Methods for adjusting and evaluating light intensity distribution of illumination apparatus, illumination apparatus, exposure apparatus, and device manufacturing method

A method for adjusting a first multipolar light intensity distribution formed on a pupil plane of an illumination apparatus configured to illuminate a surface based on a light flux from a light source to a light intensity distribution substantially equivalent to a targeted second multipolar light intensity distribution, the method comprising:

• measuring the first multipolar light intensity distribution;
• obtaining a first light intensity angle distribution by integrating a light intensity of each point in an area in a light intensity distribution of a first pole in the measured first multipolar light intensity distribution in a radial direction with respect to a predetermined central point and a second light intensity angle distribution by integrating a light intensity of each point in an area in a light distribution of a second pole, corresponding to the first pole, in the second multipolar light intensity distribution in the radial direction with respect to a predetermined central point;
• obtaining a first cumulative light quantity distribution in a circumferential direction by integrating the first light intensity angle distribution in the circumferential direction with respect to the central point and a second cumulative light quantity distribution in the circumferential direction by integrating the second light intensity angle distribution in the circumferential direction with respect to the central point;
• obtaining a difference at each of at least two points between the first cumulative light quantity distribution of the first pole in the first multipolar light intensity distribution and the second cumulative light quantity distribution of the second pole in the second multipolar light intensity distribution;
• and
• adjusting the first multipolar light intensity distribution based on the difference between the first cumulative light quantity distribution and the second cumulative light quantity distribution.

A method for evaluating a first light intensity distribution formed on a pupil plane in an illumination apparatus as a second light intensity distribution that is uniform and equivalent to the first light intensity distribution, the method comprising:

• obtaining a light intensity radial distribution by integrating a light intensity of each point in an area in the first light intensity distribution in a circumferential direction with respect to a predetermined central point;
• obtaining a cumulative light quantity distribution in a radial direction by integrating the light intensity radial distribution in the radial direction with respect to the central point;
• and
• obtaining a parameter of the second light intensity distribution with a minimum square sum of difference at each of at least three points between the cumulative light quantity distribution obtained from the first light intensity distribution and a cumulative light quantity distribution obtained from the second light intensity distribution.

A method for evaluating a first multipolar light intensity distribution formed on a pupil plane in an illumination apparatus as a second multipolar light intensity distribution that is uniform and equivalent to the first multipolar light intensity distribution, the method comprising:

• obtaining a light intensity angle distribution by integrating a light intensity of each point in an area in the first multipolar light intensity distribution in a radial direction with respect to a predetermined central point;
• obtaining a cumulative light quantity distribution in a circumferential direction by integrating the light intensity angle distribution corresponding to a first pole in the first multipolar light intensity distribution with respect to the predetermined central point from a predetermined angle;
• and
• obtaining an aperture angle of a second pole, corresponding to the first pole, in the second multipolar light intensity distribution with a minimum square sum of difference at each of at least two points between the cumulative light quantity distribution of the first pole and a cumulative light quantity distribution of the second pole.