Abstract

An innovative technique for reducing speckle noise and improving the intensity profile of the speckle correlation fringes is presented. The method is based on reducing the range of the modulation intensity values of the speckle interference pattern. After the fringe pattern is corrected adaptively at each pixel, a simple morphological filtering of the fringes is sufficient to obtain smoothed fringes. The concept is presented both analytically and by simulation by using computer-generated speckle patterns. The experimental verification is performed by using an amplitude-only spatial light modulator (SLM) in a conventional electronic speckle pattern interferometry setup. The optical arrangement for tuning a commercially available LCD array for amplitude-only behavior is described. The method of feedback to the LCD SLM to modulate the intensity of the reference beam in order to reduce the modulation intensity values is explained, and the resulting fringe pattern and increase in the signal-to-noise ratio are discussed.

© 2005 Optical Society of America

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  13. P. Varman, C. Wykes, “Smoothing of speckle and moiré fringes by computer processing,” Opt. Lasers Eng. 3, 87–100 (1981).
    [CrossRef]
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    [CrossRef]
  15. A. Federico, G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598–2604 (2001).
    [CrossRef]
  16. R. Kumar, I. P. Singh, C. Shakher, “Measurement of out-of-plane static and dynamic deformations by processing digital speckle pattern interferometry fringes using wavelet transform,” Opt. Lasers Eng. 41, 81–93 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
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  22. M. Lehmann, “Phase-shifting speckle interferometry with unresolved speckles: a theoretical investigation,” Opt. Commun. 128, 325–340 (1996).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  27. S. Krueger, G. Wernicke, H. Gruber, N. Demoli, M. Duerr, S. Teiwes, “Liquid-crystal display as dynamic diffractive element,” in Projection Displays VII, M. H. Wu, ed., Proc. SPIE4294, 84–91 (2001).
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  31. J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
    [CrossRef]
  32. I. Moreno, J. A. Davis, K. G. D'Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998).
    [CrossRef]
  33. A. Marquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted-nematic liquid-crystal displays based on simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
    [CrossRef]

2004 (1)

R. Kumar, I. P. Singh, C. Shakher, “Measurement of out-of-plane static and dynamic deformations by processing digital speckle pattern interferometry fringes using wavelet transform,” Opt. Lasers Eng. 41, 81–93 (2004).
[CrossRef]

2003 (2)

F. Chen, W. D. Luo, M. Dale, A. Petniunas, P. Harwood, G. M. Brown, “High-speed ESPI and related techniques: overview and its applications in the automotive industry,” Opt. Lasers Eng. 40, 459–485 (2003).
[CrossRef]

B. Kemper, J. Kandulla, D. Dirksen, G. V. Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
[CrossRef]

2001 (4)

A. Achim, A. Bezerianos, P. Tsakalides, “Novel Bayesian multiscale method for speckle removal in medical ultrasound images,” IEEE Trans. Med. Imaging 20, 772–783 (2001).
[CrossRef] [PubMed]

A. Federico, G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598–2604 (2001).
[CrossRef]

A. Marquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted-nematic liquid-crystal displays based on simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

J. S. Jang, D. H. Shin, “Optical representation of binary data based on both intensity and phase modulation with a twisted-nematic liquid-crystal display for holographic digital data storage,” Opt. Lett. 26, 1797–1799 (2001).
[CrossRef]

2000 (1)

1998 (2)

J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D'Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

1996 (2)

M. Lehmann, “Phase-shifting speckle interferometry with unresolved speckles: a theoretical investigation,” Opt. Commun. 128, 325–340 (1996).
[CrossRef]

Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt. 35, 51–60 (1996).
[CrossRef] [PubMed]

1994 (1)

1993 (1)

1992 (1)

1990 (1)

L. M. Novak, M. C. Burl, “Optimal speckle reduction in polarimetric SAR imagery,” IEEE Trans. Aerosp. Electron. Syst. 26, 293–305 (1990).
[CrossRef]

1989 (1)

D. Kerr, F. M. Santoyo, J. R. Tyrer, “Manipulation of Fourier components of speckle fringe patterns as part of an interferometric analysis process,” J. Mod. Opt. 36, 195–203 (1989).
[CrossRef]

1987 (2)

1985 (1)

1981 (1)

P. Varman, C. Wykes, “Smoothing of speckle and moiré fringes by computer processing,” Opt. Lasers Eng. 3, 87–100 (1981).
[CrossRef]

1980 (1)

1976 (1)

H. H. Arsenault, G. April, “Speckle removal by optical and digital processing,” J. Opt. Soc. Am. 66, 177 (1976).

Achim, A.

