A new method of synthesizing an image is presented, which is essential for integral photography, using high-resolution printer output and a fly's eye lens sheet. Integral photography (IP) is one of the best stereoscopic viewing systems available because not only horizontal but also full parallax can be obtained without the need for wearing special glasses. A special image, called an IP image, is synthesized with a computer using this technology, and is output with a high-resolution printer. When the image is observed through a special lens sheet, called a fly's eye lens, superb binocular vision can be obtained. The lens sheet consists of an array of minute convex lenses. Each lens is either square or hexagonal and the latter has the advantage that the number of lenses for each unit area can be increased. However, the existing method of synthesis is no longer applicable. Therefore, we propose a method of synthesis that can be applied to these cases. Half the proposed method is the same as the existing one in which hundreds of still images are taken with a real or virtual camera from different angles. However, the next stage of the method is only for cases using the hexagonal fly's eye lens. The displacement from the center of the nearest hexagonal lens is calculated for all pixels of in the IP image. Since the displacement corresponds to the direction of a ray emitted from a pixel, the nearest camera position to the ray is calculated from hundreds of camera positions. A pixel position that corresponds to the hexagonal lens is calculated from the image taken from the camera position, and the pixel value is set to the pixel of the IP image. Finally, the IP image is scaled to the final IP image so that the size matches the hexagonal fly's eye lens sheet. Experiments demonstrated that excellent binocular vision could be obtained using the new method.