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  1. B. P. Ramsay, O. T. Koppius, and E. L. Cleveland, “The prism and the theory of optical resolution,” J. Opt. Soc. Am. 30, 439 (1940).
    [CrossRef]
  2. E. L. Cleveland, B. P. Ramsay, and O. T. Koppius, “Optical resolving power and the photon theory,” J. Opt. Soc. Am., forthcoming issue.
  3. In this paper, primes are used to indicate maximum values, double primes to indicate minimum values, and an asterisk to denote the value of a quantity at the criterion point which is sometimes called the point of overlap.
  4. For a catalog of intensity functions appropriate to various interferential devices, see L. Sturkey and B. P. Ramsay, “A general interferential method.” This paper will shortly appear in Phil. Mag.
  5. W. E. Williams, Applications of Interferometry (E. P. Dutton and Company, 1930), p. 79.
  6. A. Schuster, Theory of Optics (E. Arnold and Company, 1924), p. 158.
  7. C. M. Sparrow, Astrophys. J. 44, 76–86 (1916).
    [CrossRef]
  8. F. L. O. Wadsworth, Phil. Mag. 5, 355–374 (1903).
    [CrossRef]
  9. T. Preston, Theory of Light, fifth edition (Macmillan and Company, 1928), p. 266.
  10. R. W. Ditchburn, Proc. Roy. Irish Acad. 39, 58–72 (1930).
  11. W. V. Houston, Phys. Rev. 29, 480 (1927).
    [CrossRef]
  12. A. Buxton, Phil. Mag. 23, 440–442 (1937).
  13. R. W. Ditchburn and E. J. Power-Steele, Proc. Roy. Irish Acad. 41, 137–149 (1933).
  14. C. Fabry, Les Applications des Interferences Lumineuses (Rev. d’optique, 1923), pp. 28–29.
  15. In the mathematical development, R appears as the geometric ratio of the amplitudes of the compatible beams whose superposition produces the intensity function (26). Its physical significance appears on applying the Stokes amplitude coefficient of reflection (sometimes called the reflecting power) to the incident beam at each reflection. Then, since internal reflections in the interferometer occur in pairs, the amplitude of each emerging beam is the product of the amplitude of the incident beam by some integral power of the square of the Stokes coefficient; and this square is the intensity coefficient, R.
  16. C. Fabry, Optique (Les Presses Universitaires de France, 1934), 70.
  17. A. A. Michelson, Phil. Mag. (5) 31, 338 (1891); Phil. Mag. 34, 280 (1892).
    [CrossRef]
  18. R. C. Williams and R. C. Gibbs, Phys. Rev. 45, 475 (1934); Phys. Rev. 45, 491 (1934).
    [CrossRef]

1940 (1)

1937 (1)

A. Buxton, Phil. Mag. 23, 440–442 (1937).

1934 (1)

R. C. Williams and R. C. Gibbs, Phys. Rev. 45, 475 (1934); Phys. Rev. 45, 491 (1934).
[CrossRef]

1933 (1)

R. W. Ditchburn and E. J. Power-Steele, Proc. Roy. Irish Acad. 41, 137–149 (1933).

1930 (1)

R. W. Ditchburn, Proc. Roy. Irish Acad. 39, 58–72 (1930).

1927 (1)

W. V. Houston, Phys. Rev. 29, 480 (1927).
[CrossRef]

1916 (1)

C. M. Sparrow, Astrophys. J. 44, 76–86 (1916).
[CrossRef]

1903 (1)

F. L. O. Wadsworth, Phil. Mag. 5, 355–374 (1903).
[CrossRef]

1891 (1)

A. A. Michelson, Phil. Mag. (5) 31, 338 (1891); Phil. Mag. 34, 280 (1892).
[CrossRef]

Buxton, A.

A. Buxton, Phil. Mag. 23, 440–442 (1937).

Cleveland, E. L.

B. P. Ramsay, O. T. Koppius, and E. L. Cleveland, “The prism and the theory of optical resolution,” J. Opt. Soc. Am. 30, 439 (1940).
[CrossRef]

E. L. Cleveland, B. P. Ramsay, and O. T. Koppius, “Optical resolving power and the photon theory,” J. Opt. Soc. Am., forthcoming issue.

Ditchburn, R. W.

