  For quality control in the factory, 3D-metrology faces increasing demands for
high precision and for more space-bandwidth-speed-product SBSP (number of
3D-points/sec). As a potential solution, we will discuss
Structured-Illumination Microscopy (SIM). We distinguish optically smooth and
rough surfaces and develop a theoretical model of the signal formation for both
surface species. This model is exploited to investigate the physical limits of
the precision and to give rules to optimize the sensor parameters for best
precision or high speed. This knowledge can profitably be combined with fast
scanning strategies, to maximize the SBSP, which will be discussed in paper
part II.
