Abstract

We propose a new digital holography method using an ultra-broadband light source and a chromatic phase-shifter. The chromatic phase-shifter gives different frequency shifts for respective spectral frequencies so that the spectrum of the light reflected from the object can be measured to reveal the spectral property of the object, and arbitrary selection of signals in the temporal frequency domain enables single- and multi-wavelength measurements with wide dynamic range. A theoretical analysis, computer simulations, and optical experiments were performed to verify the advantages of the proposed method.

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  1. J. W. Goodman and R. W. Lawrence, “Digital image formation from electrically detected holograms,” Appl. Phys. Lett.11(3), 77–79 (1967).
    [CrossRef]
  2. C. Depeursinge, “Digital holography applied to microscopy,” in Digital Holography and Three-Dimensional Display, T. C. Poon, ed. (Springer, 2006), 104–147.
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  4. I. Yamaguchi, T. Ida, M. Yokota, and K. Yamashita, “Surface shape measurement by phase-shifting digital holography with a wavelength shift,” Appl. Opt.45(29), 7610–7616 (2006).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. P. Hariharan, “Achromatic phase-shifting for white-light interferometry,” Appl. Opt.35(34), 6823–6824 (1996).
    [CrossRef] [PubMed]
  8. S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “White-light interferometry with polarization phase-shifter at the input of the interferometer,” J. Mod. Opt.47(6), 1137–1145 (2000).
    [CrossRef]
  9. S. Tamano, Y. Hayasaki, and N. Nishida, “Phase-shifting digital holography with a low-coherence light source for reconstruction of a digital relief object hidden behind a light-scattering medium,” Appl. Opt.45(5), 953–959 (2006).
    [CrossRef] [PubMed]
  10. P. S. Lam, J. D. Gaskill, and J. C. Wyant, “Two-wavelength holographic interferometer,” Appl. Opt.23(18), 3079–3081 (1984).
    [CrossRef] [PubMed]
  11. J. C. Wyant, “Testing aspherics using two-wavelength holography,” Appl. Opt.10(9), 2113–2118 (1971).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  13. S. Tamano, M. Otaka, and Y. Hayasaki, “Two-wavelength phase-shifting low-coherence digital holography,” Jpn. J. Appl. Phys.47(12), 8844–8847 (2008).
    [CrossRef]
  14. C. Wagner, W. Osten, and S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng.39(1), 79–85 (2000).
    [CrossRef]
  15. A. Wada, M. Kato, and Y. Ishii, “Multiple-wavelength digital holographic interferometry using tunable laser diodes,” Appl. Opt.47(12), 2053–2060 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  22. T. Dresel, G. Häusler, and H. Venzke, “Three-dimensional sensing of rough surfaces by coherence radar,” Appl. Opt.31(7), 919–925 (1992).
    [CrossRef] [PubMed]
  23. G. S. Kino and S. S. C. Chim, “Mirau correlation microscope,” Appl. Opt.29(26), 3775–3783 (1990).
    [CrossRef] [PubMed]
  24. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005), 17–27.
  25. S. De Nicola, A. Finizio, G. Pierattini, P. Ferraro, and D. Alfieri, “Angular spectrum method with correction of an aphorism for numerical reconstruction of digital holograms on tilted planes,” Opt. Express13(24), 9935–9940 (2005).
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  26. X. Y. Su and W. J. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng.42(3), 245–261 (2004).
    [CrossRef]

2011 (1)

2010 (2)

2008 (3)

2006 (2)

2005 (1)

2004 (1)

X. Y. Su and W. J. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng.42(3), 245–261 (2004).
[CrossRef]

2000 (2)

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “White-light interferometry with polarization phase-shifter at the input of the interferometer,” J. Mod. Opt.47(6), 1137–1145 (2000).
[CrossRef]

C. Wagner, W. Osten, and S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng.39(1), 79–85 (2000).
[CrossRef]

1999 (1)

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt.46, 993–1001 (1999).

