Abstract

Noncoherent light speckle methods have been successfully applied to gauge the motion of glaciers and buildings. Resolution of the optical method was limited by the aberrating turbulent atmosphere through which the images were collected. Sensitivity limitations regarding this particular application of speckle interferometry are discussed and analyzed. Resolution limit experiments that were incidental to glacier flow studies are related to the basic theory of astronomical imaging. Optical resolution of the ice flow measurement technique is shown to be in substantial agreement with the sensitivity predictions of astronomy theory.

© 1991 Optical Society of America

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References

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  1. A. Asundi, F. P. Chiang, “Theory and Applications of the White Light Speckle Method for Strain Analysis,” Opt. Eng. 21, 570–580 (1982).
    [CrossRef]
  2. G. L. Cloud, E. G. Conley, “A Whole-Field Interferometric Scheme for Measuring Strain and Flow Rates of Glacier and Other Naturally Occurring Surfaces,” J. Glaciol. 29, 492–497 (1983).
  3. E. G. Conley, G. L. Cloud, “Stereo Interferometric Measurement of Glacier Ice Strain Rates,” in Proceedings, Spring 1985 Conference of the Society of Experimental Mechanics (Soc. Exp. Mech., Bethel, CT, 1985), pp. 452–453.
  4. E. G. Conley, G. L. Cloud, “Whole-Field Measurement of Ice Displacement and Strain Rates,” in Proceedings, Fifth International Offshore Mechanics and Artic Engineering Symposium (ASME, NY, NY, 1986), pp. 432–435.
  5. E. G. Conley, G. L. Cloud, “Practical Applications of Double-Exposure Noncoherent-Light Speckle Photography,” Appl. Opt. 25, 2246–2248 (1986).
    [CrossRef] [PubMed]
  6. E. G. Conley, J. Genin, “Application of Speckle Metrology at a Nuclear Waste Repository,” Proc. Soc. Photo-Opt. Instrum. Eng., Bellingham, WA 1332, 798–802 (1990).
  7. E. G. Conley, G. L. Cloud, “White-Light Speckle for Measuring Glacier Surface Displacements,” in Proceedings, International Conference on Hologram Interferometry and Speckle Metrology (Soc. Exp. Mech., Bethel, CT, 1990), pp. 88–94.
  8. S. Worden, “High Angular Resolution Techniques: Speckle Interferometry and Related Methods,” Proc. Soc. Photo-Opt. Instrum. Eng. 43, 66–73 (1973).
  9. D. L. Fried, “Optical Resolution Through a Randomly Inhomogeneous Medium for Very Long and Very Short Exposures,” J. Opt. Soc. Am. 56, 1372–1379 (1966).
    [CrossRef]
  10. D. Korff, “Analysis of a Method for Obtaining Near-Diffraction-Limited Information in the Presence of Atmospheric Turbulence,” J. Opt. Soc. Am. 63, 971–980 (1973).
    [CrossRef]
  11. R. E. Hufnagel, N. R. Stanley, “Modulation Transfer Function Associated with Image Transmission Through Turbulent Media,” J. Opt. Soc. Am. 54, 52–61 (1964).
    [CrossRef]
  12. O. von der Luhe, “Estimating Fried’s Parameter from a Time Series of an Arbitrarily Resolved Object Imaged Through Atmospheric Turbulence,” J. Opt. Soc. Am. A 1, 510–519 (1984).
    [CrossRef]
  13. D. P. Karo, A. M. Schneiderman, “Speckle Interferometry Lens-Atmosphere MTF Measurements,” J. Opt. Soc. Am. 66, 1252–1256 (1976).
    [CrossRef]
  14. J. Goodman, Introduction to Fourier Optics (Holt, Rinehart & Winston, New York, 1968).
  15. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1973), Sec. 9.5.2.
  16. R. P. Khetan, F.-P. Chiang, “Strain Analysis by One-Beam Laser Speckle Interferometry. I: Single Aperture Method,” Appl. Opt. 15, 2205–2215 (1976).
    [CrossRef] [PubMed]
  17. F.-P. Chiang, D. W. Li, “Diffraction Halo Functions of Coherent and Incoherent Random Speckle Patterns,” Appl. Opt. 24, 2166–2171 (1985).
    [CrossRef] [PubMed]
  18. R. Meynart, “Diffraction Halo in Speckle Photography,” Appl. Opt. 23, 2235–2236 (1984).
    [CrossRef] [PubMed]
  19. J. M. Burch, J. M. J. Tokarski, “Production of Multiple Beam Fringes from Photographic Scatterers,” Opt. Acta 15, 101–111 (1968).
  20. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).
  21. F. Roddier, “The Effects of Atmospheric Turbulence in Optical Astronomy,” Prog. Opt. 19, 281–376 (1981).
    [CrossRef]
  22. J. C. Dainty, Stellar Speckle Interferometry (Springer-Verlag, New York1975), pp. 255–280.
  23. A. P. Odell, J. A. Weinman, “The Effect of Atmospheric Haze on Images of the Earth’s Surface,” J. Geophys. Res. 80, 5035–5040 (1975).
    [CrossRef]
  24. Y. Mekler, Y. J. Kaufman, “The Effect of Earth’s Atmosphere on Contrast Reduction for a Nonuniform Surface Albedo and ‘Two-Halves’ Field,” J. Geophys. Res. 85, 4067–4083 (1980).
    [CrossRef]
  25. J. Sherman, “Speckle Imaging Under Non-Isoplanatic Conditions,” Proc. Soc. Photo-Opt. Instrum. Eng. 243, 51–57 (1980).
  26. See Ref. 10; reproduces results of Hufnagel.
  27. G. E. Maddux, “A Programmable Data Retrieval System for In-Plane Displacements from Speckle Photographs,” Air Force Flight Dynamics Laboratory, Technical Report AFFDL-TM-78-109, Wright-Patterson AFB, OH (1978).
  28. D. L. Walters, “Atmospheric Modulation Transfer Function for Desert and Mountain Locations: r0 Measurements,” J. Opt. Soc. Am. 71, 406–409 (1981).
    [CrossRef]
  29. A. Labeyrie, “Attainment of Diffraction Limited Resolution in Large Telescopes by Fourier Analyzing Spectral Patterns in Star Images,” Astron. Astrophys. 6, 85–89 (1970).

