An error adding portion adds together input multi-tone image data and peripheral error information. The received e-mails are analyzed to determine patterns of similarity. The connecting assembly is has a connecting tube and a leash tie hole. The optical elements are set between the first object and the second object, and has rotationally asymmetric powers with respect to an optical axis of the projection optical system. More specifically, the path length L1 of the lower plate 3 is 40-60% longer than the path length L2 of the upper plate 2.