Wave-optical formation of the intensity distribution and diffraction limit of picture-generating freeform surfaces

Recent developments in design algorithm enable to design freeform surfaces that generate intensity distributions with middle to high spatial frequency. Such freeform surfaces can generate a picture in a defined plane. In contrast to conventional imaging, the light modulation is done by a ray-optical redistribution of the incident light comparable to incoherent beam shaping. Such picture-generating freeform surfaces have various advantages. As only one single optical element is needed to generate the intensity distribution, very compact optical systems can be designed. Additionally, they are highly energy efficient, as nearly 100% of the incident light is directed into the image plane. In case of a freeform mirror, the system is wavelength independent, which offers the possibility for applications in UV or IR spectral range, as well as the polychromatic projection without any chromatic aberration. As no classical imaging is performed, conventional evaluation criteria concerning the resolution of this picturegenerating system like e.g. the Rayleigh criterion cannot be applied. In order to simulate diffraction effects in the picture plane, the wave-optical propagation has to be simulated. However, depending on the geometrical arrangement of such systems, the surface modulation of the freeform can be up to several millimeters. This leads to a violation of the thin element approximation and to significant sampling problems using conventional propagation algorithms. Therefore, we used a propagation method based on the Huygens-Fresnel principle. The physical formation of the intensity distribution of a picture-generating freeform system was simulated and the diffraction limit evaluated. We will show that such systems have a significantly lower resolution than conventional imaging systems. However, they are very well suited for middle- and low-resolution.