1998 (1)

1997 (1)

1996 (1)

1995 (1)

1994 (1)

P. Hariharan and M. Roy, “White-light phase-stepping interferometry for surface profiling,” J. Mod. Opt.41(11), 2197–2201 (1994).
[CrossRef]

1992 (1)

1990 (1)

1984 (1)

1971 (1)

1967 (2)

B. P. Hildebrand and K. A. Haines, “Multiple-wavelength and multiple-source holography applied to contour generation,” J. Opt. Soc. Am.57(2), 155–157 (1967).
[CrossRef]

J. W. Goodman and R. W. Lawrence, “Digital image formation from electrically detected holograms,” Appl. Phys. Lett.11(3), 77–79 (1967).
[CrossRef]

Alfieri, D.

Barada, D.

Chen, W. J.

X. Y. Su and W. J. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng.42(3), 245–261 (2004).
[CrossRef]

Chim, S. S. C.

De Nicola, S.

Dresel, T.

Ferraro, P.

Finizio, A.

Gaskill, J. D.

Georges, M. P.

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electrically detected holograms,” Appl. Phys. Lett.11(3), 77–79 (1967).
[CrossRef]

Haines, K. A.

Hariharan, P.

P. Hariharan, “Achromatic phase-shifting for white-light interferometry,” Appl. Opt.35(34), 6823–6824 (1996).
[CrossRef] [PubMed]

P. Hariharan and M. Roy, “White-light phase-stepping interferometry for surface profiling,” J. Mod. Opt.41(11), 2197–2201 (1994).
[CrossRef]

Häusler, G.

Hayasaki, Y.

Helen, S. S.

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “White-light interferometry with polarization phase-shifter at the input of the interferometer,” J. Mod. Opt.47(6), 1137–1145 (2000).
[CrossRef]

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt.46, 993–1001 (1999).

Hildebrand, B. P.

Ida, T.

Ishii, Y.

Iwai, H.

Kato, M.

Kawata, S.

Kiire, T.

Kikuchi, Y.

Kim, S. W.

Kino, G. S.

Kothiyal, M. P.

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “White-light interferometry with polarization phase-shifter at the input of the interferometer,” J. Mod. Opt.47(6), 1137–1145 (2000).
[CrossRef]

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt.46, 993–1001 (1999).

Lam, P. S.

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electrically detected holograms,” Appl. Phys. Lett.11(3), 77–79 (1967).
[CrossRef]

Miwa, M.

Ninane, N.

Nishida, N.

Osten, W.

C. Wagner, W. Osten, and S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng.39(1), 79–85 (2000).
[CrossRef]

Otaka, M.

S. Tamano, M. Otaka, and Y. Hayasaki, “Two-wavelength phase-shifting low-coherence digital holography,” Jpn. J. Appl. Phys.47(12), 8844–8847 (2008).
[CrossRef]

Park, J.

Pierattini, G.

Roy, M.

P. Hariharan and M. Roy, “White-light phase-stepping interferometry for surface profiling,” J. Mod. Opt.41(11), 2197–2201 (1994).
[CrossRef]

Seebacher, S.

C. Wagner, W. Osten, and S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng.39(1), 79–85 (2000).
[CrossRef]

Sirohi, R. S.

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “White-light interferometry with polarization phase-shifter at the input of the interferometer,” J. Mod. Opt.47(6), 1137–1145 (2000).
[CrossRef]

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt.46, 993–1001 (1999).

Su, X. Y.

X. Y. Su and W. J. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng.42(3), 245–261 (2004).
[CrossRef]

Sugisaka, J.

Tamano, S.

Venzke, H.

Wada, A.

Wagner, C.

C. Wagner, W. Osten, and S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng.39(1), 79–85 (2000).
[CrossRef]

Wyant, J. C.

Yamaguchi, I.

Yamashita, K.

Yamashita, Y.

Yamauchi, T.

Yatagai, T.

Yokota, M.

Zhang, T.

