Abstract

In this paper, the properties of the speckle that is observed by humans in laser projection systems are theoretically analyzed. The speckle pattern on the fovea of the human retina is numerically simulated by introducing a chromatic human eye model. The results show that the speckle contrast experienced by humans is affected by the light intensity of the projected images and the wavelength of the laser source when considering the paracentral vision. Furthermore, the image quality is also affected by these two parameters. We believe that these results are useful for evaluating the speckle noise in laser projection systems.

© 2014 Optical Society of America

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References

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  1. K. V. Chellappan, E. Erden, and H. Urey, “Laser-based displays: a review,” Appl. Opt. 49, F79–F98 (2010).
    [CrossRef]
  2. J. Gollier, “Speckle measurement procedure,” (Corning Incorporated, May2010).
  3. S. Roelandt, Y. Meuret, G. Craggs, G. Verschaffelt, P. Janssens, and H. Thienpont, “Standardized speckle measurement method matched to human speckle perception in laser projection systems,” Opt. Express 20, 8770–8783 (2012).
    [CrossRef]
  4. D. Kang, E. Clarkson, and T. D. Milster, “Effect of optical aberrations on Gaussian laser speckle,” Opt. Express 17, 3084–3100 (2009).
    [CrossRef]
  5. J. C. Dainty, Laser Speckle and Related Phenomena (Springer, 1984).
  6. J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2007).
  7. D. Middleton, An Introduction to Statistical Communication Theory (IEEE, 1996).
  8. C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neural. 292, 497–523 (1990).
  9. J. Pokorny and V. C. Smith, “How much light reaches the retina?” Doc. Ophthal. Proc. Ser. 59, 491–512 (1997).
    [CrossRef]
  10. L. N. Thibos, M. Ye, X. Zhang, and A. Bradley, “The chromatic eye: a new reduced-eye model of ocular chromatic aberration in humans,” Appl. Opt. 31, 3594–3600 (1992).
    [CrossRef]
  11. S. Ravikumar, L. N. Thibos, and A. Bradley, “Calculation of retinal image quality for polychromatic light,” J. Opt. Soc. Am. A 25, 2395–2407 (2008).
    [CrossRef]
  12. B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
    [CrossRef]

2012 (2)

2010 (1)

2009 (1)

2008 (1)

1997 (1)

J. Pokorny and V. C. Smith, “How much light reaches the retina?” Doc. Ophthal. Proc. Ser. 59, 491–512 (1997).
[CrossRef]

1992 (1)

1990 (1)

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neural. 292, 497–523 (1990).

Bradley, A.

Cao, H.

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
[CrossRef]

Chellappan, K. V.

Choma, M. A.

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
[CrossRef]

Clarkson, E.

Craggs, G.

Curcio, C. A.

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neural. 292, 497–523 (1990).

Dainty, J. C.

J. C. Dainty, Laser Speckle and Related Phenomena (Springer, 1984).

Erden, E.

Gollier, J.

J. Gollier, “Speckle measurement procedure,” (Corning Incorporated, May2010).

Goodman, J. W.

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2007).

Hendrickson, A. E.

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neural. 292, 497–523 (1990).

Janssens, P.

Kalina, R. E.

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neural. 292, 497–523 (1990).

Kang, D.

Meuret, Y.

Middleton, D.

D. Middleton, An Introduction to Statistical Communication Theory (IEEE, 1996).

Milster, T. D.

Pokorny, J.

J. Pokorny and V. C. Smith, “How much light reaches the retina?” Doc. Ophthal. Proc. Ser. 59, 491–512 (1997).
[CrossRef]

Ravikumar, S.

Redding, B.

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
[CrossRef]

Roelandt, S.

Sloan, K. R.

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neural. 292, 497–523 (1990).

Smith, V. C.

J. Pokorny and V. C. Smith, “How much light reaches the retina?” Doc. Ophthal. Proc. Ser. 59, 491–512 (1997).
[CrossRef]

Thibos, L. N.

Thienpont, H.

Urey, H.

Verschaffelt, G.

Ye, M.

Zhang, X.

