Abstract

As the feature size decreases, degradation of image quality caused by wavefront aberrations of projection optics in lithographic tools has become a serious problem in the low-k1 process. We propose a novel measurement technique for in situ characterizing aberrations of projection optics in lithographic tools. Considering the impact of the partial coherence illumination, we introduce a novel algorithm that accurately describes the pattern displacement and focus shift induced by aberrations. Employing the algorithm, the measurement condition is extended from three-beam interference to two-, three-, and hybrid-beam interferences. The experiments are performed to measure the aberrations of projection optics in an ArF scanner.

© 2006 Optical Society of America

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  1. A. Hand, "Mix-and-match lithography tackles tighter requirements," Semicond. Int. 25(2), 46-51 (2003).
  2. T. Brunner, "Impact of lens aberrations on optical lithography," IBM J. Res. Dev. 41, 57-67 (1997).
    [CrossRef]
  3. P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, "Impact of wavefront errors on low k1 processes at extremely high NA," in Optical Microlithography XVI, A. Yen, ed., Proc. SPIE 5040, 119-130 (2003).
    [CrossRef]
  4. K. Lai, G. M. Gallatin, and M. A. van de Kerkhof, "New paradigm in lens metrology for lithographic scanner: evaluation and exploration," in Optical Microlithography XVII, B. W. Smith, ed., Proc. SPIE 5377, 160-171 (2004).
    [CrossRef]
  5. Y. Chiba and K. Takahashi, "New-generation projection optics for ArF lithography," in Optical Microlithography XV, A. Yen, ed., Proc. SPIE 4691, 679-686 (2002).
    [CrossRef]
  6. B. W. Smith, W. Conley, and C. M. Garza, "Aberration determination in early 157-nm exposure system," in Optical Microlithography XV, A. Yen, ed., Proc. SPIE 4691, 1635-1643 (2002).
    [CrossRef]
  7. H. Nomura and T. Sato, "Techniques for measuring aberrations in lenses used in photolithography with printed patterns," Appl. Opt. 38, 2800-2807 (1999).
    [CrossRef]
  8. H. Nomura, K. Tawarayama, and T. Kohno, "Aberration measurement from specific photolithographic images: a different approach," Appl. Opt. 39, 1136-1147 (2000).
    [CrossRef]
  9. M. Born and E. Wolf, Principles of Optics, (Cambridge U. Press, 1999).
  10. T. E. Adams, "Application of latent image metrology in microlithography," in Integrated Circuit Metrology, Inspection, and Process Control V, W. H. Arnold, ed., Proc. SPIE 1464, 294-312 (1991).
    [CrossRef]
  11. P. Dirksen, W. de Laat, and H. Megens, "Latent image metrology for production wafer steppers," in Optical/Laser Microlithography VIII, T. A. Brunner, ed., Proc. SPIE 2440, 701-711 (1995).
    [CrossRef]
  12. E. L. Raab, C. Pierrat, C. H. Fields, R. L. Kostelak, W. G. Oldham, and S. Vaidya, "Analyzing deep-uv lens aberrations using aerial image and latent image metrologies," in Optical/Laser Microlithography VII, T. A. Brunner, ed., Proc. SPIE 2197, 550-565 (1994).
    [CrossRef]
  13. B. Vleeming, B. Heskamp, and H. Bakker, "ArF Step and Scan system with 0.75 NA for the 0.10 μm node," in Optical Microlithography XIV, C. J. Progler, ed., Proc. SPIE 4346, 634-650 (2001).
    [CrossRef]
  14. H. D. Betz, "An asymmetry method for high precision alignment with laser light," Appl. Opt. 8, 1007-1013 (1969).
    [CrossRef] [PubMed]
  15. M. Gruber, D. Hagedorn, and W. Eckery, "Precise and simple optical alignment method for double-sided lithography," Appl. Opt. 40, 5052-5055 (2001).
    [CrossRef]
  16. W. Shi, X. Wang, D. Zhang, and O. Sasaki, "A method for measuring the lateral aberrations of a lithographic projection system with mirror-symmetry FOCAL marks," Opt. Eng. 45, 053201 (2006).
    [CrossRef]

