Abstract

A diffractive optical element (DOE) is presented to simultaneously manipulate the coherence plane tilt of a beam containing a plurality of discrete wavelengths. The DOE is inserted into the reference arm of an off-axis dual wavelength low coherence digital holographic microscope (DHM) to provide a coherence plane tilt so that interference with the object beam generates fringes over the full detector area. The DOE maintains the propagation direction of the reference beam and thus it can be inserted in-line in existing DHM set-ups. We demonstrate full field imaging in a reflection commercial DHM with two wavelengths, 685 nm and 794 nm, resulting in an unambiguous range of 2.494 micrometers.

© 2011 OSA

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    [CrossRef]
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2011 (1)

2009 (1)

2005 (2)

2002 (1)

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–101 (2002).
[CrossRef]

2001 (1)

1999 (3)

1998 (1)

1996 (1)

J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. 28(12), 1759–1763 (1996).
[CrossRef]

1993 (1)

Zs. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32(10), 2501–2504 (1993).
[CrossRef]

1986 (1)

O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59(3), 229–232 (1986).
[CrossRef]

1985 (1)

Zs. Bor and B. Racz, “Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,” Opt. Commun. 54(3), 165–170 (1985).
[CrossRef]

1980 (2)

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for bragg regime diffraction by phase gratings,” Opt. Commun. 32(1), 14–18 (1980).
[CrossRef]

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Raman-Nath regime diffraction by phase gratings,” Opt. Commun. 32(1), 19–23 (1980).
[CrossRef]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Andres, P.

R. M. Cuenca, L. M. Leon, J. Lancis, G. M. Vega, O. M. Yero, E. Tajahuerce, and P. Andres, “Diffractive pulse-front tilt for low-coherence digital holography,” J. Opt. Soc. B 16, 267–269 (1999).

Ansari, Z.

Balcunas, T.

Bevilacqua, F.

Bor, Zs.

Zs. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32(10), 2501–2504 (1993).
[CrossRef]

Zs. Bor and B. Racz, “Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,” Opt. Commun. 54(3), 165–170 (1985).
[CrossRef]

Charrière, F.

Choi, W.

Crimmins, T. F.

Cuche, E.

Cuenca, R. M.

R. M. Cuenca, L. M. Leon, J. Lancis, G. M. Vega, O. M. Yero, E. Tajahuerce, and P. Andres, “Diffractive pulse-front tilt for low-coherence digital holography,” J. Opt. Soc. B 16, 267–269 (1999).

Dasari, R. R.

Depeursinge, C.

Depeursinge, C. D.

Feld, M. S.

French, P. M. W.

Fu, D.

Gaylord, T. K.

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for bragg regime diffraction by phase gratings,” Opt. Commun. 32(1), 14–18 (1980).
[CrossRef]

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Raman-Nath regime diffraction by phase gratings,” Opt. Commun. 32(1), 19–23 (1980).
[CrossRef]

Gu, Y.

Hazim, H. A.

Zs. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32(10), 2501–2504 (1993).
[CrossRef]

Hebling, J.

J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. 28(12), 1759–1763 (1996).
[CrossRef]

Hilbert, M.

Zs. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32(10), 2501–2504 (1993).
[CrossRef]

Jones, R.

Jüptner, W. P. O.

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–101 (2002).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Lancis, J.

R. M. Cuenca, L. M. Leon, J. Lancis, G. M. Vega, O. M. Yero, E. Tajahuerce, and P. Andres, “Diffractive pulse-front tilt for low-coherence digital holography,” J. Opt. Soc. B 16, 267–269 (1999).

Leon, L. M.

R. M. Cuenca, L. M. Leon, J. Lancis, G. M. Vega, O. M. Yero, E. Tajahuerce, and P. Andres, “Diffractive pulse-front tilt for low-coherence digital holography,” J. Opt. Soc. B 16, 267–269 (1999).

Magnusson, R.

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Raman-Nath regime diffraction by phase gratings,” Opt. Commun. 32(1), 19–23 (1980).
[CrossRef]

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for bragg regime diffraction by phase gratings,” Opt. Commun. 32(1), 14–18 (1980).
[CrossRef]

Marquet, P.