Appl. Opt. (10)

G. S. Kino and S. S. C. Chim, “Mirau correlation microscope,” Appl. Opt.29(26), 3775–3783 (1990).
[CrossRef] [PubMed]

N. Ninane and M. P. Georges, “Holographic interferometry using two-wavelength holography for the measurement of large deformations,” Appl. Opt.34(11), 1923–1928 (1995).
[CrossRef] [PubMed]

T. Dresel, G. Häusler, and H. Venzke, “Three-dimensional sensing of rough surfaces by coherence radar,” Appl. Opt.31(7), 919–925 (1992).
[CrossRef] [PubMed]

P. Hariharan, “Achromatic phase-shifting for white-light interferometry,” Appl. Opt.35(34), 6823–6824 (1996).
[CrossRef] [PubMed]

J. C. Wyant, “Testing aspherics using two-wavelength holography,” Appl. Opt.10(9), 2113–2118 (1971).
[CrossRef] [PubMed]

S. Tamano, Y. Hayasaki, and N. Nishida, “Phase-shifting digital holography with a low-coherence light source for reconstruction of a digital relief object hidden behind a light-scattering medium,” Appl. Opt.45(5), 953–959 (2006).
[CrossRef] [PubMed]

I. Yamaguchi, T. Ida, M. Yokota, and K. Yamashita, “Surface shape measurement by phase-shifting digital holography with a wavelength shift,” Appl. Opt.45(29), 7610–7616 (2006).
[CrossRef] [PubMed]

A. Wada, M. Kato, and Y. Ishii, “Multiple-wavelength digital holographic interferometry using tunable laser diodes,” Appl. Opt.47(12), 2053–2060 (2008).
[CrossRef] [PubMed]

P. S. Lam, J. D. Gaskill, and J. C. Wyant, “Two-wavelength holographic interferometer,” Appl. Opt.23(18), 3079–3081 (1984).
[CrossRef] [PubMed]

D. Barada, T. Kiire, J. Sugisaka, S. Kawata, and T. Yatagai, “Simultaneous two-wavelength Doppler phase-shifting digital holography,” Appl. Opt.50(34), H237–H244 (2011).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electrically detected holograms,” Appl. Phys. Lett.11(3), 77–79 (1967).
[CrossRef]

J. Mod. Opt. (3)

P. Hariharan and M. Roy, “White-light phase-stepping interferometry for surface profiling,” J. Mod. Opt.41(11), 2197–2201 (1994).
[CrossRef]

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt.46, 993–1001 (1999).

S. S. Helen, M. P. Kothiyal, and R. S. Sirohi, “White-light interferometry with polarization phase-shifter at the input of the interferometer,” J. Mod. Opt.47(6), 1137–1145 (2000).
[CrossRef]

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (1)

S. Tamano, M. Otaka, and Y. Hayasaki, “Two-wavelength phase-shifting low-coherence digital holography,” Jpn. J. Appl. Phys.47(12), 8844–8847 (2008).
[CrossRef]

Opt. Eng. (1)

C. Wagner, W. Osten, and S. Seebacher, “Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring,” Opt. Eng.39(1), 79–85 (2000).
[CrossRef]

Opt. Express (2)

Opt. Lasers Eng. (1)

X. Y. Su and W. J. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng.42(3), 245–261 (2004).
[CrossRef]

Opt. Lett. (4)

Other (2)

J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005), 17–27.

C. Depeursinge, “Digital holography applied to microscopy,” in Digital Holography and Three-Dimensional Display, T. C. Poon, ed. (Springer, 2006), 104–147.

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Figures (15)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

The spectrum of the light reflected from the object is separated into many sections.

Fig. 3
Fig. 3

Actual spectrum of the light source measured with a spectrometer.

Fig. 4
Fig. 4

(a) Time-varying intensity profile of one pixel simulated using actual spectrum of the light source and PZT velocity of 10 μm/s, and (b) experimental profile obtained from the center pixel of the recorded holograms for comparison.

Fig. 5
Fig. 5

(a) Time-varying intensity profile of one pixel simulated using actual spectrum of the light source and PZT velocity of 20 μm/s, and (b) experimental profile obtained from the center pixel of the recorded holograms for comparison.