1990 (1)

E. G. Conley, J. Genin, “Application of Speckle Metrology at a Nuclear Waste Repository,” Proc. Soc. Photo-Opt. Instrum. Eng., Bellingham, WA 1332, 798–802 (1990).

1986 (1)

1985 (1)

1984 (2)

1983 (1)

G. L. Cloud, E. G. Conley, “A Whole-Field Interferometric Scheme for Measuring Strain and Flow Rates of Glacier and Other Naturally Occurring Surfaces,” J. Glaciol. 29, 492–497 (1983).

1982 (1)

A. Asundi, F. P. Chiang, “Theory and Applications of the White Light Speckle Method for Strain Analysis,” Opt. Eng. 21, 570–580 (1982).
[CrossRef]

1981 (2)

1980 (2)

Y. Mekler, Y. J. Kaufman, “The Effect of Earth’s Atmosphere on Contrast Reduction for a Nonuniform Surface Albedo and ‘Two-Halves’ Field,” J. Geophys. Res. 85, 4067–4083 (1980).
[CrossRef]

J. Sherman, “Speckle Imaging Under Non-Isoplanatic Conditions,” Proc. Soc. Photo-Opt. Instrum. Eng. 243, 51–57 (1980).

1976 (2)

1975 (1)

A. P. Odell, J. A. Weinman, “The Effect of Atmospheric Haze on Images of the Earth’s Surface,” J. Geophys. Res. 80, 5035–5040 (1975).
[CrossRef]

1973 (2)

S. Worden, “High Angular Resolution Techniques: Speckle Interferometry and Related Methods,” Proc. Soc. Photo-Opt. Instrum. Eng. 43, 66–73 (1973).

D. Korff, “Analysis of a Method for Obtaining Near-Diffraction-Limited Information in the Presence of Atmospheric Turbulence,” J. Opt. Soc. Am. 63, 971–980 (1973).
[CrossRef]

1970 (1)

A. Labeyrie, “Attainment of Diffraction Limited Resolution in Large Telescopes by Fourier Analyzing Spectral Patterns in Star Images,” Astron. Astrophys. 6, 85–89 (1970).

1968 (1)

J. M. Burch, J. M. J. Tokarski, “Production of Multiple Beam Fringes from Photographic Scatterers,” Opt. Acta 15, 101–111 (1968).

1966 (1)

1964 (1)

Asundi, A.

A. Asundi, F. P. Chiang, “Theory and Applications of the White Light Speckle Method for Strain Analysis,” Opt. Eng. 21, 570–580 (1982).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1973), Sec. 9.5.2.

