System and method for polarization characteristic measurement of optical systems via centroid analysis
A method for irradiating onto a target optical system plural linearly polarized rays having different polarization directions, and for measuring a polarization characteristic of the target optical system including a birefringence amount R and a fast axis Φ includes the steps of irradiating linearly polarized ray having a polarization direction θ onto the target optical system and obtaining a centroid amount P of the ray that has transmitted through the target optical system, and obtaining the birefringence amount R and the fast axis Φ from P=−R·cos(2θ−Φ) or P=R·cos(2θ−Φ).
1. A method for irradiating onto a target optical system plural linearly polarized rays having different polarization directions, and for measuring a polarization characteristic of the target optical system including a birefringence amount R and a fast axis Φ, said method comprising the steps of:
irradiating linearly polarized ray having a polarization direction θ onto the target optical system and obtaining a centroid amount P of the ray that has transmitted through the target optical system; and
obtaining the birefringence amount R and the fast axis Φ from P=−R·cos(2θ−Φ) or P=R·cos (2θ−Φ).
2. A method according to claim 1 , wherein the polarization characteristic further includes a Jones matrix M defined in the following equation, and said method further comprising the step of obtaining the Jones matrix M by irradiating two linearly polarized rays having different polarization directions onto the target optical system and measuring transmittances A and A′ of the target optical system for the two linearly polarized rays:
M=[A ·exp( −i·m ), a ·exp( −i·b ); a ·exp( −i·b ), A ′·exp( i·m )]
a= 2 A ″·sin R·Ex·Ey,
A″ =( A+A′ )/2,
b±π/ 2,
m=Arg{A·Ey 2 ·exp( −i·R )+ A′·Ex 2 ·exp( i·R )},
Ex =√{(1+cos Φ)2},
Ex 2 +Ey 2 =1.
3. A method for irradiating onto a target optical system plural linearly polarized rays having different polarization directions, and for measuring a polarization characteristic of the target optical system, said method comprising the steps of:
obtaining a relationship between an actual value of the polarization characteristic of the target optical system and a value of the polarization characteristic obtained under an approximation of an eigenvector of a Jones matrix of the target optical system to a linearly polarized ray;
obtaining a centroid amount determined by light intensities and phases of two rays divided due to birefringence of the target optical system; and
calculating the polarization characteristic based on the relationship and the centroid amount of the rays.
4. A method according to claim 3 , wherein the relationship is a proportion.
5. A method according to claim 3 , wherein the target optical system includes plural lenses, and a distribution range of the birefringence amount falls within 30°.
6. A method according to claim 3 , further comprising the step of changing the polarization direction of the ray.
7. A method according to claim 3 , wherein said centroid obtaining step utilizes a point diffraction interferometry, a lateral shearing interferometry, or Hartmann method.
8. An exposure apparatus comprising a projection optical system for projecting a reticle pattern onto a substrate, the projection optical system being adjusted based on a polarization characteristic measured by a method that irradiates onto the projection optical system plural linearly polarized rays having different polarization directions, the polarization characteristic including a birefringence amount R and a fast axis Φ of the target optical system, the method including the steps of irradiating the linearly polarized ray having a polarization direction θ onto the target optical system and obtaining a centroid amount P of the ray that has transmitted through the target optical system, and obtaining the birefringence amount R and the fast axis Φ from P=−R·cos(2θ−Φ) or P=R·cos(2θ−Φ).
9. A device manufacturing method comprising the steps of:
exposing a substrate using an exposure apparatus; and
developing the substrate exposed,
wherein the exposure apparatus includes a projection optical system for projecting a reticle pattern onto a substrate, the projection optical system being adjusted based on a polarization characteristic measured by a measurement method that irradiates onto the projection optical system plural linearly polarized rays having different polarization directions, the polarization characteristic including a birefringence amount R and a fast axis Φ of the target optical system, the measurement method including the steps of irradiating the linearly polarized ray having a polarization direction θ onto the target optical system and obtaining a centroid amount P of the ray that has transmitted through the target optical system, and obtaining the birefringence amount R and the fast axis Φ from P=−R·cos(2θ−Φ) or P=R·cos(2θ−Φ).