Martinez, O. E.

O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59(3), 229–232 (1986).
[CrossRef]

Martínez-León, L.

Massatsch, P.

Maznev, A. A.

Melloch, M. R.

Melninkaitis, A.

Moharam, M. G.

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Raman-Nath regime diffraction by phase gratings,” Opt. Commun. 32(1), 19–23 (1980).
[CrossRef]

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for bragg regime diffraction by phase gratings,” Opt. Commun. 32(1), 14–18 (1980).
[CrossRef]

Nelson, K. A.

Nolte, D. D.

Osten, W.

Pedrini, G.

Racz, B.

Zs. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32(10), 2501–2504 (1993).
[CrossRef]

Zs. Bor and B. Racz, “Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,” Opt. Commun. 54(3), 165–170 (1985).
[CrossRef]

Schnars, U.

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–101 (2002).
[CrossRef]

Sirutkaitis, V.

Szabo, G.

Zs. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32(10), 2501–2504 (1993).
[CrossRef]

Tajahuerce, E.

R. M. Cuenca, L. M. Leon, J. Lancis, G. M. Vega, O. M. Yero, E. Tajahuerce, and P. Andres, “Diffractive pulse-front tilt for low-coherence digital holography,” J. Opt. Soc. B 16, 267–269 (1999).

Tziraki, M.

Vanagas, A.

Vega, G. M.

R. M. Cuenca, L. M. Leon, J. Lancis, G. M. Vega, O. M. Yero, E. Tajahuerce, and P. Andres, “Diffractive pulse-front tilt for low-coherence digital holography,” J. Opt. Soc. B 16, 267–269 (1999).

Yamauchi, T.

Yaqoob, Z.

Yero, O. M.

R. M. Cuenca, L. M. Leon, J. Lancis, G. M. Vega, O. M. Yero, E. Tajahuerce, and P. Andres, “Diffractive pulse-front tilt for low-coherence digital holography,” J. Opt. Soc. B 16, 267–269 (1999).

Appl. Opt. (3)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

J. Opt. Soc. B (1)

R. M. Cuenca, L. M. Leon, J. Lancis, G. M. Vega, O. M. Yero, E. Tajahuerce, and P. Andres, “Diffractive pulse-front tilt for low-coherence digital holography,” J. Opt. Soc. B 16, 267–269 (1999).

Meas. Sci. Technol. (1)

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), R85–101 (2002).
[CrossRef]

Opt. Commun. (4)

Zs. Bor and B. Racz, “Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,” Opt. Commun. 54(3), 165–170 (1985).
[CrossRef]

O. E. Martinez, “Pulse distortions in tilted pulse schemes for ultrashort pulses,” Opt. Commun. 59(3), 229–232 (1986).
[CrossRef]

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for bragg regime diffraction by phase gratings,” Opt. Commun. 32(1), 14–18 (1980).
[CrossRef]

M. G. Moharam, T. K. Gaylord, and R. Magnusson, “Criteria for Raman-Nath regime diffraction by phase gratings,” Opt. Commun. 32(1), 19–23 (1980).
[CrossRef]

Opt. Eng. (1)

Zs. Bor, B. Racz, G. Szabo, M. Hilbert, and H. A. Hazim, “Femtosecond pulse front tilt caused by angular dispersion,” Opt. Eng. 32(10), 2501–2504 (1993).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Opt. Quantum Electron. (1)

J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt. Quantum Electron. 28(12), 1759–1763 (1996).
[CrossRef]

Other (2)

T. C. Poon, Digital Holography and Three-Dimensional Display (Springer, 2006).

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

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Figures (15)

Fig. 1
Fig. 1

Interference of two short coherence length light beams.

Fig. 2
Fig. 2

Coherence plane tilt: the phase fronts of the pulse are always perpendicular to the pulse propagation direction. The pulse front (i.e. the plane of the maximum of the pulse envelope) is tilted by an angle γt.with respect to the propagation direction.

Fig. 3
Fig. 3

Wedge-phase grating combination to produce a coherence plane tilt (a) collinear device structure. (b) general structure.

Fig. 4
Fig. 4

Diffractive optical element and diffraction orders.

