Abstract

A discussion is presented of the practical considerations involved in wavelength-scanning polarization-modulation ellipsometry. Emphasis is placed on factors affecting accuracy and precision and on the alignment of the optical elements. The system described is used to measure the optical properties of air-cleaved KC1 and of clean and tarnished Ag surfaces in ultrahigh vacuum in the 250–650-nm range.

© 1978 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. N. Jasperson, S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969);Rev. Sci. Instrum. 41, 152 (1970).
    [CrossRef]
  2. J. I. Treu, A. B. Callender, S. E. Schnatterly, Rev. Sci. Instrum. 44, 793 (1973).
    [CrossRef]
  3. J. I. Treu, Rev. Sci. Instrum. 45, 1464 (1974).
    [CrossRef]
  4. S. N. Jasperson, Ph.D. Thesis, Princeton U. (1969 (unpublished), available from University Microfilms, Ann Arbor, Mich., Order 69-3297.
  5. A. B. Callender, Ph.D. Thesis, Princeton U. (1971) (unpublished), Order 71-23346.
  6. R. E. Palmer, Ph.D. Thesis, Princeton U. (1971) (unpublished), Order 72-14162.
  7. S. N. Jasperson, S. E. Schnatterly, Phys. Rev. 188, 759 (1969).
    [CrossRef]
  8. R. C. O'Handley, D. K. Burge, S. N. Jasperson, E. J. Ashley, Surf. Sci. 50, 407 (1975) and references quoted therein.
    [CrossRef]
  9. The reader is referred to an extensive series of paper by R. M. A. Azzam, N. M. Bashara, and co-workers, J. Opt. Soc. Am. and Appl. Opt. (1970–1976).
  10. D. E. Aspnes, J. Opt. Soc. Am. 64, 639 (1974).
    [CrossRef]
  11. D. E. Aspnes, A. A. Studna, Appl. Opt. 14, 220 (1975).
    [CrossRef] [PubMed]
  12. R. C. O'Handley, J. Opt. Soc. Am. 63, 523 (1973).
    [CrossRef]
  13. R. M. A. Azzam, Optik 45, 209 (1976).
  14. V. M. Bermudez, Computer Phys. Commun. 13, 207 (1977).The program described in this reference treats measurement of N and S in Config. III and of C in Config. II. For the present discussion, a simple modification of the program has been made to allow analysis of N in Config. I and of S and C in Config. II.
    [CrossRef]
  15. R. J. King, J. Sci. Instrum. 43, 617 (1966).
    [CrossRef]
  16. RCA Photomultiplier Manual, Technical Series PT-61 (RCA, Harrison, N.J., 1970).
  17. R. T. Williams, private communication.
  18. G. K. Wertheim, Rev. Sci. Instrum. 46, 1414 (1975).
    [CrossRef]
  19. W. R. Hunter, J. Opt. Soc. Am. 63, 951 (1973).
    [CrossRef]
  20. C. E. Moeller, D. R. Grieser, Appl. Opt. 8, 206 (1969).
    [CrossRef] [PubMed]
  21. J. C. Cheng, L. A. Nafie, S. D. Allen, A. I. Braunstein, Appl. Opt. 15, 1960 (1976).
    [CrossRef] [PubMed]
  22. D. E. Aspnes, A. A. Studna, Rev. Sci. Instrum. 41, 966 (1970).
    [CrossRef]
  23. F. B. Hildebrand, Advanced Calculus for Applications (Prentice-Hall, Englewood Cliffs, N.J., 1962), p. 143.
  24. S. N. Jasperson, D. K. Burge, R. C. O'Handley, Surf. Sci. 37, 548 (1973).
    [CrossRef]
  25. L. G. Schulz, J. Opt. Soc. Am. 44, 357 (1954);L. G. Schulz, F. R. Tangherlini, J. Opt. Soc. Am. 44, 362 (1954).
    [CrossRef]
  26. R. H. Huebner, E. T. Arakawa, R. A. MacRae, R. N. Hamm, J. Opt. Soc. Am. 54, 1434 (1964).
    [CrossRef]
  27. D. K. Burge (Michelson Labs.,), private communication.See D. L. Decker, J. L. Stanford, J. Opt. Soc. Am. 61, 679 (1971), Abstract WD14.
  28. P. B. Johnson, R. W. Christy, Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  29. W. Köster, R. Stahl, Z. Metallkd. 58, 768 (1967).
  30. Z. Gyulai, Z. Phys. 46, 80 (1927).
    [CrossRef]

