Optical apparatus, method of determining position of optical element in optical system, and device manufacturing method

摘要

An optical apparatus including an image forming optical system having a movable optical element, and a driving mechanism. A first block obtains a linear evaluation value by normalizing, by a first tolerance, an aberration expressed by a linear function of a position of the movable optical element and normalizing, by a second tolerance, an aberration expressed by a quadratic function of the position out of the aberrations of the optical system. A second block obtains a minimum value of a dummy variable by linear programming. A third block determines a position of the optical element to be moved by the driving mechanism using a value prepared by adding a relaxation amount to the minimum value obtained by the second block and minimizes the weighted sum of the quadratic evaluation values by adjusting the weights assigned to the quadratic evaluation values and a relaxation amount.