Abstract

Speckle noise reduction is best tested on a precise speckle contrast measurement bench, which should be able to measure 100% contrast in fully developed speckle as well as the smallest contrast (for example, less than 10%) after its reduction. On such a test bench, we have measured very efficient speckle contrast reduction by temporal averaging using a moving diffuser on a tuning fork, which vibrates at 100Hz over 60μm in amplitude, a distance that is three times the surface roughness correlation length of the diffuser.

© 2010 Optical Society of America

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References

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  1. D. Bloom, “Grating Light Valve: revolutionizing display technology,” Proc. SPIE 3013, 165–171 (1997).
    [CrossRef]
  2. J. I. T. Trisnadi, “Speckle contrast reduction in laser projection displays,” Proc. SPIE 4657, 131–137 (2002).
    [CrossRef]
  3. J. I. T. Trisnadi, “Hadamard speckle contrast reduction,” Opt. Lett. 29, 11–13 (2004).
    [CrossRef] [PubMed]
  4. J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2007).
  5. H. Fuji and T. Asakura, “Effects of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11, 35–38 (1974).
    [CrossRef]
  6. J. M. Elson and J. M. Bennett, “Relation between the angular dependence of scattering and the statistical properties of optical surfaces,” J. Opt. Soc. Am. 69, 31–47 (1979).
    [CrossRef]
  7. J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).
  8. J. W. Goodman, Statistical Optics (Wiley, 1985).
  9. S. Kubota, T. Matsumoto, and T. Shimura, “An integrating sphere system to realize very-low-luminance reference light sources,” in Proceedings of IDW’08 (Society for Information Display, 2008), Vol. 3, p. 2115.
  10. S. Moriguchi, K. Udagawa, and S. Hitotsumatsu, The Mathematical Formulae I (Iwanami, 1956), in Japanese.
  11. L. Mandel, “Phenomenological theory of laser beam fluctuation and beam mixing,” Phys. Rev. 138, B753–B762 (1965).
    [CrossRef]
  12. M.Abramowitz and I.A.Stegun, eds., Handbook of Mathematical Functions (Dover, 1972).
  13. C. Hastings, Jr., Approximations for Digital Computers(Princeton U. Press, 1955).

2008 (1)

S. Kubota, T. Matsumoto, and T. Shimura, “An integrating sphere system to realize very-low-luminance reference light sources,” in Proceedings of IDW’08 (Society for Information Display, 2008), Vol. 3, p. 2115.

2007 (1)

J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2007).

2005 (1)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).

2004 (1)

2002 (1)

J. I. T. Trisnadi, “Speckle contrast reduction in laser projection displays,” Proc. SPIE 4657, 131–137 (2002).
[CrossRef]

1997 (1)

D. Bloom, “Grating Light Valve: revolutionizing display technology,” Proc. SPIE 3013, 165–171 (1997).
[CrossRef]

1985 (1)

J. W. Goodman, Statistical Optics (Wiley, 1985).

1979 (1)

1974 (1)

H. Fuji and T. Asakura, “Effects of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11, 35–38 (1974).
[CrossRef]

1972 (1)

M.Abramowitz and I.A.Stegun, eds., Handbook of Mathematical Functions (Dover, 1972).

1965 (1)

L. Mandel, “Phenomenological theory of laser beam fluctuation and beam mixing,” Phys. Rev. 138, B753–B762 (1965).
[CrossRef]

1956 (1)

S. Moriguchi, K. Udagawa, and S. Hitotsumatsu, The Mathematical Formulae I (Iwanami, 1956), in Japanese.

1955 (1)

C. Hastings, Jr., Approximations for Digital Computers(Princeton U. Press, 1955).

Asakura, T.

H. Fuji and T. Asakura, “Effects of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11, 35–38 (1974).
[CrossRef]

Bennett, J. M.

Bloom, D.

D. Bloom, “Grating Light Valve: revolutionizing display technology,” Proc. SPIE 3013, 165–171 (1997).
[CrossRef]

Elson, J. M.

Fuji, H.

H. Fuji and T. Asakura, “Effects of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11, 35–38 (1974).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2007).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).

J. W. Goodman, Statistical Optics (Wiley, 1985).

Hastings, C.

C. Hastings, Jr., Approximations for Digital Computers(Princeton U. Press, 1955).

Hitotsumatsu, S.

S. Moriguchi, K. Udagawa, and S. Hitotsumatsu, The Mathematical Formulae I (Iwanami, 1956), in Japanese.

Kubota, S.

S. Kubota, T. Matsumoto, and T. Shimura, “An integrating sphere system to realize very-low-luminance reference light sources,” in Proceedings of IDW’08 (Society for Information Display, 2008), Vol. 3, p. 2115.

Mandel, L.

L. Mandel, “Phenomenological theory of laser beam fluctuation and beam mixing,” Phys. Rev. 138, B753–B762 (1965).
[CrossRef]

Matsumoto, T.

S. Kubota, T. Matsumoto, and T. Shimura, “An integrating sphere system to realize very-low-luminance reference light sources,” in Proceedings of IDW’08 (Society for Information Display, 2008), Vol. 3, p. 2115.

Moriguchi, S.

S. Moriguchi, K. Udagawa, and S. Hitotsumatsu, The Mathematical Formulae I (Iwanami, 1956), in Japanese.

Shimura, T.

S. Kubota, T. Matsumoto, and T. Shimura, “An integrating sphere system to realize very-low-luminance reference light sources,” in Proceedings of IDW’08 (Society for Information Display, 2008), Vol. 3, p. 2115.

Trisnadi, J. I. T.