1977

V. M. Bermudez, Computer Phys. Commun. 13, 207 (1977).The program described in this reference treats measurement of N and S in Config. III and of C in Config. II. For the present discussion, a simple modification of the program has been made to allow analysis of N in Config. I and of S and C in Config. II.
[CrossRef]

1976

1975

G. K. Wertheim, Rev. Sci. Instrum. 46, 1414 (1975).
[CrossRef]

R. C. O'Handley, D. K. Burge, S. N. Jasperson, E. J. Ashley, Surf. Sci. 50, 407 (1975) and references quoted therein.
[CrossRef]

D. E. Aspnes, A. A. Studna, Appl. Opt. 14, 220 (1975).
[CrossRef] [PubMed]

1974

D. E. Aspnes, J. Opt. Soc. Am. 64, 639 (1974).
[CrossRef]

J. I. Treu, Rev. Sci. Instrum. 45, 1464 (1974).
[CrossRef]

1973

J. I. Treu, A. B. Callender, S. E. Schnatterly, Rev. Sci. Instrum. 44, 793 (1973).
[CrossRef]

R. C. O'Handley, J. Opt. Soc. Am. 63, 523 (1973).
[CrossRef]

W. R. Hunter, J. Opt. Soc. Am. 63, 951 (1973).
[CrossRef]

S. N. Jasperson, D. K. Burge, R. C. O'Handley, Surf. Sci. 37, 548 (1973).
[CrossRef]

1972

P. B. Johnson, R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

1970

D. E. Aspnes, A. A. Studna, Rev. Sci. Instrum. 41, 966 (1970).
[CrossRef]

1969

C. E. Moeller, D. R. Grieser, Appl. Opt. 8, 206 (1969).
[CrossRef] [PubMed]

S. N. Jasperson, S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969);Rev. Sci. Instrum. 41, 152 (1970).
[CrossRef]

S. N. Jasperson, S. E. Schnatterly, Phys. Rev. 188, 759 (1969).
[CrossRef]

1967

W. Köster, R. Stahl, Z. Metallkd. 58, 768 (1967).

1966

R. J. King, J. Sci. Instrum. 43, 617 (1966).
[CrossRef]

1964

1954

1927

Z. Gyulai, Z. Phys. 46, 80 (1927).
[CrossRef]

Allen, S. D.

Arakawa, E. T.

Ashley, E. J.

R. C. O'Handley, D. K. Burge, S. N. Jasperson, E. J. Ashley, Surf. Sci. 50, 407 (1975) and references quoted therein.
[CrossRef]

Aspnes, D. E.

Azzam, R. M. A.

R. M. A. Azzam, Optik 45, 209 (1976).

The reader is referred to an extensive series of paper by R. M. A. Azzam, N. M. Bashara, and co-workers, J. Opt. Soc. Am. and Appl. Opt. (1970–1976).

Bashara, N. M.

The reader is referred to an extensive series of paper by R. M. A. Azzam, N. M. Bashara, and co-workers, J. Opt. Soc. Am. and Appl. Opt. (1970–1976).

Bermudez, V. M.

V. M. Bermudez, Computer Phys. Commun. 13, 207 (1977).The program described in this reference treats measurement of N and S in Config. III and of C in Config. II. For the present discussion, a simple modification of the program has been made to allow analysis of N in Config. I and of S and C in Config. II.
[CrossRef]

Braunstein, A. I.

Burge, D. K.

R. C. O'Handley, D. K. Burge, S. N. Jasperson, E. J. Ashley, Surf. Sci. 50, 407 (1975) and references quoted therein.
[CrossRef]

S. N. Jasperson, D. K. Burge, R. C. O'Handley, Surf. Sci. 37, 548 (1973).
[CrossRef]

D. K. Burge (Michelson Labs.,), private communication.See D. L. Decker, J. L. Stanford, J. Opt. Soc. Am. 61, 679 (1971), Abstract WD14.

Callender, A. B.

J. I. Treu, A. B. Callender, S. E. Schnatterly, Rev. Sci. Instrum. 44, 793 (1973).
[CrossRef]

A. B. Callender, Ph.D. Thesis, Princeton U. (1971) (unpublished), Order 71-23346.

Cheng, J. C.

