1. A two-dimensional lattice calibrating device, comprising: a measuring unit that measures positions of a plurality of marks within a plane of an artifact as a standard gauge, the positions of the plurality of marks being measured per a plurality of measurement dispositions in which at least a part of the plurality of marks is superposed; a coordinate setting unit in which a coordinate relational equation is set in advance, the coordinate relational equation representing a relationship between a measurement coordinate system of the measuring unit and an artifact coordinate system for specifying the positions of the plurality of marks on the artifact for each of the plurality of measurement dispositions; a simultaneous-equations generating unit that generates simultaneous equations for acquiring deviations of the plurality of marks using a coordinate relational equation and a conditional equation that sets a coordinate axis of the artifact coordinate system based on a measurement value of the plurality of marks; and a simultaneous-equations calculating unit that solves the simultaneous equations generated by the simultaneous-equations generating unit.