A. Achim, A. Bezerianos, P. Tsakalides, “Novel Bayesian multiscale method for speckle removal in medical ultrasound images,” IEEE Trans. Med. Imaging 20, 772–783 (2001).
[CrossRef] [PubMed]

Allison, D. B.

I. Moreno, J. A. Davis, K. G. D'Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

April, G.

H. H. Arsenault, G. April, “Speckle removal by optical and digital processing,” J. Opt. Soc. Am. 66, 177 (1976).

Arsenault, H. H.

H. H. Arsenault, G. April, “Speckle removal by optical and digital processing,” J. Opt. Soc. Am. 66, 177 (1976).

Bally, G. V.

B. Kemper, J. Kandulla, D. Dirksen, G. V. Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
[CrossRef]

Benediktsson, J. A.

J. R. Sveinsson, J. A. Benediktsson, “Review of applications of wavelets in speckle reduction and enhancement of SAR images,” in Image and Signal Processing for Remote Sensing VII, S. B. Serpico, ed., Proc. SPIE4541, 47–58 (2002).
[CrossRef]

Bezerianos, A.

A. Achim, A. Bezerianos, P. Tsakalides, “Novel Bayesian multiscale method for speckle removal in medical ultrasound images,” IEEE Trans. Med. Imaging 20, 772–783 (2001).
[CrossRef] [PubMed]

Boucher, J. M.

K. Lebart, J. M. Boucher, “Speckle filtering by wavelet analysis and synthesis,” in Wavelet Applications in Signal and Image Processing IV, M. A. Unser, A. Aldroubi, A. F. Laine, eds., Proc. SPIE2825, 644–651 (1996).
[CrossRef]

Brown, G. M.

F. Chen, W. D. Luo, M. Dale, A. Petniunas, P. Harwood, G. M. Brown, “High-speed ESPI and related techniques: overview and its applications in the automotive industry,” Opt. Lasers Eng. 40, 459–485 (2003).
[CrossRef]

Burl, M. C.

L. M. Novak, M. C. Burl, “Optimal speckle reduction in polarimetric SAR imagery,” IEEE Trans. Aerosp. Electron. Syst. 26, 293–305 (1990).
[CrossRef]

Campos, J.

A. Marquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted-nematic liquid-crystal displays based on simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

Carnicer, A.

Chen, F.

F. Chen, W. D. Luo, M. Dale, A. Petniunas, P. Harwood, G. M. Brown, “High-speed ESPI and related techniques: overview and its applications in the automotive industry,” Opt. Lasers Eng. 40, 459–485 (2003).
[CrossRef]

Chipaman, R. A.

Christensen, C. R.

A. K. Jain, C. R. Christensen, “Digital processing of images in speckle noise,” in Applications of Speckle Phenomena, W. H. Carter, ed., Proc. SPIE243, 46–50 (1980).
[CrossRef]

Creath, K.

K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24, 3053–3058 (1985).
[CrossRef] [PubMed]

K. Creath, “Phase-shifting holographic interferometry,” in Holographic Interferometry, Vol. 68 (Springer-Verlag, Berlin, 1994), pp. 109–150.
[CrossRef]

Dale, M.

F. Chen, W. D. Luo, M. Dale, A. Petniunas, P. Harwood, G. M. Brown, “High-speed ESPI and related techniques: overview and its applications in the automotive industry,” Opt. Lasers Eng. 40, 459–485 (2003).
[CrossRef]

Davila, A.

Davis, J. A.

A. Marquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted-nematic liquid-crystal displays based on simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D'Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
[CrossRef]

Demoli, N.

S. Krueger, G. Wernicke, H. Gruber, N. Demoli, M. Duerr, S. Teiwes, “Liquid-crystal display as dynamic diffractive element,” in Projection Displays VII, M. H. Wu, ed., Proc. SPIE4294, 84–91 (2001).
[CrossRef]

G. Wernicke, S. Krüger, H. Gruber, N. Demoli, M. Dürr, S. Teiwes, “Liquid crystal display as spatial light modulator for diffractive optical elements and the reconstruction of digital holograms,” in Advanced Photonic Sensors and Applications II, A. K. Asundi, W. Osten, V. J. Varadan, eds., Proc. SPIE4596, 182–190 (2001).
[CrossRef]

Dirksen, D.

B. Kemper, J. Kandulla, D. Dirksen, G. V. Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
[CrossRef]

D'Nelly, K. G.

I. Moreno, J. A. Davis, K. G. D'Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

Duerr, M.