Christy, R. W.

P. B. Johnson, R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Grieser, D. R.

Gyulai, Z.

Z. Gyulai, Z. Phys. 46, 80 (1927).
[CrossRef]

Hamm, R. N.

Hildebrand, F. B.

F. B. Hildebrand, Advanced Calculus for Applications (Prentice-Hall, Englewood Cliffs, N.J., 1962), p. 143.

Huebner, R. H.

Hunter, W. R.

Jasperson, S. N.

R. C. O'Handley, D. K. Burge, S. N. Jasperson, E. J. Ashley, Surf. Sci. 50, 407 (1975) and references quoted therein.
[CrossRef]

S. N. Jasperson, D. K. Burge, R. C. O'Handley, Surf. Sci. 37, 548 (1973).
[CrossRef]

S. N. Jasperson, S. E. Schnatterly, Phys. Rev. 188, 759 (1969).
[CrossRef]

S. N. Jasperson, S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969);Rev. Sci. Instrum. 41, 152 (1970).
[CrossRef]

S. N. Jasperson, Ph.D. Thesis, Princeton U. (1969 (unpublished), available from University Microfilms, Ann Arbor, Mich., Order 69-3297.

Johnson, P. B.

P. B. Johnson, R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

King, R. J.

R. J. King, J. Sci. Instrum. 43, 617 (1966).
[CrossRef]

Köster, W.

W. Köster, R. Stahl, Z. Metallkd. 58, 768 (1967).

MacRae, R. A.

Moeller, C. E.

Nafie, L. A.

O'Handley, R. C.

R. C. O'Handley, D. K. Burge, S. N. Jasperson, E. J. Ashley, Surf. Sci. 50, 407 (1975) and references quoted therein.
[CrossRef]

R. C. O'Handley, J. Opt. Soc. Am. 63, 523 (1973).
[CrossRef]

S. N. Jasperson, D. K. Burge, R. C. O'Handley, Surf. Sci. 37, 548 (1973).
[CrossRef]

Palmer, R. E.

R. E. Palmer, Ph.D. Thesis, Princeton U. (1971) (unpublished), Order 72-14162.

Schnatterly, S. E.

J. I. Treu, A. B. Callender, S. E. Schnatterly, Rev. Sci. Instrum. 44, 793 (1973).
[CrossRef]

S. N. Jasperson, S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969);Rev. Sci. Instrum. 41, 152 (1970).
[CrossRef]

S. N. Jasperson, S. E. Schnatterly, Phys. Rev. 188, 759 (1969).
[CrossRef]

Schulz, L. G.

Stahl, R.

W. Köster, R. Stahl, Z. Metallkd. 58, 768 (1967).

Studna, A. A.

D. E. Aspnes, A. A. Studna, Appl. Opt. 14, 220 (1975).
[CrossRef] [PubMed]

D. E. Aspnes, A. A. Studna, Rev. Sci. Instrum. 41, 966 (1970).
[CrossRef]

Treu, J. I.

J. I. Treu, Rev. Sci. Instrum. 45, 1464 (1974).
[CrossRef]

J. I. Treu, A. B. Callender, S. E. Schnatterly, Rev. Sci. Instrum. 44, 793 (1973).
[CrossRef]

Wertheim, G. K.

G. K. Wertheim, Rev. Sci. Instrum. 46, 1414 (1975).
[CrossRef]

Williams, R. T.

R. T. Williams, private communication.

Appl. Opt.

Computer Phys. Commun.

V. M. Bermudez, Computer Phys. Commun. 13, 207 (1977).The program described in this reference treats measurement of N and S in Config. III and of C in Config. II. For the present discussion, a simple modification of the program has been made to allow analysis of N in Config. I and of S and C in Config. II.
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. and Appl. Opt.

The reader is referred to an extensive series of paper by R. M. A. Azzam, N. M. Bashara, and co-workers, J. Opt. Soc. Am. and Appl. Opt. (1970–1976).

J. Sci. Instrum.

R. J. King, J. Sci. Instrum. 43, 617 (1966).
[CrossRef]

Optik

R. M. A. Azzam, Optik 45, 209 (1976).

Phys. Rev.

