Geometric aberrations in the plano-convex lens

Introduction

Plano-convex lenses present a curved interface and a planar interface. They are for instance the microlenses situated on top of a wafer, but can also encountered in macroscopic optical systems. Their asymetrical nature influences their properties of bending the light. Depending on their role in an optical system, their orientation has to be taken into account.

The focusing case

On axis, the main aberration is the spherical aberration. A common mistake is not to care about the lens orientation in the system. However, if the purpose is the focusing of parallel rays (a plane wave), the aberrations can vary of a factor four, depending on this "detail" (n=1.5 in the equation n³/(n³ - 2n² +2)). The curved surface should be placed first on the light's path, as you can experiment in the following applet.

This difference can be understood simply: As you can see in the previous applet, if the light falls upon the planar interface, it is not bent, and the whole effect will be done by the curved interface. On the other way, the whole lens effect is shared between the two interfaces. Their "effort" is smaller for each interface, so the aberrations are smaller.

The collimating case

Symetrically, the collimating set-up requires the lens to be placed the other way around. The following applet demonstrates this principle.

Conclusion

For both situations, the good position is the one where the center of curvature of the lens is in the direction of the focus.

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