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References

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  1. L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, Inst. Radio Engrs. Trans. IT-6, 386 (1960).
  2. M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), p 385.
  3. J. W. Cooley, J. W. Tukey, Math. Computation 19, No. 90, 297 (1965).
    [CrossRef]
  4. H. C. Andrews, A High Speed Algorithm for the Computer Generation of Fourier Transforms, IEEE Computer Group Repository, R–67–126, 1967.
  5. A. A. Michelson, Studies in Optics (University of Chicago Press, Chicago, Illinois, 1927), p. 70.

1967 (1)

H. C. Andrews, A High Speed Algorithm for the Computer Generation of Fourier Transforms, IEEE Computer Group Repository, R–67–126, 1967.

1965 (1)

J. W. Cooley, J. W. Tukey, Math. Computation 19, No. 90, 297 (1965).
[CrossRef]

1960 (1)

L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, Inst. Radio Engrs. Trans. IT-6, 386 (1960).

Andrews, H. C.

H. C. Andrews, A High Speed Algorithm for the Computer Generation of Fourier Transforms, IEEE Computer Group Repository, R–67–126, 1967.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), p 385.

Cooley, J. W.

J. W. Cooley, J. W. Tukey, Math. Computation 19, No. 90, 297 (1965).
[CrossRef]

Cutrona, L. J.

L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, Inst. Radio Engrs. Trans. IT-6, 386 (1960).

Leith, E. N.

L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, Inst. Radio Engrs. Trans. IT-6, 386 (1960).

Michelson, A. A.

A. A. Michelson, Studies in Optics (University of Chicago Press, Chicago, Illinois, 1927), p. 70.

Palermo, C. J.

L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, Inst. Radio Engrs. Trans. IT-6, 386 (1960).

Porcello, L. J.

L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, Inst. Radio Engrs. Trans. IT-6, 386 (1960).

Tukey, J. W.

J. W. Cooley, J. W. Tukey, Math. Computation 19, No. 90, 297 (1965).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), p 385.

IEEE Computer Group Repository, R–67–126 (1)

H. C. Andrews, A High Speed Algorithm for the Computer Generation of Fourier Transforms, IEEE Computer Group Repository, R–67–126, 1967.

Inst. Radio Engrs. Trans. (1)

L. J. Cutrona, E. N. Leith, C. J. Palermo, L. J. Porcello, Inst. Radio Engrs. Trans. IT-6, 386 (1960).

Math. Computation (1)

J. W. Cooley, J. W. Tukey, Math. Computation 19, No. 90, 297 (1965).
[CrossRef]

Other (2)

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), p 385.

A. A. Michelson, Studies in Optics (University of Chicago Press, Chicago, Illinois, 1927), p. 70.

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Figures (3)

Fig. 1
Fig. 1

Fraunhofer diffraction pattern geometry.

Fig. 2
Fig. 2

Diffraction pattern of an unsymmetrical cross: (a) aperture; (b) diffraction pattern; (c) log of diffraction pattern.

Fig. 3
Fig. 3

Diffraction pattern of four rectangles: (a) aperture; (b) diffraction pattern; (c) log of diffraction pattern.

Equations (6)

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a ( u , v ) = ( 1 / λ ) ( E / D ) 1 2 f ( x , y ) exp [ - ( 2 π i / λ r ) ( u x + u y ) ] d x d y ,
a ( u s , v t ) = 1 λ ( E D ) 1 2 j = 0 N - 1 k = 0 N - 1 f ( x j , y k ) × exp [ - 2 π i λ r ( u s x j + v t y k ) ] ,
j = x j ( N / 2 L ) , k = y k ( N / 2 L ) .
a ( u s , v t ) = 1 λ ( E D ) 1 2 j = 0 N - 1 k = 0 N - 1 f ( j , k ) × exp [ - 2 π i λ r ( 2 L N ) ( u s j + v t k ) ] .
F ( m , n ) = 1 N j = 0 N - 1 k = 0 N - 1 f ( j , k ) exp [ 2 π i N ( j m + k n ) ] ,
a ( u s , v t ) = ( N / λ ) ( E / D ) 1 2 F [ m = ( 2 L / λ r ) u s , n = ( 2 L / λ r ) v t ] .

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