Abstract

The appropriate reference wave in single-exposure phase-shifting digital holography using a random-complex-amplitude encoded reference wave is experimentally investigated. Although the reference wave is generalized, the quality of reconstructed images depends on it. Furthermore, when the reference wave satisfies a certain condition, reconstructed images cannot be obtained in this method. After the certain condition is presented, the appropriate condition is studied using a speckle property. Experimental results are given to investigate the relations between the quality of reconstructed images and the sizes of speckles of the reference waves. The results prove that the appropriate reference wave exists in this method.

© 2013 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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2013 (2)

2012 (3)

2011 (3)

2010 (2)

H.  Suzuki, T.  Nomura, E.  Nitanai, T.  Numata, “Dynamic recording of a digital hologram with single exposure by a wave-splitting phase-shifting method,” Opt. Rev. 17, 176–180 (2010).
[CrossRef]

T.  Nomura M.  Imbe, “Single-exposure phase-shifting digital holography using a random-phase reference wave,” Opt. Lett. 35, 2281–2283 (2010).
[CrossRef]

2009 (2)

2008 (1)

2005 (1)

2004 (2)

Y.  Awatsuji, M.  Sasada, T.  Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

J.  Millerd, N.  Brock, J.  Hayes, M.  North-Morris, M.  Novak, J.  Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Andrés, P.

Andrews, M.

Araiza-E, M.

Araiza-Esquivel, M.

Asundi, A.

Awatsuji, Y.

T.  Kakue, S.  Itoh, P.  Xia, T.  Tahara, Y.  Awatsuji, K.  Nishio, S.  Ura, T.  Kubota, O.  Matoba, “Single-shot femtosecond-pulsed phase-shifting digital holography,” Opt. Express 20, 20286–20291 (2012).
[CrossRef]

M.  Lin, K.  Nitta, O.  Matoba, Y.  Awatsuji, “Parallel phase-shifting digital holography with adaptive function using phase-mode spatial light modulator,” Appl. Opt. 51, 2633–2637 (2012).
[CrossRef]

Y.  Awatsuji, M.  Sasada, T.  Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

M.  Sasada, Y.  Awatsuji, T.  Kubota, “Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187–188.

M.  Sasada, A.  Fujii, Y.  Awatsuji, T.  Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357–358.

Brock, N.

J.  Millerd, N.  Brock, J.  Hayes, M.  North-Morris, M.  Novak, J.  Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Chen, P.

Climent, V.

Duncan, D.

Fujii, A.

M.  Sasada, A.  Fujii, Y.  Awatsuji, T.  Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357–358.

Gao, F.

Guo, Z.

Han, G.

Hayes, J.

J.  Millerd, N.  Brock, J.  Hayes, M.  North-Morris, M.  Novak, J.  Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Hirst, E.

Imbe, M.

Itoh, S.

Javidi, B.

Jhou, G.

Jiao, Z.

Kakue, T.

Kelly, D.

Kirkpatrick, S.

Kreis, T.

T.  Kreis, “Speckle Size,” in Handbook of Holographic Interferometry (Wiley-VCH, 2005), pp. 34–36.

Kubota, T.

T.  Kakue, S.  Itoh, P.  Xia, T.  Tahara, Y.  Awatsuji, K.  Nishio, S.  Ura, T.  Kubota, O.  Matoba, “Single-shot femtosecond-pulsed phase-shifting digital holography,” Opt. Express 20, 20286–20291 (2012).
[CrossRef]

Y.  Awatsuji, M.  Sasada, T.  Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

M.  Sasada, Y.  Awatsuji, T.  Kubota, “Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187–188.

M.  Sasada, A.  Fujii, Y.  Awatsuji, T.  Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357–358.

Lancis, J.

Lin, M.

Liu, J.

Lu, G.

Martínez-León, L.

Matoba, O.

Meinecke, T.

Miao, J.

Miao, X.

Millerd, J.

J.  Millerd, N.  Brock, J.  Hayes, M.  North-Morris, M.  Novak, J.  Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Nishio, K.

Nitanai, E.

H.  Suzuki, T.  Nomura, E.  Nitanai, T.  Numata, “Dynamic recording of a digital hologram with single exposure by a wave-splitting phase-shifting method,” Opt. Rev. 17, 176–180 (2010).
[CrossRef]

Nitta, K.

Nomura, T.

North-Morris, M.

J.  Millerd, N.  Brock, J.  Hayes, M.  North-Morris, M.  Novak, J.  Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Novak, M.

J.  Millerd, N.  Brock, J.  Hayes, M.  North-Morris, M.  Novak, J.  Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Numata, T.

H.  Suzuki, T.  Nomura, E.  Nitanai, T.  Numata, “Dynamic recording of a digital hologram with single exposure by a wave-splitting phase-shifting method,” Opt. Rev. 17, 176–180 (2010).
[CrossRef]

Peng, X.