2006 (1)

W. Shi, X. Wang, D. Zhang, and O. Sasaki, "A method for measuring the lateral aberrations of a lithographic projection system with mirror-symmetry FOCAL marks," Opt. Eng. 45, 053201 (2006).
[CrossRef]

2004 (1)

K. Lai, G. M. Gallatin, and M. A. van de Kerkhof, "New paradigm in lens metrology for lithographic scanner: evaluation and exploration," in Optical Microlithography XVII, B. W. Smith, ed., Proc. SPIE 5377, 160-171 (2004).
[CrossRef]

2003 (2)

A. Hand, "Mix-and-match lithography tackles tighter requirements," Semicond. Int. 25(2), 46-51 (2003).

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, "Impact of wavefront errors on low k1 processes at extremely high NA," in Optical Microlithography XVI, A. Yen, ed., Proc. SPIE 5040, 119-130 (2003).
[CrossRef]

2002 (2)

Y. Chiba and K. Takahashi, "New-generation projection optics for ArF lithography," in Optical Microlithography XV, A. Yen, ed., Proc. SPIE 4691, 679-686 (2002).
[CrossRef]

B. W. Smith, W. Conley, and C. M. Garza, "Aberration determination in early 157-nm exposure system," in Optical Microlithography XV, A. Yen, ed., Proc. SPIE 4691, 1635-1643 (2002).
[CrossRef]

2001 (2)

B. Vleeming, B. Heskamp, and H. Bakker, "ArF Step and Scan system with 0.75 NA for the 0.10 μm node," in Optical Microlithography XIV, C. J. Progler, ed., Proc. SPIE 4346, 634-650 (2001).
[CrossRef]

M. Gruber, D. Hagedorn, and W. Eckery, "Precise and simple optical alignment method for double-sided lithography," Appl. Opt. 40, 5052-5055 (2001).
[CrossRef]

2000 (1)

1999 (1)

1997 (1)

T. Brunner, "Impact of lens aberrations on optical lithography," IBM J. Res. Dev. 41, 57-67 (1997).
[CrossRef]

1995 (1)

P. Dirksen, W. de Laat, and H. Megens, "Latent image metrology for production wafer steppers," in Optical/Laser Microlithography VIII, T. A. Brunner, ed., Proc. SPIE 2440, 701-711 (1995).
[CrossRef]

1994 (1)

E. L. Raab, C. Pierrat, C. H. Fields, R. L. Kostelak, W. G. Oldham, and S. Vaidya, "Analyzing deep-uv lens aberrations using aerial image and latent image metrologies," in Optical/Laser Microlithography VII, T. A. Brunner, ed., Proc. SPIE 2197, 550-565 (1994).
[CrossRef]

1991 (1)

T. E. Adams, "Application of latent image metrology in microlithography," in Integrated Circuit Metrology, Inspection, and Process Control V, W. H. Arnold, ed., Proc. SPIE 1464, 294-312 (1991).
[CrossRef]

1969 (1)

Adams, T. E.

T. E. Adams, "Application of latent image metrology in microlithography," in Integrated Circuit Metrology, Inspection, and Process Control V, W. H. Arnold, ed., Proc. SPIE 1464, 294-312 (1991).
[CrossRef]

Bakker, H.

B. Vleeming, B. Heskamp, and H. Bakker, "ArF Step and Scan system with 0.75 NA for the 0.10 μm node," in Optical Microlithography XIV, C. J. Progler, ed., Proc. SPIE 4346, 634-650 (2001).
[CrossRef]

Betz, H. D.

Born, M.

M. Born and E. Wolf, Principles of Optics, (Cambridge U. Press, 1999).

Brunner, T.

