Complex surfaces in optical system design
Complex surfaces
Most optical systems and also most methods in describing and minimizing aberrations in optical systems are still based on rotational symmetric systems consisting of spherical refractive lenses. However todays fabrication technologies allow the reliable and accurate manufacturing of:
- Diffractive optical surfaces
- Non-spherical surfaces, such as rotational-symmetric aspheres
- Non-rotational symmetric surfaces, so-called free-form surfaces
- Facetted optical surfaces, e.g. Fresnel lenses in illumination design
Diffractive Surfaces in optical design
Recent lithographic technologies allow for the fabrication of high period diffractive structures. Such diffractive surfaces offer the optical designer extra degrees of freedom for the correction of aberrations in optical systems. For example diffractive surfaces are very well suited for color correction of broad-band optical systems. Since recently, diffractive surfaces can also be applied to curved optical surfaces with very high precision. This allows for addressing other third order aberrations, like field curvature and astigmatism.

Fig. 1: A diffractive singlet with f/#=1.0 and focal length f=50mm. The top figures illustrate the performance for a planar substrate, whereas the bottom figures correspond to curved substrates.
Non-rotational-symmetric surfaces in illumination design
Several laser illumination systems require special illumination field geometries, like narrow illumination lines, or custom 2d-intensity profiles. This class of systems thus requires anamorphic or even free-form surfaces for the homogenization and formation of the illumination pattern. Aberrations within such systems, as for example induced by cylindrical or non-symmetric optical components, need to be analyzed and controlled. 
Fig. 2: Anamorphic optical system for laser-line-illumination employing cylindrical optical components.
Facetted and Fresnel-surfaces
Other types of complex surfaces, mainly employed in illumination design, are facetted surfaces and Fresnel structures. Such elements are for example used in LED illumination systems or solar concentrator systems.

Fig. 3: Fresnel lens in combination with freeform secondary collector optics for solar concentration.
Recent Publications
Herkommer A. M., Münz H., Reichle R., "Design of extreme anamorphic laser illumination systems", Proc. SPIE Vol. 8170, 81700B (2011).
Herkommer A. M., Reichle R., Häfner M., et al., "Design and simulation of diffractive optical components in fast optical imaging systems," Proc. SPIE Vol. 8167, 816708 (2011).
Herkommer, A. M., "Variable Beleuchtungssysteme - Konzepte und Limitationen am Beispiel Lithographie, DGaO Proceedings (2011).
