Abstract

We present a simultaneous dual-wavelength phase-imaging digital holographic technique demonstrated on porous coal samples. The use of two wavelengths enables us to increase the axial range at which the unambiguous phase imaging can be performed, but also increases the noise. We employ a noise reduction “fine map” algorithm, which uses the two-wavelength phase map as a guide to correct a single-wavelength phase image. Then, the resulting noise of a fine map is reduced to the level of single-wavelength noise. A comparison to software unwrapping is also presented. A simple way of correcting a curvature mismatch between the reference and the object beams is offered.

© 2008 Optical Society of America

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    [CrossRef]
  25. A. Khmaladze, C. J. Mann, and M. K. Kim, “Phase contrast movies of cell migration by multi-wavelength digital holography,” in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD), (Optical Society of America, 2007), paper DMB3.

2007 (3)

2006 (1)

2005 (1)

K. Tobin and P. Bingham, “Optical spatial heterodyned interferometry for applications in semiconductor inspection and metrology,” Proc. SPIE 6162 (2005).

2004 (1)

W. Branch and H. J. Mesa, “Caracterización de poros de carbones tratados térmicamente empleando procesamiento digital de imágenes y microscopía asistida por computador,” Adv. Comput. Syst. 1, 35-39 (2004).

2003 (3)

2002 (1)

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

2001 (4)

1999 (1)

1998 (1)

1994 (2)

1992 (1)

Asundi, A K.

Barty, A.

Bevilacqua, F.

Bingham, P.

K. Tobin and P. Bingham, “Optical spatial heterodyned interferometry for applications in semiconductor inspection and metrology,” Proc. SPIE 6162 (2005).

Boyer, K.

Branch, W.

W. Branch and H. J. Mesa, “Caracterización de poros de carbones tratados térmicamente empleando procesamiento digital de imágenes y microscopía asistida por computador,” Adv. Comput. Syst. 1, 35-39 (2004).

Cai, L. L.

Charrière, F.

Colomb, T.

Coppola, G.

Cuche, E.

Cullen, D.

Dakoff, A.

De Nicola, S.

Depeursinge, C.

Emery, Y.

Ferraro, P.

Finizio, A.

Gass, J.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Grilli, S.

Haddad, W. S.

Hariharan, P.

P. Hariharan, Optical Holography, 2nd ed. (Cambridge University, 2004).

Jericho, M. H.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, "Digital in-line holography for biological applications," Proc. Natl. Acad. Sci. (U.S.) 98, 11301-11305 (2001).
[CrossRef]

Jueptner, W.

W. Jueptner and U. Schnars, Digital Holography, (Springer Verlag, 2004).

Jueptner, W. P.

Jueptner, W. P. O.

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

Khmaladze, A.

A. Khmaladze, C. J. Mann, and M. K. Kim, “Phase contrast movies of cell migration by multi-wavelength digital holography,” in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD), (Optical Society of America, 2007), paper DMB3.

A. Khmaladze and M. Kim, "Quantitative phase contrast imaging of cells by multi-wavelength digital holography," in Conference on Lasers and Electro-Optics (CLEO), Technical Digest (CD), (Optical Society of America, 2007), paper JTuA52A.
[CrossRef]

Kim, M.

A. Khmaladze and M. Kim, "Quantitative phase contrast imaging of cells by multi-wavelength digital holography," in Conference on Lasers and Electro-Optics (CLEO), Technical Digest (CD), (Optical Society of America, 2007), paper JTuA52A.
[CrossRef]

Kim, M. K.

N. Warnasooriya and M. K. Kim, “LED-based multi-wavelength phase imaging interference microscopy,” Opt. Express 15, 9239-9247 (2007).
[CrossRef] [PubMed]

D. Parshall and M. K. Kim, “Digital holographic microscopy with dual wavelength phase unwrapping,” Appl. Opt. 45, 451-459 (2006).
[CrossRef] [PubMed]

J. Gass, A. Dakoff, and M. K. Kim, “Phase imaging without 2π-ambiguity by multiple-wavelength digital holography,” Opt. Lett. 28, 1141-1143 (2003).
[CrossRef] [PubMed]

M. K. Kim, L. Yu, and C. J. Mann, “Digital holography and multi-wavelength interference techniques,” in Digital Holography and Three-Dimensional Display, T. C. Poon, ed. (Springer, 2006), Chap. 2.
[CrossRef]

A. Khmaladze, C. J. Mann, and M. K. Kim, “Phase contrast movies of cell migration by multi-wavelength digital holography,” in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD), (Optical Society of America, 2007), paper DMB3.