T. Brunner, "Impact of lens aberrations on optical lithography," IBM J. Res. Dev. 41, 57-67 (1997).
[CrossRef]

Chiba, Y.

Y. Chiba and K. Takahashi, "New-generation projection optics for ArF lithography," in Optical Microlithography XV, A. Yen, ed., Proc. SPIE 4691, 679-686 (2002).
[CrossRef]

Conley, W.

B. W. Smith, W. Conley, and C. M. Garza, "Aberration determination in early 157-nm exposure system," in Optical Microlithography XV, A. Yen, ed., Proc. SPIE 4691, 1635-1643 (2002).
[CrossRef]

de Laat, W.

P. Dirksen, W. de Laat, and H. Megens, "Latent image metrology for production wafer steppers," in Optical/Laser Microlithography VIII, T. A. Brunner, ed., Proc. SPIE 2440, 701-711 (1995).
[CrossRef]

Dirksen, P.

P. Dirksen, W. de Laat, and H. Megens, "Latent image metrology for production wafer steppers," in Optical/Laser Microlithography VIII, T. A. Brunner, ed., Proc. SPIE 2440, 701-711 (1995).
[CrossRef]

Eckery, W.

Fields, C. H.

E. L. Raab, C. Pierrat, C. H. Fields, R. L. Kostelak, W. G. Oldham, and S. Vaidya, "Analyzing deep-uv lens aberrations using aerial image and latent image metrologies," in Optical/Laser Microlithography VII, T. A. Brunner, ed., Proc. SPIE 2197, 550-565 (1994).
[CrossRef]

Flagello, D. G.

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, "Impact of wavefront errors on low k1 processes at extremely high NA," in Optical Microlithography XVI, A. Yen, ed., Proc. SPIE 5040, 119-130 (2003).
[CrossRef]

Gallatin, G. M.

K. Lai, G. M. Gallatin, and M. A. van de Kerkhof, "New paradigm in lens metrology for lithographic scanner: evaluation and exploration," in Optical Microlithography XVII, B. W. Smith, ed., Proc. SPIE 5377, 160-171 (2004).
[CrossRef]

Garreis, R. B.

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, "Impact of wavefront errors on low k1 processes at extremely high NA," in Optical Microlithography XVI, A. Yen, ed., Proc. SPIE 5040, 119-130 (2003).
[CrossRef]

Garza, C. M.

B. W. Smith, W. Conley, and C. M. Garza, "Aberration determination in early 157-nm exposure system," in Optical Microlithography XV, A. Yen, ed., Proc. SPIE 4691, 1635-1643 (2002).
[CrossRef]

Goehnermeier, A.

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, "Impact of wavefront errors on low k1 processes at extremely high NA," in Optical Microlithography XVI, A. Yen, ed., Proc. SPIE 5040, 119-130 (2003).
[CrossRef]

Graeupner, P.

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, "Impact of wavefront errors on low k1 processes at extremely high NA," in Optical Microlithography XVI, A. Yen, ed., Proc. SPIE 5040, 119-130 (2003).
[CrossRef]

Gruber, M.

Hagedorn, D.

Hand, A.

A. Hand, "Mix-and-match lithography tackles tighter requirements," Semicond. Int. 25(2), 46-51 (2003).

Heil, T.

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, "Impact of wavefront errors on low k1 processes at extremely high NA," in Optical Microlithography XVI, A. Yen, ed., Proc. SPIE 5040, 119-130 (2003).
[CrossRef]

Heskamp, B.

B. Vleeming, B. Heskamp, and H. Bakker, "ArF Step and Scan system with 0.75 NA for the 0.10 μm node," in Optical Microlithography XIV, C. J. Progler, ed., Proc. SPIE 4346, 634-650 (2001).
[CrossRef]

Kohno, T.

Kostelak, R. L.

