Hidden Rainbows: How to Measure Chromatic Aberrations in Eyeglasses

Mark Valentine, Electrical Engineer

If you wear glasses, you may have noticed red and blue fringes along opposite edges of an incandescent light bulb, such as the virtual one in Fig. 1, or perhaps even a full moon. You may also have noticed that the placement of the fringes will depend on the type of eyeglasses you are wearing and on the direction you are facing with respect to the light bulb. For example, I wear concave glasses (to correct for near sightedness), and when I face the region of space to the left side of a light bulb, I see blue and red fringes on the left and right edges of the light bulb, respectively. These fringes are examples of color distortions, also referred to as chromatic aberrations.

Figure 1. Colored fringes can appear around the edges of an incandescent lamp.

While this information may seem as elementary as the anatomy of the solar system (with its nine planets, or is it now eight, or ten?), Newton's research had a deeper significance because it shattered the notion that a prism created colors, revealing instead that each primary color remained unchanged and was bent by the same amount when refracted by a second prism. However, we can certainly excuse the presumptions made about the nature of light prior to Newton's experiments when we consider that the study of the solar system in our own time has been largely confined to the plane of the ecliptic.

We can also excuse presumptions about the insignificance of chromatic aberrations caused by eyeglasses. This is a position I'm inclined to take, because I haven't noticed any difficulties caused by chromatic aberrations, and I wear glasses every day. In fact, it almost seems inappropriate to search for any potential distortions caused by the very instruments that are compensating for defects in my own eyesight!

While the remainder of this article deals with testing this assumption by quantifying chromatic aberrations, it's worth noting that Isaac Newton found a way to eliminate them in optical instruments by eliminating refraction altogether, inventing the reflecting telescope in 1668. It wasn't until 1729 that Chester Moor Hall invented the first achromatic lens and, shortly thereafter, the first refracting achromatic telescope .

When the challenge of measuring the chromatic aberrations specific to eyeglasses was addressed, the visible fringes around the light bulb discussed earlier hinted that red and blue could be used as reference colors. Specifically, differences between the angles of refraction for these two colors were used to indicate the potential severity of the aberrations in a given pair of eyeglasses.

The measuring method developed was inspired by the vernier calipers, occasionally referred to as the nonius. It also utilized the benefits inherent in using a computer monitor to display images.

The vernier calipers is a measuring device that acts as a type of mechanical magnifier. It uses two slightly different numerical scales to perform measurements having a resolution that is much finer than that defined by the individual tick marks of either scale. If one of these scales is red, and the other blue, as shown in Fig. 2, the two scales should appear to slide in opposite directions when you view them through a pair of eyeglasses while turning your head from side to side. The resulting displacements between them can be measured by the same technique used to read a vernier scale.

Figure 2. A bi-directional vernier scale can indicate shifts between red and blue caused by the chromatic aberrations of eyeglasses.

Figure 3. A modification to the vernier scale allows chromatic aberrations in eyeglasses to be measured effectively.

While Fig. 3 gave improved results, there seemed to be an inherent offset in which the blue scale was slightly shifted to the right of the red scale. The cause of this was determined to be the red-green-blue horizontal arrangement of the tiny rectangular elements within each square pixel of the LCD monitor (which I observed in reverse order by viewing the borders of black and white objects on the screen with a low-power microscope).

When Fig. 3 was rotated in software by 90°, there was no corresponding vertical offset, probably because there is no vertical offset between the red and blue rectangles within each pixel. When the original Fig. 3, with its horizontal orientation, was viewed on another computer with a CRT display, the offset present in the LCD disappeared. This might be explained by the different arrangement and finer geometry of red, green, and blue elements in a CRT monitor .

Satisfied with these results, I then used Fig. 3 to characterize the chromatic aberrations in my eyeglasses. The basic process was to note the displacement between the red and blue scales in Fig. 3 and then to translate that displacement into angles measured in degrees. To do that, the angles of measurement were first approximated as radians, which are unitless (dimensionless) numbers used in calculus (yet another tool first developed by Isaac Newton) to represent angles for trigonometric functions. The angles were only approximations because computer monitors are essentially flat (LCDs) or curved slightly outward (CRTs), whereas ideally Fig. 3 would have been displayed on a spherical surface that curved inward.

