A joint transform correlation incorporating the coordinate transformation technique is proposed to perform invariant pattern recognition. Instead of an input image or its Fourier transform intensity being mapped, the Fourier transform of the input image is directly transformed from rectangular into logarithmic-polar coordinates. All information is saved, and as a result, multiple objects can be processed simultaneously. A binary optical component is designed and fabricated to perform coordinate transformation with high efficiency. Further, a Dammann grating is applied to generate a two-periodicity mapped reference image to overcome correlation peak dropping due to the cyclic shift of the mapped image along the (theta) axis when the target is rotated.