. . "Since the generation factors of the errors dFXk(i11, j11) are considered to be random, the mark information calculation device 32 assumes that their distribution is a normal distribution, and that a probability density function fX11(dx) of the errors dFXk(i11, j11) is given by f X11 ??? ( d ??? ??? x ) = 1 2 ??? ??? ?? ??? ?? ??? ??? X ??? ( i 11 , j 11 ) ??? exp ??? [ { d ??? ??? x - d ??? ??? F" . .