Fig. 6
Fig. 6

(a) Time-varying intensity profile of one pixel simulated using actual spectrum of the light source and PZT velocity of 30 μm/s, and (b) experimental profile obtained from the center pixel of the recorded holograms for comparison.

Fig. 7
Fig. 7

The intensity spectrum of the hologram obtained from the Fourier transform of the center pixel of the recorded holograms with PZT velocities of (a) 10 μm/s, (b) 20 μm/s, and (c) 30 μm/s.

Fig. 8
Fig. 8

The effect of errors caused by environmental disturbances or experimental devices on the reconstructed 3D information of the object with different selected wavelengths.

Fig. 9
Fig. 9

(a) Surface of an object reconstructed by TW-LCDH, (b) cross-section, and (c) error profile along center line.

Fig. 10
Fig. 10

(a) Surface of the object reconstructed by SW-LCDH, (b) cross-section, and (c) error profile along center line.

Fig. 11
Fig. 11

The color object.

Fig. 12
Fig. 12

Time-varying intensity profile of one pixel obtained from (a) the red, (b) green, (c) blue and (d) back-ground pixels of the recorded holograms.

Fig. 13
Fig. 13

The intensity spectrum of the hologram obtained from the Fourier transform of the red, green, blue and back-ground pixels of the recorded holograms.

Fig. 14
Fig. 14

The intensity image corresponding to selected frequency.

Fig. 15
Fig. 15

(a) Surface of the object reconstructed by SW-LCDH, cross-section along (b) red, (c) green and (d) blue color character.

Tables (2)

Tables Icon

Table 1 The effect of errors caused by environmental disturbances or experimental devices on the reconstructed 3D information of the object with different selected equivalent wavelengths

Tables Icon

Table 2 The dependence of the quality of the reconstructed 3D image of the object on the velocity of the PZT when employing two-wavelength DH

Equations (18)

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U O [z(x,y),t,k]= A O (x,y) e j[ w O t2z(x,y)k θ O ] ,
U R [z(x,y),t,k]= A R (x,y) e j w R t ,
I[z(x,y),t]= { U O [z(x,y),t,k]+ U R (t,k)} 2 = I O {1+Mcos[( w R w O )t+2z(x,y)k+ θ o ]},
w R ( v R )= w O 1+2 v R /c 12 v R /c w O (1+2 v R c ),
w b = w R ( v R ) w O 2 v R c w O =2k v R .
I[z(x,y),t]= I O {1+Mcos[ θ o + w b t+2z(x,y)k]}.
I i [z(x,y),t]= k i k i+1 I[z(x,y),t] dk.
I WL [z(x,y),t]= i=1 N1 I[z(x,y),t,k] = i=1 N1 k i k i+1 I Oi {1+ M i cos[ θ o + w b t+2z(x,y)k]} dk = i=1 N1 ( k i+1 k i ) I 0 + i=1 N1 M i I 0i ( k i+1 k i )sinc{ k i+1 k i π [ v R t+z(x,y)]} ×cos[ θ 0i +z(x,y)( k i+1 + k i )+ v R t( k i+1 + k i )].
F I WL [z(x,y),w]= i=1 N1 ( k i+1 k i ) I Oi δ(w) + i=1 N1 I Oi π M i 2 v R { e j θ o +jz(x,y)w/(2 v R ) rect[ w v R ( k i+1 + k i ) 2( k i+1 k i ) v R ] + e j θ o jz(x,y)w/(2 v R ) rect[ w+ v R ( k i+1 + k i ) 2( k i+1 k i ) v R ]},
f min f f max ,
f max = v R k N π ,
f min = v R k 1 π
f= v R k π ,
f s 2 v R k N π .
F I WL [z(x,y), w m ]=DFT{ I WL [z(x,y), t n ]} = n=0 N s 1 I WL [z(x,y), t n ]exp(j n f S w m ) ,
1 λ e = 1 λ s2 1 λ s1 .
Δ f min =min( f 1 f 2 )= f s N s ,
λ e max = 2 v R Δ f min .

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