Abstract

Two wavelength coherent imaging is a digital holographic technique that offers several advantages over conventional coherent imaging. One of the most significant advantages is the ability to extract 3D target information from the phase contrast image at a known difference frequency. However, phase noise detracts from the accuracy at which the target can be faithfully identified. We therefore describe a method for relating phase noise to the correlation of the image planes corresponding to each wavelength, among other parameters. The prediction of the phase noise spectrum of a scene will aid in determining our ability to reconstruct the target.

© 2013 Optical Society of America

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References

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2012 (1)

J. W.  Haus, B.  Dapore, N.  Miller, P.  Banerjee, G.  Nehmetallah, P.  Powers, P.  McManamon, “Instantaneously captured images using multi-wavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
[CrossRef]

2011 (2)

2010 (1)

2009 (1)

2008 (2)

2007 (2)

2002 (1)

1992 (1)

J. C.  Marron, “Wavelength decorrelation of laser speckle from three-dimensional diffuse objects,” Opt. Commun. 88(4-6), 305–308 (1992).
[CrossRef]

1990 (1)

1981 (1)

Banerjee, P.

J. W.  Haus, B.  Dapore, N.  Miller, P.  Banerjee, G.  Nehmetallah, P.  Powers, P.  McManamon, “Instantaneously captured images using multi-wavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
[CrossRef]

Banerjee, P. P.

Beghuin, D.

Charrière, F.

Colomb, T.

Cuche, E.

Dahlgren, P.

Dapore, B.

J. W.  Haus, B.  Dapore, N.  Miller, P.  Banerjee, G.  Nehmetallah, P.  Powers, P.  McManamon, “Instantaneously captured images using multi-wavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
[CrossRef]

Depeursinge, C.

Emery, Y.

Fienup, J. R.

Grow, T. D.

Guizar-Sicairos, M.

Haus, J. W.

J. W.  Haus, B.  Dapore, N.  Miller, P.  Banerjee, G.  Nehmetallah, P.  Powers, P.  McManamon, “Instantaneously captured images using multi-wavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
[CrossRef]

N. J.  Miller, J. W.  Haus, P.  McManamon, D.  Shemano, “Multi-aperture coherent imaging,” Proc. SPIE 8052, 805207 (2011).
[CrossRef]

Höft, T. A.

Jameson, D. F.

Kendrick, R. L.

Kowalczyk, A. M.

Kühn, J.

Kukhtarev, N.

Lee, M.

Machida, H.

Marquet, P.

Marron, J. C.

J. C.  Marron, R. L.  Kendrick, N.  Seldomridge, T. D.  Grow, T. A.  Höft, “Atmospheric turbulence correction using digital holographic detection: experimental results,” Opt. Express 17(14), 11638–11651 (2009).
[CrossRef] [PubMed]

J. C.  Marron, R. L.  Kendrick, “Distributed aperture active Imaging,” Proc. SPIE 6550, 65500A(2007).
[CrossRef]

J. C.  Marron, “Wavelength decorrelation of laser speckle from three-dimensional diffuse objects,” Opt. Commun. 88(4-6), 305–308 (1992).
[CrossRef]

McManamon, P.

J. W.  Haus, B.  Dapore, N.  Miller, P.  Banerjee, G.  Nehmetallah, P.  Powers, P.  McManamon, “Instantaneously captured images using multi-wavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
[CrossRef]

N. J.  Miller, J. W.  Haus, P.  McManamon, D.  Shemano, “Multi-aperture coherent imaging,” Proc. SPIE 8052, 805207 (2011).
[CrossRef]

Miller, N.

J. W.  Haus, B.  Dapore, N.  Miller, P.  Banerjee, G.  Nehmetallah, P.  Powers, P.  McManamon, “Instantaneously captured images using multi-wavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
[CrossRef]

Miller, N. J.

N. J.  Miller, J. W.  Haus, P.  McManamon, D.  Shemano, “Multi-aperture coherent imaging,” Proc. SPIE 8052, 805207 (2011).
[CrossRef]

Montfort, F.

