Pattern inspection apparatus, pattern position measurement apparatus, aerial image measurement system, method for measuring aerial image, pattern position repairing apparatus, method for repairing pattern position, aerial image data processing apparatus, method for processing aerial image data, pattern exposure apparatus, method for exposing pattern, method for manufacturing mask, and mask manufacturing system

A pattern inspection apparatus includes: an optical image acquiring mechanism to acquire optical image data of a corresponding divided pattern for each of masks for multiple patterning has been formed; a position deviation map generating processing circuitry to generate position deviation maps regarding the corresponding divided pattern; a difference position value map generating processing circuitry to generate one difference position value map defining a difference value between relative position deviation amounts of the each minimum element of the position deviation maps; a region specifying processing circuitry to specify at least one region having the difference value exceeding a threshold of distance between patterns laying side-by-side by using the difference position value map; and an output mechanism to output at least coordinates, a type of defect, and information of a reference image of each region specified for the each region specified.