Abstract

Calculations are performed to study the noise in the detector plane of an optical data-storage system with Fourier-transform holograms, caused by noise in the storage material. The signal-to-background ratio (SBR) and the signal-to-noise ratio (SNR) of the output signals in the detector plane are defined and calculated. Exact solutions are obtained by assuming gaussian-probability densities for amplitude and phase noise in the storage material.

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  1. V. A. Vitals, IBM Tech. Disclosure Bull. 8, 1581 (1966).
  2. F. M. Smits and L. E. Gallaher, Bell System Tech. J. 46, 1267 (1968).
  3. L. K. Anderson, Bell Lab. Record 46, 318 (1968).
  4. R. M. Langdon, Radio. Electr. Eng. 38, 369 (1969).
  5. A. L. Mikaeliane, V. I. Bobrinev, S. M. Naumov, and L. Z. Sokolova, IEEE J. QE-6, 4, 193 (1970).
  6. J. W. Goodman, J. Opt. Soc. Am. 57, 493 (1967).
  7. A. Kozma, J. Opt. Soc. Am. 58, 436 (1968).
  8. S. Löwenthal, J. Serres, and H. Arsenault, Opt. Commun. 1, 438 (1970).
  9. R. Röhler, Informationstheorie in der Optik (Wissenschaftliche Verlagsgesellschaft, Stuttgart, 1967).
  10. N. D. Diamantides, Appl. Opt. 8, 819 (1969).
  11. W. B. Davenport, Jr. and W. L. Root, Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).
  12. F. H. Lange, Korrelationselektronik (VEB Verlag, Berlin, 1962).
  13. I. J. Freeman, Principles of Noise (Wiley, New York, 1958).
  14. K. Stange and H. J. Henning, Formeln und Tabellen der Mathematischen Statistik (Springer, Berlin, 1966).
  15. E. L. O'Neill, Introduction to Statistical Optics (Addison–Wesley, Reading, Mass., 1963), p. 100.
  16. The assumption of a gaussian probability density for the noise function t˜N(x,y) apparently contradicts the restriction | t(x,y)|≤1. Nevertheless, the assumption can still be true if σt is small compared to 1, because in this case, the values of t˜N for which | tN|≥1≫σt have a very small probability density and may therefore be neglected.
  17. F. T. S. Yu, Appl. Opt. 8, 2483 (1969).
  18. C. B. Burckhardt, Appl. Opt. 9, 3, 695 (1970).
  19. G. W. Stroke, An Introduction to Coherent Optics and Holography (Academic, New York, 1966), p. 196.

Anderson, L. K.

L. K. Anderson, Bell Lab. Record 46, 318 (1968).

Arsenault, H.

S. Löwenthal, J. Serres, and H. Arsenault, Opt. Commun. 1, 438 (1970).

Bobrinev, V. I.

A. L. Mikaeliane, V. I. Bobrinev, S. M. Naumov, and L. Z. Sokolova, IEEE J. QE-6, 4, 193 (1970).

Burckhardt, C. B.

C. B. Burckhardt, Appl. Opt. 9, 3, 695 (1970).

Davenport, Jr., W. B.

W. B. Davenport, Jr. and W. L. Root, Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).

Diamantides, N. D.

N. D. Diamantides, Appl. Opt. 8, 819 (1969).

Freeman, I. J.

I. J. Freeman, Principles of Noise (Wiley, New York, 1958).

Gallaher, L. E.

F. M. Smits and L. E. Gallaher, Bell System Tech. J. 46, 1267 (1968).

Goodman, J. W.

J. W. Goodman, J. Opt. Soc. Am. 57, 493 (1967).

Henning, H. J.

K. Stange and H. J. Henning, Formeln und Tabellen der Mathematischen Statistik (Springer, Berlin, 1966).

Kozma, A.

A. Kozma, J. Opt. Soc. Am. 58, 436 (1968).

Langdon, R. M.

R. M. Langdon, Radio. Electr. Eng. 38, 369 (1969).

Lange, F. H.

