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  1. P. Elias, D. S. Grey, and D. Z. Robinson, J. Opt. Soc. Am. 42, 127 (1952).
    [Crossref]
  2. P. Elias, J. Opt. Soc. Am. 43, 229 (1953).
    [Crossref]
  3. Y. W. Lee, Statistical Theory of Communication (John Wiley & Sons, Inc., New York, 1960), p. 481.
  4. S. J. Mason and H. J. Zimmermann, Electronic Circuits, Signals and Systems (John Wiley & Sons, Inc., New York, 1960), p. 350.
  5. P. M. Duffieux, L’Integrale de Fourier et ses applications à l’oplique (Besançon, 1946).
  6. J. A. MacDonald, Proc. Phys. Soc. (London) 72, 749 (1958).
    [Crossref]

1958 (1)

J. A. MacDonald, Proc. Phys. Soc. (London) 72, 749 (1958).
[Crossref]

1953 (1)

1952 (1)

Duffieux, P. M.

P. M. Duffieux, L’Integrale de Fourier et ses applications à l’oplique (Besançon, 1946).

Elias, P.

Grey, D. S.

Lee, Y. W.

Y. W. Lee, Statistical Theory of Communication (John Wiley & Sons, Inc., New York, 1960), p. 481.

MacDonald, J. A.

J. A. MacDonald, Proc. Phys. Soc. (London) 72, 749 (1958).
[Crossref]

Mason, S. J.

S. J. Mason and H. J. Zimmermann, Electronic Circuits, Signals and Systems (John Wiley & Sons, Inc., New York, 1960), p. 350.

Robinson, D. Z.

Zimmermann, H. J.

S. J. Mason and H. J. Zimmermann, Electronic Circuits, Signals and Systems (John Wiley & Sons, Inc., New York, 1960), p. 350.

J. Opt. Soc. Am. (2)

Proc. Phys. Soc. (London) (1)

J. A. MacDonald, Proc. Phys. Soc. (London) 72, 749 (1958).
[Crossref]

Other (3)

Y. W. Lee, Statistical Theory of Communication (John Wiley & Sons, Inc., New York, 1960), p. 481.

S. J. Mason and H. J. Zimmermann, Electronic Circuits, Signals and Systems (John Wiley & Sons, Inc., New York, 1960), p. 350.

P. M. Duffieux, L’Integrale de Fourier et ses applications à l’oplique (Besançon, 1946).

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Figures (2)

Fig. 1
Fig. 1

Upper bounds for the modulation transfer function |D(R,ψ)| (for constant azimuth ψ) of linear low-pass filters with nonnegative spread functions and cutoff frequency R(ψ). The well-known optical transfer functions of aberration-free systems (all for azimuth ψ parallel to one side of the rectangular aperture, respectively, perpendicular to the slits) are seen to reach the fundamental upper bounds at one frequency.——— rectangular aperture of uniform transparency.— – — – rectangular aperture apodized according to Wiener [N. Wiener: cf R. C. Spencer, “Optical Image Evaluation” (NBS circular 526, Washington, 1954) p. 249]. — – – — – – two-slit aperture.

Fig. 2
Fig. 2

(a) Definition of the “spread” Δx of the line-source image G L ( x ˜ ): Δ x ( G L ) Max = + G L ( x ˜ ) d x ˜ .

Equations (22)

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G ( t ) = 0 for t < 0 .
G P ( x , y ) 0 ; G L ( x ˜ ) 0.
R = ( R x 2 + R y 2 ) 1 2 , tan g ψ = R y / R x ;
D ( R x , R y ) = + + f ( r x , r y ) f * ( r x R x , r y R y ) d r x d r y + + | f ( r x , r y ) | 2 d r x d r y .
I ( x , y ) = + + I ( x ˜ , y ˜ ) G P ( x x ˜ , y y ˜ ) d x ˜ d y ˜
I ( x ˜ ) = 1 + 2 n = 1 , 2 , cos 2 π n R x ˜ .
I ( x ˜ ) = 1 + 2 / D ( R , ψ ) / cos [ 2 π R x ˜ + θ ( R , ψ ) ] .
| D ( R , ψ ) | 1 2 for R 1 2 R ( ψ )
| D ( R , ψ ) | cos [ π / ( N + 1 ) ]
R [ R ( ψ ) / N ] ( N = 1 , 2 , 3 , ) .
| D ( R , ψ ) | 1 1 2 π 2 [ R / R ( ψ ) ] 2 .
| D ( R , ψ = const ) | av 1 2 .
| D ( R , ψ = const ) | av = 1 R ( ψ ) 0 R ( ψ ) | D ( R ; ψ = const ) | d R
| D ( R ; ψ = const ) | av = 1 N n = 1 , 2 , | D ( n R ˆ ; ψ = const ) |
Δ x 1 / R ( ψ ) .
| D ( R , ψ ) | av 1 4 ,
| D ( R , ψ ) | av = 1 [ B ] ψ = 0 2 π R = 0 R ( ψ ) | D ( R , ψ ) | d R d ψ = 1 [ B ] ( B ) | D ( R x , R y ) | d R x d R y .
Δ f ψ / [ B ] .
Δ f · ( G P ) Max = + + G P ( x , y ) d x d y .
Δ x ( G L ) Max = + G L ( x ˜ ) d x ˜ .
Δ x ( d I E / d x ˜ ) Max = I E ( x ˜ ) .
I E ( x ˜ ) = + G L ( x ¯ ) d x ¯ .