S. N. Jasperson, S. E. Schnatterly, Phys. Rev. 188, 759 (1969).
[CrossRef]

Phys. Rev. B

P. B. Johnson, R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Rev. Sci. Instrum.

D. E. Aspnes, A. A. Studna, Rev. Sci. Instrum. 41, 966 (1970).
[CrossRef]

S. N. Jasperson, S. E. Schnatterly, Rev. Sci. Instrum. 40, 761 (1969);Rev. Sci. Instrum. 41, 152 (1970).
[CrossRef]

J. I. Treu, A. B. Callender, S. E. Schnatterly, Rev. Sci. Instrum. 44, 793 (1973).
[CrossRef]

J. I. Treu, Rev. Sci. Instrum. 45, 1464 (1974).
[CrossRef]

G. K. Wertheim, Rev. Sci. Instrum. 46, 1414 (1975).
[CrossRef]

Surf. Sci.

R. C. O'Handley, D. K. Burge, S. N. Jasperson, E. J. Ashley, Surf. Sci. 50, 407 (1975) and references quoted therein.
[CrossRef]

S. N. Jasperson, D. K. Burge, R. C. O'Handley, Surf. Sci. 37, 548 (1973).
[CrossRef]

Z. Metallkd.

W. Köster, R. Stahl, Z. Metallkd. 58, 768 (1967).

Z. Phys.

Z. Gyulai, Z. Phys. 46, 80 (1927).
[CrossRef]

Other

D. K. Burge (Michelson Labs.,), private communication.See D. L. Decker, J. L. Stanford, J. Opt. Soc. Am. 61, 679 (1971), Abstract WD14.

F. B. Hildebrand, Advanced Calculus for Applications (Prentice-Hall, Englewood Cliffs, N.J., 1962), p. 143.

S. N. Jasperson, Ph.D. Thesis, Princeton U. (1969 (unpublished), available from University Microfilms, Ann Arbor, Mich., Order 69-3297.

A. B. Callender, Ph.D. Thesis, Princeton U. (1971) (unpublished), Order 71-23346.

R. E. Palmer, Ph.D. Thesis, Princeton U. (1971) (unpublished), Order 72-14162.

RCA Photomultiplier Manual, Technical Series PT-61 (RCA, Harrison, N.J., 1970).

R. T. Williams, private communication.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

The three different configurations of optical components used in polarization-modulation ellipsometry. In each case, the upper diagram is for measurement and the lower for calibration; the compensator (C) is present only in recording R ω cal. Positive azimuth angles are measured counterclockwise from the +ŝ axis as the observer faces the source.

Fig. 2
Fig. 2

Section through the midplane, viewed from above, of the ultrahigh vacuum system for optical and electronic spectroscopy.

Fig. 3
Fig. 3

Details of the arrangement used to transfer the sample back and forth between the two vacuum chambers.

Fig. 4
Fig. 4

The imaginary component of the dielectric function of a vacuum-evaporated silver film, measured at room temperature in vacuum (∼10−9 Torr). The solid and dashed curves, respectively, were obtained before and after cleaning by 2-kV argon–ion sputtering. The spectral slit width (5 nm) is indicated at both ends of the spectrum. The literature values2528 were all obtained by reflection and/or transmission measurements on vacuum evaporated films.

Fig. 5
Fig. 5

The real component of the dielectric function of a silver film, as in Fig. 4.

Fig. 6
Fig. 6

The real component of the index of refraction of KCl, measured at room temperature in vacuum. The broken curve is the data of Gyulai30 obtained from prism measurements. The solid curve is the WSPME results, and the vertical bars indicate the scatter about the smooth curve.

Tables (2)

Tables Icon

Table I J0(A), J1(A), J2(A), and Derived Quantities near A = 138°

Tables Icon

Table II Ellipsometer Error Quantities, by Component

Equations (42)

