Device manufacturing method, computer program and lithographic apparatus

A device manufacturing method using a lithographic apparatus comprising:

• an illuminator configured to illuminate a patterning device with a radiation beam having an illumination arrangement, and
• a projection system configured to project radiation in a modulated beam to form an image of the pattern onto a substrate, the projection system having a pupil plane and an adjustable element configured to adjust an aberration of the projection system in response to a control setting,
• the method comprising:
• receiving information regarding the pattern and the illumination arrangement;
• determining a region of interest based on the information regarding the pattern and the illumination arrangement using a non-transitory computer system comprising a computer program to execute the determining, the region of interest being a non-circular region of the pupil plane through which substantially all of the radiation of the modulated beam that contributes to formation of the image passes;
• determining a weighting function for the pupil plane, the weighting function weighting the region of interest higher than parts of the pupil plane not in the region of interest;
• obtaining a set of basis functions that are orthogonal over the weighted pupil plane;
• expressing the wavefront in the pupil plane in terms of the basis functions that are orthogonal over the weighted pupil plane and a set of coefficients;
• and
• determining a value of the control setting to minimize the values of the coefficients.

A non-transitory computer readable storage medium comprising a computer program recorded thereon, the computer program configured to cause a computer system to determine a value for a control setting for a device manufacturing method using a lithographic apparatus comprising:

• an illuminator configured to illuminate a patterning device with a radiation beam having an illumination arrangement, and
• a projection system configured to project radiation in a modulated beam to form an image of the pattern onto a substrate, the projection system having a pupil plane and an adjustable element configured to adjust an aberration of the projection system in response to a control setting,
• the computer program comprising instructions to instruct the computer system to perform a method comprising:
• receiving information regarding the pattern and the illumination arrangement;
• determining a region of interest based on the information regarding the pattern and the illumination arrangement, the region of interest being a non-circular region of the pupil plane through which substantially all of the radiation of the modulated beam that contributes to formation of the image passes;
• obtaining a set of basis functions that are orthogonal over the region of interest;
• expressing the wavefront in the pupil plane in terms of the basis functions that are orthogonal over the region of interest and a set of coefficients;
• and
• determining a value of the control setting to minimize the values of the coefficients.

A lithographic apparatus comprising:

• an illuminator configured to illuminate a patterning device with a radiation beam having an illumination arrangement;
• a projection system configured to project radiation in a modulated beam to form an image of the pattern onto a substrate, the projection system having a pupil plane and an adjustable element configured to adjust an aberration of the projection system in response to a control setting;
• and
• a control system comprising:
• an input device arranged to receive information regarding the pattern and the illumination arrangement,
• a first calculating device arranged to determine a region of interest based on the information regarding the pattern and the illumination arrangement, the region of interest being a non-circular region of the pupil plane through which substantially all of the radiation of the modulated beam that contributes to formation of the image passes,
• a second calculating device arranged to obtain a set of basis functions that are orthogonal over the region of interest,
• a third calculating device arranged to express the wavefront in the pupil plane in terms of the basis functions that are orthogonal over the region of interest and a set of coefficients, and
• a fourth calculating device arranged to determine a value of the control setting to minimize the values of the coefficients.