Section 27–6 Aberrations

 (Spherical aberration / Chromatic aberration / Comatic aberration)

 

In this section, Feynman discusses spherical aberration, chromatic aberration, and comatic aberration (or coma).

 

1. Spherical aberration:

“This effect is called spherical aberration, because it is a property of the spherical surfaces we use in place of the right shape (Feynman et al., 1963, section 27–6 Aberrations).”

 

According to Feynman, a real lens having a finite size will exhibit aberrations, for example, spherical aberration is a smear in an image. The word spherical is used because spherical aberration is related to the spherical surfaces of the lenses that enlarge an image imperfectly. Simply phrased, an aberration is an image error of an optical system that may manifest as an unclear or distorted image. Spherical aberration is classified as a type of monochromatic (or quasi-monochromatic) aberrations, however, other types of monochromatic aberrations include coma, astigmatism, field curvature, and distortion. More important, one should emphasize that spherical aberration is observable even for objects that are located on the optical axis (or principal axis).

 

Feynman elaborates that the spherical aberration could be remedied by re-forming the shape of the lens surface or using several lenses arranged so that the aberrations of the individual lenses tend to cancel each other. One may include more methods to resolve this aberration such as using an aperture stop or computerized lens design. In short, the aperture stop can affect the amount of light closer to the optical axis that passes through the lens. Perhaps Feynman should mention that computerized lens design is a useful tool that was used by manufacturers worldwide in the early 1960s (when this lecture was delivered). Currently, there are more sophisticated computer programs that help to design and analyze more complicated optical systems (Hecht, 2002).

 

2. Chromatic aberration:

“So if we image a white spot, the image will have colors, because when we focus for the red, the blue is out of focus, or vice versa. This property is called chromatic aberration (Feynman et al., 1963, section 27–6 Aberrations).”

 

According to Feynman, another fault of the lens is its refractive index which is color-dependent, and thus, light of different colors travels at different speeds in a glass. That is, a white spot has chromatic aberration in the sense that its image has different colors. Chromatic aberration is also known as “color fringing” or “splitting of light” because the lens is unable to let colored light rays meet at the same point in the focal plane. Specifically, lens dispersion is observed as a result of a higher refractive index for light rays that have shorter wavelengths. In other words, the image appears blurred with colored edges because light of different colors reaches different points along the optical axis.

 

Instead of providing a specific solution to compensate for chromatic aberration, Feynman asks how careful do we have to be to eliminate aberrations. Then, he says that the theory of geometrical optics does not work here and the principle of least time is only an approximation. Perhaps Feynman should discuss how achromatic lenses can resolve the chromatic aberration from the perspective of Fermat’s principle of least time. For example, one may explain to what extent the light path of each ray has the same length by having a good design of lens surface with the appropriate refractive index. In essence, Fermat’s principle of least time is a first-order approximation in the sense that the optimum light path could have the longest-time or shortest-time provided all nearby paths take approximately the same time (δT = 0).

 

3. Comatic aberration: “If the object is off the axis, then the focus really isn’t perfect anymore, when it gets far enough off the axis (Feynman et al., 1963, section 27–6 Aberrations).”

 

Feynman says that the focus isn’t perfect anymore if the object is located off the optical axis. (Strictly speaking, the focus isn’t perfect even if the object is located on the optical axis depending on its size and colors.) He elaborates that the image will usually be quite crude, and there may be no place where it focuses well. One may clarify that this image error is also known as coma or comatic aberration. In short, coma is a monochromatic aberration that occurs for an object located a distance from the optical axis; the light rays reach points on the focal plane that are farther from the optical axis. A good example is the appearance of comet-shaped stars when they are located at an angle to the optical axis of a telescope.

 

Feynman mentions that the optical designer tries to remedy aberrations by using many lenses to compensate for each other’s errors. Then, he explains that if we have arranged the time difference for different light rays is less than about a period, there is no use going any further. One may add that comatic aberration can be compensated by using an aperture stop at the proper location. However, if the time difference for different light rays is less than about a period, then there would be interference between the light rays such that it is more difficult to improve the resolution of the image. This is a limitation of geometrical optics because of the diffraction and interference of light waves.

 

Review Questions:

1. How would you define the concept of spherical aberration?

2. How would you resolve the problems of chromatic aberration?

3. Do you agree with Feynman when he says that the focus isn’t perfect anymore if the object is located off the optical axis?

 

The moral of the lesson: aberrations (image errors) are due to the faults of lenses (spherical surface and refractive index) that cause light rays not to meet at the focal point and at the same time (Fermat’s principle of least time).

 

References:

1. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

2. Hecht, E. (2002). Optics (4th ed.). San Francisco, Addison-Wesley.