Abstract

We describe a scheme in which a camera is turned into an efficient tunable frequency filter of a few-Hertz bandwidth in an off-axis, heterodyne optical mixing configuration, enabling one to perform parallel, high-resolution coherent spectral imaging. This approach is made possible through the combination of a spatial and temporal modulation of the signal to reject noise contributions. Experimental data obtained with dynamically scattered light by a suspension of particles in Brownian motion is interpreted.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [PubMed]
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    [CrossRef]
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2006 (4)

M. Atlan and M. Gross, "Laser Doppler imaging, revisited," Rev. Sci. Instrum. 77, 1161031-1161034 (2006).
[CrossRef]

M. Atlan, M. Gross, and J. Leng, "Laser Doppler imaging of microflow," J. Eur. Opt. Soc. Rapid Publications 1:06025-1 (2006).

M. Lesaffre, M. Atlan, and M. Gross, "Effect of the photon's Brownian Doppler shift on the weak-localization coherent-backscattering cone," Phys. Rev. Lett. 97, 033901 (2006).
[CrossRef] [PubMed]

M. Atlan, M. Gross, T. Vitalis, A. Rancillac, B. C. Forget, and A. K. Dunn, "Frequency-domain, wide-field laser Doppler in vivo imaging," Opt. Lett. 31, 2762-2764 (2006).
[CrossRef] [PubMed]

2005 (4)

2003 (2)

2002 (2)

U. Schnars and W. P. O. Juptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

T. M. Kreis, "Frequency analysis of digital holography," Opt. Lett. 41, 771-778 (2002).

2001 (2)

J. D. Briers, "Laser Doppler, speckle, and related techniques for blood perfusion mapping and imaging," Physiol. Meas 22, R35-R66 (2001).
[CrossRef]

G. Indebetouw and P. Klysubun, "Spatiotemporal digital microholography," J. Opt. Soc. Am. A 18, 319-325 (2001).
[CrossRef]

2000 (1)

1999 (2)

G. Indebetouw and P. Klysubun, "Space-time digital holography, a three-dimensional microscopic imaging scheme with an arbitrary degree of spatial coherence," Appl. Phys. Lett. 75, 2017-2019 (1999).
[CrossRef]

C. Wagner, S. Seebacher, W. Osten, and W. Jüptner, "Digital recording and numerical reconstruction of lensless Fourier holograms in optical metrology," Appl. Opt. 38, 4812-4820 (1999).
[CrossRef]

1997 (2)

I. Yamaguchi and T. Zhang, "Phase-shifting digital holography," Opt. Lett. 22, 1268-1270 (1997).
[CrossRef] [PubMed]

D. S. Chung, K. Y. Lee, and E. Mazur, "Fourier-transform heterodyne spectroscopy of liquid and solid surfaces," Appl. Phys. (N.Y.) 64, 1-13 (1997).
[CrossRef]

1994 (1)

1991 (1)

T. J. H. Essex and P. O. Byrne, "A laser Doppler scanner for imaging blood flow in skin," J. Biomed. Eng. 13, 189-194 (1991).
[CrossRef] [PubMed]

1985 (1)

1984 (1)

O. J. Lokberg, "Espi-the ultimate holographic tool for vibration analysis," J. Acoust. Soc. Am. 55, 1783-1791 (1984).
[CrossRef]

1983 (1)

J. C. Brown, "Optical correlations and spectra," Am. J. Phys. 51, 1008-1011 (1983).
[CrossRef]

1977 (1)

M. D. Stern, D. L. Lappe, P. D. Bowen, J. E. Chimosky, G. A. Holloway, H. R. Keiser, and R. L. Bowman, "Continuous measurement of tissue blood flow by laser-Doppler spectroscopy," Am. J. Physiol. 232, H441-H448 (1977).
[PubMed]

1969 (1)

C. C. Aleksoff, "Time average holography extended," Appl. Phys. Lett. 14, 23-24 (1969).
[CrossRef]

1967 (1)