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

Config . I I = 1 + ρ 2 + ( 1 ρ 2 ) cos δ , Config . II I = 1 + ρ 2 2 ρ sin Δ sin δ + 2 ρ cos Δ cos δ , Config . III I = 1 + ρ 2 + ( 1 ρ 2 ) cos δ 2 ρ sin Δ sin δ ,
sin ( δ ) = sin ( A sin ω t ) = 2 k = 0 J 2 k + 1 ( A ) sin [ ( 2 k + 1 ) ω t ] , cos ( δ ) = cos ( A sin ω t ) = J 0 ( A ) + 2 k = 1 J 2 k ( A ) cos ( 2 k ω t ) ,
Config . I R 2 ω = 1 ρ 2 1 + ρ 2 [ 2 J 2 ( A ) ] , Config . II R ω = 2 ρ 1 + ρ 2 sin Δ [ 2 J 1 ( A ) ] , R 2 ω = 2 ρ 1 + ρ 2 cos Δ [ 2 J 2 ( A ) ] , Config . III R ω = 2 ρ 1 + ρ 2 sin Δ [ 2 J 1 ( A ) ] , R ω = 1 ρ 2 1 + ρ 2 [ 2 J 2 ( A ) ] ,
I = 1 ± sin δ , R ω cal = ± 2 J 1 ( A ) ;
I = 1 + cos δ , R 2 ω cal = 2 J 2 ( A ) ,
N = R 2 ω / R 2 ω cal = ( 1 ρ 2 ) / ( 1 + ρ 2 ) = cos ( 2 ψ ) ;
S = R ω / R ω cal = 2 ρ sin Δ / ( 1 + ρ 2 ) = ( 1 N 2 ) 1 / 2 sin Δ = sin ( 2 ψ ) sin Δ , C = R 2 ω / R 2 ω cal = 2 ρ cos Δ / ( 1 + ρ 2 ) = ( 1 N 2 ) 1 / 2 cos Δ = sin ( 2 ψ ) cos Δ ;
N = R 2 ω / R 2 ω cal S = R ω / R ω cal .
1 = n 2 k 2 = sin 2 θ + sin 2 θ tan 2 θ [ N 2 S 2 ( 1 + C ) 2 ] , 2 = 2 n k = 2 sin 2 θ tan 2 θ [ N S ( 1 + C ) 2 ] , α = 4 π k / λ ,
I = cos 2 φ A cos 2 φ P + sin 2 φ A sin 2 φ P + ½ sin ( 2 φ A ) sin ( 2 φ P ) cos δ ,
I 0 = cos 2 φ A cos 2 φ P + sin 2 φ A sin 2 φ P + ½ sin ( 2 φ A ) sin ( 2 φ P ) J 0 ( A ) , I 2 ω = ½ sin ( 2 φ A ) sin ( 2 φ P ) [ 2 J 2 ( A ) ] .
I 0 ( φ A = 0 ) = cos 2 φ P I 0 ( φ A = π / 2 ) = sin 2 φ P ,
| cos 2 ϕ P sin 2 ϕ P cos 2 ϕ P + sin 2 ϕ P | = | I 0 ( ϕ A = 0 ) I 0 ( ϕ A = π / 2 ) I 0 ( ϕ A = 0 ) + I 0 ( ϕ A = π / 2 ) | = | cos ( 2 ϕ P ) | ,
R 2 ω = sin ( 2 ϕ A ) [ 2 J 2 ( A ) ] 1 + sin ( 2 ϕ A ) J 0 ( A ) .
R 2 ω ( ϕ A = ± π / 4 ) = ± 2 J 2 ( A ) 1 ± J 0 ( A ) ,
J 0 ( A ) = R 2 ω ( ϕ A = + π / 4 ) + R 2 ω ( ϕ A = π / 4 ) R 2 ω ( ϕ A = + π / 4 ) R 2 ω ( ϕ A = π / 4 ) .
I = sin 2 ψ M cos 2 ( ψ M ψ P ) + cos 2 ψ M sin 2 ( ψ M ψ P ) + ρ 2 [ cos 2 ψ M cos 2 ( ψ M ψ P ) + sin 2 ψ M sin 2 ( ψ M ψ P ) ] + ½ ( ρ 2 1 ) sin ( 2 ψ M ) sin [ 2 ( ψ M ψ P ) ] cos δ ,
R 2 ω = N sin ( 2 ψ M ) [ 2 J 2 ( A ) ] .
sin ( 2 ψ M ) 2 ψ M = [ R 2 ω min / R 2 ω max ] ,