F. H. Lange, Korrelationselektronik (VEB Verlag, Berlin, 1962).

Löwenthal, S.

S. Löwenthal, J. Serres, and H. Arsenault, Opt. Commun. 1, 438 (1970).

Mikaeliane, A. L.

A. L. Mikaeliane, V. I. Bobrinev, S. M. Naumov, and L. Z. Sokolova, IEEE J. QE-6, 4, 193 (1970).

Naumov, S. M.

A. L. Mikaeliane, V. I. Bobrinev, S. M. Naumov, and L. Z. Sokolova, IEEE J. QE-6, 4, 193 (1970).

O’Neill, E. L.

E. L. O'Neill, Introduction to Statistical Optics (Addison–Wesley, Reading, Mass., 1963), p. 100.

Röhler, R.

R. Röhler, Informationstheorie in der Optik (Wissenschaftliche Verlagsgesellschaft, Stuttgart, 1967).

Root, W. L.

W. B. Davenport, Jr. and W. L. Root, Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).

Serres, J.

S. Löwenthal, J. Serres, and H. Arsenault, Opt. Commun. 1, 438 (1970).

Smits, F. M.

F. M. Smits and L. E. Gallaher, Bell System Tech. J. 46, 1267 (1968).

Sokolova, L. Z.

A. L. Mikaeliane, V. I. Bobrinev, S. M. Naumov, and L. Z. Sokolova, IEEE J. QE-6, 4, 193 (1970).

Stange, K.

K. Stange and H. J. Henning, Formeln und Tabellen der Mathematischen Statistik (Springer, Berlin, 1966).

Stroke, G. W.

G. W. Stroke, An Introduction to Coherent Optics and Holography (Academic, New York, 1966), p. 196.

Vitals, V. A.

V. A. Vitals, IBM Tech. Disclosure Bull. 8, 1581 (1966).

Yu, F. T. S.

F. T. S. Yu, Appl. Opt. 8, 2483 (1969).

Other (19)

V. A. Vitals, IBM Tech. Disclosure Bull. 8, 1581 (1966).

F. M. Smits and L. E. Gallaher, Bell System Tech. J. 46, 1267 (1968).

L. K. Anderson, Bell Lab. Record 46, 318 (1968).

R. M. Langdon, Radio. Electr. Eng. 38, 369 (1969).

A. L. Mikaeliane, V. I. Bobrinev, S. M. Naumov, and L. Z. Sokolova, IEEE J. QE-6, 4, 193 (1970).

J. W. Goodman, J. Opt. Soc. Am. 57, 493 (1967).

A. Kozma, J. Opt. Soc. Am. 58, 436 (1968).

S. Löwenthal, J. Serres, and H. Arsenault, Opt. Commun. 1, 438 (1970).

R. Röhler, Informationstheorie in der Optik (Wissenschaftliche Verlagsgesellschaft, Stuttgart, 1967).

N. D. Diamantides, Appl. Opt. 8, 819 (1969).

W. B. Davenport, Jr. and W. L. Root, Introduction to the Theory of Random Signals and Noise (McGraw-Hill, New York, 1958).

F. H. Lange, Korrelationselektronik (VEB Verlag, Berlin, 1962).

I. J. Freeman, Principles of Noise (Wiley, New York, 1958).

K. Stange and H. J. Henning, Formeln und Tabellen der Mathematischen Statistik (Springer, Berlin, 1966).

E. L. O'Neill, Introduction to Statistical Optics (Addison–Wesley, Reading, Mass., 1963), p. 100.

The assumption of a gaussian probability density for the noise function t˜N(x,y) apparently contradicts the restriction | t(x,y)|≤1. Nevertheless, the assumption can still be true if σt is small compared to 1, because in this case, the values of t˜N for which | tN|≥1≫σt have a very small probability density and may therefore be neglected.

F. T. S. Yu, Appl. Opt. 8, 2483 (1969).

C. B. Burckhardt, Appl. Opt. 9, 3, 695 (1970).

G. W. Stroke, An Introduction to Coherent Optics and Holography (Academic, New York, 1966), p. 196.

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