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

1966 (1)

1965 (2)

G. W. Stroke, "Lensless Fourier-transform method for optical holography," Appl. Phys. Lett. 6, 201-203 (1965).
[CrossRef]

R. L. Powell and K. A. Stetson, "Interferometric vibration analysis by wavefront reconstruction," J. Opt. Soc. Am. 55, 1593-1598 (1965).
[CrossRef]

1961 (1)

1948 (1)

D. Gabor, "A new microscopic principle," Nature (London) 161, 777-778 (1948).
[CrossRef]

Aleksoff, C. C.

C. C. Aleksoff, "Time average holography extended," Appl. Phys. Lett. 14, 23-24 (1969).
[CrossRef]

Al-Koussa, M.

Atlan, M.

Berne, B. J.

B. J. Berne and R. Pecora, Dynamic Light Scattering (Dover, 2000).

Boccara, A. C.

Bowen, P. D.

M. D. Stern, D. L. Lappe, P. D. Bowen, J. E. Chimosky, G. A. Holloway, H. R. Keiser, and R. L. Bowman, "Continuous measurement of tissue blood flow by laser-Doppler spectroscopy," Am. J. Physiol. 232, H441-H448 (1977).
[PubMed]

Bowman, R. L.

M. D. Stern, D. L. Lappe, P. D. Bowen, J. E. Chimosky, G. A. Holloway, H. R. Keiser, and R. L. Bowman, "Continuous measurement of tissue blood flow by laser-Doppler spectroscopy," Am. J. Physiol. 232, H441-H448 (1977).
[PubMed]

Briers, J. D.

J. D. Briers, "Laser Doppler, speckle, and related techniques for blood perfusion mapping and imaging," Physiol. Meas 22, R35-R66 (2001).
[CrossRef]

Brown, J. C.

J. C. Brown, "Optical correlations and spectra," Am. J. Phys. 51, 1008-1011 (1983).
[CrossRef]

Byrne, P. O.

T. J. H. Essex and P. O. Byrne, "A laser Doppler scanner for imaging blood flow in skin," J. Biomed. Eng. 13, 189-194 (1991).
[CrossRef] [PubMed]

Chimosky, J. E.

M. D. Stern, D. L. Lappe, P. D. Bowen, J. E. Chimosky, G. A. Holloway, H. R. Keiser, and R. L. Bowman, "Continuous measurement of tissue blood flow by laser-Doppler spectroscopy," Am. J. Physiol. 232, H441-H448 (1977).
[PubMed]

Chung, D. S.

D. S. Chung, K. Y. Lee, and E. Mazur, "Fourier-transform heterodyne spectroscopy of liquid and solid surfaces," Appl. Phys. (N.Y.) 64, 1-13 (1997).
[CrossRef]

Collot, L.

Creath, K.

Demoli, I.

Demoli, N.

Dunn, A. K.

Essex, T. J. H.

T. J. H. Essex and P. O. Byrne, "A laser Doppler scanner for imaging blood flow in skin," J. Biomed. Eng. 13, 189-194 (1991).
[CrossRef] [PubMed]

Forget, B. C.

Forrester, A. T.

Gabor, D.

D. Gabor, "A new microscopic principle," Nature (London) 161, 777-778 (1948).
[CrossRef]

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Goy, P.

Gross, M.

Holloway, G. A.

M. D. Stern, D. L. Lappe, P. D. Bowen, J. E. Chimosky, G. A. Holloway, H. R. Keiser, and R. L. Bowman, "Continuous measurement of tissue blood flow by laser-Doppler spectroscopy," Am. J. Physiol. 232, H441-H448 (1977).
[PubMed]

Indebetouw, G.

