Chromatic Aberration

What is chromatic aberration?

Idealized optics makes the assumption that light is monochromatic or its frequency does not affect its propagation through a system.  However, for a real system, this is never true.  The frequency of light does affect its propagation through a system.  The index of refraction of a material is generally higher for shorter wavelengths, causing them to be more strongly refracted.  This dependence of frequency results in chromatic aberration.

Why does the frequency of light affect its propagation through a system?

The propagation of light through a system is dependent on the index of refraction.  This can be seen in the ray tracing equation ( ), which describes the path of a ray of light.  Since  (where κE is the dielectric constant and κM is the relative permeability) and κE is frequency dependent, N is frequency dependent.  This means that the propagation must, therefore, be frequency dependent.

How does the frequency of light affect its propagation?

 figure 1. Different frequencies ("colors") travel different paths.
If a white light is shown into a system that has chromatic aberration, each of the composite frequencies that make up that white light will be focused in a different location.  The different frequency ("colors") travel a different path (figure 1).

How can chromatic aberration be measured?

 •
 •
 FB
 FR
 figure 2. Lateral chromatic aberration (indicated by the purple arrow)
 Hecht, Optics, 2002.
Chromatic aberration can be described in terms of lateral chromatic aberration or axial chromatic aberration.  Lateral chromatic aberration is the distance between the off-axis blue focus and the off-axis red focus (figure 2), while axial chromatic aberration is the distance between an on-axis blue focus and on-axis red focus (figure 3).

 •
 •
 FB
 FR
 a. positive
 •
 FB
 •
 FR
 b. negative
 figure 3. Axial chromatic aberrations (indicated by purple arrow).
 Hecht, Optics, 2002.
 Hecht, Optics, 2000.
The axial chromatic aberration is positive if the blue focus is left of the red focus (figure 3a).  Conversely, the aberration is negative if the blue rays are more strongly deviated, and, therefore originate at the right of the red focus (figure 3b).

 figure 4. The color of the spot and halo depend on the location.
What does chromatic aberration look like?

When white light is passed through a system with chromatic aberration, the image depends on the location on the other side.  The frequency of light that is in focus at a particular point will form a bright colored dot, while the frequencies that are out of focus form a halo around the dot.  The color of both the dot and the halo will change as the position is varied (figure 4).

How is chromatic aberration corrected?

A combination of two lenses - one positive and one negative can cancel out the aberration from each individual lens, causing the system to have a net aberration of zero.  When a system is designed to exactly overlap the red and blue focus (resulting in no aberration) the system is achromatized.  Therefore an achromatic doublet (stem of two lenses) will be free of chromatic aberration.

Hecht, Eugene, Optics, 4th Edition, San Francisco: Addison-Wesley, 2002.