Burch, J. M.

J. M. Burch, J. M. J. Tokarski, “Production of Multiple Beam Fringes from Photographic Scatterers,” Opt. Acta 15, 101–111 (1968).

Chiang, F. P.

A. Asundi, F. P. Chiang, “Theory and Applications of the White Light Speckle Method for Strain Analysis,” Opt. Eng. 21, 570–580 (1982).
[CrossRef]

Chiang, F.-P.

Cloud, G. L.

E. G. Conley, G. L. Cloud, “Practical Applications of Double-Exposure Noncoherent-Light Speckle Photography,” Appl. Opt. 25, 2246–2248 (1986).
[CrossRef] [PubMed]

G. L. Cloud, E. G. Conley, “A Whole-Field Interferometric Scheme for Measuring Strain and Flow Rates of Glacier and Other Naturally Occurring Surfaces,” J. Glaciol. 29, 492–497 (1983).

E. G. Conley, G. L. Cloud, “Stereo Interferometric Measurement of Glacier Ice Strain Rates,” in Proceedings, Spring 1985 Conference of the Society of Experimental Mechanics (Soc. Exp. Mech., Bethel, CT, 1985), pp. 452–453.

E. G. Conley, G. L. Cloud, “Whole-Field Measurement of Ice Displacement and Strain Rates,” in Proceedings, Fifth International Offshore Mechanics and Artic Engineering Symposium (ASME, NY, NY, 1986), pp. 432–435.

E. G. Conley, G. L. Cloud, “White-Light Speckle for Measuring Glacier Surface Displacements,” in Proceedings, International Conference on Hologram Interferometry and Speckle Metrology (Soc. Exp. Mech., Bethel, CT, 1990), pp. 88–94.

Conley, E. G.

E. G. Conley, J. Genin, “Application of Speckle Metrology at a Nuclear Waste Repository,” Proc. Soc. Photo-Opt. Instrum. Eng., Bellingham, WA 1332, 798–802 (1990).

E. G. Conley, G. L. Cloud, “Practical Applications of Double-Exposure Noncoherent-Light Speckle Photography,” Appl. Opt. 25, 2246–2248 (1986).
[CrossRef] [PubMed]

G. L. Cloud, E. G. Conley, “A Whole-Field Interferometric Scheme for Measuring Strain and Flow Rates of Glacier and Other Naturally Occurring Surfaces,” J. Glaciol. 29, 492–497 (1983).

E. G. Conley, G. L. Cloud, “Stereo Interferometric Measurement of Glacier Ice Strain Rates,” in Proceedings, Spring 1985 Conference of the Society of Experimental Mechanics (Soc. Exp. Mech., Bethel, CT, 1985), pp. 452–453.

E. G. Conley, G. L. Cloud, “Whole-Field Measurement of Ice Displacement and Strain Rates,” in Proceedings, Fifth International Offshore Mechanics and Artic Engineering Symposium (ASME, NY, NY, 1986), pp. 432–435.

E. G. Conley, G. L. Cloud, “White-Light Speckle for Measuring Glacier Surface Displacements,” in Proceedings, International Conference on Hologram Interferometry and Speckle Metrology (Soc. Exp. Mech., Bethel, CT, 1990), pp. 88–94.

Dainty, J. C.

J. C. Dainty, Stellar Speckle Interferometry (Springer-Verlag, New York1975), pp. 255–280.

Fried, D. L.

Genin, J.

E. G. Conley, J. Genin, “Application of Speckle Metrology at a Nuclear Waste Repository,” Proc. Soc. Photo-Opt. Instrum. Eng., Bellingham, WA 1332, 798–802 (1990).

Goodman, J.

J. Goodman, Introduction to Fourier Optics (Holt, Rinehart & Winston, New York, 1968).

Hufnagel, R. E.

Karo, D. P.

Kaufman, Y. J.

Y. Mekler, Y. J. Kaufman, “The Effect of Earth’s Atmosphere on Contrast Reduction for a Nonuniform Surface Albedo and ‘Two-Halves’ Field,” J. Geophys. Res. 85, 4067–4083 (1980).
[CrossRef]

Khetan, R. P.

Korff, D.

Labeyrie, A.

A. Labeyrie, “Attainment of Diffraction Limited Resolution in Large Telescopes by Fourier Analyzing Spectral Patterns in Star Images,” Astron. Astrophys. 6, 85–89 (1970).

Li, D. W.

Maddux, G. E.