Fig. 5
Fig. 5

Optical set-up of the digital holographic microscope.

Fig. 6
Fig. 6

(a) Interferogram (left panel) and fringe modulation (right panel) without DOE in the reference arm. (b) Interferogram (left panel) and fringe modulation (right panel) after inserting DOE in the reference arm.

Fig. 7
Fig. 7

Grating-wedge-Grating sequence for generating a coherence plan tilt in the Bragg regime.

Fig. 8
Fig. 8

Diffractive optical element and Bragg diffracted order.

Fig. 9
Fig. 9

Diffraction efficiency of: (a) top grating; (b) bottom grating; (c) combined top and bottom gratings, in 794nm (solid) and 685nm (dashed), measured efficiency in 685nm (cross)

Fig. 10
Fig. 10

Parasitic beams at the output of the DOE.

Fig. 11
Fig. 11

Efficiency ratio between the unfiltered cross-talk beam and the desired output beam of the DOE. The dot on the figure shows the measured relative efficiency of the DOE in the experiment.

Fig. 12
Fig. 12

Spatial walk-off of the Bragg order for material thickness 17μm (solid) and 50μm (dashed). The dot shows the measured walk-off of the DOE in the experiment.

Fig. 13
Fig. 13

(a) Intensity(685nm) (b) phase(685nm) (c) intensity(794nm) (d) phase(794nm) without the DOEs.

Fig. 14
Fig. 14

(a) Intensity(685nm) (b) phase(685nm) (c) intensity(794nm) (d) phase(794nm) with the DOEs in the reference arms.

Fig. 15
Fig. 15

(a) 3D perspective; (b) Profile line; of the measured staircase object.

Equations (21)

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L= 1 2sin( α/2 ) λ 2 Δλ
tan γ t =λ dδ dλ ,
δ= θ 4 θ 0 +ε,
dδ dλ = d θ 4 dλ
sin θ 0 = n w sin θ 0
n w sin( θ 0 ε)= n w sin θ 0
n g sin θ 4 = n w sin θ 4
n g cos θ 2 sin θ 4 = λ Λ cosϕ
n g cos θ 2 sin θ 4 = λ Λ cosϕ
cos θ 4 tan γ t λ = cosϕ Λ sinε 1 ( sin θ 0 n w ) 2 d n w dλ
η= J 1 2 ( 2πdΔn λcosθ ),
cos ϕ 2 Λ 2 = cos ϕ 1 Λ 1 + 1 2 sinε× ( n w 2 ( n g n w ) 2 ( λ cos ϕ 1 Λ 1 sin θ 0 ) 2 ) 1 /2 × ( 2 n w n w 2 n g 2 n w 2 cos ϕ 1 Λ 1 ( λ cos ϕ 1 Λ 1 sin θ 0 )+ 2 n g n g n w 2 +2 n w n w n g 2 n w 4 ( λ cos ϕ 1 Λ 1 sin θ 0 ) 2 ) +cos θ 4 tan γ t λ
sin θ 0 = n w sin θ 0
n g sin θ 1 = n w sin θ 1
n w sin( θ 1 +ε)= n g sin θ 2
n g sin θ 4 =sin θ 4
sin θ 0 + n g sin θ 1 = λ Λ 1 cos ϕ 1
n g cos θ 0 n g cos θ 1 = λ Λ 1 sin ϕ 1
n g sin θ 2 +sin θ 4 = λ Λ 2 cos ϕ 2
n g cos θ 2 + n g cos θ 2 ' = λ Λ 2 sin ϕ 2
cos ϕ 2 Λ 2 = cos ϕ 1 Λ 1 + 1 2 sinε× ( n w 2 ( n g n w ) 2 ( λ cos ϕ 1 Λ 1 sin θ 0 ) 2 ) 1 /2 × ( 2 n w n w 2 n g 2 n w 2 cos ϕ 1 Λ 1 ( λ cos ϕ 1 Λ 1 sin θ 0 )+ 2 n g n g n w 2 +2 n w n w n g 2 n w 4 ( λ cos ϕ 1 Λ 1 sin θ 0 ) 2 ) +cos θ 4 tan γ t λ

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