  Knowledge of the transverse four-dimensional beam rms-parameters is essential
for applications that involve lattice elements that couple the two transverse
degrees of freedom (planes). Of special interest is the removal of inter-plane
correlations to reduce the projected emittances. A dedicated ROtating System
for Emittance measurements (ROSE) has been proposed, developed, and
successfully commissioned to fully determine the four-dimensional beam matrix.
This device has been used at the High Charge injector (HLI) at GSI using a beam
line which is composed of a skew quadrupole triplet, a normal quadrupole
doublet, and ROSE. Mathematical algorithms, measurements, and results for ion
beams of 83Kr13+ at 1.4 MeV/u are reported in this paper.