S. Krueger, G. Wernicke, H. Gruber, N. Demoli, M. Duerr, S. Teiwes, “Liquid-crystal display as dynamic diffractive element,” in Projection Displays VII, M. H. Wu, ed., Proc. SPIE4294, 84–91 (2001).
[CrossRef]

Dürr, M.

G. Wernicke, S. Krüger, H. Gruber, N. Demoli, M. Dürr, S. Teiwes, “Liquid crystal display as spatial light modulator for diffractive optical elements and the reconstruction of digital holograms,” in Advanced Photonic Sensors and Applications II, A. K. Asundi, W. Osten, V. J. Varadan, eds., Proc. SPIE4596, 182–190 (2001).
[CrossRef]

Eiju, T.

Federico, A.

A. Federico, G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598–2604 (2001).
[CrossRef]

Ferritsen, H. J.

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1993).

Gruber, H.

G. Wernicke, S. Krüger, H. Gruber, N. Demoli, M. Dürr, S. Teiwes, “Liquid crystal display as spatial light modulator for diffractive optical elements and the reconstruction of digital holograms,” in Advanced Photonic Sensors and Applications II, A. K. Asundi, W. Osten, V. J. Varadan, eds., Proc. SPIE4596, 182–190 (2001).
[CrossRef]

S. Krueger, G. Wernicke, H. Gruber, N. Demoli, M. Duerr, S. Teiwes, “Liquid-crystal display as dynamic diffractive element,” in Projection Displays VII, M. H. Wu, ed., Proc. SPIE4294, 84–91 (2001).
[CrossRef]

Hack, E.

E. Hack, “ESPI—principles and prospects,” in Trends in Optical Nondestructive Testing and Inspection, P. K. Rastogi, D. Inaudi, eds. (Elsevier, Oxford, 2000), pp. 207–239.

Hariharan, P.

Harwood, P.

F. Chen, W. D. Luo, M. Dale, A. Petniunas, P. Harwood, G. M. Brown, “High-speed ESPI and related techniques: overview and its applications in the automotive industry,” Opt. Lasers Eng. 40, 459–485 (2003).
[CrossRef]

Iemmi, C.

A. Marquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted-nematic liquid-crystal displays based on simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

Jain, A. K.

A. K. Jain, C. R. Christensen, “Digital processing of images in speckle noise,” in Applications of Speckle Phenomena, W. H. Carter, ed., Proc. SPIE243, 46–50 (1980).
[CrossRef]

Jang, J. S.

Jepsen, M. L.

Juvells, I.

Kandulla, J.

B. Kemper, J. Kandulla, D. Dirksen, G. V. Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
[CrossRef]

Kaufmann, G. H.

A. Federico, G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle pattern interferometry fringes,” Opt. Eng. 40, 2598–2604 (2001).
[CrossRef]

A. Davila, D. Kerr, G. H. Kaufmann, “Digital processing of electronic speckle pattern interferometry addition fringes,” Appl. Opt. 33, 5964–5969 (1994).
[CrossRef] [PubMed]

Kemper, B.

B. Kemper, J. Kandulla, D. Dirksen, G. V. Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
[CrossRef]

Kerr, D.

A. Davila, D. Kerr, G. H. Kaufmann, “Digital processing of electronic speckle pattern interferometry addition fringes,” Appl. Opt. 33, 5964–5969 (1994).
[CrossRef] [PubMed]

D. Kerr, F. M. Santoyo, J. R. Tyrer, “Manipulation of Fourier components of speckle fringe patterns as part of an interferometric analysis process,” J. Mod. Opt. 36, 195–203 (1989).
[CrossRef]

Krueger, S.

S. Krueger, G. Wernicke, H. Gruber, N. Demoli, M. Duerr, S. Teiwes, “Liquid-crystal display as dynamic diffractive element,” in Projection Displays VII, M. H. Wu, ed., Proc. SPIE4294, 84–91 (2001).
[CrossRef]

Krüger, S.

G. Wernicke, S. Krüger, H. Gruber, N. Demoli, M. Dürr, S. Teiwes, “Liquid crystal display as spatial light modulator for diffractive optical elements and the reconstruction of digital holograms,” in Advanced Photonic Sensors and Applications II, A. K. Asundi, W. Osten, V. J. Varadan, eds., Proc. SPIE4596, 182–190 (2001).
[CrossRef]

Kumar, R.

R. Kumar, I. P. Singh, C. Shakher, “Measurement of out-of-plane static and dynamic deformations by processing digital speckle pattern interferometry fringes using wavelet transform,” Opt. Lasers Eng. 41, 81–93 (2004).
[CrossRef]

Labastida, I.

