Abstract

The influence of birefringence on high-resolution projection optics used for microlithography is investigated theoretically. A formula for partially coherent imaging that is based on the scalar diffraction theory is extended to include the birefringent properties of lens materials. By the determination of the birefringent properties of lens materials by use of random numbers, data on 200 lenses, each composed of 10 birefringent elements, are generated to estimate statistically the degree of imaging-performance degradation. As a result, it was found that the image contrast of a five-bar pattern decreases as a quadratic function of the maximum magnitude of the birefringence that was set in common for all elements in each lens data set.

© 2000 Optical Society of America

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References

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  1. Y. Unno, “Distorted wave front produced by a high-resolution projection optical system having rotationally symmetric birefringence,” Appl. Opt. 37, 7241–7247 (1998).
    [CrossRef]
  2. F. Ratajczyk, “A method of calculation of permissible birefringence in lenses of the optical instruments,” Optik 68, 61–68 (1984).
  3. H. Fukuda, A. Imai, T. Terasawa, S. Okazaki, “New approach to resolution limit and advanced image formation techniques in optical lithography,” IEEE Trans. Electron Devices 38, 67–75 (1991).
    [CrossRef]
  4. Related papers can be found in L. Van den Hove, ed., Optical Microlithography XII, Proc. SPIE3679, (1999).
  5. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 10.
  6. A. Takahashi, M. Mieda, Y. Murakami, K. Ohta, H. Yamaoka, “Influence of birefringence on the signal quality of magneto-optic disks using polycarbonate substrates,” Appl. Opt. 27, 2863–2866 (1988).
    [CrossRef] [PubMed]
  7. B. E. Bernacki, M. Mansuripur, “Investigation of substrate birefringence effects on optical-disk performance,” Appl. Opt. 32, 6547–6555 (1993).
    [CrossRef] [PubMed]
  8. S. Sugaya, M. Mansuripur, “Effects of substrate birefringence on focusing and tracking servo signals in magneto-optical disk data storage,” Appl. Opt. 33, 5073–5079 (1994).
    [CrossRef] [PubMed]
  9. R. E. Gerber, M. Mansuripur, “Effects of substrate birefringence and tilt on the irradiance and phase patterns of the return beam in magneto-optical disk data storage,” Appl. Opt. 33, 5999–6008 (1994).
    [CrossRef]
  10. R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).
  11. R. A. Chipman, L. J. Chipman, “Polarization aberration diagrams,” Opt. Eng. 28, 100–106 (1989).
    [CrossRef]
  12. J. P. McGuire, R. A. Chipman, “Diffraction image formation in optical systems with polarization aberrations. I: formulation and example,” J. Opt. Soc. Am. A 7, 1614–1626 (1990).
    [CrossRef]
  13. R. C. Jones, “A new calculus for the treatment of optical systems. I. Description and discussion of the calculus,” J. Opt. Soc. Am. 31, 488–493 (1941).
    [CrossRef]
  14. J. P. McGuire, R. A. Chipman, “Polarization aberrations in optical systems,” in Current Developments in Optical Engineering II, R. E. Fisher, W. J. Smith, eds., Proc. SPIE818, 240–257 (1987).
  15. J. P. McGuire, R. A. Chipman, “Polarization aberrations. 1. Rotationally symmetric optical systems,” Appl. Opt. 33, 5080–5100 (1994).
    [CrossRef] [PubMed]
  16. J. P. McGuire, R. A. Chipman, “Polarization aberrations. 2. Tilted and decentered optical systems,” Appl. Opt. 33, 5101–5107 (1994).
    [CrossRef] [PubMed]
  17. A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991), Chap. 1.
  18. Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
    [CrossRef]
  19. Y. Otani, T. Shimada, T. Yoshizawa, “The local-sampling phase shifting technique for precise two-dimensional birefringence measurement,” Opt. Rev. 1, 103–106 (1994).
    [CrossRef]
  20. B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
    [CrossRef]
  21. M. S. Yeung, “Modeling high numerical aperture optical lithography,” in Optical/Laser Microlithography, B. J. Lin, ed., Proc. SPIE922, 149–164 (1988).
    [CrossRef]
  22. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 6.
  23. K. Yamamoto, Y. Ichioda, T. Suzuki, “Influence of light coherence at the exit pupil of the condenser on the image formation,” Opt. Acta 23, 987–996 (1976).
    [CrossRef]
  24. M. Yeung, “Modeling aerial images in two and three dimensions,” in Proceedings of the Kodak Microelectronics Seminar INTERFACE ’85 (Eastman Kodak Co., Rochester, N.Y., 1986), pp. 115–126.
  25. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 5.
  26. D. L. Fried, J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992).
    [CrossRef] [PubMed]
  27. M. Harris, C. A. Hill, J. M. Vaughan, “Optical helices and spiral interference fringes,” Opt. Commun. 106, 161–166 (1994).
    [CrossRef]
  28. H. Aben, J. Josepson, “Strange interference blots in the interferometry of inhomogeneous objects,” Appl. Opt. 36, 7172–7179 (1997).
    [CrossRef]
  29. D. H. Sanders, Statistics: A First Course, 5th ed. (McGraw-Hill, New York, 1995), Chap. 3.4.