E. L. Raab, C. Pierrat, C. H. Fields, R. L. Kostelak, W. G. Oldham, and S. Vaidya, "Analyzing deep-uv lens aberrations using aerial image and latent image metrologies," in Optical/Laser Microlithography VII, T. A. Brunner, ed., Proc. SPIE 2197, 550-565 (1994).
[CrossRef]

Lai, K.

K. Lai, G. M. Gallatin, and M. A. van de Kerkhof, "New paradigm in lens metrology for lithographic scanner: evaluation and exploration," in Optical Microlithography XVII, B. W. Smith, ed., Proc. SPIE 5377, 160-171 (2004).
[CrossRef]

Lowisch, M.

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, "Impact of wavefront errors on low k1 processes at extremely high NA," in Optical Microlithography XVI, A. Yen, ed., Proc. SPIE 5040, 119-130 (2003).
[CrossRef]

Megens, H.

P. Dirksen, W. de Laat, and H. Megens, "Latent image metrology for production wafer steppers," in Optical/Laser Microlithography VIII, T. A. Brunner, ed., Proc. SPIE 2440, 701-711 (1995).
[CrossRef]

Nomura, H.

Oldham, W. G.

E. L. Raab, C. Pierrat, C. H. Fields, R. L. Kostelak, W. G. Oldham, and S. Vaidya, "Analyzing deep-uv lens aberrations using aerial image and latent image metrologies," in Optical/Laser Microlithography VII, T. A. Brunner, ed., Proc. SPIE 2197, 550-565 (1994).
[CrossRef]

Pierrat, C.

E. L. Raab, C. Pierrat, C. H. Fields, R. L. Kostelak, W. G. Oldham, and S. Vaidya, "Analyzing deep-uv lens aberrations using aerial image and latent image metrologies," in Optical/Laser Microlithography VII, T. A. Brunner, ed., Proc. SPIE 2197, 550-565 (1994).
[CrossRef]

Raab, E. L.

E. L. Raab, C. Pierrat, C. H. Fields, R. L. Kostelak, W. G. Oldham, and S. Vaidya, "Analyzing deep-uv lens aberrations using aerial image and latent image metrologies," in Optical/Laser Microlithography VII, T. A. Brunner, ed., Proc. SPIE 2197, 550-565 (1994).
[CrossRef]

Sasaki, O.

W. Shi, X. Wang, D. Zhang, and O. Sasaki, "A method for measuring the lateral aberrations of a lithographic projection system with mirror-symmetry FOCAL marks," Opt. Eng. 45, 053201 (2006).
[CrossRef]

Sato, T.

Shi, W.

W. Shi, X. Wang, D. Zhang, and O. Sasaki, "A method for measuring the lateral aberrations of a lithographic projection system with mirror-symmetry FOCAL marks," Opt. Eng. 45, 053201 (2006).
[CrossRef]

Smith, B. W.

B. W. Smith, W. Conley, and C. M. Garza, "Aberration determination in early 157-nm exposure system," in Optical Microlithography XV, A. Yen, ed., Proc. SPIE 4691, 1635-1643 (2002).
[CrossRef]

Takahashi, K.

Y. Chiba and K. Takahashi, "New-generation projection optics for ArF lithography," in Optical Microlithography XV, A. Yen, ed., Proc. SPIE 4691, 679-686 (2002).
[CrossRef]

Tawarayama, K.

Vaidya, S.

E. L. Raab, C. Pierrat, C. H. Fields, R. L. Kostelak, W. G. Oldham, and S. Vaidya, "Analyzing deep-uv lens aberrations using aerial image and latent image metrologies," in Optical/Laser Microlithography VII, T. A. Brunner, ed., Proc. SPIE 2197, 550-565 (1994).
[CrossRef]

van de Kerkhof, M. A.

K. Lai, G. M. Gallatin, and M. A. van de Kerkhof, "New paradigm in lens metrology for lithographic scanner: evaluation and exploration," in Optical Microlithography XVII, B. W. Smith, ed., Proc. SPIE 5377, 160-171 (2004).
[CrossRef]

Vleeming, B.