Appl. Opt. (2)

Doc. Ophthal. Proc. Ser. (1)

J. Pokorny and V. C. Smith, “How much light reaches the retina?” Doc. Ophthal. Proc. Ser. 59, 491–512 (1997).
[CrossRef]

J. Comp. Neural. (1)

C. A. Curcio, K. R. Sloan, R. E. Kalina, and A. E. Hendrickson, “Human photoreceptor topography,” J. Comp. Neural. 292, 497–523 (1990).

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

Nat. Photonics (1)

B. Redding, M. A. Choma, and H. Cao, “Speckle-free laser imaging using random laser illumination,” Nat. Photonics 6, 355–359 (2012).
[CrossRef]

Opt. Express (2)

Other (4)

J. Gollier, “Speckle measurement procedure,” (Corning Incorporated, May2010).

J. C. Dainty, Laser Speckle and Related Phenomena (Springer, 1984).

J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts, 2007).

D. Middleton, An Introduction to Statistical Communication Theory (IEEE, 1996).

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Figures (5)

Fig. 1.
Fig. 1.

Setup of a laser-based projector–observer system. The random surface is Gaussian. The image on the screen will be received by the human eye.

Fig. 2.
Fig. 2.

Average speckle size at different wavelengths and varying light intensity; the dotted line is the average size of a visual cell.

Fig. 3.
Fig. 3.

Image field on the frequency domain. The high-frequency components can be considered as the speckle noise in the image.

Fig. 4.
Fig. 4.

Speckle contrast experienced by humans after the averaging process. The two speckle patterns above are numerically simulated.

Fig. 5.
Fig. 5.

Image quality (CNR) at different wavelengths and varying light intensity.

Equations (17)

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τi(Δxi)=Ii(xi)Ii(xi+Δxi)=I¯2[1+|μi(Δxi)|2],
gi(xi)=gRi(xi)+igIi(xi),
μi(Δxi)=gi(xi)gi*(xi+Δxi)=RRRi(Δxi)+RIIi(Δxi)+i[RIRi(Δxi)RRIi(Δxi)],
Rmni(Δxi)=gmi(xi)gni*(xi+Δxi)m,n=R,I.
gi(xi)=fo(xo)hcoh(xixo)dxo,
fo(xo)=exp[i2πλl(xo)]
hcoh(xixo)=P(ξ)exp[i2πW(ξ)]×exp[i2π(xixo)ξ]dξ,
fo(xo)=fRo(xo)+ifIo(xo),
hcoh(xixo)=hRcoh(xixo)+ihIcoh(xixo).
{P(ξ)=P(ξ)W(ξ)=W(ξ)
{hRcoh(xixo)=P(ξ)cos[2πW(ξ)]×cos[2π(xixo)ξ]dξhIcoh(xixo)=P(ξ)sin[2πW(ξ)]×cos[2π(xixo)ξ]dξ.
{fRo(xo)fRo(xo+Δxo)=δ(Δxo)fIo(xo)fIo(xo+Δxo)=δ(Δxo)fIo(xo)fRo(xo+Δxo)=fRo(xo)fIo(xo+Δxo)=0.
{RRRi(Δxi)=RIIi(Δxi)=ξ1,ξ2P(ξ1)P(ξ2)α(xo,Δxi,ξ1,ξ2)×cos{2π[W(ξ1)W(ξ2)]}dξ1dξ2RIRi(Δxi)=RRIi(Δxi)=ξ1,ξ2P(ξ1)P(ξ2)β(xo,Δxi,ξ1,ξ2)×cos[2πW(ξ1)]sin[2πW(ξ2)]dξ1dξ2,
{α(xo,Δxi,ξ1,ξ2)=12xo{cos[2π(xixo)(ξ1+ξ2)+Δxiξ2]+cos[2π(xixo)(ξ1ξ2)Δxiξ2]}dxoβ(xo,Δxi,ξ1,ξ2)=xo{cos[2π(xixo)ξ2]cos[2π(xi+Δxixo)ξ1]cos[2π(xixo)ξ1]cos[2π(xi+Δxixo)ξ2]}dxo.
p(h(x,y))=12πexp(h(x,y)22σh2),
R(x,y)=12πexp(x2+y22lcorr2),
CNR=2(IfIb)σf+σb,

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