Abstract

We examine the statistical basis of the shift-and-add technique, by which true images of objects (viewed through fluctuating, distorting media) are formed by a particular kind of averaging of speckle images Our theory agrees with experimental results for objects consisting of isolated unresolvable points We develop a preliminary analysis for extended objects (i e, objects having continuous, resolvable brightness distributions)

© 1983 Optical Society of America

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  1. A Labeyrie, "Attainment of diffraction-limited resolution in large telescopes by Fourier analyzing speckle patterns in star images," Astron Astrophys 6, 85–87 (1970)
  2. R H T Bates and F M Cady, "Towards true imaging by wideband speckle interferometry," Opt Commun 32, 365-369 (1980), F M Cady and R H T Bates, "Speckle processing gives diffraction- limited true images from severely aberrated instruments," Opt Lett 5, 438–440 (1980)
  3. J C Dainty, Institute of Optics, University of Rochester, Rochester, New York 14627
  4. 4 C R Lynds, S P Worden, and J W Harvey, Astrophys J 207, 174–179 (1976)
  5. 5 K T Knox and B J Thompson, "Recovery of images from atmospherically- degraded short-exposure photographs," Astrophys J 193, L45–L48 (1974)
  6. 6 W T Rhodes and J W Goodman, "Interferometric technique for recording and restoring images degraded by unknown aberrations," J Opt Soc Am 63, 647–657 (1973)
  7. 7 R H T Bates and W R Fright, "Towards imaging with a speckle interferometric optical synthesis telescope," Mon Not R Astron Soc 198, 1017–1031 (1982)
  8. 8 J W Goodman, "Statistical properties of laser speckle patterns," in Laser Speckle and Related Phenomena, Vol 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap 2
  9. 9 A Papoullis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965)
  10. 10 J C Dainty, "Stellar speckle interferometry," in Laser Speckle and Related Phenomena, Vol 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap 7
  11. 11 E J Gumbel, Statistics of Extreme Values (Columbia U Press, New York, 1958)
  12. 12 F Mosteller and J W Tukey, Data Analysis and Regression (Addison-Wesley, New York, 1976)
  13. 13 H Andrews and B R Hunt, Digital Image Restoration (Prentice- Hall, Englewood Cliffs, N J, 1977)
  14. 14 I Gradshteyn and S Rizhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p 721

1982 (1)

7 R H T Bates and W R Fright, "Towards imaging with a speckle interferometric optical synthesis telescope," Mon Not R Astron Soc 198, 1017–1031 (1982)

1980 (1)

R H T Bates and F M Cady, "Towards true imaging by wideband speckle interferometry," Opt Commun 32, 365-369 (1980), F M Cady and R H T Bates, "Speckle processing gives diffraction- limited true images from severely aberrated instruments," Opt Lett 5, 438–440 (1980)

1974 (1)

5 K T Knox and B J Thompson, "Recovery of images from atmospherically- degraded short-exposure photographs," Astrophys J 193, L45–L48 (1974)

1973 (1)

6 W T Rhodes and J W Goodman, "Interferometric technique for recording and restoring images degraded by unknown aberrations," J Opt Soc Am 63, 647–657 (1973)

1970 (1)

A Labeyrie, "Attainment of diffraction-limited resolution in large telescopes by Fourier analyzing speckle patterns in star images," Astron Astrophys 6, 85–87 (1970)

Andrews, H

13 H Andrews and B R Hunt, Digital Image Restoration (Prentice- Hall, Englewood Cliffs, N J, 1977)

Bates, R H T

7 R H T Bates and W R Fright, "Towards imaging with a speckle interferometric optical synthesis telescope," Mon Not R Astron Soc 198, 1017–1031 (1982)

R H T Bates and F M Cady, "Towards true imaging by wideband speckle interferometry," Opt Commun 32, 365-369 (1980), F M Cady and R H T Bates, "Speckle processing gives diffraction- limited true images from severely aberrated instruments," Opt Lett 5, 438–440 (1980)

Cady, F M

R H T Bates and F M Cady, "Towards true imaging by wideband speckle interferometry," Opt Commun 32, 365-369 (1980), F M Cady and R H T Bates, "Speckle processing gives diffraction- limited true images from severely aberrated instruments," Opt Lett 5, 438–440 (1980)

Dainty, J C

10 J C Dainty, "Stellar speckle interferometry," in Laser Speckle and Related Phenomena, Vol 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap 7

J C Dainty, Institute of Optics, University of Rochester, Rochester, New York 14627

