Abstract

Diffraction has been numerically modeled using a Monte Carlo statistical analysis. The Heisenberg uncertainty principle has been applied to attain this goal. Example solutions have been studied and are presented to illustrate the utility and accuracy of the technique.

© 1971 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).
  2. J. R. Howell, “Calculation of Radiant Heat Exchange by the Monte Carlo Method,” ASME paper 65-WA/HT-54 (1965); also “Application of Monte Carlo to Heat Transfer Problems,” in Advances in Heat Transfer (1968), Vol. 5.
  3. P. W. Carlin, Proc. IEEE 52, 1371 (1964).
    [CrossRef]
  4. J. R. Schornhorst, R. Viskanta, AIAAJ. 6, 1450 (1968).
    [CrossRef]
  5. J. S. Toor, R. Viskanta, E. R. F. Winter, “Radiant Heat Transfer Between Simply Arranged Surfaces with Direction Dependent Properties,” AIAA Paper 69-624 (June1969).

1968 (1)

J. R. Schornhorst, R. Viskanta, AIAAJ. 6, 1450 (1968).
[CrossRef]

1964 (1)

P. W. Carlin, Proc. IEEE 52, 1371 (1964).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).

Carlin, P. W.

P. W. Carlin, Proc. IEEE 52, 1371 (1964).
[CrossRef]

Howell, J. R.

J. R. Howell, “Calculation of Radiant Heat Exchange by the Monte Carlo Method,” ASME paper 65-WA/HT-54 (1965); also “Application of Monte Carlo to Heat Transfer Problems,” in Advances in Heat Transfer (1968), Vol. 5.

Schornhorst, J. R.

J. R. Schornhorst, R. Viskanta, AIAAJ. 6, 1450 (1968).
[CrossRef]

Toor, J. S.

J. S. Toor, R. Viskanta, E. R. F. Winter, “Radiant Heat Transfer Between Simply Arranged Surfaces with Direction Dependent Properties,” AIAA Paper 69-624 (June1969).

Viskanta, R.

J. R. Schornhorst, R. Viskanta, AIAAJ. 6, 1450 (1968).
[CrossRef]

J. S. Toor, R. Viskanta, E. R. F. Winter, “Radiant Heat Transfer Between Simply Arranged Surfaces with Direction Dependent Properties,” AIAA Paper 69-624 (June1969).

Winter, E. R. F.

J. S. Toor, R. Viskanta, E. R. F. Winter, “Radiant Heat Transfer Between Simply Arranged Surfaces with Direction Dependent Properties,” AIAA Paper 69-624 (June1969).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).

AIAAJ. (1)

J. R. Schornhorst, R. Viskanta, AIAAJ. 6, 1450 (1968).
[CrossRef]

Proc. IEEE (1)

P. W. Carlin, Proc. IEEE 52, 1371 (1964).
[CrossRef]

Other (3)

J. S. Toor, R. Viskanta, E. R. F. Winter, “Radiant Heat Transfer Between Simply Arranged Surfaces with Direction Dependent Properties,” AIAA Paper 69-624 (June1969).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).

J. R. Howell, “Calculation of Radiant Heat Exchange by the Monte Carlo Method,” ASME paper 65-WA/HT-54 (1965); also “Application of Monte Carlo to Heat Transfer Problems,” in Advances in Heat Transfer (1968), Vol. 5.

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Figures (6)

Fig. 1
Fig. 1

Photon bundle incident upon an arbitrary aperture.

Fig. 2
Fig. 2

Angular distribution of photons upon applying the uncertainty principle.

Fig. 3
Fig. 3

Far field diffraction schematically illustrated from a square aperture.

Fig. 4
Fig. 4

Results of Monte Carlo and closed form solutions for far field diffraction from a square aperture.

Fig. 5
Fig. 5

Near field diffraction from a semi-infinite knife edge.

Fig. 6
Fig. 6

Results of Monte Carlo and closed form solutions for near field diffraction from a semi-infinite knife edge.

Equations (2)

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θ * = tan - 1 ( f / 2 k Δ ξ ) ,
F ( θ ) = [ 1 / ( 2 π ) 1 2 ] exp ( - θ / 2 θ * ) .

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