J. I. T. Trisnadi, “Hadamard speckle contrast reduction,” Opt. Lett. 29, 11–13 (2004).
[CrossRef] [PubMed]

J. I. T. Trisnadi, “Speckle contrast reduction in laser projection displays,” Proc. SPIE 4657, 131–137 (2002).
[CrossRef]

Udagawa, K.

S. Moriguchi, K. Udagawa, and S. Hitotsumatsu, The Mathematical Formulae I (Iwanami, 1956), in Japanese.

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

H. Fuji and T. Asakura, “Effects of surface roughness on the statistical distribution of image speckle intensity,” Opt. Commun. 11, 35–38 (1974).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. (1)

L. Mandel, “Phenomenological theory of laser beam fluctuation and beam mixing,” Phys. Rev. 138, B753–B762 (1965).
[CrossRef]

Proc. SPIE (2)

D. Bloom, “Grating Light Valve: revolutionizing display technology,” Proc. SPIE 3013, 165–171 (1997).
[CrossRef]

J. I. T. Trisnadi, “Speckle contrast reduction in laser projection displays,” Proc. SPIE 4657, 131–137 (2002).
[CrossRef]

Other (7)

J. W. Goodman, Speckle Phenomena in Optics (Roberts, 2007).

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts, 2005).

J. W. Goodman, Statistical Optics (Wiley, 1985).

S. Kubota, T. Matsumoto, and T. Shimura, “An integrating sphere system to realize very-low-luminance reference light sources,” in Proceedings of IDW’08 (Society for Information Display, 2008), Vol. 3, p. 2115.

S. Moriguchi, K. Udagawa, and S. Hitotsumatsu, The Mathematical Formulae I (Iwanami, 1956), in Japanese.

M.Abramowitz and I.A.Stegun, eds., Handbook of Mathematical Functions (Dover, 1972).

C. Hastings, Jr., Approximations for Digital Computers(Princeton U. Press, 1955).

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Figures (6)

Fig. 1
Fig. 1

Speckle measuring geometry.

Fig. 2
Fig. 2

(a) Hermetically sealed frosted glass diffuser and (b) its cross-sectional view.

Fig. 3
Fig. 3

(a) Simulated light intensity distribution that obeys the negative exponential function type PDF, which gives C = 1 , (b) measured light intensity distribution, which gives C = 0.995 after apparent dark current bias correction, (c) two-dimensional light intensity distribution pattern on CCD camera, and (d) separately taken histogram approximating the negative exponential function type PDF.

Fig. 4
Fig. 4

(a) Diode-pumped solid-state second harmonic generation green laser illuminated vibrating diffuser attached on tuning forks with piezoelectric vibration sensor electromagnetically driven by a coil in a plastic box. (b) Back in the diffuser, the projection lens locates the image scattered light onto a screen diffuser with a magnification of 6.25.

Fig. 5
Fig. 5

(a) Light intensity distribution measured with a vibrating diffuser with amplitude of 60 μm , where speckle contrast C measured 0.034, and (b) its two-dimensional light intensity distribution pattern.

Fig. 6
Fig. 6

Simulated window weighting function K x ( ξ ) / K x ( 0 ) for an oscillating diffuser as a function of displacement ξ in micrometers, where the diffuser correlation length r c is 20 μm . The integer pa rameter i corresponds to the truncation point ξ i used in the approximation for the complete elliptic integral. The dashed line shows the corresponding window weighting function for a rotating diffuser when v T / r c = 4 with rotation velocity v and integration time T.

Equations (16)

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C = 8 ( N 1 ) [ N 1 + cosh ( x 2 ) ] sinh 2 ( x 2 / 2 ) N ( N 1 + exp ( x 2 ) ) 2 .
N = N 0 exp ( x 2 ) 1 Ei ( x 2 ) γ ln ( x 2 ) ,
C = x erf ( π / x ) x / π [ 1 exp ( π / x ) ] ,
C = ( K + M ± 1 ) / K M ,
C 1 / K C s .
1 K = 1 A e 2 P e ( Δ x , Δ y ) | μ A ( Δ x , Δ y ) | 2 d Δ x d Δ y ,
K 5.91 × 10 7 z e 2 / A m ,
K 5.91 × 10 7 z e 2 / A m = 853 .
M = K x ( 0 ) K x ( ξ ) | μ A ( ξ ) | 2 d ξ ,
Γ A ( τ ) A ( 0 , 0 ; ξ ) A * ( 0 , 0 ; t τ ) ¯ = | a 0 | 2 K ( Δ α , Δ β ) e σ o 2 [ 1 μ o ( Δ α , Δ β ) ] e σ d 2 [ 1 μ d ( Δ α v t , Δ β ) ] d Δ α d Δ β ,
C A ( τ ) = [ exp ( σ o 2 e Δ α 2 + Δ β 2 r o 2 ) 1 ] [ exp ( σ o 2 e ( Δ α v t ) 2 + Δ β 2 r o 2 ) 1 ] d Δ α d Δ β ,
μ ( ξ ) = C A ( ξ ) / C A ( 0 ) .
K x ( ξ ) = P x ( x ) P x ( ξ x ) d x .
π 2 K ( ξ ) x = ξ 1 1 d x 1 x 2 1 ( x ξ ) 2 = F ( π 2 , 1 ( ξ 2 ) 2 ) = K ( 1 ( ξ 2 ) 2 ) K ( ( ξ 2 ) 2 ) ,
J = 0 | μ A ( e s ) | 2 [ p 1 ( e s ) + t p 2 ( e s ) ] e s / 2 d s < ,
0 s α e a s d s = Γ ( 1 + α ) a 1 + α ( α > 1 , a > 0 ) .

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