Design of two-dimensional zero reference codes by means of a global optimization method.

A method to obtain the absolute measure of the position is by means of the autocorrelation of two zero reference marks. In one-axis measurement systems one dimensional mark are used and the design of these marks is relatively complex. When the movement is in two-axes, two dimensional reference marks are required and they are even harder to design. We report a method of global optimization to calculate the optimal two dimensional zero reference marks which generate the reference signal with the highest central peak. This method proves to be a powerful tool for solving this problem.