Measurement apparatus, exposure apparatus, and device manufacturing method to measure numerical aperture of the optical system using interference fringe

An exposure apparatus which projects a pattern of an original onto a substrate using a projection optical system to expose the substrate, the exposure apparatus comprising:

• a mirror configured to reflect test light which passes through the projection optical system;
• an interferometer unit which includes an image sensor and is configured to form an interference fringe on an image sensing plane of the image sensor by reference light and the test light reflected by the mirror;
• and
• a controller configured to control the interferometer unit, and compute a numerical aperture NA of the projection optical system based on the interference fringe captured by the image sensor,
• wherein the controller computes the numerical aperture NA of the projection optical system by multiplying a quotient ΔNA/ΔR describing a change ΔNA in the numerical aperture NA of the projection optical system with respect to a change ΔR in pupil radius R of the projection optical system in the image sensing plane by the pupil radius R of the projection optical system in the image sensing plane,
• wherein the controller is configured to compute, using a first radius R1 as the pupil radius R of the projection optical system in the image sensing plane, a wavefront difference W1 that is a difference between a first wavefront of the projection optical system computed based on a first interference fringe formed on the image sensing plane when a position of the mirror relative to the projection optical system is in a first state and a second wavefront of the projection optical system computed based on a second interference fringe formed on the image sensing plane when the position of the mirror relative to the projection optical system is in a second state which is obtained by a movement of a movement amount ΔX from the position of the first state,
• to compute, using a second radius R2 that differs from the first radius R1 as the pupil radius R of the projection optical system in the image sensing plane, a wavefront difference W2 that is a difference between a third wavefront of the projection optical system computed based on the first interference fringe, and a fourth wavefront of the projection optical system computed based on the second interference fringe, and
• to compute the quotient ΔNA/ΔR using the following equation:
• ΔNA/ΔR=(W1−W2)/{(R1−R2)ΔX}.

A device manufacturing method comprising the steps of:

• exposing a substrate coated with a photosensitive agent using an exposure apparatus configured to project a pattern of an original onto the substrate using a projection optical system to expose the photosensitive agent on the substrate;
• and
• developing the photosensitive agent,
• wherein the exposure apparatus comprises:
• a mirror configured to reflect test light which passes through the projection optical system;
• an interferometer unit which includes an image sensor and is configured to form an interference fringe on an image sensing plane of the image sensor by reference light and the test light reflected by the mirror;
• and
• a controller configured to control the interferometer unit, and compute a numerical aperture NA of the projection optical system based on the interference fringe captured by the image sensor, wherein the controller computes the numerical aperture NA of the projection optical system by multiplying a quotient ΔNA/ΔR describing a change ΔNA in the numerical aperture NA of the projection optical system with respect to a change ΔR in pupil radius R of the projection optical system in the image sensing plane by the pupil radius R of the projection optical system in the image sensing plane,
• wherein the controller is configured to compute, using a first radius R1 as the pupil radius R of the projection optical system in the image sensing plane, a wavefront difference W1 that is a difference between a first wavefront of the projection optical system computed based on a first interference fringe formed on the image sensing plane when a position of the mirror relative to the projection optical system is in a first state and a second wavefront of the projection optical system computed based on a second interference fringe formed on the image sensing plane when the position of the mirror relative to the projection optical system is in a second state which is obtained by a movement of a movement amount ΔX from the position of the first state,
• to compute, using a second radius R2 that differs from the first radius R1 as the pupil radius R of the projection optical system in the image sensing plane, a wavefront difference W2 that is a difference between a third wavefront of the projection optical system computed based on the first interference fringe, and a fourth wavefront of the projection optical system computed based on the second interference fringe, and
• to compute the quotient ΔNA/ΔR using the following equation:
• ΔNA/ΔR=(W1−W2)/{(R1−R2)ΔX}.