1998 (1)

1997 (1)

1994 (7)

1993 (1)

1992 (1)

1991 (1)

H. Fukuda, A. Imai, T. Terasawa, S. Okazaki, “New approach to resolution limit and advanced image formation techniques in optical lithography,” IEEE Trans. Electron Devices 38, 67–75 (1991).
[CrossRef]

1990 (1)

1989 (2)

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

R. A. Chipman, L. J. Chipman, “Polarization aberration diagrams,” Opt. Eng. 28, 100–106 (1989).
[CrossRef]

1988 (1)

1984 (1)

F. Ratajczyk, “A method of calculation of permissible birefringence in lenses of the optical instruments,” Optik 68, 61–68 (1984).

1976 (1)

K. Yamamoto, Y. Ichioda, T. Suzuki, “Influence of light coherence at the exit pupil of the condenser on the image formation,” Opt. Acta 23, 987–996 (1976).
[CrossRef]

1959 (1)

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
[CrossRef]

1941 (1)

Aben, H.

Bernacki, B. E.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 5.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 10.

Chipman, L. J.

R. A. Chipman, L. J. Chipman, “Polarization aberration diagrams,” Opt. Eng. 28, 100–106 (1989).
[CrossRef]

Chipman, R. A.

J. P. McGuire, R. A. Chipman, “Polarization aberrations. 1. Rotationally symmetric optical systems,” Appl. Opt. 33, 5080–5100 (1994).
[CrossRef] [PubMed]

J. P. McGuire, R. A. Chipman, “Polarization aberrations. 2. Tilted and decentered optical systems,” Appl. Opt. 33, 5101–5107 (1994).
[CrossRef] [PubMed]

J. P. McGuire, R. A. Chipman, “Diffraction image formation in optical systems with polarization aberrations. I: formulation and example,” J. Opt. Soc. Am. A 7, 1614–1626 (1990).
[CrossRef]

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

R. A. Chipman, L. J. Chipman, “Polarization aberration diagrams,” Opt. Eng. 28, 100–106 (1989).
[CrossRef]

J. P. McGuire, R. A. Chipman, “Polarization aberrations in optical systems,” in Current Developments in Optical Engineering II, R. E. Fisher, W. J. Smith, eds., Proc. SPIE818, 240–257 (1987).

Fried, D. L.

Fukuda, H.

H. Fukuda, A. Imai, T. Terasawa, S. Okazaki, “New approach to resolution limit and advanced image formation techniques in optical lithography,” IEEE Trans. Electron Devices 38, 67–75 (1991).
[CrossRef]

Gerber, R. E.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 6.

Harris, M.

M. Harris, C. A. Hill, J. M. Vaughan, “Optical helices and spiral interference fringes,” Opt. Commun. 106, 161–166 (1994).
[CrossRef]

Hill, C. A.

M. Harris, C. A. Hill, J. M. Vaughan, “Optical helices and spiral interference fringes,” Opt. Commun. 106, 161–166 (1994).
[CrossRef]

Ichioda, Y.

K. Yamamoto, Y. Ichioda, T. Suzuki, “Influence of light coherence at the exit pupil of the condenser on the image formation,” Opt. Acta 23, 987–996 (1976).
[CrossRef]

Imai, A.

H. Fukuda, A. Imai, T. Terasawa, S. Okazaki, “New approach to resolution limit and advanced image formation techniques in optical lithography,” IEEE Trans. Electron Devices 38, 67–75 (1991).
[CrossRef]

Jones, R. C.

Josepson, J.

Mansuripur, M.

McGuire, J. P.

Mieda, M.

Murakami, Y.

Ohta, K.

Okazaki, S.

H. Fukuda, A. Imai, T. Terasawa, S. Okazaki, “New approach to resolution limit and advanced image formation techniques in optical lithography,” IEEE Trans. Electron Devices 38, 67–75 (1991).
[CrossRef]

Otani, Y.

Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

Y. Otani, T. Shimada, T. Yoshizawa, “The local-sampling phase shifting technique for precise two-dimensional birefringence measurement,” Opt. Rev. 1, 103–106 (1994).
[CrossRef]

Ratajczyk, F.

F. Ratajczyk, “A method of calculation of permissible birefringence in lenses of the optical instruments,” Optik 68, 61–68 (1984).

Richards, B.

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
[CrossRef]

Sanders, D. H.

D. H. Sanders, Statistics: A First Course, 5th ed. (McGraw-Hill, New York, 1995), Chap. 3.4.

Shimada, T.

Y. Otani, T. Shimada, T. Yoshizawa, “The local-sampling phase shifting technique for precise two-dimensional birefringence measurement,” Opt. Rev. 1, 103–106 (1994).
[CrossRef]

Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

Sugaya, S.

Suzuki, T.

K. Yamamoto, Y. Ichioda, T. Suzuki, “Influence of light coherence at the exit pupil of the condenser on the image formation,” Opt. Acta 23, 987–996 (1976).
[CrossRef]

Takahashi, A.

Terasawa, T.

H. Fukuda, A. Imai, T. Terasawa, S. Okazaki, “New approach to resolution limit and advanced image formation techniques in optical lithography,” IEEE Trans. Electron Devices 38, 67–75 (1991).
[CrossRef]

Umeda, N.

Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

Unno, Y.

Vaughan, J. M.

M. Harris, C. A. Hill, J. M. Vaughan, “Optical helices and spiral interference fringes,” Opt. Commun. 106, 161–166 (1994).
[CrossRef]

Vaughn, J. L.

Wolf, E.

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 10.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 5.

Yamamoto, K.

K. Yamamoto, Y. Ichioda, T. Suzuki, “Influence of light coherence at the exit pupil of the condenser on the image formation,” Opt. Acta 23, 987–996 (1976).
[CrossRef]

Yamaoka, H.

Yariv, A.

A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991), Chap. 1.

Yeung, M.

M. Yeung, “Modeling aerial images in two and three dimensions,” in Proceedings of the Kodak Microelectronics Seminar INTERFACE ’85 (Eastman Kodak Co., Rochester, N.Y., 1986), pp. 115–126.

Yeung, M. S.

M. S. Yeung, “Modeling high numerical aperture optical lithography,” in Optical/Laser Microlithography, B. J. Lin, ed., Proc. SPIE922, 149–164 (1988).
[CrossRef]

Yoshizawa, T.

Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

Y. Otani, T. Shimada, T. Yoshizawa, “The local-sampling phase shifting technique for precise two-dimensional birefringence measurement,” Opt. Rev. 1, 103–106 (1994).
[CrossRef]

Appl. Opt. (9)

A. Takahashi, M. Mieda, Y. Murakami, K. Ohta, H. Yamaoka, “Influence of birefringence on the signal quality of magneto-optic disks using polycarbonate substrates,” Appl. Opt. 27, 2863–2866 (1988).
[CrossRef] [PubMed]

D. L. Fried, J. L. Vaughn, “Branch cuts in the phase function,” Appl. Opt. 31, 2865–2882 (1992).
[CrossRef] [PubMed]

B. E. Bernacki, M. Mansuripur, “Investigation of substrate birefringence effects on optical-disk performance,” Appl. Opt. 32, 6547–6555 (1993).
[CrossRef] [PubMed]

S. Sugaya, M. Mansuripur, “Effects of substrate birefringence on focusing and tracking servo signals in magneto-optical disk data storage,” Appl. Opt. 33, 5073–5079 (1994).
[CrossRef] [PubMed]

J. P. McGuire, R. A. Chipman, “Polarization aberrations. 1. Rotationally symmetric optical systems,” Appl. Opt. 33, 5080–5100 (1994).
[CrossRef] [PubMed]

J. P. McGuire, R. A. Chipman, “Polarization aberrations. 2. Tilted and decentered optical systems,” Appl. Opt. 33, 5101–5107 (1994).
[CrossRef] [PubMed]

R. E. Gerber, M. Mansuripur, “Effects of substrate birefringence and tilt on the irradiance and phase patterns of the return beam in magneto-optical disk data storage,” Appl. Opt. 33, 5999–6008 (1994).
[CrossRef]

H. Aben, J. Josepson, “Strange interference blots in the interferometry of inhomogeneous objects,” Appl. Opt. 36, 7172–7179 (1997).
[CrossRef]

