Abstract

This paper concerns the calculation of autocovariance (autocorrelation) functions and the corresponding power spectra from a set of finite samples selected from the infinite population. In many optical experiments involving statistical fluctuations we wish to subtract the population mean from each measurement when the population mean is unknown. It is shown that subtracting the sample mean from each sample measurement leads to definite and predictable errors in the autocovariance function and its corresponding power spectrum. We show in a computer-generated example that the error introduced has significance in the autocovariance function but has much less significance in the power spectrum.

© 1978 Optical Society of America

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  1. J. C. Dainty and R. Shaw, Image Science (Academic, New York, 1974), Chap. 8.
  2. S. A. Armstrong and B. J. Thompson, "Comparison of Coherent and Incoherent Spectral Analysis Techniques in Image Evaluation," in Data Extraction and Classification from Film (SPIE publication, 1977), Vol. 117.
  3. D. Korff, G. Dryden, and M. G. Miller, "Information Retrieval from Atmospheric Induced Speckle Patterns," Opt. Commun. 5, 187 (1972).
  4. S. P. Worden, "The Angular Diameter of Vesta from Speckle Interferometry," Icarus (to be published).
  5. P. Dobberstein, "Coupling Between Light and Surface Plasma- Waves Via Non-Gaussian Surface Roughness," Phys. Lett. A 31, 307 (1970).
  6. M. Rasigni, G. Rasigni, C. T. Hua, and J. Pons, "Determination of Surface Structure Autocorrelation Function for Rough Deposits of Magnesium," Opt. Lett. 1, 127 (1977).
  7. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 21.
  8. Reference. 1, pp. 277–279.
  9. G. M. Jenkins and D. G. Watts, Spectral Analysis and Its Applications (Holden-Day, San Francisco, 1968), p. 179.
  10. E. L. O'Neill and A. Walther, "A problem in the determination of correlation functions," J. Opt. Soc. Am. 67, 1125 (1977).
  11. Ref. 9, pp. 179–180.
  12. W. Davenport and W. Root, Random Signals and Noise (McGraw-Hill, New York, 1958), p. 69.
  13. Reference. 9, Sec. 6.3.4.
  14. E. O. Brigham, The Fast Fourier Transform, (Prentice-Hall, Englewood Cliffs, NJ, 1974), p. 98.

1977

M. Rasigni, G. Rasigni, C. T. Hua, and J. Pons, "Determination of Surface Structure Autocorrelation Function for Rough Deposits of Magnesium," Opt. Lett. 1, 127 (1977).

E. L. O'Neill and A. Walther, "A problem in the determination of correlation functions," J. Opt. Soc. Am. 67, 1125 (1977).

1972

D. Korff, G. Dryden, and M. G. Miller, "Information Retrieval from Atmospheric Induced Speckle Patterns," Opt. Commun. 5, 187 (1972).

1970

P. Dobberstein, "Coupling Between Light and Surface Plasma- Waves Via Non-Gaussian Surface Roughness," Phys. Lett. A 31, 307 (1970).

Armstrong, S. A.

S. A. Armstrong and B. J. Thompson, "Comparison of Coherent and Incoherent Spectral Analysis Techniques in Image Evaluation," in Data Extraction and Classification from Film (SPIE publication, 1977), Vol. 117.

Brigham, E. O.

E. O. Brigham, The Fast Fourier Transform, (Prentice-Hall, Englewood Cliffs, NJ, 1974), p. 98.

Dainty, J. C.

J. C. Dainty and R. Shaw, Image Science (Academic, New York, 1974), Chap. 8.

Davenport, W.

W. Davenport and W. Root, Random Signals and Noise (McGraw-Hill, New York, 1958), p. 69.

Dobberstein, P.

P. Dobberstein, "Coupling Between Light and Surface Plasma- Waves Via Non-Gaussian Surface Roughness," Phys. Lett. A 31, 307 (1970).

Dryden, G.

D. Korff, G. Dryden, and M. G. Miller, "Information Retrieval from Atmospheric Induced Speckle Patterns," Opt. Commun. 5, 187 (1972).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 21.