Kreuzer, H. J.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, "Digital in-line holography for biological applications," Proc. Natl. Acad. Sci. (U.S.) 98, 11301-11305 (2001).
[CrossRef]

Kühn, J.

Laporta, P.

Longworth, J. W.

Magro, C.

Mann, C. J.

M. K. Kim, L. Yu, and C. J. Mann, “Digital holography and multi-wavelength interference techniques,” in Digital Holography and Three-Dimensional Display, T. C. Poon, ed. (Springer, 2006), Chap. 2.
[CrossRef]

A. Khmaladze, C. J. Mann, and M. K. Kim, “Phase contrast movies of cell migration by multi-wavelength digital holography,” in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD), (Optical Society of America, 2007), paper DMB3.

Marquet, P.

Matsushima, K.

McPherson, A.

Meinertzhagen, I. A.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, "Digital in-line holography for biological applications," Proc. Natl. Acad. Sci. (U.S.) 98, 11301-11305 (2001).
[CrossRef]

Mesa, H. J.

W. Branch and H. J. Mesa, “Caracterización de poros de carbones tratados térmicamente empleando procesamiento digital de imágenes y microscopía asistida por computador,” Adv. Comput. Syst. 1, 35-39 (2004).

Meucci, R.

Miao, J.

Miccio, L.

Montfort, F.

Nugent, K. A.

Osellame, R.

Paganin, D.

Parshall, D.

Paturzo, M.

Peng, X.

Pierattini, G.

Rhodes, C. K.

Roberts, A.

Schimmel, H.

Schnars, U.

Solem, J. C.

Tobin, K.

K. Tobin and P. Bingham, “Optical spatial heterodyned interferometry for applications in semiconductor inspection and metrology,” Proc. SPIE 6162 (2005).

Warnasooriya, N.

Wyrowski, F.

Xu, L.

Xu, W.

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, "Digital in-line holography for biological applications," Proc. Natl. Acad. Sci. (U.S.) 98, 11301-11305 (2001).
[CrossRef]

Yu, L.

M. K. Kim, L. Yu, and C. J. Mann, “Digital holography and multi-wavelength interference techniques,” in Digital Holography and Three-Dimensional Display, T. C. Poon, ed. (Springer, 2006), Chap. 2.
[CrossRef]

Yu, L. F.

Adv. Comput. Syst. (1)

W. Branch and H. J. Mesa, “Caracterización de poros de carbones tratados térmicamente empleando procesamiento digital de imágenes y microscopía asistida por computador,” Adv. Comput. Syst. 1, 35-39 (2004).

Appl. Opt. (5)

J. Opt. Soc. Am. A (3)

Meas. Sci. Technol. (1)

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

Opt. Express (4)

Opt. Lett. (3)

Proc. Natl. Acad. Sci. (U.S.) (1)

W. Xu, M. H. Jericho, I. A. Meinertzhagen, and H. J. Kreuzer, "Digital in-line holography for biological applications," Proc. Natl. Acad. Sci. (U.S.) 98, 11301-11305 (2001).
[CrossRef]

Proc. SPIE (1)

K. Tobin and P. Bingham, “Optical spatial heterodyned interferometry for applications in semiconductor inspection and metrology,” Proc. SPIE 6162 (2005).

Other (6)

M. K. Kim, L. Yu, and C. J. Mann, “Digital holography and multi-wavelength interference techniques,” in Digital Holography and Three-Dimensional Display, T. C. Poon, ed. (Springer, 2006), Chap. 2.
[CrossRef]

A. Khmaladze and M. Kim, "Quantitative phase contrast imaging of cells by multi-wavelength digital holography," in Conference on Lasers and Electro-Optics (CLEO), Technical Digest (CD), (Optical Society of America, 2007), paper JTuA52A.
[CrossRef]

A. Khmaladze, C. J. Mann, and M. K. Kim, “Phase contrast movies of cell migration by multi-wavelength digital holography,” in Digital Holography and Three-Dimensional Imaging (DH), Technical Digest (CD), (Optical Society of America, 2007), paper DMB3.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