Nehmetallah, G.

J. W.  Haus, B.  Dapore, N.  Miller, P.  Banerjee, G.  Nehmetallah, P.  Powers, P.  McManamon, “Instantaneously captured images using multi-wavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
[CrossRef]

P. P.  Banerjee, G.  Nehmetallah, N.  Kukhtarev, S. C.  Praharaj, “Dynamic holographic interferometry of diffuse objects and its application to determination of airplane attitudes,” Appl. Opt. 47, 3877–3885 (2008).
[CrossRef] [PubMed]

Nishisaka, T.

Ozcan, A.

Powers, P.

J. W.  Haus, B.  Dapore, N.  Miller, P.  Banerjee, G.  Nehmetallah, P.  Powers, P.  McManamon, “Instantaneously captured images using multi-wavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
[CrossRef]

Praharaj, S. C.

Rabb, D. J.

Seldomridge, N.

Shemano, D.

N. J.  Miller, J. W.  Haus, P.  McManamon, D.  Shemano, “Multi-aperture coherent imaging,” Proc. SPIE 8052, 805207 (2011).
[CrossRef]

Stafford, J. W.

Stokes, A. J.

Thurman, S. T.

Yaglidere, O.

Yonemura, M.

Appl. Opt. (3)

Biomed. Opt. Express (1)

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

Opt. Commun. (1)

J. C.  Marron, “Wavelength decorrelation of laser speckle from three-dimensional diffuse objects,” Opt. Commun. 88(4-6), 305–308 (1992).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Proc. SPIE (3)

J. W.  Haus, B.  Dapore, N.  Miller, P.  Banerjee, G.  Nehmetallah, P.  Powers, P.  McManamon, “Instantaneously captured images using multi-wavelength digital holography,” Proc. SPIE 8493, 84930W (2012).
[CrossRef]

N. J.  Miller, J. W.  Haus, P.  McManamon, D.  Shemano, “Multi-aperture coherent imaging,” Proc. SPIE 8052, 805207 (2011).
[CrossRef]

J. C.  Marron, R. L.  Kendrick, “Distributed aperture active Imaging,” Proc. SPIE 6550, 65500A(2007).
[CrossRef]

Other (3)

J. W. Goodman, Speckle Phenomena in Optics (Theory and Applications) (Roberts & Company, Englewood, Colorado, 2007).

G. Nehmetallah, P. Banerjee and N. Kukhtarev, “Single-beam holographic tomography creates images in three dimensions,” SPIE Newsroom (2011). doi: 10.1117/ 2.1201102.003474.

U. Schnars and W. Jueptner, Digital Holography, (Springer, Berlin, 2005).

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Figures (10)

Fig. 1
Fig. 1

Theoretical probability curves for various correlation values. The parameter μ is varied from 0 to 0.9.

Fig. 2
Fig. 2

Image of target corresponding to one wavelength.

Fig. 3
Fig. 3

(a) Synthetic angle image before processing; (b) Synthetic angle image after processing.

Fig. 4
Fig. 4

(a) Comparison of simulation and theoretical PDFs for a target tilt of 10°, which corrseponds to a value of fx that is 19% fc; (b) PDF comparison, for a target tilt of 22° and the value of fx is 44% fc.

Fig. 5
Fig. 5

Simplified schematic of experimental setup.

Fig. 6
Fig. 6

(a) Pupil plane image of the digital holograms at the synthetic wavelength. (b) The image plane data at the synthetic wavelength obtained by Fourier transforming the dual-wavelength pupil plane data as shown in Eq. (14) or Eq. (15). The LO and signal autocorrelation contributions are removed.

Fig. 7
Fig. 7

(a) PDFs corresponding to five degree target tilt, (b) PDFs corresponding to twenty degree target tilt.

Fig. 8
Fig. 8

The μ parameter from theory and experiment as a function of target tilt.

