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References

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  1. C. B. Burckhardt, J. Opt. Soc. Am. 56, 1502 (1966).
    [Crossref]
  2. P. Phariseau, Proc. Ind. Acad. Sci. 44A, 165 (1956). A. B. Bathia and W. J. Noble, Proc. Roy. Soc. 220A, 369 (1953).
  3. W. R. Klein, C. B. Tipnis, and E. A. Hiedemann, J. Acoust. Soc. Am. 38, 229 (1965). W. R. Klein, Proc. 5th Congrès International D’Acoustique, Liège (1965).
    [Crossref]
  4. M. G. Cohen and E. I. Gordon, Bell Syst. Tech. J. 45, 945 (1966).
    [Crossref]
  5. Note that the factor R is equal to the square of the amplitude reflectance and corresponds to two reflections. The factor (1 − R) is equal to the product of amplitude transmittances of the two grating boundaries.

1966 (2)

C. B. Burckhardt, J. Opt. Soc. Am. 56, 1502 (1966).
[Crossref]

M. G. Cohen and E. I. Gordon, Bell Syst. Tech. J. 45, 945 (1966).
[Crossref]

1965 (1)

W. R. Klein, C. B. Tipnis, and E. A. Hiedemann, J. Acoust. Soc. Am. 38, 229 (1965). W. R. Klein, Proc. 5th Congrès International D’Acoustique, Liège (1965).
[Crossref]

1956 (1)

P. Phariseau, Proc. Ind. Acad. Sci. 44A, 165 (1956). A. B. Bathia and W. J. Noble, Proc. Roy. Soc. 220A, 369 (1953).

Burckhardt, C. B.

Cohen, M. G.

M. G. Cohen and E. I. Gordon, Bell Syst. Tech. J. 45, 945 (1966).
[Crossref]

Gordon, E. I.

M. G. Cohen and E. I. Gordon, Bell Syst. Tech. J. 45, 945 (1966).
[Crossref]

Hiedemann, E. A.

W. R. Klein, C. B. Tipnis, and E. A. Hiedemann, J. Acoust. Soc. Am. 38, 229 (1965). W. R. Klein, Proc. 5th Congrès International D’Acoustique, Liège (1965).
[Crossref]

Klein, W. R.

W. R. Klein, C. B. Tipnis, and E. A. Hiedemann, J. Acoust. Soc. Am. 38, 229 (1965). W. R. Klein, Proc. 5th Congrès International D’Acoustique, Liège (1965).
[Crossref]

Phariseau, P.

P. Phariseau, Proc. Ind. Acad. Sci. 44A, 165 (1956). A. B. Bathia and W. J. Noble, Proc. Roy. Soc. 220A, 369 (1953).

Tipnis, C. B.

W. R. Klein, C. B. Tipnis, and E. A. Hiedemann, J. Acoust. Soc. Am. 38, 229 (1965). W. R. Klein, Proc. 5th Congrès International D’Acoustique, Liège (1965).
[Crossref]

Bell Syst. Tech. J. (1)

M. G. Cohen and E. I. Gordon, Bell Syst. Tech. J. 45, 945 (1966).
[Crossref]

J. Acoust. Soc. Am. (1)

W. R. Klein, C. B. Tipnis, and E. A. Hiedemann, J. Acoust. Soc. Am. 38, 229 (1965). W. R. Klein, Proc. 5th Congrès International D’Acoustique, Liège (1965).
[Crossref]

J. Opt. Soc. Am. (1)

Proc. Ind. Acad. Sci. (1)

P. Phariseau, Proc. Ind. Acad. Sci. 44A, 165 (1956). A. B. Bathia and W. J. Noble, Proc. Roy. Soc. 220A, 369 (1953).

Other (1)

Note that the factor R is equal to the square of the amplitude reflectance and corresponds to two reflections. The factor (1 − R) is equal to the product of amplitude transmittances of the two grating boundaries.

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Figures (1)

Fig. 1
Fig. 1

Multiple reflections in a hologram grating.

Tables (1)

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Table I Results for light of wavelength λ=0.6328 μ and grating thicknesses of 15 and 50 μ.

Equations (11)

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S ( d ) = - j sin ν d · e - j β d ,
β = ( 2 π n / λ ) cos ϑ ,
ν = π n 1 / λ cos ϑ .
R = sin 2 ( θ - ϑ ) / sin 2 ( θ + ϑ ) ,
S tot = ( 1 - R ) [ S ( d ) + R S ( 3 d ) + R 2 S ( 5 d ) + ] .
S tot = - j sin ν d · e - j β d · ( 1 - R ) 1 + R e - 2 j β d 1 - 2 R e - 2 j β d · cos 2 ν d + R 2 e - 4 j β d .
S tot S tot * = τ S S * ,
τ = ( 1 - R ) 2 ( 1 + 2 R cos 2 β d + R 2 ) ( 1 - R 2 ) 2 + 4 R 2 ( cos 2 2 ν d + cos 2 2 β d ) - 4 R ( 1 + R 2 ) cos 2 ν d cos 2 β d .
R = 0.062             for             θ = 30 °
R = 0.097             for             θ = 45 ° ,
I tot = ( 1 - R ) 2 { S ( d ) 2 + R 2 S ( 3 d ) 2 + } .