R. W. Ditchburn and E. J. Power-Steele, Proc. Roy. Irish Acad. 41, 137–149 (1933).

R. W. Ditchburn, Proc. Roy. Irish Acad. 39, 58–72 (1930).

Fabry, C.

C. Fabry, Les Applications des Interferences Lumineuses (Rev. d’optique, 1923), pp. 28–29.

C. Fabry, Optique (Les Presses Universitaires de France, 1934), 70.

Gibbs, R. C.

R. C. Williams and R. C. Gibbs, Phys. Rev. 45, 475 (1934); Phys. Rev. 45, 491 (1934).
[CrossRef]

Houston, W. V.

W. V. Houston, Phys. Rev. 29, 480 (1927).
[CrossRef]

Koppius, O. T.

B. P. Ramsay, O. T. Koppius, and E. L. Cleveland, “The prism and the theory of optical resolution,” J. Opt. Soc. Am. 30, 439 (1940).
[CrossRef]

E. L. Cleveland, B. P. Ramsay, and O. T. Koppius, “Optical resolving power and the photon theory,” J. Opt. Soc. Am., forthcoming issue.

Michelson, A. A.

A. A. Michelson, Phil. Mag. (5) 31, 338 (1891); Phil. Mag. 34, 280 (1892).
[CrossRef]

Power-Steele, E. J.

R. W. Ditchburn and E. J. Power-Steele, Proc. Roy. Irish Acad. 41, 137–149 (1933).

Preston, T.

T. Preston, Theory of Light, fifth edition (Macmillan and Company, 1928), p. 266.

Ramsay, B. P.

B. P. Ramsay, O. T. Koppius, and E. L. Cleveland, “The prism and the theory of optical resolution,” J. Opt. Soc. Am. 30, 439 (1940).
[CrossRef]

E. L. Cleveland, B. P. Ramsay, and O. T. Koppius, “Optical resolving power and the photon theory,” J. Opt. Soc. Am., forthcoming issue.

For a catalog of intensity functions appropriate to various interferential devices, see L. Sturkey and B. P. Ramsay, “A general interferential method.” This paper will shortly appear in Phil. Mag.

Schuster, A.

A. Schuster, Theory of Optics (E. Arnold and Company, 1924), p. 158.

Sparrow, C. M.

C. M. Sparrow, Astrophys. J. 44, 76–86 (1916).
[CrossRef]

Sturkey, L.

For a catalog of intensity functions appropriate to various interferential devices, see L. Sturkey and B. P. Ramsay, “A general interferential method.” This paper will shortly appear in Phil. Mag.

Wadsworth, F. L. O.

F. L. O. Wadsworth, Phil. Mag. 5, 355–374 (1903).
[CrossRef]

Williams, R. C.

R. C. Williams and R. C. Gibbs, Phys. Rev. 45, 475 (1934); Phys. Rev. 45, 491 (1934).
[CrossRef]

Williams, W. E.

W. E. Williams, Applications of Interferometry (E. P. Dutton and Company, 1930), p. 79.

Astrophys. J. (1)

C. M. Sparrow, Astrophys. J. 44, 76–86 (1916).
[CrossRef]

J. Opt. Soc. Am. (1)

Phil. Mag. (2)

A. Buxton, Phil. Mag. 23, 440–442 (1937).

F. L. O. Wadsworth, Phil. Mag. 5, 355–374 (1903).
[CrossRef]

Phil. Mag. (5) (1)

A. A. Michelson, Phil. Mag. (5) 31, 338 (1891); Phil. Mag. 34, 280 (1892).
[CrossRef]

Phys. Rev. (2)

R. C. Williams and R. C. Gibbs, Phys. Rev. 45, 475 (1934); Phys. Rev. 45, 491 (1934).
[CrossRef]

W. V. Houston, Phys. Rev. 29, 480 (1927).
[CrossRef]

Proc. Roy. Irish Acad. (2)

R. W. Ditchburn, Proc. Roy. Irish Acad. 39, 58–72 (1930).

R. W. Ditchburn and E. J. Power-Steele, Proc. Roy. Irish Acad. 41, 137–149 (1933).

Other (9)

C. Fabry, Les Applications des Interferences Lumineuses (Rev. d’optique, 1923), pp. 28–29.

In the mathematical development, R appears as the geometric ratio of the amplitudes of the compatible beams whose superposition produces the intensity function (26). Its physical significance appears on applying the Stokes amplitude coefficient of reflection (sometimes called the reflecting power) to the incident beam at each reflection. Then, since internal reflections in the interferometer occur in pairs, the amplitude of each emerging beam is the product of the amplitude of the incident beam by some integral power of the square of the Stokes coefficient; and this square is the intensity coefficient, R.