Fig. 9
Fig. 9

(a) Side view of a complex rendered scene; (b) MATLAB point cloud image showing a top view of the scene with multiple tilts and facets for a synthetic wavelength of 0.5 m. The truck appears in the top center of the scene in yellow.

Fig. 10
Fig. 10

Simulated PDFs from the scene in Fig. 9 compared to (a) the PDF from a single μ value and (b) the PDF generated by ensemble average using Eq. (18). The synthetic wavelength is 0.5 m.

Equations (19)

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λ s = λ 1 λ 2 | λ 1 λ 2 | ,
μ= U 1 U 2 * ¯ | U 1 | 2 ¯ | U 2 | 2 ¯ .
p(Δθ)=( 1 μ 2 2π ) (1 β 2 ) 1/2 +βπβ cos 1 β (1 β 2 ) 3/2 ,
| σ( z ) | 2 = | σ(x,y,z) | 2 dxdy ,
| σ(z) | 2 0 =exp{ 1 2 ( z σ R ) 2 },
| σ( z ) | 2 T = δ( z( tan θ x )x ) | sinc( Dx λL )sinc( Dy λL ) | 2 dxdy,
| σ( z ) | 2 T = | sinc( Dz λ( tan θ x )L ) | 2 .
| σ(z) | 2 = | σ(z) | 2 0 | σ(z) | 2 T =exp{ 1 2 ( z σ R ) 2 }sin c 2 { Dz tan θ x λL }.
μ( Δυ )= | σ( z ) | 2 exp( 4iπz( Δυ ) c ) dz,
μ=exp{ 8 π 2 σ R 2 Δ ν 2 c 2 }Λ( f x λL D ),
f x = 2tan θ x Δυ c = 2tan θ x λ s .
θ c = tan 1 ( λ s D 2λL ).
I(x,y)= | U LO1 (x,y) | 2 + | U s 1 (x,y) | 2 + U LO1 (x,y) U s 1 * (x,y)+ U LO1 * (x,y) U s 1 (x,y) + | U LO2 (x,y) | 2 + | U s 2 (x,y) | 2 + U LO2 (x,y) U s 2 * (x,y)+ U LO2 * (x,y) U s 2 (x,y) ,
{ I(x,y) }={ | U LO1 (x,y) | 2 }+{ | U s 1 (x,y) | 2 }+{ U LO1 (x,y) U s 1 * (x,y) }+{ U LO1 * (x,y) U s 1 (x,y) } +{ | U LO2 (x,y) | 2 }+{ | U s 2 (x,y) | 2 }+{ U LO2 (x,y) U s 2 * (x,y) }+{ U LO2 * (x,y) U s 2 (x,y) } .
{ I(x,y) }= A LO1 2 δ( f x , f y )+ A LO2 2 δ( f x , f y ) + | { U s1 (x,y) } | 2 + | { U s1 (x,y) } | 2 + A LO1 { U s 1 * ( x,y ) }*δ( f x f x1 , f y f y1 ) , + A LO2 { U s 2 * ( x,y ) }*δ( f x f x2 , f y f y2 ) + A LO1 { U s 1 (x,y) }*δ( f x + f x1 , f y + f y1 ) + A LO2 { U s 2 (x,y) }*δ( f x + f x2 , f y + f y2 )
U 1 = A LO1 { U s 1 * ( x,y ) }*δ( f x f x1 , f y f y1 ) U 2 = A LO2 { U s 2 * ( x,y ) }*δ( f x f x2 , f y f y2 ) .
μ( f x , f y )=exp( 8 π 2 σ T 2 Δ υ 2 c 2 )Λ( λL f x D )Λ( λL f y D ),
Overall_PDF= f x , f y pdf( μ( f x , f y ) ) | spectrum( f x , f y ) | 2 f x , f y | spectrum( f x , f y ) | 2 ,
spectrum( f x , f y )={ exp( 4iπh( x,y ) λ s ) }.

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