Geometrical transformations in optics*

Optical techniques are introduced for performing general types of map transformations. Geometrical image modifications like coordinate transformations and local translation, inversion, reflection, stretching, and rotation require highly space-variant systems. Filters can be introduced into optical coherent systems in such a way that their local phase variations are able to influence light from local object areas. Experimental results of typical optical geometrical transformations like conformal mapping of object distributions are presented. Another capability of this technique is to image a specific, arbitrary surface onto another surface of general shape.