 4, 2013

Visual accuity and color

As the only John the Math Guy around, you can imagine that I get a lot of questions.  I do. Thousands of questions a month. Normally they start out with "when are you gonna..." and end with "pick up your dirty socks?" or "get home from the bar?" or "fix the door knob?" But every so often, I get a question that isn't a thinly veiled command. Here is an example.

"How does visual perception of sharpness (acutance, resolution, and contrast all considered) vary with color?"

    - if fine marks need to be visually evaluated and black is not an option, what other color is the next best choice?
    - where has an MTF at one frequency vs wavelength plot been published?

    My usual references; Wyzecki and Stiles, Hunt, Zakia and Todd, etc.
    don't seem to address this particular issue. A new edition by
    Lambrecht and Woodhouse gets tantalizing close, but their emphasis is
    primarily black and white photography.

    Any suggestions?

Wow! An intelligent and interesting question! And I think I can provide a decent answer!

I am sure you have noticed that when you look at yellow halftones with the naked eye, you really can't see the dots, even when you can see the color. This fact leads to your question, since it implies that visual acuity somehow depends on wavelength.

The sensors in the eye are either rods or cones. The rods are largely active when old guys like me get up in the middle of the night to go to the bathroom. In normal daylight, these are pretty much saturated, so they don't have much effect on vision.

The cones are the sensors in the eye that are most important under daylight. If I were haughty, I would say something like "under photopic rather than scotopic conditions." And I would likely slip those words into casual conversation whenever possible. Much like ice cream cones, the cones in the eye come in several flavors. Not quite as many as Baskin Robbins, though. There are only three flavors of sensors in our eyes: cherry, mint, and blueberry.

Unretouched photomicrograph of Burt Baskins' retina

Some sadly mistaken people call the sensors in our eyes "red, green, and blue". Real color scientists who don't like ice cream call them L, M, and S for long, medium, and short wavelength. Red, green, and blue are not quite appropriate since the cones don't exactly line up with what we would think of as red, green, and blue. The L cone (the reddish one) overlaps quite a bit with the M cone (the greenish one).

The spectral response of the S, M, and L cones

Here comes the important part. There are more of certain types of cones per square millimeter than there are of others. In the fovea (that's the very central part of the retina in the center of our field of view), only about 5% of the cones are S cones. So... these cones are less tightly packed than others. So... our resolution (visual acuity) is less with the S cones. 

Look at the spectra of yellow ink. 

The reflectance of yellow ink is down at 5% to 10% in the 400 nm to 500 nm range, and close to the reflectance of paper above 500 nm. The S cones are the only cones that are sensitive in this range, so our ability to see yellow halftone dots is because of the sparsity of S cones in the fovea. And that, my friends, is why you can't see yellow halftone dots without a magnifier.

By the way... there is this company called Beta Industries that sells this really cool microscope that illuminates a sample with blue light so that you can look at yellow ink with just your S cones. You can illuminate with red light to see cyan, and green light to see magenta as well. But the really fun one is yellow ink and blue light.

Let's get back to the original question. Clearly yellow would be the worst possible choice for making dots on the paper that are just barely visible. Clearly, black is the best ink. Of the other two, which is preferred?

Generally speaking, there are twice as many M cones as there are L cones, but this varies from individual to individual. This means that, in general, the eye has better visual acuity in the green region of the spectrum, and somewhat less visual acuity in the red.

Let's say we are considering what is going on in the green region of the spectrum, from 500 nm to roughly 600 nm. Which ink shows the most contrast against white?  In other words, which ink has the lowest reflectance in this region? If we are limited to the four basic inks, both black and magenta have low reflectance in this region. So, if we want a single ink, then magenta would be the second choice if black is unavailable.

Cyan ink shows a bit of contrast against white in the green region (look at cyan ink under green illumination to see this), but has a fairly decent contrast in the red region. Thus, one would expect that cyan would have decent visual acuity, but not quite so much as the magenta.

But, as I said: 1) there is a wide overlap between the spectral range of the L and M cones, so we can't really think of there being a sharp distinction between L and M in terms of wavelength, and 2) there is quite a bit of variability in the relative number of L and M cones in different people, so one rule may not apply to all people.

If you are allowed a bit larger range of inks, then blue ink would be best, since it has good contrast both in the green and red regions of the spectrum. But if blue is being made by overprinting cyan and magenta inks, then register could cause problems.

One more consideration is the strength of the ink. Obviously, if you print at a higher density, you have better contrast. This would tend to favor black ink over cyan and magenta (which are typically printed at comparable densities), and both would be favored over yellow.

So, all in all, I would go with magenta ink, if all you have available is CMYK. If you have a spot color available, I would go for a dark blue. You can quickly check the contrast by viewing the ink under green illumination.


  1. Hence, Blueberry Ice Cream should be a favorite. It not only tastes good but looks good too!

  2. Just to point out some errata: There are no S cones in the fovea, and 2% to 7% S cones elsewhere. And there are twice as many L cones as M cones, not the other way around.