Freeform optics offer new opportunities for optical system design by providing greater flexibility in aberration correction than traditional rotationally symmetric surfaces. This short course introduces the fundamentals of freeform optics and their application to modern optical systems.

Participants will learn what defines a freeform optical surface, how freeform surfaces are mathematically represented and how breaking rotational symmetry can provide additional degrees of freedom for correcting aberrations, reducing system size and complexity and improving optical performance. The course will explore applications of freeform optics for imaging and will highlight the advantages and challenges of incorporating freeform surfaces into optical designs.

The course will also introduce the fundamentals of freeform optical design, including when, how and where to include freeform surfaces in a system. Through representative design examples, participants will gain insight into how freeform surfaces can enable optical architectures that are difficult or impractical to achieve using conventional optical design approaches.

Designed for optical engineers, researchers and students, this course provides a foundation for understanding the capabilities of freeform optics and evaluating when and how freeform surfaces can benefit an optical design.

Session 1 frames illumination design as an inverse problem: given a source and a desired target illuminance, find the optical surfaces. The session develops point-source tailoring of a single freeform surface, deriving the tailoring ODE in 2D and showing why the 3D case becomes a difficult PDE constrained by surface-normal integrability. We then cover generalized Cartesian ovals: surfaces mapping one given wavefront exactly into another via constant optical path length. Participants learn the construction method, its numerical implementation and the crucial limitation — wavefront matching controls phase, not illuminance.

Session 2 presents the synthesis: tailor the output wavefront's own ray density so it carries the desired illuminance distribution, then use wavefront matching to deliver that wavefront exactly. This combines illuminance control (tailoring) with phase control (ovals), and the session treats consistency conditions and failure modes such as caustics. Finally, we confront extended sources. The point-source solution blurs predictably; strategies include centroid design, pre-compensation (deconvolving the source's image from the target), étendue-aware specifications and iterative re-tailoring. The course closes with an honest outlook: 3D SMS for extended sources is documented but not available as software, and direct single-surface tailoring for extended sources is still an open research problem.

Two running examples anchor the material: a street-lighting reflector and a refractive illuminator homogenizing a rectangle, each developed fully, including extended-source compensation.
 

This course will teach the principles and applications of optical metasurfaces. Metaoptics rely on sub-wavelength structures to engineer the optical response of a surface. Like this optical functionalities such as lensing, beam shaping and many other can be added to flat surfaces. Metaoptics are especially promising for miniaturization of optical systems and optical functions that are difficult to impossible to achieve by conventional components. These properties led to their recent mass scale application in smartphones.   

The mechanisms by which nano-structures can be used to control the optical behaviour of a surfaces will be explained starting from their influence on light on the sub-wavelength scale to form meta-atoms. We will investigate the different types of interactions as well as the practical steps needed to design and optimize a meta-atom library. Including material choice and fabrication considerations. Understanding of the physical principles employed in the meta-atom design will clarify the capabilities and limitations of metasurfaces.

Afterwards we will move on to applying the nano-structures to form optical components / meta-surfaces with unique properties such as polarization control, wavefront shaping etc. Both as single components and integrated into systems of multiple metasurfaces or combining refractive optics with metasurfaces in a hybrid system. We will show how to combine wave and ray optics to design systems. Several example applications in sensing, imaging and beamforming will be examined.

The course will conclude with an overview of manufacturing technologies for metaoptics. Namely e-beam, nano-imprint, two photon and photo lithography. A detailed look will be taken into the effect of manufacturing imperfections and alignment on the metasurface and system performance. Notably the differences with classical optical components and failure mechanisms.

The next generation of optical systems demands components with increased degrees of freedom to achieve enhanced performance, compactness, reduced weight and multifunctionality. Freeform optical elements offer opportunities to improve optical performance, reduce system complexity and enable innovative designs. Integrating diffractive features with freeform surfaces provides additional control over the amplitude, phase and propagation of light, enabling compact and lightweight optical systems. Such elements are promising for advanced imaging, space optics, augmented and virtual reality, beam shaping and optical instrumentation. However, their fabrication presents significant challenges in simultaneously achieving complex surface geometries and precisely defined micro- and nanoscale diffractive structures while maintaining surface accuracy, feature dimensions and quality.

The course will describe and discuss the methodologies and technologies involved in precision optical manufacturing and metrology, focusing on off-axis aspheres, freeforms and diffractive-freeform optics. It will cover advanced fabrication techniques, including ultra-precision diamond turning, grinding, polishing, lithography and etching, along with metrology for absolute measurement of surface shape and figure and characterisation of diffractive features. The capabilities and limitations of different manufacturing and metrology techniques will be compared through practical case studies. Fabrication of freeform optical components for imaging and spectroscopic applications will also be discussed, highlighting design requirements, manufacturing considerations and metrology challenges.

Participants will be able to identify suitable fabrication and characterisation approaches, determine critical process parameters, measure surface and feature characteristics and evaluate their impact on optical system performance.