Recent developments in design algorithm allow the calculation of free form surfaces that generate a picture in
the target plane with the help of one optical surface. In contrast to conventional imaging, light modulation is
done by a ray-optical redistribution of the incident light which is comparable to incoherent beam shaping.
Such picture-generating surfaces normally exhibit very complex surface sags, that are manufactured using
diamond turning machining. The knowledge of manufacturing tolerances is important to generate the desired
intensity distribution with the required accuracy and at the same time reduce manufacturing effort.
However, compared to the tolerancing of conventional optical elements (e.g. spheres), the tolerancing of
picture-generating free form optical elements is a demanding task. The complexity of their surface shapes and
the target intensity distribution are challenging considering the finding of tolerance parameters and performance
Tolerance parameters strongly depend on the manufacturing process. Therefore they can be obtained by a
detailed analysis of their manufacturing process. In this contribution we focused on picture-generating free form
optical elements manufactured using diamond turning with slow tool servo support. Astigmatism and spherical
aberration are typical manufacturing errors caused by this tool exhibiting low spatial frequency. Errors with
middle to high spatial frequency have not been investigated so far.
Conventional software tools for tolerancing, as e.g. implemented in Zemax, provide only such tolerance
parameters as radius, thickness or tilt, corresponding to conventional manufacturing methods of classical optical
elements (e.g. spheres). Therefore we implemented a software tool developed in Matlab and using Zemax for
raytracing in order to perform sensitivity analysis and Monte Carlo analysis.
Conventional performance criteria like spot radius or wavefront error to evaluate the tolerance analysis cannot
be applied for picture-generating free from elements. Consequently, other performance criteria were investigated.
The correlation between the desired and the generated intensity distribution was chosen to be an appropriate
performance criterion for the tolerancing analysis.