Abstract: A method of predicting thermally induced aberrations of a projection system for projecting a radiation beam, the method comprising: calculating an irradiance profile for at least one optical element of the projection system from a power and illumination source pupil of the radiation beam, estimating a temperature distribution as a function of time in the at least one optical element of the projection system using the calculated irradiance profile for the at least one optical element of the projection system; calculating the thermally induced aberrations of the projection system based on the estimated temperature distribution and a thermal expansion parameter map associated with the at least one optical element of the projection system, wherein the thermal expansion parameter map is a spatial map indicating spatial variations of thermal expansion parameters in the at least one optical element of the projection system or a uniform map.

Abstract: A control system for a positioning system, for positioning a driven object, e.g. in a lithographic apparatus, in N dimensions has M sensors, where M>N. A transformation module converts the M measurements by the sensors into a positional estimate in N dimensions taking into account compliance of the driven object.

Abstract: A control system for a positioning system, for positioning a driven object, e.g. in a lithographic apparatus, in N dimensions has M sensors, where M>N. A transformation module converts the M measurements by the sensors into a positional estimate in N dimensions taking into account compliance of the driven object.

Abstract: A lithographic apparatus includes a driven object having compliant dynamics; a plurality of actuators configured to act on the driven object, wherein the plurality of actuators are over-determined in an actuator degree of freedom; a control system including a transformation matrix configured to generate controller output signals for each of the plurality of actuators in response to a setpoint, wherein the transformation matrix is configured such that the controller output signals do not excite the compliant dynamics of the driven object in at least one degree of freedom.

Abstract: There is provided a positioning system for positioning an object in a lithographic apparatus. The positioning system includes a support, a position measurement device, a deformation sensor and a processor. The support is constructed to hold the object. The position measurement device is configured to measure a position of the support. The position measurement device includes at least one position sensor target and a plurality of position sensors to cooperate with the at least one position sensor target to provide a redundant set of position signals representing the position of the support. The deformation sensor is arranged to provide a deformation signal representing a deformation of one of the support and the position measurement device. The processor is configured to calibrate one of the position measurement device and the deformation sensor based on the deformation signal and the redundant set of position signals.

Abstract: A lithographic apparatus includes a driven object having compliant dynamics; a plurality of actuators configured to act on the driven object, wherein the plurality of actuators are over-determined in an actuator degree of freedom; a control system including a transformation matrix configured to generate controller output signals for each of the plurality of actuators in response to a setpoint, wherein the transformation matrix is configured such that the controller output signals do not excite the compliant dynamics of the driven object in at least one degree of freedom.

Abstract: A lithographic apparatus includes: an illumination system configured to condition a radiation beam; a support constructed to support a patterning device, the patterning device being capable of imparting the radiation beam with a pattern in its cross-section to form a patterned radiation beam; a substrate table constructed to hold a substrate; a projection system configured to project the patterned radiation beam onto a target portion of the substrate, and a deformation sensor to determine deformations of an object of the lithographic apparatus, wherein the deformation sensor includes at least one optical fiber arranged on or in the object, the optical fiber including one or more Bragg gratings, and an interrogation system to interrogate the one or more Bragg gratings.

Abstract: There is provided a positioning system for positioning an object in a lithographic apparatus. The positioning system includes a support, a position measurement device, a deformation sensor and a processor. The support is constructed to hold the object. The position measurement device is configured to measure a position of the support. The position measurement device includes at least one position sensor target and a plurality of position sensors to cooperate with the at least one position sensor target to provide a redundant set of position signals representing the position of the support. The deformation sensor is arranged to provide a deformation signal representing a deformation of one of the support and the position measurement device. The processor is configured to calibrate one of the position measurement device and the deformation sensor based on the deformation signal and the redundant set of position signals.

Abstract: A controller is provided that controls an actuator system having a plurality of actuators arranged to act on an object. The controller uses a gain balancing matrix to convert a first control signal, representing a set of forces desired to be provided to the center of gravity of the object into a second control signal, representing an equivalent set of forces to be provided by the plurality of actuators. The system is further configured such that a first gain balancing matrix is used at a first frequency band and a second gain balancing matrix is used at a second frequency band.

Abstract: A lithographic apparatus includes: an illumination system configured to condition a radiation beam; a support constructed to support a patterning device, the patterning device being capable of imparting the radiation beam with a pattern in its cross-section to form a patterned radiation beam; a substrate table constructed to hold a substrate; a projection system configured to project the patterned radiation beam onto a target portion of the substrate, and a deformation sensor to determine deformations of an object of the lithographic apparatus, wherein the deformation sensor includes at least one optical fiber arranged on or in the object, the optical fiber including one or more Bragg gratings, and an interrogation system to interrogate the one or more Bragg gratings.

Abstract: A controller is provided that controls an actuator system having a plurality of actuators arranged to act on an object. The controller uses a gain balancing matrix to convert a first control signal, representing a set of forces desired to be provided to the centre of gravity of the object into a second control signal, representing an equivalent set of forces to be provided by the plurality of actuators. The system is further configured such that a first gain balancing matrix is used at a first frequency band and a second gain balancing matrix is used at a second frequency band.