Lebart, K.

K. Lebart, J. M. Boucher, “Speckle filtering by wavelet analysis and synthesis,” in Wavelet Applications in Signal and Image Processing IV, M. A. Unser, A. Aldroubi, A. F. Laine, eds., Proc. SPIE2825, 644–651 (1996).
[CrossRef]

Lehmann, M.

M. Lehmann, “Phase-shifting speckle interferometry with unresolved speckles: a theoretical investigation,” Opt. Commun. 128, 325–340 (1996).
[CrossRef]

Lim, J. S.

J. S. Lim, H. Nawab, “Techniques for speckle noise removal,” in Applications of Speckle Phenomena, W. H. Carter, ed., Proc. SPIE243, 35–44 (1980).
[CrossRef]

Luo, W. D.

F. Chen, W. D. Luo, M. Dale, A. Petniunas, P. Harwood, G. M. Brown, “High-speed ESPI and related techniques: overview and its applications in the automotive industry,” Opt. Lasers Eng. 40, 459–485 (2003).
[CrossRef]

Marquez, A.

A. Marquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted-nematic liquid-crystal displays based on simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

Martin-Badosa, E.

Moreno, I.

A. Marquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, M. J. Yzuel, “Quantitative prediction of the modulation behavior of twisted-nematic liquid-crystal displays based on simple physical model,” Opt. Eng. 40, 2558–2564 (2001).
[CrossRef]

I. Moreno, J. A. Davis, K. G. D'Nelly, D. B. Allison, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid-crystal spatial light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
[CrossRef]

Nawab, H.

J. S. Lim, H. Nawab, “Techniques for speckle noise removal,” in Applications of Speckle Phenomena, W. H. Carter, ed., Proc. SPIE243, 35–44 (1980).
[CrossRef]

Novak, L. M.

L. M. Novak, M. C. Burl, “Optimal speckle reduction in polarimetric SAR imagery,” IEEE Trans. Aerosp. Electron. Syst. 26, 293–305 (1990).
[CrossRef]

Orbel, B. F.

Petniunas, A.

F. Chen, W. D. Luo, M. Dale, A. Petniunas, P. Harwood, G. M. Brown, “High-speed ESPI and related techniques: overview and its applications in the automotive industry,” Opt. Lasers Eng. 40, 459–485 (2003).
[CrossRef]

Pezzaniti, J. L.

Santoyo, F. M.

D. Kerr, F. M. Santoyo, J. R. Tyrer, “Manipulation of Fourier components of speckle fringe patterns as part of an interferometric analysis process,” J. Mod. Opt. 36, 195–203 (1989).
[CrossRef]

Shakher, C.

R. Kumar, I. P. Singh, C. Shakher, “Measurement of out-of-plane static and dynamic deformations by processing digital speckle pattern interferometry fringes using wavelet transform,” Opt. Lasers Eng. 41, 81–93 (2004).
[CrossRef]

Shin, D. H.

Singh, I. P.

R. Kumar, I. P. Singh, C. Shakher, “Measurement of out-of-plane static and dynamic deformations by processing digital speckle pattern interferometry fringes using wavelet transform,” Opt. Lasers Eng. 41, 81–93 (2004).
[CrossRef]

Slettemoen, G. A.

Surrel, Y.

Sveinsson, J. R.

J. R. Sveinsson, J. A. Benediktsson, “Review of applications of wavelets in speckle reduction and enhancement of SAR images,” in Image and Signal Processing for Remote Sensing VII, S. B. Serpico, ed., Proc. SPIE4541, 47–58 (2002).
[CrossRef]

Teiwes, S.

G. Wernicke, S. Krüger, H. Gruber, N. Demoli, M. Dürr, S. Teiwes, “Liquid crystal display as spatial light modulator for diffractive optical elements and the reconstruction of digital holograms,” in Advanced Photonic Sensors and Applications II, A. K. Asundi, W. Osten, V. J. Varadan, eds., Proc. SPIE4596, 182–190 (2001).
[CrossRef]

S. Krueger, G. Wernicke, H. Gruber, N. Demoli, M. Duerr, S. Teiwes, “Liquid-crystal display as dynamic diffractive element,” in Projection Displays VII, M. H. Wu, ed., Proc. SPIE4294, 84–91 (2001).
[CrossRef]

Tsai, P.

Tsakalides, P.

A. Achim, A. Bezerianos, P. Tsakalides, “Novel Bayesian multiscale method for speckle removal in medical ultrasound images,” IEEE Trans. Med. Imaging 20, 772–783 (2001).
[CrossRef] [PubMed]

Tyrer, J. R.