Hua, C. T.

M. Rasigni, G. Rasigni, C. T. Hua, and J. Pons, "Determination of Surface Structure Autocorrelation Function for Rough Deposits of Magnesium," Opt. Lett. 1, 127 (1977).

Jenkins, G. M.

G. M. Jenkins and D. G. Watts, Spectral Analysis and Its Applications (Holden-Day, San Francisco, 1968), p. 179.

Korff, D.

D. Korff, G. Dryden, and M. G. Miller, "Information Retrieval from Atmospheric Induced Speckle Patterns," Opt. Commun. 5, 187 (1972).

Miller, M. G.

D. Korff, G. Dryden, and M. G. Miller, "Information Retrieval from Atmospheric Induced Speckle Patterns," Opt. Commun. 5, 187 (1972).

O’Neill, E. L.

Pons, J.

M. Rasigni, G. Rasigni, C. T. Hua, and J. Pons, "Determination of Surface Structure Autocorrelation Function for Rough Deposits of Magnesium," Opt. Lett. 1, 127 (1977).

Rasigni, G.

M. Rasigni, G. Rasigni, C. T. Hua, and J. Pons, "Determination of Surface Structure Autocorrelation Function for Rough Deposits of Magnesium," Opt. Lett. 1, 127 (1977).

Rasigni, M.

M. Rasigni, G. Rasigni, C. T. Hua, and J. Pons, "Determination of Surface Structure Autocorrelation Function for Rough Deposits of Magnesium," Opt. Lett. 1, 127 (1977).

Root, W.

W. Davenport and W. Root, Random Signals and Noise (McGraw-Hill, New York, 1958), p. 69.

Shaw, R.

J. C. Dainty and R. Shaw, Image Science (Academic, New York, 1974), Chap. 8.

Thompson, B. J.

S. A. Armstrong and B. J. Thompson, "Comparison of Coherent and Incoherent Spectral Analysis Techniques in Image Evaluation," in Data Extraction and Classification from Film (SPIE publication, 1977), Vol. 117.

Walther, A.

Watts, D. G.

G. M. Jenkins and D. G. Watts, Spectral Analysis and Its Applications (Holden-Day, San Francisco, 1968), p. 179.

Worden, S. P.

S. P. Worden, "The Angular Diameter of Vesta from Speckle Interferometry," Icarus (to be published).

J. Opt. Soc. Am.

Opt. Commun.

D. Korff, G. Dryden, and M. G. Miller, "Information Retrieval from Atmospheric Induced Speckle Patterns," Opt. Commun. 5, 187 (1972).

Opt. Lett.

M. Rasigni, G. Rasigni, C. T. Hua, and J. Pons, "Determination of Surface Structure Autocorrelation Function for Rough Deposits of Magnesium," Opt. Lett. 1, 127 (1977).

Phys. Lett. A

P. Dobberstein, "Coupling Between Light and Surface Plasma- Waves Via Non-Gaussian Surface Roughness," Phys. Lett. A 31, 307 (1970).

Other

Ref. 9, pp. 179–180.

W. Davenport and W. Root, Random Signals and Noise (McGraw-Hill, New York, 1958), p. 69.

Reference. 9, Sec. 6.3.4.

E. O. Brigham, The Fast Fourier Transform, (Prentice-Hall, Englewood Cliffs, NJ, 1974), p. 98.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 21.

Reference. 1, pp. 277–279.

G. M. Jenkins and D. G. Watts, Spectral Analysis and Its Applications (Holden-Day, San Francisco, 1968), p. 179.

S. P. Worden, "The Angular Diameter of Vesta from Speckle Interferometry," Icarus (to be published).

J. C. Dainty and R. Shaw, Image Science (Academic, New York, 1974), Chap. 8.

S. A. Armstrong and B. J. Thompson, "Comparison of Coherent and Incoherent Spectral Analysis Techniques in Image Evaluation," in Data Extraction and Classification from Film (SPIE publication, 1977), Vol. 117.

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