Abstract: In determining a relative position between a chip lattice including rectangular cells, each of which has a size of a chip to be formed on a substrate and an effective area on the substrate, one representative cell in the chip lattice is divided into a plurality of partial areas in accordance with an existing area, of a representative point of the effective area, in which chip sets trimmed from the chip lattice with the effective area are identical. A partial area corresponding to a chip set including a maximum number of chips is specified from the plurality of partial areas, and the representative point is set in the specified partial area.

Abstract: An optical apparatus which includes an image forming optical system having a movable optical element, and a driving mechanism configured to move the optical element. The apparatus includes a first block which measures a wavefront aberration of the optical system. A second block obtains a linear evaluation value of an aberration expressed by a linear function of a position of the movable optical element out of aberrations of the optical system, and a quadratic evaluation value of a square of a root mean square of the wavefront aberration measured by the first block expressed by a quadratic function of the position. A third block uses a dummy variable as an upper limit value of the linear evaluation value and obtains a minimum value of the dummy variable by a linear programming. A fourth block determines a position of the optical element to be moved by the driving mechanism.

Abstract: 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.

Abstract: An optical apparatus including an image forming optical system having a movable optical element, and a driving mechanism which moves the optical element is disclosed.

Abstract: In determining a relative position between a chip lattice comprised of rectangular cells each of which has a size of a chip to be formed on a substrate and an effective area on the substrate, one representative cell in the chip lattice is divided into a plurality of partial areas in accordance with an existing area, of a representative point of the effective area, in which chip sets trimmed from the chip lattice with the effective area are identical. A partial area corresponding to a chip set including a maximum number of chips is specified from the plurality of partial areas, and the representative point is set in the specified partial area.

Abstract: An optical apparatus including an image forming optical system having a movable optical element, and a driving mechanism which moves the optical element is disclosed.