# On Lens Aberration

## When reality is wrong.

A 3 minute read, posted on 5 May 2019

Tags computer vision, optics

When I first encountered the topic “lens aberration” I expected to find content on how some manufacturing defect in a particular lens causes it to behave differently from other normal lenses. This must be a common enough assumption as the Wikipedia entry on optical aberration1 includes a statement specifically to clarify it.

Aberrations occur because the simple paraxial theory is not a completely accurate model of the effect of an optical system on light, rather than due to flaws in the optical elements.

To understand aberrations in lenses, we must first understand what is considered “normal” behavior in lenses. After all, an aberration can only exist in relation to the norm as a deviation from it.

Lenses are considered “normal” when the horizontal distances (depth) of a point on the object and its image from the optical center are related to the focal length of a lens in the following manner.

$$\dfrac{1}{f} = \dfrac{1}{d_{obj}} + \dfrac{1}{d_{img}}.$$

This is called the thin lens equation. This equation implies that all rays coming from the same point at a depth $d_{obj}$ from the optical center of the lens, regardless of the angle of incidence, point of incidence or wavelength of the ray, will focus at a single point at a depth $d_{img}$ from the optical center on the imaging surface.

In reality (which is ultimately what we’re trying to model), this is of course not true2. Lenses refract different rays coming from a point in the scene to different, albeit close, points on the imaging surface causing the dreaded aberration. By this definition however, there exists no normal lens in the world. In other words, all lenses are aberrant! The only “normal” lens exists in our imagination. Go figure! Isn’t science supposed to be the objective study of the world around us? This is the same as claiming that the reality that we set out to study is aberrant. Talk about a contradiction in terms!

We (myself included) have this curious habit of not accepting things as they are. We love to create ideal versions of everything, as per our cultural context, and compare reality with this idealized version, insisting all along that reality should not be as it is. Somehow the simple tautology evades us that reality is. We see the world through our conditioned and mostly skewed lenses (pun intended) leading to absurd, sometimes hilarious and other times downright dangerous conclusions 3.

## Acknowledgments

Thanks to automoto for your invaluable review.

## References and footnotes

1. Wikipedia. Optical Aberration. https://en.wikipedia.org/wiki/Optical_aberration. [return]
2. The thin lens equation only works for those rays that are very close to the optical axis (paraxial) and make a small angle with it. This is what is referred to as the paraxial approximation. [return]
3. Pol Pot’s dangerous conclusion was that the Marxist ideal >> reality. It is futile and painful to think something to be better than reality because reality already is. [return]