Poon, T.

Sabitov, N.

Sasada, M.

Y.  Awatsuji, M.  Sasada, T.  Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

M.  Sasada, Y.  Awatsuji, T.  Kubota, “Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187–188.

M.  Sasada, A.  Fujii, Y.  Awatsuji, T.  Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357–358.

Sinzinger, S.

Suzuki, H.

H.  Suzuki, T.  Nomura, E.  Nitanai, T.  Numata, “Dynamic recording of a digital hologram with single exposure by a wave-splitting phase-shifting method,” Opt. Rev. 17, 176–180 (2010).
[CrossRef]

Tahara, T.

Tajahuerce, E.

Thompson, O.

Tian, Y.

Ura, S.

Voelz, D.

D.  Voelz, “Rayleigh-Sommerfeld solution I,” in Computational Fourier Optics: A MATLAB Tutorial (SPIE, 2011), pp. 51–53.

Wells-Gray, E.

Wyant, J.

J.  Millerd, N.  Brock, J.  Hayes, M.  North-Morris, M.  Novak, J.  Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Xia, P.

Xu, L.

Xu, X.

Yuan, H.

Appl. Opt. (6)

Appl. Phys. Lett. (1)

Y.  Awatsuji, M.  Sasada, T.  Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069–1071 (2004).
[CrossRef]

Biomed. Opt. Express (1)

Opt. Express (3)

Opt. Lett. (3)

Opt. Rev. (1)

H.  Suzuki, T.  Nomura, E.  Nitanai, T.  Numata, “Dynamic recording of a digital hologram with single exposure by a wave-splitting phase-shifting method,” Opt. Rev. 17, 176–180 (2010).
[CrossRef]

Proc. SPIE (1)

J.  Millerd, N.  Brock, J.  Hayes, M.  North-Morris, M.  Novak, J.  Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Other (4)

T.  Kreis, “Speckle Size,” in Handbook of Holographic Interferometry (Wiley-VCH, 2005), pp. 34–36.

D.  Voelz, “Rayleigh-Sommerfeld solution I,” in Computational Fourier Optics: A MATLAB Tutorial (SPIE, 2011), pp. 51–53.

M.  Sasada, Y.  Awatsuji, T.  Kubota, “Parallel quasi-phase-shifting digital holography that can achieve instantaneous measurement,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 187–188.

M.  Sasada, A.  Fujii, Y.  Awatsuji, T.  Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of the 2004 ICO International Conference: Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357–358.

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Figures (7)

Fig. 1.
Fig. 1.

Arbitrary four neighboring pixels on the hologram, the reference wave, and the object wave.

Fig. 2.
Fig. 2.

Example of the condition for which S equals zero: the two vectors Ru and Rl are parallel.

Fig. 3.
Fig. 3.

Object used in the experiments: surrounding area by a yellow broken line is used to obtain N. This figure is an illustration, not a real object. In the real object, the letters of numbers and the small resolution patterns are written at the outside and the inside, respectively.

Fig. 4.
Fig. 4.

Optical setup: OL, object lens; L1, collimating lens; L2, imaging lens; BS1, BS2, beam splitters; M1, M2, mirrors; P, polarizer; QWP, quarter wavelength plate; ND, neutral density filter.

Fig. 5.
Fig. 5.

Relations between E values and average diameters of speckles of reference waves.

Fig. 6.
Fig. 6.

Reconstructed images: the average diameters of speckles of the reference waves are (a) 4.02 pixels, (b) 2.39 pixels, (c) 1.63 pixels, (d) 1.20 pixels, (e) 1.12 pixels, and (f) 1.06 pixels, respectively.

Fig. 7.
Fig. 7.

Reconstructed image obtained by four-exposure quadrature phase-shifting technique.

Equations (18)

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

I1=AoAo*+Ar1Ar1*+AoAr1*+Ao*Ar1,
I2=AoAo*+Ar2Ar2*+AoAr2*+Ao*Ar2,
I3=AoAo*+Ar3Ar3*+AoAr3*+Ao*Ar3,
I4=AoAo*+Ar4Ar4*+AoAr4*+Ao*Ar4.
Ao=HuRlHlRuRu*RlRuRl*,
Hu=I1I2(|Ar1|2|Ar2|2),
Hl=I3I4(|Ar3|2|Ar4|2),
Ru=Ar1Ar2,
Rl=Ar3Ar4.
S=|Ru*RlRuRl*|.
S=|2i|Ru||Rl|sin(ϕuϕl)|,
ϕu=tan1Im[Ru]Re[Ru],
ϕl=tan1Im[Rl]Re[Rl].
|Ru|=0,
|Rl|=0,
ϕuϕl=mπ.
ρ=2.44λld,
E=(1NM)×100[%].

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