Y. Unno, “Distorted wave front produced by a high-resolution projection optical system having rotationally symmetric birefringence,” Appl. Opt. 37, 7241–7247 (1998).
[CrossRef]

IEEE Trans. Electron Devices (1)

H. Fukuda, A. Imai, T. Terasawa, S. Okazaki, “New approach to resolution limit and advanced image formation techniques in optical lithography,” IEEE Trans. Electron Devices 38, 67–75 (1991).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

K. Yamamoto, Y. Ichioda, T. Suzuki, “Influence of light coherence at the exit pupil of the condenser on the image formation,” Opt. Acta 23, 987–996 (1976).
[CrossRef]

Opt. Commun. (1)

M. Harris, C. A. Hill, J. M. Vaughan, “Optical helices and spiral interference fringes,” Opt. Commun. 106, 161–166 (1994).
[CrossRef]

Opt. Eng. (3)

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

R. A. Chipman, L. J. Chipman, “Polarization aberration diagrams,” Opt. Eng. 28, 100–106 (1989).
[CrossRef]

Y. Otani, T. Shimada, T. Yoshizawa, N. Umeda, “Two-dimensional birefringence measurement using the phase shifting technique,” Opt. Eng. 33, 1604–1609 (1994).
[CrossRef]

Opt. Rev. (1)

Y. Otani, T. Shimada, T. Yoshizawa, “The local-sampling phase shifting technique for precise two-dimensional birefringence measurement,” Opt. Rev. 1, 103–106 (1994).
[CrossRef]

Optik (1)

F. Ratajczyk, “A method of calculation of permissible birefringence in lenses of the optical instruments,” Optik 68, 61–68 (1984).

Proc. R. Soc. London A (1)

B. Richards, E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. London A 253, 358–379 (1959).
[CrossRef]

Other (9)

M. S. Yeung, “Modeling high numerical aperture optical lithography,” in Optical/Laser Microlithography, B. J. Lin, ed., Proc. SPIE922, 149–164 (1988).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), Chap. 6.

Related papers can be found in L. Van den Hove, ed., Optical Microlithography XII, Proc. SPIE3679, (1999).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 10.

A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991), Chap. 1.

D. H. Sanders, Statistics: A First Course, 5th ed. (McGraw-Hill, New York, 1995), Chap. 3.4.

J. P. McGuire, R. A. Chipman, “Polarization aberrations in optical systems,” in Current Developments in Optical Engineering II, R. E. Fisher, W. J. Smith, eds., Proc. SPIE818, 240–257 (1987).

M. Yeung, “Modeling aerial images in two and three dimensions,” in Proceedings of the Kodak Microelectronics Seminar INTERFACE ’85 (Eastman Kodak Co., Rochester, N.Y., 1986), pp. 115–126.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 5.

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Figures (11)

Fig. 1
Fig. 1

Change in the polarization state during transmission of a linearly polarized beam onto a birefringent plate. The linearly polarized beam represented by the orthogonal components p f and p s is transformed into elliptical polarization with the introduction of a wave-front displacement ZΨ(x, y) after transmission.

Fig. 2
Fig. 2

Projection lens composed of K birefringent elements. Along a beam path designated by the object point R and the pupil coordinates (ρ x , ρ y) the entrance point at the kth element and the path length therein are denoted by Q k (x k , y k) and Z k (x k , y k), respectively.

Fig. 3
Fig. 3

Configuration of a stepper optical system. In addition to the conjugate relation that is set between the object and the image planes, the effective source is set to be conjugate with the pupil plane.

Fig. 4
Fig. 4

Positions where the values that represent birefringent properties are generated by use of random numbers. The point P 1 coincides with the coordinate origin, whereas the points P 2P 9 and P 10P 17 are located on circles x k 2 + y k 2 = (a k /2)2 and x k 2 + y k 2 = a k 2, respectively.

Fig. 5
Fig. 5

Birefringence distributions determined for 10 elements by use of random numbers. The line length represents the magnitude of the birefringence, whereas the line inclination corresponds to the fast-axis direction.

Fig. 6
Fig. 6

Configuration of a lens model for use in imaging calculations. The flat-surface elements labeled 1–10 are birefringent, and the system is assumed to be aberration free in the case of zero birefringence.

Fig. 7
Fig. 7

Distributions of the Jones matrix elements m 11 x , ρ y) and m 12 x , ρ y) on the pupil plane as calculated with br/λ = 0.04 cm-1. A 11 x , ρ y) and A 12 x , ρ y) represent the amplitude transmittances, whereas W 11 x , ρ y) and W 12 x , ρ y) are the associated wave-front deviations for m 11 x , ρ y) and m 12 x , ρ y), respectively.