G. E. Maddux, “A Programmable Data Retrieval System for In-Plane Displacements from Speckle Photographs,” Air Force Flight Dynamics Laboratory, Technical Report AFFDL-TM-78-109, Wright-Patterson AFB, OH (1978).

Mekler, Y.

Y. Mekler, Y. J. Kaufman, “The Effect of Earth’s Atmosphere on Contrast Reduction for a Nonuniform Surface Albedo and ‘Two-Halves’ Field,” J. Geophys. Res. 85, 4067–4083 (1980).
[CrossRef]

Meynart, R.

Odell, A. P.

A. P. Odell, J. A. Weinman, “The Effect of Atmospheric Haze on Images of the Earth’s Surface,” J. Geophys. Res. 80, 5035–5040 (1975).
[CrossRef]

Roddier, F.

F. Roddier, “The Effects of Atmospheric Turbulence in Optical Astronomy,” Prog. Opt. 19, 281–376 (1981).
[CrossRef]

Schneiderman, A. M.

Sherman, J.

J. Sherman, “Speckle Imaging Under Non-Isoplanatic Conditions,” Proc. Soc. Photo-Opt. Instrum. Eng. 243, 51–57 (1980).

Stanley, N. R.

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

Tokarski, J. M. J.

J. M. Burch, J. M. J. Tokarski, “Production of Multiple Beam Fringes from Photographic Scatterers,” Opt. Acta 15, 101–111 (1968).

von der Luhe, O.

Walters, D. L.

Weinman, J. A.

A. P. Odell, J. A. Weinman, “The Effect of Atmospheric Haze on Images of the Earth’s Surface,” J. Geophys. Res. 80, 5035–5040 (1975).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1973), Sec. 9.5.2.

Worden, S.

S. Worden, “High Angular Resolution Techniques: Speckle Interferometry and Related Methods,” Proc. Soc. Photo-Opt. Instrum. Eng. 43, 66–73 (1973).

Appl. Opt. (4)

Astron. Astrophys. (1)

A. Labeyrie, “Attainment of Diffraction Limited Resolution in Large Telescopes by Fourier Analyzing Spectral Patterns in Star Images,” Astron. Astrophys. 6, 85–89 (1970).

J. Geophys. Res. (2)

A. P. Odell, J. A. Weinman, “The Effect of Atmospheric Haze on Images of the Earth’s Surface,” J. Geophys. Res. 80, 5035–5040 (1975).
[CrossRef]

Y. Mekler, Y. J. Kaufman, “The Effect of Earth’s Atmosphere on Contrast Reduction for a Nonuniform Surface Albedo and ‘Two-Halves’ Field,” J. Geophys. Res. 85, 4067–4083 (1980).
[CrossRef]

J. Glaciol. (1)

G. L. Cloud, E. G. Conley, “A Whole-Field Interferometric Scheme for Measuring Strain and Flow Rates of Glacier and Other Naturally Occurring Surfaces,” J. Glaciol. 29, 492–497 (1983).

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (1)

Opt. Acta (1)

J. M. Burch, J. M. J. Tokarski, “Production of Multiple Beam Fringes from Photographic Scatterers,” Opt. Acta 15, 101–111 (1968).

Opt. Eng. (1)

A. Asundi, F. P. Chiang, “Theory and Applications of the White Light Speckle Method for Strain Analysis,” Opt. Eng. 21, 570–580 (1982).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

J. Sherman, “Speckle Imaging Under Non-Isoplanatic Conditions,” Proc. Soc. Photo-Opt. Instrum. Eng. 243, 51–57 (1980).

S. Worden, “High Angular Resolution Techniques: Speckle Interferometry and Related Methods,” Proc. Soc. Photo-Opt. Instrum. Eng. 43, 66–73 (1973).

Proc. Soc. Photo-Opt. Instrum. Eng., Bellingham, WA (1)

E. G. Conley, J. Genin, “Application of Speckle Metrology at a Nuclear Waste Repository,” Proc. Soc. Photo-Opt. Instrum. Eng., Bellingham, WA 1332, 798–802 (1990).

Prog. Opt. (1)

F. Roddier, “The Effects of Atmospheric Turbulence in Optical Astronomy,” Prog. Opt. 19, 281–376 (1981).
[CrossRef]

Other (9)

J. C. Dainty, Stellar Speckle Interferometry (Springer-Verlag, New York1975), pp. 255–280.

See Ref. 10; reproduces results of Hufnagel.