C. Fabry, Optique (Les Presses Universitaires de France, 1934), 70.

T. Preston, Theory of Light, fifth edition (Macmillan and Company, 1928), p. 266.

E. L. Cleveland, B. P. Ramsay, and O. T. Koppius, “Optical resolving power and the photon theory,” J. Opt. Soc. Am., forthcoming issue.

In this paper, primes are used to indicate maximum values, double primes to indicate minimum values, and an asterisk to denote the value of a quantity at the criterion point which is sometimes called the point of overlap.

For a catalog of intensity functions appropriate to various interferential devices, see L. Sturkey and B. P. Ramsay, “A general interferential method.” This paper will shortly appear in Phil. Mag.

W. E. Williams, Applications of Interferometry (E. P. Dutton and Company, 1930), p. 79.

A. Schuster, Theory of Optics (E. Arnold and Company, 1924), p. 158.

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Figures (1)

Fig. 1
Fig. 1

Diagram to show the application of the Rayleigh criterion to the prism distribution functions. I1 and I2 are the intensity curves, J is the composite curve, x is the parameter in terms of which the distribution is described, and b is the criterion value. The limit of resolution is 2b.

Equations (42)

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J = I 1 + I 2 .
I = I ( sin 2 α ) / α 2 .
J = I { sin 2 ( x - b ) ( x - b ) 2 + sin 2 ( x + b ) ( x + b ) 2 } .
ϕ = 2 b = π .
ϕ = 2 b = 2 π .
J = I ( 4 / π 2 + 4 / π 2 ) .
J / J = 8 / π 2 = 0.810.
2 J / x 2 = 0             at             x = 0.
ϕ = 2 b = 2.606.
ρ s = ( - π / 2.606 ) T ( d μ / d λ ) or             ρ s = - 1.206 T ( d μ / d λ ) .
ρ s = 1.206 k m .
I = { 2 z J 1 ( z ) } 2 ,
z = 2 π R y 1 / λ f .
d 2 d z 2 { J 1 ( z ) z } = 0.
J 1 ( z ) { 2 z - z 3 } = J 0 ( z ) .
ϕ B = 2 b = 2 y 1 / f
ϕ B = 4.60 λ / 2 π R = 1.46 λ / 2 R .
ϕ R = 3.83 λ / 2 π R = 1.2197 λ / 2 R .
Δ α = b = π Δ I = 1
Δ I / Δ α = 1 / π .
Δ α = π / k ,             Δ I = 1
Δ I / Δ α = k / π .
Δ α = b = π / 2 ,
Δ I = ( 1 - 4 / π 2 ) ,
Δ I Δ α = ( 1 - 0.405 ) π / 2 = 1.19 π .
Δ I = ( 1 - 4 / π 2 ) .
I f = I / ( 1 + F sin 2 α ) ,
α = m π .
I * = 0.405 = 1 / ( 1 + F sin 2 α * ) ,
sin 2 α * = ( 1 - 0.405 ) / 0.405 F ,
α * = m π + sin - 1 ( 1.469 / F ) 1 2 ,
Δ α = α - α * = sin - 1 ( 1.21 / F 1 2 ) .
Δ I Δ α = ( 1 - 0.405 ) sin - 1 ( 1.21 / F 1 2 ) .
F = 4 R / ( 1 - R ) 2 ,
Δ I / Δ α = 0.595 F 1 2 / 1.21 ,
Δ I / Δ α = 1.19 R 1 2 / 1.21 ( 1 - R ) ,
Δ I Δ α = 1.19 π [ π 1.21 R 1 2 ( 1 - R ) ] .
Δ I / Δ α = ( 1.19 / π ) k ,
N = [ π 1.21 R 1 2 ( 1 - R ) ] .
I f = Z 2 / ( 1 + R 2 - 2 R cos γ ) .
I = Z 2 / ( 1 - R ) 2
α = γ / 2.