B. Vleeming, B. Heskamp, and H. Bakker, "ArF Step and Scan system with 0.75 NA for the 0.10 μm node," in Optical Microlithography XIV, C. J. Progler, ed., Proc. SPIE 4346, 634-650 (2001).
[CrossRef]

Wang, X.

W. Shi, X. Wang, D. Zhang, and O. Sasaki, "A method for measuring the lateral aberrations of a lithographic projection system with mirror-symmetry FOCAL marks," Opt. Eng. 45, 053201 (2006).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, (Cambridge U. Press, 1999).

Zhang, D.

W. Shi, X. Wang, D. Zhang, and O. Sasaki, "A method for measuring the lateral aberrations of a lithographic projection system with mirror-symmetry FOCAL marks," Opt. Eng. 45, 053201 (2006).
[CrossRef]

Appl. Opt. (4)

IBM J. Res. Dev. (1)

T. Brunner, "Impact of lens aberrations on optical lithography," IBM J. Res. Dev. 41, 57-67 (1997).
[CrossRef]

Opt. Eng. (1)

W. Shi, X. Wang, D. Zhang, and O. Sasaki, "A method for measuring the lateral aberrations of a lithographic projection system with mirror-symmetry FOCAL marks," Opt. Eng. 45, 053201 (2006).
[CrossRef]

Proc. SPIE (8)

P. Graeupner, R. B. Garreis, A. Goehnermeier, T. Heil, M. Lowisch, and D. G. Flagello, "Impact of wavefront errors on low k1 processes at extremely high NA," in Optical Microlithography XVI, A. Yen, ed., Proc. SPIE 5040, 119-130 (2003).
[CrossRef]

K. Lai, G. M. Gallatin, and M. A. van de Kerkhof, "New paradigm in lens metrology for lithographic scanner: evaluation and exploration," in Optical Microlithography XVII, B. W. Smith, ed., Proc. SPIE 5377, 160-171 (2004).
[CrossRef]

Y. Chiba and K. Takahashi, "New-generation projection optics for ArF lithography," in Optical Microlithography XV, A. Yen, ed., Proc. SPIE 4691, 679-686 (2002).
[CrossRef]

B. W. Smith, W. Conley, and C. M. Garza, "Aberration determination in early 157-nm exposure system," in Optical Microlithography XV, A. Yen, ed., Proc. SPIE 4691, 1635-1643 (2002).
[CrossRef]

T. E. Adams, "Application of latent image metrology in microlithography," in Integrated Circuit Metrology, Inspection, and Process Control V, W. H. Arnold, ed., Proc. SPIE 1464, 294-312 (1991).
[CrossRef]

P. Dirksen, W. de Laat, and H. Megens, "Latent image metrology for production wafer steppers," in Optical/Laser Microlithography VIII, T. A. Brunner, ed., Proc. SPIE 2440, 701-711 (1995).
[CrossRef]

E. L. Raab, C. Pierrat, C. H. Fields, R. L. Kostelak, W. G. Oldham, and S. Vaidya, "Analyzing deep-uv lens aberrations using aerial image and latent image metrologies," in Optical/Laser Microlithography VII, T. A. Brunner, ed., Proc. SPIE 2197, 550-565 (1994).
[CrossRef]

B. Vleeming, B. Heskamp, and H. Bakker, "ArF Step and Scan system with 0.75 NA for the 0.10 μm node," in Optical Microlithography XIV, C. J. Progler, ed., Proc. SPIE 4346, 634-650 (2001).
[CrossRef]

Semicond. Int. (1)

A. Hand, "Mix-and-match lithography tackles tighter requirements," Semicond. Int. 25(2), 46-51 (2003).

Other (1)

M. Born and E. Wolf, Principles of Optics, (Cambridge U. Press, 1999).

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Figures (8)

Fig. 1
Fig. 1

Coordinate systems of the lithographic tool.

