Patent ID: 7948695

Claim:
An apparatus that includes an optical element and positions the optical element, the apparatus comprising: a holder configured to hold the optical element; a back plate configured to support the optical element via the holder; a mechanism configured to move the optical element in six-degrees-of-freedom; a base plate configured to support the back plate via the mechanism; three first displacement sensors disposed on the base plate and configured to measure respective displacement amounts of three mutually different points on the back plate in a first direction; a second displacement sensor disposed on the base plate and configured to measure a displacement amount of one point on the back plate in a second direction different from the first direction; two third displacement sensors disposed on the base plate and configured to measure respective displacement amounts of two mutually different points on the back plate in a third direction different from the first and second directions; a transformation processor configured to transform the six displacement amounts measured by the first, second and third displacement sensors into displacement amounts of the optical element in the six-degrees-of-freedom; a calibration processor configured to calibrate the displacement amounts transformed by the transformation processor with a calibration matrix, of which coefficients are previously obtained, to calibrate the displacement amounts in the six-degrees-of-freedom, which have errors due to measurement errors of the first, second and third displacement sensors; and a controller configured to output command values to the mechanism based on differences between the displacement amounts calibrated by the calibration processor and target displacement amounts of the optical element.