Beam expansion - A unique system made of aspheric lenses

(3) \(z(h) = \frac {h^2}{R(1+\sqrt{(1-(1+k) \frac{h^2}{R^2}}} + \sum_{i=2}^{n} A_{2i} h^{2i}\)

These beam expansion systems are typically optimized for one wavelength in terms of the shape of optical surface and lens distance. Spheric aberrations can be reduced to a minimum.

By adding an additional optical group, the beam expansion system receives additional flexibility with regard to the adjustable magnification levels. This can be done most easily with a symmetrical zoom system, which consists of three single optical lenses (converging lens-diverging lens-converging lens). Therby two lenses must be able to change their position so that an afocal beam path is ensured for each magnification level. Depending on requirements, such a system can become very complex, whereby the demands increas in terms of the mechanical mount.

Monolithic beam expansion systems

A slightly different approach is taken by monolithic beam expansion systems that are similar in operating principle to a Galilean telescope, but consists only of one optical element – a meniscus lens. The two optically active surfaces have a common center of curvature. The principle of this so-called zero lenses has been known for a very long time, but they show strong spherical aberration in their original design with two spherical surfaces and thus are only suitable for very small beam diameters and very low magnifications.

In Figure 2 (a) the beam path in such a spherical lens is shown schematically. If these optical elements are aspherized to one of the two surfaces, the spherical aberration can be corrected as shown in Figure 2 (b) and an afocal system for large beam diameters can be implemented.

The improvement in the optical properties can be clearly seen in comparison to Figure 1. The magnification in both cases corresponds to V = 2, whereby the beam diameter is different by the factor 2. The maximum attainable magnification of such a single element is V = 2. This is estimated by the paraxial magnification

(4) \(V = \frac {d}{r} * \frac {n-1}{n}\)

whereby n is the refractive index of the glass, r is the radius of the concave side, and d is the center thickness.

It turns out that the single element magnifications of the monolithic Galilean telescopes are comparatively low due to the overall length limitation. Since it is an afocal beam expansion systems, they can gradually increase the input beam while they are “connected in series” in succession in the beam path (Figure 3c).