Fright, W R

7 R H T Bates and W R Fright, "Towards imaging with a speckle interferometric optical synthesis telescope," Mon Not R Astron Soc 198, 1017–1031 (1982)

Goodman, J W

6 W T Rhodes and J W Goodman, "Interferometric technique for recording and restoring images degraded by unknown aberrations," J Opt Soc Am 63, 647–657 (1973)

8 J W Goodman, "Statistical properties of laser speckle patterns," in Laser Speckle and Related Phenomena, Vol 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap 2

Gradshteyn, I

14 I Gradshteyn and S Rizhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p 721

Gumbel, E J

11 E J Gumbel, Statistics of Extreme Values (Columbia U Press, New York, 1958)

Harvey, J W

4 C R Lynds, S P Worden, and J W Harvey, Astrophys J 207, 174–179 (1976)

Hunt, B R

13 H Andrews and B R Hunt, Digital Image Restoration (Prentice- Hall, Englewood Cliffs, N J, 1977)

Knox, K T

5 K T Knox and B J Thompson, "Recovery of images from atmospherically- degraded short-exposure photographs," Astrophys J 193, L45–L48 (1974)

Labeyrie, A

A Labeyrie, "Attainment of diffraction-limited resolution in large telescopes by Fourier analyzing speckle patterns in star images," Astron Astrophys 6, 85–87 (1970)

Lynds, C R

4 C R Lynds, S P Worden, and J W Harvey, Astrophys J 207, 174–179 (1976)

Mosteller, F

12 F Mosteller and J W Tukey, Data Analysis and Regression (Addison-Wesley, New York, 1976)

Papoullis, A

9 A Papoullis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965)

Rhodes, W T

6 W T Rhodes and J W Goodman, "Interferometric technique for recording and restoring images degraded by unknown aberrations," J Opt Soc Am 63, 647–657 (1973)

Rizhik, S

14 I Gradshteyn and S Rizhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p 721

Thompson, B J

5 K T Knox and B J Thompson, "Recovery of images from atmospherically- degraded short-exposure photographs," Astrophys J 193, L45–L48 (1974)

Tukey, J W

12 F Mosteller and J W Tukey, Data Analysis and Regression (Addison-Wesley, New York, 1976)

Worden, S P

4 C R Lynds, S P Worden, and J W Harvey, Astrophys J 207, 174–179 (1976)

Astron Astrophys (1)

A Labeyrie, "Attainment of diffraction-limited resolution in large telescopes by Fourier analyzing speckle patterns in star images," Astron Astrophys 6, 85–87 (1970)

Astrophys J (1)

5 K T Knox and B J Thompson, "Recovery of images from atmospherically- degraded short-exposure photographs," Astrophys J 193, L45–L48 (1974)

J Opt Soc Am (1)

6 W T Rhodes and J W Goodman, "Interferometric technique for recording and restoring images degraded by unknown aberrations," J Opt Soc Am 63, 647–657 (1973)

Mon Not R Astron Soc (1)

7 R H T Bates and W R Fright, "Towards imaging with a speckle interferometric optical synthesis telescope," Mon Not R Astron Soc 198, 1017–1031 (1982)

Opt Commun (1)

R H T Bates and F M Cady, "Towards true imaging by wideband speckle interferometry," Opt Commun 32, 365-369 (1980), F M Cady and R H T Bates, "Speckle processing gives diffraction- limited true images from severely aberrated instruments," Opt Lett 5, 438–440 (1980)

Other (9)

J C Dainty, Institute of Optics, University of Rochester, Rochester, New York 14627

4 C R Lynds, S P Worden, and J W Harvey, Astrophys J 207, 174–179 (1976)

8 J W Goodman, "Statistical properties of laser speckle patterns," in Laser Speckle and Related Phenomena, Vol 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap 2

9 A Papoullis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965)

10 J C Dainty, "Stellar speckle interferometry," in Laser Speckle and Related Phenomena, Vol 9 of Topics in Applied Physics (Springer-Verlag, Berlin, 1975), Chap 7

11 E J Gumbel, Statistics of Extreme Values (Columbia U Press, New York, 1958)

12 F Mosteller and J W Tukey, Data Analysis and Regression (Addison-Wesley, New York, 1976)

13 H Andrews and B R Hunt, Digital Image Restoration (Prentice- Hall, Englewood Cliffs, N J, 1977)

14 I Gradshteyn and S Rizhik, Table of Integrals, Series, and Products (Academic, New York, 1965), p 721

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