G. E. Maddux, “A Programmable Data Retrieval System for In-Plane Displacements from Speckle Photographs,” Air Force Flight Dynamics Laboratory, Technical Report AFFDL-TM-78-109, Wright-Patterson AFB, OH (1978).

E. G. Conley, G. L. Cloud, “White-Light Speckle for Measuring Glacier Surface Displacements,” in Proceedings, International Conference on Hologram Interferometry and Speckle Metrology (Soc. Exp. Mech., Bethel, CT, 1990), pp. 88–94.

E. G. Conley, G. L. Cloud, “Stereo Interferometric Measurement of Glacier Ice Strain Rates,” in Proceedings, Spring 1985 Conference of the Society of Experimental Mechanics (Soc. Exp. Mech., Bethel, CT, 1985), pp. 452–453.

E. G. Conley, G. L. Cloud, “Whole-Field Measurement of Ice Displacement and Strain Rates,” in Proceedings, Fifth International Offshore Mechanics and Artic Engineering Symposium (ASME, NY, NY, 1986), pp. 432–435.

J. Goodman, Introduction to Fourier Optics (Holt, Rinehart & Winston, New York, 1968).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1973), Sec. 9.5.2.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961).

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Figures (5)

Fig. 1
Fig. 1

Imaging system geometry.

Fig. 2
Fig. 2

Pointwise specklegram interrogation geometry.

Fig. 3
Fig. 3

Geometric interpretation of autocorrelation function.

Fig. 4
Fig. 4

Hufnagel’s night turbulence model which gives Fried’s turbulence parameter r0 as a function of imaging wavelength, station altitude, and inclination (abstracted from Ref. 10).

Fig. 5
Fig. 5

Relative frequency response as a function of the parameter α = r0/D (abstracted from Ref. 12).

Tables (1)

Tables Icon

Table I Glacier Imaging System Performance For Two Field Studies

Equations (24)

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I i ( x i ) = ± I o ( x o ) PSF ( x i x o ) d x o ,
Φ i ( f ) = Φ o ( f ) τ ( f ) ,
FT { I i ( x i ) } = Φ i ( f ) , FT { I o ( x o ) } = Φ o ( f ) , FT { PSF ( x i x o ) } = τ ( f ) .
κ ( f ) = ± K ( x ) exp ( 2 π i f x ) d x = F T { K ( x ) } , K ( x ) = ± κ ( f ) exp ( 2 π i x f ) d f = FT 1 { κ ( f ) } ,
τ ( λ n R f ) = ± P ( r ) P * ( r + λ n R f ) d r ,
P ( r ) = 1 for r D / 2 , P ( r ) = 0 for r > D / 2 ,
I i ( x i ) = FT 1 { Φ o ( f ) τ ( λ n R f ) } .
A ( x i ) = I i ( x i ) I i ( x i + d ) ,
ω = s λ c L ,
U t ( ω ) = A ( x ) exp ( 2 π i ω x ) d x = FT { A ( x ) } ,
I t ( ω ) = [ FT { A ( x ) } ] 2 = [ FT { I ( x ) I ( x + d ) } ] 2 .
I t ( ω ) = [ F T { I ( x ) } ] 2 [ 1 + exp ( 2 π i ω d ) ] 2 .
I t ( ω ) = [ FT [ FT 1 { Φ o ( f ) τ ( λ n R f ) ] } ] 2 .
I t ( ω ) = { [ Φ o ( f ) τ ( λ n R f ) exp ( 2 π i f x ) d f ] exp ( 2 π i ω x ) d x } 2 .
I t ( ω ) = { Φ o ( f ) τ ( λ n R f ) [ exp ( 2 π i ( ω f ) x ) d x ] d f } 2 .
exp [ 2 π i ( ω f ) x ] d x = δ ( ω f ) = δ ( f + ω ) = δ ( f ω ) .
I t ( ω ) = { Φ o ( f ) τ ( λ n R f ) δ ( f ω ) d f } 2 .
I t ( ω ) = [ Φ o ( ω ) τ ( λ n R ω ) ] 2 .
I t ( ω ) = [ τ ( λ n R ω ) ] 2
0 = I t ( ω max ) = [ τ ( λ n R ω max ) ] 2 .
ω max = s max λ c L ,
f max = D λ n R .
0 = I t ( s max λ c L ) = [ τ ( λ n R s max λ c L ) ] 2 .
D sqrt ( λ n l ) for near field , D sqrt ( λ n l ) for far field ,

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