Fig. 2
Fig. 2

Imaging of a grating pattern in a lithographic tool.

Fig. 3
Fig. 3

Four imaging conditions: (a) three-beam interference, (b) hybrid-beam interference, (c) two-beam interference, and (d) multiple-beam interference.

Fig. 4
Fig. 4

Relationship between illumination coherence σ and pupil radius ρ at the center of the ±1st diffraction orders.

Fig. 5
Fig. 5

Diffraction beams in pupil coordinates.

Fig. 6
Fig. 6

Sketch map of the mirror-symmetry FOCAL mark.

Fig. 7
Fig. 7

Experimental results of odd aberrations measured in different field positions. (a) Z7 measuring results and (b) Z14 measuring results.

Fig. 8
Fig. 8

Experimental results of odd aberrations measured in different field positions. (a) Z9 measuring results and (b) Z16 measuring results.

Tables (1)

Tables Icon

Table 1 Illumination Settings Used in the Experiment and Corresponding Sensitivities

Equations (33)

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ω ( ρ ) = n = 1 Z n R n ( ρ , θ ) = Z 1 + Z 2 ρ cos θ + Z 3 ρ sin θ + Z 4 ( 2 ρ 2 1 ) + Z 5 ρ 2 cos 2 θ + Z 6 ρ 2 sin 2 θ + Z 7 ( 3 ρ 3 2 ρ ) cos θ + Z 8 ( 3 ρ 3 2 ρ ) sin θ + Z 9 ( 6 ρ 4 6 ρ 4 + 1 ) + ,
λ NA ( 1 σ ) P m λ NA ( 1 + σ ) ,
λ NA P λ NA ( 1 σ ) , P m λ NA ( 1 + σ ) .
λ N A ( 1 + σ ) P λ NA .
P m λ NA ( 1 + σ ) .
ϕ i ( ρ i ) = 2 π λ ω ( ρ i ) ( i = 1 , 0 , 1 ) ,
ρ i = ρ i , 0 + ρ ill .
I coh ( x ) = | A 0 exp [ j ϕ 0 ( ρ 0 ) ] + A 1 exp ( j 2 π x P ) exp [ j ϕ 1 ( ρ 1 ) ] | 2 = A 0 2 + A 1 2 + 2 A 0 A 1 × cos [ 2 π x P + ϕ 1 ( ρ 1 ) ϕ 0 ( ρ 0 ) ] ,
Δ x = P λ [ ω ( ρ 1 ) ω ( ρ 0 ) ] .
Δ x = P λ [ ω ( ρ 0 ) ω ( ρ 1 ) ] .
I coh ( x ) = | A 0 exp ( j ϕ 0 ) + A 1 exp ( j 2 π x P + j ϕ 1 ) + A 1 exp ( j 2 π x P + j ϕ 1 ) | 2 = A 0 2 + 2 A 1 2 + 2 A 0 A 1 × cos [ 2 π x P + ϕ 1 ( ρ - 1 ) ϕ 0 ( ρ 0 ) ] + 2 A 0 A 1 cos [ 2 π x P + ϕ 1 ( ρ 1 ) ϕ 0 ( ρ 0 ) ] + 2 A 1 2 cos [ 4 π x P + ϕ 1 ( ρ 1 ) ϕ 1 ( ρ - 1 ) ] .
