On designing an isotropic fiducial mark

The Crame´r-Rao lower bound (CRLB) of image registration error using an isotropic fiducial mark is derived. The derived CRLB is a function of the intensity profile of the fiducial mark. Following the development of the CRLB, a new method for designing an isotropic fiducial mark, suitable for digital image registration, is presented. A parameterization method of the fiducial intensity profile is introduced which guarantees no aliasing effect when the fiducial mark is digitized with the proper sampling rate. A method for computing the fiducial intensity profile, based on minimization of the CRLB registration error, and subject to certain practical constraints, is developed. For imaging systems with a significant low-pass effect, it is proposed to pre-emphasize the high frequency components of the fiducial mark by converting the designed gray-scale fiducial marks into binary fiducial marks. Experimental results show that the designed fiducial mark can provide very accurate registration results and that the registration accuracy is independent of its location.