G. Indebetouw and P. Klysubun, "Spatiotemporal digital microholography," J. Opt. Soc. Am. A 18, 319-325 (2001).
[CrossRef]

G. Indebetouw and P. Klysubun, "Space-time digital holography, a three-dimensional microscopic imaging scheme with an arbitrary degree of spatial coherence," Appl. Phys. Lett. 75, 2017-2019 (1999).
[CrossRef]

Juptner, W. P. O.

U. Schnars and W. P. O. Juptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

Jüptner, W.

Keiser, H. R.

M. D. Stern, D. L. Lappe, P. D. Bowen, J. E. Chimosky, G. A. Holloway, H. R. Keiser, and R. L. Bowman, "Continuous measurement of tissue blood flow by laser-Doppler spectroscopy," Am. J. Physiol. 232, H441-H448 (1977).
[PubMed]

Klysubun, P.

G. Indebetouw and P. Klysubun, "Spatiotemporal digital microholography," J. Opt. Soc. Am. A 18, 319-325 (2001).
[CrossRef]

G. Indebetouw and P. Klysubun, "Space-time digital holography, a three-dimensional microscopic imaging scheme with an arbitrary degree of spatial coherence," Appl. Phys. Lett. 75, 2017-2019 (1999).
[CrossRef]

Kreis, T. M.

T. M. Kreis, "Frequency analysis of digital holography," Opt. Lett. 41, 771-778 (2002).

Lappe, D. L.

M. D. Stern, D. L. Lappe, P. D. Bowen, J. E. Chimosky, G. A. Holloway, H. R. Keiser, and R. L. Bowman, "Continuous measurement of tissue blood flow by laser-Doppler spectroscopy," Am. J. Physiol. 232, H441-H448 (1977).
[PubMed]

Lasser, T.

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

LeClerc, F.

Lee, K. Y.

D. S. Chung, K. Y. Lee, and E. Mazur, "Fourier-transform heterodyne spectroscopy of liquid and solid surfaces," Appl. Phys. (N.Y.) 64, 1-13 (1997).
[CrossRef]

Leng, J.

M. Atlan, M. Gross, and J. Leng, "Laser Doppler imaging of microflow," J. Eur. Opt. Soc. Rapid Publications 1:06025-1 (2006).

Lesaffre, M.

M. Lesaffre, M. Atlan, and M. Gross, "Effect of the photon's Brownian Doppler shift on the weak-localization coherent-backscattering cone," Phys. Rev. Lett. 97, 033901 (2006).
[CrossRef] [PubMed]

Lokberg, O. J.

O. J. Lokberg, "Espi-the ultimate holographic tool for vibration analysis," J. Acoust. Soc. Am. 55, 1783-1791 (1984).
[CrossRef]

Mazur, E.

D. S. Chung, K. Y. Lee, and E. Mazur, "Fourier-transform heterodyne spectroscopy of liquid and solid surfaces," Appl. Phys. (N.Y.) 64, 1-13 (1997).
[CrossRef]

Moisson, E.

Mounier, D.

Osten, W.

Pecora, R.

B. J. Berne and R. Pecora, Dynamic Light Scattering (Dover, 2000).

Picart, P.

Powell, R. L.

Ramaz, F.

Rancillac, A.

Schnars, U.

U. Schnars and W. P. O. Juptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

U. Schnars, "Direct phase determination in hologram interferometry with use of digitally recorded holograms," J. Opt. Soc. Am. A 11, 2011-2015 (1994).
[CrossRef]

Seebacher, S.

Serov, A.

Siegman, A. E.

Steinacher, B.

Stern, M. D.

M. D. Stern, D. L. Lappe, P. D. Bowen, J. E. Chimosky, G. A. Holloway, H. R. Keiser, and R. L. Bowman, "Continuous measurement of tissue blood flow by laser-Doppler spectroscopy," Am. J. Physiol. 232, H441-H448 (1977).
[PubMed]

Stetson, K. A.

Stroke, G. W.