I coh ( x ) = A 0 2 + 2 A 1 2 + 4 A 0 A 1 × cos [ 2 π x P + ϕ 1 ( ρ 1 ) ϕ 1 ( ρ - 1 ) 2 ] × cos [ ϕ 1 ( ρ 1 ) + ϕ 1 ( ρ - 1 ) 2 ϕ 0 ] + 2 A 1 2 × cos [ 4 π x P + ϕ 1 ( ρ 1 ) ϕ 1 ( ρ - 1 ) ] .
Δ x = P 2 λ [ ω ( ρ 1 ) ω ( ρ - 1 ) ] .
I part ( x ) = S σ I coh ( x , ρ ill ) d ρ ill ,
Δ x = P 2 λ × s 1 ω ( ρ 1 ) ω ( ρ 0 ) d ρ 1 + s 1 ω ( ρ 0 ) ω ( ρ - 1 ) d ρ - 1 S 1 + S 1 .
s 1 ω ( ρ 1 ) ω ( ρ 0 ) d ρ 1 = s 1 ω ( ρ 0 ) ω ( ρ - 1 ) d ρ - 1 .
Δ x = - P λ s 1 ω ( ρ 1 ) ω ( ρ 0 ) d ρ 1 S 1 .
s 1 ω ( ρ 1 ) ω ( ρ 0 ) d ρ 1 = s 1 ω ( ρ 0 ) ω ( ρ - 1 ) d ρ - 1 .
Δ x = k 2 Z 2 + k 7 Z 7 + k 10 Z 10 + k 14 Z 14 ,
k n = P λ s 1 R ( ρ 1 ) R ( ρ 0 ) d ρ 1 S 1 .
Δ y = k 3 Z 3 + k 8 Z 8 + k 11 Z 11 + k 15 Z 15 .
I coh ( x , z ) = | A 0 exp [ j ϕ 0 ( ρ 0 ) ] + A 1 exp ( j 2 π x P ) exp [ j ϕ 1 ( ρ 1 ) + j πz λ P 2 ] | 2 = A 0 2 + A 1 2 + 2 A 0 A 1 × cos [ 2 π x P + ϕ 1 ( ρ 1 ) ϕ 0 ( ρ 0 ) + π z λ P 2 ] ,
Δ z = 2 P 2 λ 2 [ ω ( ρ 1 ) ω ( ρ 0 ) ] .
Δ z = 2 P 2 λ 2 [ ω ( ρ - 1 ) ω ( ρ 0 ) ] .
I coh ( x , z ) = | A 0 exp [ j ϕ 0 ( ρ 0 ) ] + A 1 exp ( j 2 π x P ) × exp [ j ϕ 1 ( ρ 1 ) + j π z λ P 2 ] | 2 + A 1 exp ( j 2 π x P ) exp [ j ϕ 1 ( ρ - 1 ) + j π z λ P 2 ] | + 2 A 0 2 + A 1 2 + 2 A 1 2 × cos [ 4 π x P + ϕ 1 ( ρ 1 ) ϕ 1 ( ρ - 1 ) ] + 4 A 0 A 1 × cos [ 2 π x P + ϕ 1 ( ρ 1 ) ϕ 1 ( ρ - 1 ) 2 ] × cos [ ϕ 1 ( ρ 1 ) + ϕ 1 ( ρ - 1 ) 2 ϕ 0 ( ρ 0 ) + π z λ P 2 ] ,
Δ z = P 2 λ 2 [ ω ( ρ 1 ) + ω ( ρ - 1 ) 2 ω ( ρ 0 ) ] .
Δ z = P 2 λ 2 × s 1 ω ( ρ 1 ) ω ( ρ 0 ) d ρ 1 + s 1 ω ( ρ - 1 ) ω ( ρ 0 ) d ρ - 1 S 1 + S 1 .
s 1 ω ( ρ 1 ) ω ( ρ 0 ) d ρ 1 = s 1 ω ( ρ - 1 ) ω ( ρ 0 ) d ρ - 1 .
Δ z x = n k n Z n ( n = 4 , 5 , 6 , 9 , 12 , 13 , 16 ) .
k n = 2 P 2 λ 2 s 1 R ( ρ 1 ) R ( ρ 0 ) d ρ 1 S 1 .
Δ z y = n k n Z n ( n = 4 , 5 , 6 , 9 , 12 , 13 , 16 ) .
Δ x = ( ra + 1 ) A O FOCAL , x ra A O align , x ,
Δ y = ( ra + 1 ) A O FOCAL , y ra A O align , y ,

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