  Fast characterization of 2-dimensional gratings is demonstrated using a
Fourier lens optical system and a differential optimization algorithm. It is
shown that both the grating specific parameters such as the basis vectors and
the angle between them and the alignment of the sample, such as the rotation of
the sample around the x-, y-, and z-axis, can be deduced from a single
measurement. More specifically, the lattice vectors and the angle between them
have been measured, while the corrections of the alignment parameters are used
to improve the quality of the measurement, and hence reduce the measurement
uncertainty. Alignment free characterization is demonstrated on both a 2D
hexagonal grating with a period of 700 nm and a checkerboard grating with a
pitch of 3000 nm. The method can also be used for both automatic alignment and
in-line characterization of gratings.