P. Hariharan, Optical Holography, 2nd ed. (Cambridge University, 2004).

W. Jueptner and U. Schnars, Digital Holography, (Springer Verlag, 2004).

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Figures (10)

Fig. 1
Fig. 1

Multiwavelength digital holography setup. The lateral magnification of all microscope objectives (OBJ) is 20 × . The focal lengths of lenses L21 and L22 are 17.5 cm and 10 cm , respectively. The ND filters and polarizers P1 and P2 are used to control the intensity of the laser beams. Pinholes A are used to select only the central part of the Gaussian beam. Lenses L11, L12, L21, and L22 and objectives OBJ1, OBJ21, and OBJ22 ensure an appropriate collimation of the waves (i.e., the beam waist is kept at “infinity”).

Fig. 2
Fig. 2

Two-wavelength DHM of a USAF resolution target: (a) digital hologram, (b) small section of the hologram in (a) showing two fringe patterns due to the recording wavelengths (the rectangular shadows are two bars of the target image) and (c) Fourier spectrum of the hologram in (a); the encircled sections are the first-order components for the red and the green wavelengths, respectively.

Fig. 3
Fig. 3

Reconstructed phase image of the USAF resolution target (a) without curvature correction and (b) with curvature correction (the vertical scale is in nanometers); (c) the diagram illustrating the curvature correction procedure. R is the wave’s radius of curvature, which can be determined experimentally for a given setup. r = x 2 + y 2 is the distance between the center of the CCD matrix (point o) and an arbitrary point a. x and y are the coordinates of a.

Fig. 4
Fig. 4

(a) Phase map and height profile for λ = 633 nm . The profile is taken along the line over the phase map. (b) AFM image and height profile that confirm the results in (a).

Fig. 5
Fig. 5

Phase maps for (a)  λ 1 = 532 nm and (b)  λ 2 = 633 nm . (c) Synthetic dual-phase map with beat wavelength Λ 12 = 3334 nm and (d) its 3D rendering (the images are 174 × 174 μm 2 and the vertical scale for (a)–(c) is in radians).

Fig. 6
Fig. 6

Height profiles of (a) coarse and (b) fine phase maps. (c) Final fine map and (d) 3D rendering of (c). The image sizes are 174 × 174 μm 2 .

Fig. 7
Fig. 7

Line intensity profiles of a flat area for the coarse, fine, and the single-wavelength phase maps, respectively.

Fig. 8
Fig. 8

Images of a porous coal sample: (a) amplitude image; phase maps reconstructed at (b)  λ 1 = 0.63 μm and (c)  λ 2 = 0.53 μm ; (d) the dual-wavelength coarse phase map, (e) fine map, and (f) its 3D rendering. All images are 98 × 98 μm 2 and vertical scale (b–e) is in radians.

Fig. 9
Fig. 9

Images of a porous coal sample: (a) amplitude image; phase maps reconstructed at (b)  λ 1 = 532 nm and (c)  λ 2 = 633 nm ; (d) 3D rendering of the dual-wavelength phase map; software unwrapped phase maps reconstructed at (e)  λ 1 = 633 nm and (f)  λ 2 = 532 nm for comparison. All image sizes are 98 × 98 μm 2 . The vertical scales of the phase maps are in radians.

Fig. 10
Fig. 10

(a) Coarse phase map, (b) fine phase map, and line profiles for (c) coarse and (d) fine. For comparison, (e) single- wavelength phase map at λ = 633 nm and (f) line profile (the image sizes are 138 × 138 μm 2 and the vertical scales of the phase images are in radians).

Equations (6)

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A 0 ( k x , k y ; 0 ) = E 0 ( x , y ; 0 ) exp [ - i ( k x x + k y y ) ] d x d y ,
A ( k x , k y ; z ) = A 0 ( k x , k y ; 0 ) exp [ i k z z ] ,
E ( x , y ; z ) = A ( k x , k y ; z ) exp [ i ( k x x + k y y ) ] d k x d k y .
E ( x , y ; 0 ) = E 0 ( x , y ; 0 ) exp [ i k ( ± [ R 2 + r 2 - R ] ) ] ,
h ( x , y ) = λ 4 π ϕ ( x , y ) .
Λ 12 = λ 1 λ 2 / | λ 1 λ 2 | .

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