G. W. Stroke, "Lensless Fourier-transform method for optical holography," Appl. Phys. Lett. 6, 201-203 (1965).
[CrossRef]

Vitalis, T.

Wagner, C.

Yamaguchi, I.

Zhang, T.

Am. J. Phys. (1)

J. C. Brown, "Optical correlations and spectra," Am. J. Phys. 51, 1008-1011 (1983).
[CrossRef]

Am. J. Physiol. (1)

M. D. Stern, D. L. Lappe, P. D. Bowen, J. E. Chimosky, G. A. Holloway, H. R. Keiser, and R. L. Bowman, "Continuous measurement of tissue blood flow by laser-Doppler spectroscopy," Am. J. Physiol. 232, H441-H448 (1977).
[PubMed]

Appl. Opt. (4)

Appl. Phys. (N.Y.) (1)

D. S. Chung, K. Y. Lee, and E. Mazur, "Fourier-transform heterodyne spectroscopy of liquid and solid surfaces," Appl. Phys. (N.Y.) 64, 1-13 (1997).
[CrossRef]

Appl. Phys. Lett. (4)

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

G. W. Stroke, "Lensless Fourier-transform method for optical holography," Appl. Phys. Lett. 6, 201-203 (1965).
[CrossRef]

G. Indebetouw and P. Klysubun, "Space-time digital holography, a three-dimensional microscopic imaging scheme with an arbitrary degree of spatial coherence," Appl. Phys. Lett. 75, 2017-2019 (1999).
[CrossRef]

C. C. Aleksoff, "Time average holography extended," Appl. Phys. Lett. 14, 23-24 (1969).
[CrossRef]

J. Acoust. Soc. Am. (1)

O. J. Lokberg, "Espi-the ultimate holographic tool for vibration analysis," J. Acoust. Soc. Am. 55, 1783-1791 (1984).
[CrossRef]

J. Biomed. Eng. (1)

T. J. H. Essex and P. O. Byrne, "A laser Doppler scanner for imaging blood flow in skin," J. Biomed. Eng. 13, 189-194 (1991).
[CrossRef] [PubMed]

J. Eur. Opt. Soc. Rapid Publications (1)

M. Atlan, M. Gross, and J. Leng, "Laser Doppler imaging of microflow," J. Eur. Opt. Soc. Rapid Publications 1:06025-1 (2006).

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Meas. Sci. Technol. (1)

U. Schnars and W. P. O. Juptner, "Digital recording and numerical reconstruction of holograms," Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

Nature (London) (1)

D. Gabor, "A new microscopic principle," Nature (London) 161, 777-778 (1948).
[CrossRef]

Opt. Express (2)

Opt. Lett. (7)

Phys. Rev. Lett. (1)

M. Lesaffre, M. Atlan, and M. Gross, "Effect of the photon's Brownian Doppler shift on the weak-localization coherent-backscattering cone," Phys. Rev. Lett. 97, 033901 (2006).
[CrossRef] [PubMed]

Physiol. Meas (1)

J. D. Briers, "Laser Doppler, speckle, and related techniques for blood perfusion mapping and imaging," Physiol. Meas 22, R35-R66 (2001).
[CrossRef]

Rev. Sci. Instrum. (1)

M. Atlan and M. Gross, "Laser Doppler imaging, revisited," Rev. Sci. Instrum. 77, 1161031-1161034 (2006).
[CrossRef]

Other (1)

B. J. Berne and R. Pecora, Dynamic Light Scattering (Dover, 2000).

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Figures (10)

Fig. 1
Fig. 1

Coherent spectral detection schemes: (a) homodyne and (b) heterodyne optical mixing. PM, photomixer (square-law detector); SA, spectrum analyzer; E O , object field; E LO , local oscillator field; S 1 , S 2 , first- and second-order object field spectral distributions.

Fig. 2
Fig. 2

Off-axis lensless Fourier configuration for heterodyne holography. L, laser; M, mirror; B S , beam splitter.

