Provided is a geometric transformation lens which can transform a target image geometrically as desired, achieving downsizing and reducing energy consumption. Even if another target to be observed more in detail is inside the field of view, the geometric transformation lenses (20a, 20b, 20c and 20d) can magnify optically the desired region within the target projection image by supplying the magnification instruction voltage (V2,mn) to the corresponding magnifying/demagnifying electrodes (EL2,mn) simply without moving the lens itself using heavy mechanical parts motorized. This can achieve downsizing because a space for setting the existing mechanical part to control the direction of the lens and its motion can be disregarded. This also can achieve reducing energy consumption because no space is needed to move the lenses with the heavy mechanical parts.