Abstract: A method including calculating, using an objective function, which includes a regression model used to estimate an array of a plurality of regions on a substrate and a regularization term used to limit a value of a coefficient of the regression model, a value of each of a plurality of coefficients included in the regression model, with which the objective function becomes not more than a reference value, extracting, based on the calculated values, the coefficient having the value not less than a threshold value from the plurality of coefficients, and obtaining, using a regression model including only the extracted coefficient, an array of a plurality of regions on a substrate.

Abstract: A method including calculating, using an objective function, which includes a regression model used to estimate an array of a plurality of regions on a substrate and a regularization term used to limit a value of a coefficient of the regression model, a value of each of a plurality of coefficients included in the regression model, with which the objective function becomes not more than a reference value, extracting, based on the calculated values, the coefficient having the value not less than a threshold value from the plurality of coefficients, and obtaining, using a regression model including only the extracted coefficient, an array of a plurality of regions on a substrate.

Abstract: The preset invention provides a method of obtaining an array of a plurality of regions on a substrate, including obtaining, using a prior distribution representing a probability distribution of parameters of a regression model used to estimate the array, a first posterior distribution representing the probability distribution of the parameters, obtaining, using the first posterior distribution as the prior distribution representing the probability distribution of the parameters, a second posterior distribution representing the probability distribution of the parameters, and updating the regression model by deciding the parameters based on the second posterior distribution and obtaining, using the updated regression model, the array of the plurality of regions on a substrate from the second position measurement data.

Abstract: An exposure apparatus that performs a job process of exposing each of a plurality of substrates while exchanging the substrate is provided. The apparatus comprises a substrate holder configured to hold a substrate, and a controller configured to control the job process. The controller corrects, based on a relationship between an elapsed time of the job process and a substrate deformation amount, an overlay error generated due to deformation of the substrate, and exposes the substrate. In the relationship, the substrate conveyed to the substrate holder upon a substrate exchange is given an initial deformation amount corresponding to residual heat of the substrate holder at the time of the substrate exchange.

Abstract: An exposure apparatus that projects a pattern of an original onto a substrate via a projection optical system and exposes the substrate is provided. The apparatus comprises an aberration correction member arranged on an optical path of exposure light between the original and the substrate, and a driver which drives the aberration correction member. The aberration correction member includes a first optical element including a first surface having a three-fold rotational symmetric aspherical shape with respect to an optical axis of the exposure light, and a second optical element spaced apart from the first optical element along the optical axis and including a second surface facing the first surface and having an aspherical shape that complementarily corrects an aberration generated by the first optical element.

Abstract: An exposure apparatus that performs a job process of exposing each of a plurality of substrates while exchanging the substrate is provided. The apparatus comprises a substrate holder configured to hold a substrate, and a controller configured to control the job process. The controller corrects, based on a relationship between an elapsed time of the job process and a substrate deformation amount, an overlay error generated due to deformation of the substrate, and exposes the substrate. In the relationship, the substrate conveyed to the substrate holder upon a substrate exchange is given an initial deformation amount corresponding to residual heat of the substrate holder at the time of the substrate exchange.

Abstract: An exposure apparatus that projects a pattern of an original onto a substrate via a projection optical system and exposes the substrate is provided. The apparatus comprises an aberration correction member arranged on an optical path of exposure light between the original and the substrate, and a driver which drives the aberration correction member. The aberration correction member includes a first optical element including a first surface having a three-fold rotational symmetric aspherical shape with respect to an optical axis of the exposure light, and a second optical element spaced apart from the first optical element along the optical axis and including a second surface facing the first surface and having an aspherical shape that complementarily corrects an aberration generated by the first optical element.

Abstract: In a case where a substrate is exposed to exposure light of a first wavelength band, an exposure coefficient, which is defined as an amount of fluctuation of an imaging characteristic of a projection optical system per unit of exposure energy, for the first wavelength band is calculated using data of the amount of fluctuation of the optical characteristic of the projection optical system. An exposure coefficient for a second wavelength band that is different from the first wavelength band is calculated using the exposure coefficient for the first wavelength band. In a case where the substrate is exposed to exposure light of the second wavelength band, the amount of fluctuation of the imaging characteristic of the projection optical system is calculated using the exposure coefficient for the second wavelength band.

Abstract: In a case where a substrate is exposed to exposure light of a first wavelength band, an exposure coefficient, which is defined as an amount of fluctuation of an imaging characteristic of a projection optical system per unit of exposure energy, for the first wavelength band is calculated using data of the amount of fluctuation of the optical characteristic of the projection optical system. An exposure coefficient for a second wavelength band that is different from the first wavelength band is calculated using the exposure coefficient for the first wavelength band. In a case where the substrate is exposed to exposure light of the second wavelength band, the amount of fluctuation of the imaging characteristic of the projection optical system is calculated using the exposure coefficient for the second wavelength band.