D. Kerr, F. M. Santoyo, J. R. Tyrer, “Manipulation of Fourier components of speckle fringe patterns as part of an interferometric analysis process,” J. Mod. Opt. 36, 195–203 (1989).
[CrossRef]

Vallmitjana, S.

Varman, P.

P. Varman, C. Wykes, “Smoothing of speckle and moiré fringes by computer processing,” Opt. Lasers Eng. 3, 87–100 (1981).
[CrossRef]

Wernicke, G.

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[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Probability density function of modulation IM/〈IS〉 for n = 1, 2, 4, and 8 speckles per pixel.

Fig. 2
Fig. 2

(a) Speckle correlation pattern for a linear phase change. (b) Adaptively corrected and filtered pattern of (a). (c) LIP of (a). (d) LIP of (a) after adaptive correction of IM. (e) LIP of (b) after adaptive correction followed by morphological filtering.

Fig. 3
Fig. 3

(a) Speckle correlation pattern for a spherical phase change; (b) adaptively corrected and filtered pattern of (a); (c) LIP of (a); (d) LIP of (a) after adaptive correction of IM; (e) LIP of (b) after adaptive correction followed by morphological filtering.

Fig. 4
Fig. 4

Setup for LCD characterization: BS1, BS2, nonpolarizing beam splitters; P1, P2, linear polarizers; QWP1, QWP2, quarter-wave plates; TN-LCD, twisted-nematic LCD.

Fig. 5
Fig. 5

Intensity transmission characteristic graph of amplitude-only LCD SLM along with the phase change measurements.

Fig. 6
Fig. 6

(a) Increase of IM to 2 I M; (b) decrease of IM to I M / 2 for all pixels in the central rectangular area.

Fig. 7
Fig. 7

(1) LIP of the fringe pattern when the LCD SLM is set to 50% transmission; (2) LIP of the fringes in Fig. 6(a); (c) LIP of the fringes in Fig. 6(b).

Fig. 8
Fig. 8

Adaptive ESPI setup: BS, beam splitters; IL, imaging lens; S1, S2, shutters.

Fig. 9
Fig. 9

(a) Speckle correlation pattern without adaptive correction; (b) speckle correlation pattern with adaptive correction; (c) morphological filtering of (a); (d) morphological filtering of (b); (e) histogram of the marked fringe in (a); (f) histogram of the marked fringe in (b).

Equations (19)

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I CCD , initial = I R + I S + 2 ( I R I S ) 1 / 2 cos ( ϕ S , initial ϕ R ) ,
I CCD , final = I R + I S + 2 ( I R I S ) 1 / 2 cos ( ϕ S , final ϕ R ) ,
ϕ S , final = ϕ S , initial + Δ ϕ ,
O = | I CCD , final I CCD , initial | = 2 I M | sin ( ϕ S , initial ϕ R + Δ ϕ 2 ) sin ( Δ ϕ 2 ) | ,
O = I M P S D ,
I M = 2 ( I R I S ) 1 / 2 ; P S | sin ( ϕ S , initial ϕ R + Δ ϕ 2 ) |
D 2 | sin ( Δ ϕ 2 ) |
O = I M P S D 0 = 1 k i = 1 k I Mi P Si D 0 ,
var [ O ] = ( O O ) 2 = O 2 O 2 = I M 2 P S 2 D 0 2 I M P S 2 D 0 2 .
var [ O ] = I M 2 P S 2 D 0 2 I M 2 P S 2 D 0 2 .
SNR unc 2 = O 2 var [ O ] = I M 2 P S 2 I M 2 P S 2 I M 2 P S 2 = I M 2 P S 2 I M 2 var [ P S ] + P S 2 var [ I M ] ,
I M 2 = I M 2 .
SNR MIC 2 = P S 2 P s 2 P s 2 = P S 2 var [ P S ]
Γ = SNR MIC 2 SNR unc 2 = P S 2 [ I M 2 var [ P S ] + P S 2 var [ I M ] ] var [ P S ] I M 2 P S 2 ,
Γ = 1 + var [ I M ] P S 2 I M 2 var [ P S ] > 1 .
n PA / π [ 1.2 λ F / # ( 1 + M ) ] 2 ,
P ( I M ) = n I M 2 I R I S exp ( n I M 2 4 I R I S ) , ( 0 I M ) for n 1 ,
P ( I S ) = 1 I S exp ( I S I S ) , ( I S 0 ) .
f ( x , y ) B = max β B f [ ( x , y ) β ] .

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