Fig. 8
Fig. 8

Specification of the five-bar object pattern by use of the linewidth parameter L and the angle parameter η. The intensities I max and I min are calculated to obtain the image contrast.

Fig. 9
Fig. 9

Distribution of the image-contrast data that were calculated by each combination of br/λ (=0.005, 0.010, 0.015 cm-1) and L (=0.5, 0.6, 0.7), respectively. The abscissa represents the contrast values divided with a step interval of 0.5%, whereas the ordinate represents the data frequency that is included in each contrast region.

Fig. 10
Fig. 10

Mode and the mean calculated for the contrast data shown in Fig. 9. The values for each linewidth are fitted to quadratic functions with respect to br/λ by use of a least-squares technique.

Fig. 11
Fig. 11

Standard deviations calculated for the contrast data shown in Fig. 9. The values are fitted to quadratic functions with respect to br/λ.

Equations (37)

Equations on this page are rendered with MathJax. Learn more.

φx, y=2πZ Ψx, yλ,
px,outpy,out=R-θexp-iφ/200expiφ/2Rθpx,inpy,in,
Rθ=cos θsin θ-sin θcos θ,
φkxk, yk=2πZkxk, ykΨkxk, ykλ,
px,kpy,k=Mkxk, ykpx,k-1py,k-1.
Mkxk, ykR-θkexp-iφk/200expiφk/2Rθk.
px,Kpy,K=k=K,-11Mkxk, ykpx,0py,0,
k=K,-11Mkxk, yk=m11ρx, ρym12ρx, ρym21ρx, ρym22ρx, ρy
pxρx, ρy=m11ρx, ρycos ϕ+m12ρx, ρysin ϕ,  pyρx, ρy=m21ρx, ρycos ϕ+m22ρx, ρysin ϕ.
m11ρx, ρy2+m12ρx, ρy2=1,
m21ρx, ρy=-m12*ρx, ρy,  m22ρx, ρy=m11*ρx, ρy,
oˆρx+ρx, ρy+ρy=ox, yexp-i2πρx+ρxx+ρy+ρyydxdy,
Uγx, y= oˆρx+ρx, ρy+ρypγρx, ρy×expiΦρx, ρyexp-i2πρxx+ρyydρxdρy,
ρx2+ρy21
Iˆϕx, y=|Uxx, y|2+|Uyx, y|2,
Iˆϕx, y=|u11x, y|2+|u21x, y|2cos2 ϕ+|u12x, y|2+|u22x, y|2sin2 ϕ+Reu11*x, yu12x, y+u21*x, yu22x, ysin2ϕ,
uαβx, y oˆρx+ρx, ρy+ρymαβρx, ρy×expiΦρx, ρyexp[-i2πρxx+ρyydρxdρy
Iˆx, y=0π Iˆϕx, ydϕ0πdϕ
0π cos2ϕdϕ=0π sin2 ϕdϕ=π2,
0π sin2ϕdϕ=0
Iˆx, y=12α=12β=12 |uαβx, y|2,
Ix, y= Σ Iˆx, ydρxdρy Σdρxdρy=12α=12β=12 Σ |uα,βx, y|2dρxdρy Σdρxdρy,
ρx2+ρy2σ2,
Iα,βx, y=12 Σ |uα,βx, y|2dρxdρy Σdρxdρy,
uαβx, y= oˆρx+ρx, ρy+ρyPαβρx, ρy×exp-i2πρxx+ρyydρxdρy,
Pαβρx, ρy=mαβρx, ρyexpiΦρx, ρy,
u11x, y=u22x, y=ux, y,  u12x, y=u21x, y=0,
ux, y= oˆρx+ρx, ρy+ρyexpiΦρx, ρy×exp-i2πρxx+ρyydρxdρy.
Ix, y= Σ|ux, y|2dρxdρy Σdρxdρy,
θkxk, yk=π2i=04j=0i bk,i,jxki-jykj+π2rk,
Ψkxk, yk=34+14i=04j=0i ck,i,jxki-jykj,
Ψˆkxk, yk=brkΨkxk, ykΨk,max,
mαβρx, ρy=Aαβρx, ρyexpiWαβρx, ρy,
m21ρx, ρy=A12ρx, ρyexpiπ-W12ρx, ρy,  m22ρx, ρy=A11ρx, ρyexp-iW11ρx, ρy,
contrastImax-IminImax+Imin 100  %,
gbr/λ-60,000br/λ2+63  %.
hbr/λgbr/λ/g0,

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