Abstract: A system includes a plurality of optical elements, a deformation unit configured to deform a deformable optical element satisfying a following conditional formula included in the plurality of optical elements by applying a force to the deformable optical element: 0.75<EA/EA0<0.95 where EA0 represents an effective aperture of each of the plurality of optical elements and EA represents an axial light flux diameter of each of the plurality of optical elements, and a control unit configured to control the deformation unit, wherein n positions on an outer circumference of the deformable optical element are fixed, the deformation unit includes n actuators, the n actuators apply forces to n positions on the outer circumference other than the fixed n positions, and the control unit controls each of the n actuators independently.

Abstract: In a case where a substrate is exposed to exposure light of a first wavelength band, an exposure coefficient, which is defined as an amount of fluctuation of an imaging characteristic of a projection optical system per unit of exposure energy, for the first wavelength band is calculated using data of the amount of fluctuation of the optical characteristic of the projection optical system. An exposure coefficient for a second wavelength band that is different from the first wavelength band is calculated using the exposure coefficient for the first wavelength band. In a case where the substrate is exposed to exposure light of the second wavelength band, the amount of fluctuation of the imaging characteristic of the projection optical system is calculated using the exposure coefficient for the second wavelength band.

Abstract: An exposure apparatus for exposing a substrate to a light comprises a projection optical system including an optical element and configured to project a light from an original onto the substrate, an adjusting device configured to adjust at least one of a position, an orientation and a shape of the optical element, and a controller configured to obtain an adjusting amount of the optical element based on a value of an objective function relating to an optical characteristic of the projection optical system, and to control the adjusting device based on the obtained adjusting amount. The objective function includes a variable which represents an upper limit of the adjusting amount.

Abstract: The present invention provides an exposure apparatus including a map obtaining unit configured to obtain a pupil aberration map representing saturation values of fluctuations in each of optical characteristics generated in a plurality of regions, which are obtained by dividing a pupil plane of a projection optical system, upon irradiating the plurality of regions with a unit amount of light, a distribution obtaining unit configured to obtain a light intensity distribution formed on the pupil plane of the projection optical system upon illuminating a pattern of an arbitrary reticle in an arbitrary illumination mode, and a calculation unit configured to calculate a saturation value of a fluctuation in each of the optical characteristics generated in the projection optical system upon illuminating the pattern of the arbitrary reticle in the arbitrary illumination mode, based on the obtained pupil aberration map and the obtained light intensity distribution.

Abstract: An exposure apparatus for exposing a substrate to a light comprises a projection optical system including an optical element and configured to project a light from an original onto the substrate, an adjusting device configured to adjust at least one of a position, an orientation and a shape of the optical element, and a controller configured to obtain an adjusting amount of the optical element based on a value of an objective function relating to an optical characteristic of the projection optical system, and to control the adjusting device based on the obtained adjusting amount. The objective function includes a variable which represents an upper limit of the adjusting amount.

Abstract: A system includes a plurality of optical elements, a deformation unit configured to deform a deformable optical element satisfying a following conditional formula included in the plurality of optical elements by applying a force to the deformable optical element: 0.75<EA/EA0<0.95 where EA0 represents an effective aperture of each of the plurality of optical elements and EA represents an axial light flux diameter of each of the plurality of optical elements, and a control unit configured to control the deformation unit, wherein n positions on an outer circumference of the deformable optical element are fixed, the deformation unit includes n actuators, the n actuators apply forces to n positions on the outer circumference other than the fixed n positions, and the control unit controls each of the n actuators independently.

Abstract: An exposure apparatus includes a first driving mechanism which drives a first optical element, a second driving mechanism which drives a second optical element, and a control unit which controls the first driving mechanism and the second driving mechanism so as to adjust the astigmatism of a projection optical system. The amount of change in the first order component of the astigmatism and the amount of change in the second order component of the astigmatism upon driving the first optical element by the first driving mechanism have a first ratio, and the amount of change in the first order component of the astigmatism and the amount of change in the second order component of the astigmatism upon driving the second optical element by the second driving mechanism have a second ratio which is different from the first ratio.

Abstract: The present invention provides an exposure apparatus including a map obtaining unit configured to obtain a pupil aberration map representing saturation values of fluctuations in each of optical characteristics generated in a plurality of regions, which are obtained by dividing a pupil plane of a projection optical system, upon irradiating the plurality of regions with a unit amount of light, a distribution obtaining unit configured to obtain a light intensity distribution formed on the pupil plane of the projection optical system upon illuminating a pattern of an arbitrary reticle in an arbitrary illumination mode, and a calculation unit configured to calculate a saturation value of a fluctuation in each of the optical characteristics generated in the projection optical system upon illuminating the pattern of the arbitrary reticle in the arbitrary illumination mode, based on the obtained pupil aberration map and the obtained light intensity distribution.

Abstract: An exposure apparatus includes a first driving mechanism which drives a first optical element, a second driving mechanism which drives a second optical element, and a control unit which controls the first driving mechanism and the second driving mechanism so as to adjust the astigmatism of a projection optical system. The amount of change in the first order component of the astigmatism and the amount of change in the second order component of the astigmatism upon driving the first optical element by the first driving mechanism have a first ratio, and the amount of change in the first order component of the astigmatism and the amount of change in the second order component of the astigmatism upon driving the second optical element by the second driving mechanism have a second ratio which is different from the first ratio.