The procedure used to characterize the aberrations was the following:

•  Bring up Fig. 3 on the computer's display. Center it and size it as desired. Remember, CRTs work better than LCDs.

•  Situate yourself in front of the monitor and carefully measure and record the distance between the point in Fig. 3 where the central pair of arrowheads touch and the bridge of your nose.

•  Measure and record the length of the red “100” reference line.

•  Cover one eye and turn your head to view Fig. 3 through the center, extreme left edge, or extreme right edge of the uncovered lens of your eyeglasses.

•  Record the number next to the pair of red and blue arrows that appear to be touching at the tips. When two blue arrow tips appear to be centered in the space between two red arrow tips, the displacement should be taken as a number halfway between them. Therefore, displacements should be interpreted as 0, or ± 0.5, or ± 1.0, or ± 1.5, and so on.

•  Divide the displacement recorded in Step 5 by 100; then multiply it by the number found in Step 3 and record the result.

•  The number obtained in Step 6 should now be divided by the number recorded in Step 2. Note this gives a number without any units. Record this number as the angle of displacement measured in radians.

•  Since there are 2 pi (about 6.283) radians in a circle, and 360° in a circle, the displacement in degrees is obtained by multiplying the number generated in Step 7 by 360 and then dividing the result by 2 pi.

•  Record the final number from this step as the difference in refraction, measured in degrees, between the red and blue colors in Fig. 3. Be sure to note which lens of the pair of eyeglasses and which part of that lens corresponds to this number.

Table 1: Data for author's eyeglasses when Fig. 3 was displayed on a LCD monitor.

Table 2: Data for author's eyeglasses when Fig. 3 was displayed on a CRT monitor.

A quick topside inspection of my eyeglasses revealed that the right lens is much thicker at the edges than the left lens. The virtual prisms formed by the edges of this lens should then be expected to have the greatest effect on incident light and should therefore cause the strongest aberrations. As shown in Tables 1 and 2, this was indeed the case, which is consistent with the assumption that the displacements observed between the colored scales in Fig. 3 were indeed the result of chromatic aberrations caused by refraction.

Contrary to my original assumption, the data also shows the visual displacements caused by aberrations can be significant. While the blended colors of daily life passing though my glasses usually obscure these effects, there are certain ordinary objects by which they can still be observed, such as red and blue neon signs. There are even situations where aberrations in eyeglasses could potentially affect the eye's ability to gather information.

One example might be a speedometer in which the speed scale and indicator needle are self-illuminated with blue and red colors, respectively. The fact that the previously mentioned offset caused by my laptop's LCD pixels was even noticeable, as reflected in the data in Tables 1 and 2 for the center of each lens, suggests such an effect in a speedometer could at least be perceivable, if not significant.

LEDs are wonderful things, and this experiment could be carried out just as easily, and perhaps more accurately, using them. For one thing, an instrument made with LEDs could be made more precise than an instrument based on a computer monitor, because the relative positions of the LEDs can be more carefully controlled. Also, using its data sheet, the wavelength of a particular LED can probably be determined more accurately than that of the light generated from a CRT or LCD display. This would have the advantage of making experimental results easier to replicate.

Furthermore, while the colored elements for a CRT or LCD are restricted to red, green and blue, experiments based on LEDs can be conducted with those colors as well as orange, yellow, indigo and violet, the remaining primary colors. Using red and violet LEDs, it might be possible to create a pattern (a violet LED perfectly centered among four red LEDs, for example) with enough sensitivity to determine whether or not the frames in a given pair of eyeglasses are correctly positioning the lenses in front of the wearer's eyes.

While displacements caused by chromatic aberrations are usually undesirable, they can also be fun. For instance, it may be possible to use the displacement effect occurring between two primary colors to create a new class of “Op Art” that appears animated or three-dimensional. By its very nature, it would cause heads to shake from side to side, giving it something in common with many other forms of modern art.

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