Fig. 3
Fig. 3

Measurement of the temporal frequency instrumental response. Camera frame rate, ω S ( 2 π ) = 8 Hz ; exposure time, τ e = 124 ms ; n = 4 . Representation is of instrumental responses for the true image (signal) and the twin image (ghost) in decibels. Horizontal axis, detuning frequency ( ω LO ω L ) ( 2 π ) in Hertz. Squares, signal (first heterodyne term); circles, ghost (second heterodyne term).

Fig. 4
Fig. 4

Squared amplitude of the instrumental response defined by Eq. (26). Camera frame rate, ω S ( 2 π ) = 8 Hz ; exposure time, τ e = 124 ms ; n = 4 . Representation is of 10 log 10 [ B ± ( ω LO ω L ) 2 ] in decibels. Horizontal axis, detuning frequency ( ω LO ω L ) ( 2 π ) in Hertz. Dotted curve B + ; solid curve, B .

Fig. 5
Fig. 5

Frequency diagram of spectral components in the case where the detuning frequency is set to ω LO ω L = Δ ω ω S n .

Fig. 6
Fig. 6

Images ( 1024 × 1024   pixels ) of the sample for ( ω LO ω L ) ( 2 π ) equal to (a) 0 Hz , (b) 400 Hz , (c) 4000 Hz , and (d) 8000 Hz ( 80 ms image exposure time, 4-image demodulation). Arbitrary logarithmic scale display.

Fig. 7
Fig. 7

Traces obtained by summation along columns of Fig. 6a, 6b, 6c, 6d intensities. Curves a, b, c, and d correspond to a detuning frequency ( ω LO ω L ) ( 2 π ) equal to 0, 400, 4000, and 8000 Hz , respectively. The horizontal scale is the image horizontal pixel index. The vertical scale is in linear arbitrary units.

Fig. 8
Fig. 8

Frequency spectra of the light diffused through a suspension of latex particles in Brownian motion. Exposure time, τ e = 80 ms . Curves a, b, c, and d (overlapping) correspond to demodulation performed with 4, 8, 16, and 32 images, respectively. The horizontal axis is the detuning frequency ( ω LO ω L ) ( 2 π ) in kHz. The vertical scale is in linear arbitrary units.

Fig. 9
Fig. 9

Curves (overlapping) a, b, and c correspond to spectra measured with exposure time τ e = 80 , 20, and 5 ms , respectively, and 4-image demodulation. Note that curve a is the same as in Fig. 8 (4 images and 80 ms ). The horizontal and vertical scales are as in Fig. 8.

Fig. 10
Fig. 10

Frequency line shapes of the light diffused through the cell for different concentrations of latex spheres. Exposure time, τ e = 80 ms ; 4-image demodulation. Curves a, b, c, and d correspond to volumic concentration of latex beads at 2.9 × 10 3 , 1.5 × 10 3 , 7.3 × 10 4 , and 3.6 × 10 4 , respectively. The horizontal and vertical scales are as in Fig. 8.

Equations (33)

Equations on this page are rendered with MathJax. Learn more.