E f = W 2 × R ( ψ W 2 ) × S × R ( ψ W 1 ) × W 1 × R ( ψ W 1 ψ M ) × M × R ( ψ M ψ P ) × P × ( 1 1 ) ,
E f = A × R ( ψ A ψ W 2 ) × W 2 × R ( ψ W 2 ) × S × R ( ψ W 1 ) × W 1 × R ( ψ W 1 ψ M ) × M × R ( ψ M ψ P ) × P × ( 1 1 ) ,
S = ( 1 0 0 ρ exp ( i Δ ) ) = ( 1 0 0 tan ψ exp ( i Δ ) ) ,
P = A = ( 1 0 0 α ) .
M = { 1 0 0 τ 0 exp [ i ( δ 0 + δ ) ] } .
I = 1 + cos ( δ + δ 0 ) ,
R ω / R ω cal = sin δ 0 ,
I = 1 + ρ 2 + ( 1 ρ 2 ) cos ( δ + δ )
R 2 ω / R 2 ω cal = N cos δ .
E f = A × R ( π / 4 ψ W 2 ) × W 2 × R ( ψ W 2 ) × S × R ( ψ W 1 ) × W 1 × R ( ψ W 1 ) × M × R ( π / 4 ) × P × ( 1 1 ) .
A × R ( 0 ) × W 2 × R ( π / 4 ) = ( 1 0 0 0 ) [ 1 1 τ 2 exp ( i δ 2 ) τ 2 exp ( i δ 2 ) ] = ( 1 1 0 0 )
W 2 = [ 1 0 0 τ 2 exp ( i δ 2 ) ] .
E f = [ 1 ρ exp ( i Δ ) 0 0 ] × { cos 2 Φ + τ 1 exp ( i δ 1 ) sin 2 Φ sin Φ cos Φ [ 1 τ 1 exp ( i δ 1 ) ] sin Φ cos Φ [ 1 τ 1 exp ( i δ 1 ) ] sin 2 Φ + τ 1 exp ( i δ 1 ) cos 2 Φ ] } × [ 1 exp ( i δ ) ] .
S = S cos δ 1 [ N sin ( 2 Φ ) + C ( sin 4 Φ cos 4 Φ ) ] sin δ 1 , C = C [ cos δ 1 ( 1 4 sin 2 Φ cos 2 Φ ) + 4 sin 2 Φ cos 2 Φ ] + S ( sin 4 Φ cos 4 Φ ) sin δ 1 + N sin ( 2 Φ ) cos ( 2 Φ ) ( 1 cos δ 1 ) ,
R 2 ω = ( cos 2 Φ ρ 2 sin 2 Φ ) + τ PMT 2 ( sin 2 Φ ρ 2 cos 2 Φ ) ( cos 2 Φ ρ 2 sin 2 Φ ) + τ PMT 2 ( sin 2 Φ + ρ 2 cos 2 Φ ) × [ 2 J 2 ( A ) ] ,
R ¯ 2 ω = R 2 ω ( ψ M ψ P = π / 4 ) R 2 ω ( ψ M ψ P = + π / 4 ) = 2 N [ 2 J 2 ( A ) ] 1 N 2 [ J 0 ( A ) ] 2
R ¯ 2 ω cal = R 2 ω cal ( ψ M ψ P = π / 4 ) R 2 ω cal ( ψ M ψ P = + π / 4 ) = 2 J 2 ( A ) 1 [ J 0 ( A ) ] 2 ,
R ¯ 2 ω R ¯ 2 ω cal = N { 1 [ J 0 ( A ) ] 2 1 N 2 [ J 0 ( A ) ] 2 } ,
J n ( A ) = k = 0 ( 1 ) k ( A / 2 ) 2 k + n k ! ( k + n ) !
I = ( 1 + ρ 2 ) ( 1 + α 2 ) + ( 1 ρ 2 ) ( 1 α 2 ) cos ( δ + δ 0 ) ,
I = ( 1 + α 2 ) ( 1 α ) 2 + ρ 2 ( 1 + α 2 ) ( 1 + α ) 2 + 2 ρ ( 1 α 2 ) cos ( δ + δ 0 + Δ )
N = N [ 1 + J 0 ( A ) 1 + N J 0 ( A ) ] , S = S ( 1 2 α N ) + C J 0 ( A ) S = ( 1 N 2 ) 1 / 2 sin ( Δ + δ 0 ) , C = C [ 1 + J 0 ( A ) ] ( 1 2 α N ) + C J 0 ( A ) C = ( 1 N 2 ) 1 / 2 cos ( Δ + δ 0 ) ,
N = N 1 + J 0 ( A ) ( 1 N ) , S = S [ 1 + J 0 ( A ) ] ( 1 2 α N ) 1 + J 0 ( A ) ( 1 C ) , C = C ( 1 2 α N ) 1 + J 0 ( A ) ( 1 C ) .

Metrics