I'm always in the market for surprising facts. One of my favorites is that the color blue is always out of focus for the human eye. It's hard to believe since it appears that we see blue clearly, but it's astonishing when shown an example. Here', I'll explain why we're unable to focus on blue, and show examples of what it means for image sharpness.
In order to fully appreciate what's happening in the eye, we need to understand some fundamentals of optics in order to understand how light travels and can be focused by a lens.
We've all heard that the speed of light is a universal constant. Yet, light travels at different speeds all the time. Light travels its fastest when in a vacuum, but slows down in different substances. For example, light travels at 3x108 m/s in a vacuum, but only 2x108 m/s in glass. This change in the speed of light is called the refractive index of the medium.
As light moves from one medium to another medium with a different refractive index, not only does the light change speeds, but it also changes direction. The relationship between the two angles is given by Snell's Law, which relates the direction of the light relative to the angle of the surface, the indices of refraction of the materials, and the new direction of the light beam. The animation below shows how light striking a new medium with a higher index of refraction (slower speed of light), will change direction.
We can use this fact to shape the paths of light with a lens. If the lens is spherically shaped, parallel rays approaching the lens will be deflected relative to their incident angle. Light striking a lens in the center will not be deflected at all as the incident angle is 0, while light striking towards the edge of the lens will have the greatest angle of incidence, and therefore the greatest angle of reflection. As the beams exit the lens, they are bent once more.
With a common lens, each ray of light will converge at the same position, known as the focal point. By observing the light at this location, the image would sharp and in focus. Observe in this animation how the light bends while moving through the lens, and converges on a common focal point.
In these previous examples, we've made the assumption that the color (aka wavelength) of light is constant. However, this isn't the case for most natural light sources. As we know from the rainbow, white light is composed of a full spectrum of individual colors.
Light with multiple color components causes complexities for lensmakers, as the index of refraction (speed of light in a material) is dependent on the wavelength of light. Thus, when a beam of light is passed through a lens, the white light "splits" into beams of different wavelengths as they are refracted at different angles. Because the colors take different paths, they no longer converge a single focal point. This is called chromatic aberration, and can be seen with the red, green, and blue light in the animation.
Because the different colors of light now have different focal points, there is no single position where all the light coming from the lens is in focus. Instead, there is an optimal focal plane for each wavelength of light, and all colors can not simultaneously be in focus. Modern camera lenses have multiple elements or special coatings to help combat this issue and keep all wavelengths converging to the same focal point, but simple lenses do not have this ability. In the animation, we can see that moving the focal plane (think of an image sensor) changes which color is in focus. Without chromatic abberation, the sensor would see a clean white dot. However, when outside of the focal point, each each color is blurred.
For all its complexity, the human eye cannot overcome this issue of chromatic aberration. As described in a journal review of the design of the eye:
"Another simplifying strategy in the eye is to leave chromatic aberration uncorrected. In fact, it has been shown that the LCA (longitudinal chromatic aberration) of the eye is close to that of a salty water single-surface lens. In lens design, CA is corrected by a combination of glasses with low and high dispersions (the classic flint & crown), but this strategy is difficult with biological tissues having a high water content. Thus, nature doesn’t seem to even try this hardly achievable goal."
With such strong chromatic aberration, how then is the eye able to focus on anything? It turns out, the eye doesn't! While no single color is fully in focus, the eye's focal plane is positioned for the colors where it is most sensitive.
As can be seen in the chart of spectral sensitivity, and in the animation of focusing various colors, sensitivity and focal points for the red and green receptors are very close to one another. In looking at the animation, it appears that the best position for the focal plane is between the red and green focal points. This is exactly what happens in the eye.
At long last, we can see why the human eye can't focus on blue light. The focal point is placed between the peaks of the red and green receptors and blue is left blurry.
I may have buried the lede in this explanation, since the results of chromatic aberration in the eye are so striking. To visualize how little resolving power we have for sharpness in blues, we'll take an image and split it into its red, green, and blue components. We'll then blur one of the channels, and recompose the image.
This is the original image of the earth with no edits.
On the left, I have extracted the green channel from the image and blurred it. On the right, the original red and blue channels are recombined with the blurred green channel. As expected, the resulting image is blurry.
Following the same procedure as used before, I have extracted the blue channel from the image and blurred it. On the right, the original red and green channels are recombined with the blurred blue channel. Shockingly, the image appears perfectly sharp!
What if we went even further? I blur the blue channel to the point where it's almost unrecognizable. The resulting recombined image has a fair amount of color fringing, but the sharpness remains. Amazing!
I think this concept is amazing. Our brain extracts some color information from the blue channel, but delegates sharpness to the red and green channels which are in focus. The result is so astonishing, that I have to wonder if there is something that may go awry from modifying and displaying these images on a computer. If you have any theories beyond chromatic aberration and focusing of the eye, let me know.
This is one of many examples of our brains being much more powerful than our eyes. Too often we think of our eyes as perfect cameras. However, it is the brain that is able to accomodate for all of the optical shortcomings in order to resolve the world.