1. An image pickup apparatus comprising: an image pickup portion configured to pick up an optical image of an object formed by an objective optical system configured to form the optical image of the object, and generate an image pickup signal; a zoom magnification setting portion configured to set a zoom magnification; a cut-out range setting portion configured to set a position and size of a cut-out area, which is a part of an image represented by the image pickup signal, wherein a center of the cut-out area is set at a position deviated from a field-of-view center of the objective optical system when the zoom magnification is a first magnification, and the center of the cut-out area is set to come close to the field-of-view center as the zoom magnification increases from the first magnification; and a zoom processing portion configured to cut out the cut-out area set by the cut-out range setting portion from the image represented by the image pickup signal, perform enlargement or reduction corresponding to the zoom magnification and generate a zoomed image.