E L ( t ) = A L A t ( t ) exp ( i ω L t + i ϕ ( t ) ) ,
E O ( t ) = A O X t ( t ) A t ( t ) exp ( i ω L t + i ϕ ( t ) ) ,
E LO ( t ) = A LO A t ( t ) exp ( i ω LO t + i ϕ ( t ) ) ,
i ( t ) i 0 ( Re [ E ] ) 2 ,
I ( t ) = I 0 τ e 2 τ e 2 ( E ( t + τ ) + E * ( t + τ ) ) 2 d τ ,
Y f ( ω ) = T 2 T 2 Y t ( t ) exp ( i ω t ) d t ,
Y sf ( ξ , η ) = Δ x 2 Δ x 2 Δ y 2 Δ y 2 Y s ( x , y ) exp ( 2 i π ( x ξ + y η ) ) d x d y ,
E O ( x , y , t ) = A O X s ( x , y ) A s ( x , y ) X t ( t ) A t ( t ) exp ( i ω L t + i ϕ ( t ) ) ,
E LO ( x , y , t ) = A LO A s ( x , y ) exp ( 2 i π ( x ξ 0 + y η 0 ) ) A t ( t ) exp ( i ω LO t + i ϕ ( t ) ) ,
I ( x , y , t ) = I 0 τ e 2 τ e 2 [ E O ( x , y , t + τ ) + E LO ( x , y , t + τ ) + E O * ( x , y , t + τ ) + E LO * ( x , y , t + τ ) ] 2 d τ .
I ( x , y , t ) I 0 = A O A LO I 1 ( x , y ) I 1 ( t ) + A O A LO I 2 ( x , y ) I 2 ( t ) + A LO 2 I 3 ( x , y ) I 3 ( t ) + A O 2 I 4 ( x , y ) I 4 ( t ) ,
I 1 ( t ) = τ e 2 τ e 2 X t ( t + τ ) A t ( t + τ ) 2 exp ( i ( ω LO ω L ) ( t + τ ) ) d τ ,
I 2 ( t ) = τ e 2 τ e 2 X t * ( t + τ ) A t ( t + τ ) 2 exp ( i ( ω LO ω L ) ( t + τ ) ) d τ ,
I 3 ( t ) = τ e 2 τ e 2 A t ( t + τ ) 2 d τ ,
I 4 ( t ) = τ e 2 τ e 2 X t ( t + τ ) 2 A t ( t + τ ) 2 d τ ,
I 1 ( x , y ) = A s ( x , y ) 2 X s ( x , y ) exp ( 2 i π ( x ξ 0 + y η 0 ) ) ,
I 2 ( x , y ) = A s ( x , y ) 2 X s * ( x , y ) exp ( 2 i π ( x ξ 0 + y η 0 ) ) ,
I 3 ( x , y ) = A s ( x , y ) 2 ,
I 4 ( x , y ) = X s ( x , y ) 2 A s ( x , y ) 2 .
A O A LO .
I 1 ( t ) = F ( t ) exp ( i ( ω LO ω L ) t ) ,
F ( t ) = τ e 2 τ e 2 A t ( t + τ ) 2 X t ( t + τ ) exp ( i ( ω LO ω L ) τ ) d τ .
I 1 ( ω S n ) = k = 1 n I 1 ( t k ) exp ( 2 i k π n ) ,
I 1 ( ω S n ) = k = 1 n F ( t k ) exp ( i ( ω LO ω L ) t k ) exp ( 2 i k π n ) ,
I 2 ( ω S n ) = k = 1 n F * ( t k ) exp ( i ( ω LO ω L ) t k ) exp ( 2 i k π n ) ,
B ± ( ω LO ω L ) = sinc ( ( ω LO ω L ) τ e ) k = 1 n exp ( 2 i k π n ) exp ( 2 i k π ω LO ω L ω S ) .
ω LO ω L = Δ ω ω S n ,
X sf ( ξ = x ( λ d ) , η = y ( λ d ) ) 2 X s ( x , y ) 2 ,
Δ x 2 Δ x 2 Δ y 2 Δ y 2 A s ( x , y ) 2 exp ( 2 i π λ d ( x x + y y ) ) d x d y δ ( x , y ) ;
I 1 ( ξ = x ( λ d ) , η = y ( λ d ) ) 2 X s ( x x 0 , y y 0 ) 2 .
I 2 ( ξ = x ( λ d ) , η = y ( λ d ) ) 2 X s ( x 0 x , y 0 y ) 2 .
I 3 ( ξ = x ( λ d ) , η = y ( λ d ) ) δ ( x , y ) ,
I 4 ( ξ = x ( λ d ) , η = y ( λ d ) ) X s ( x , y ) X s * ( x , y ) .

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