Abstract

A scanning full-field interferometer is a key device in the optical scheme of digital hyperspectral hologram registration. Behind the theory of hyperspectral holography is Fourier transform spectroscopy, wherein the set of spectrally resolved complex amplitudes of the object’s hyperspectral field is obtained via the Fourier transform of a series of interferograms registered in incoherent radiation. Several established approaches in digital holography, based on discrete phase-shifting techniques as well as continuous phase modulation of the reference signal by a scanning mirror, are special cases of Fourier transform spectroscopy, where a coherent light source is used for hologram registration. The proposed algorithm was found to apply to processing holograms registered by various phase-shifting techniques and can give a greater signal-to-noise ratio.

© 2019 Optical Society of America

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References

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  1. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987).
    [Crossref]
  2. Y.-Y. Cheng and J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
    [Crossref]
  3. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [Crossref]
  4. V. Micó, J. García, Z. Zalevsky, and B. Javidi, “Phase-shifting Gabor holography,” Opt. Lett. 34, 1492–1494 (2009).
    [Crossref]
  5. P. J. de Groot, “101-frame algorithm for phase-shifting interferometry,” Proc. SPIE 3098, 283–292 (1997).
    [Crossref]
  6. N. T. Shaked, Y. Zhu, M. T. Rinehart, and A. Wax, “Two-step-only phase-shifting interferometry with optimized detector bandwidth for microscopy of live cells,” Opt. Express 17, 15585–15591 (2009).
    [Crossref]
  7. J.-P. Liu, T.-C. Poon, G.-S. Jhou, and P.-J. Chen, “Comparison of two-, three-, and four-exposure quadrature phase-shifting holography,” Appl. Opt. 50, 2443–2450 (2011).
    [Crossref]
  8. J.-P. Liu and T.-C. Poon, “Two-step-only quadrature phase-shifting digital holography,” Opt. Lett. 34, 250–252 (2009).
    [Crossref]
  9. Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt. 35, 51–60 (1996).
    [Crossref]
  10. G. Lai and T. Yatagai, “Generalized phase-shifting interferometry,” J. Opt. Soc. Am. A 8, 822–827 (1991).
    [Crossref]
  11. K. G. Larkin, “A self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns,” Opt. Express 9, 236–253 (2001).
    [Crossref]
  12. J. Vargas, J. A. Quiroga, T. Belenguer, M. Servín, and J. C. Estrada, “Two-step self-tuning phase-shifting interferometry,” Opt. Express 19, 638–648 (2011).
    [Crossref]
  13. M. Gross and M. Atlan, “Digital holography with ultimate sensitivity,” Opt. Lett. 32, 909–911 (2007).
    [Crossref]
  14. F. L. Clerc, L. Collot, and M. Gross, “Numerical heterodyne holography with two-dimensional photodetector arrays,” Opt. Lett. 25, 716–718 (2000).
    [Crossref]
  15. M. Gross, “Heterodyne holography with full control of both the signal and reference arms,” Appl. Opt. 55, A8–A16 (2016).
    [Crossref]
  16. X. Lv, B. Xiangli, W. Zhang, Z. Wu, Y. Li, X. Kong, and Z. Zhou, “Multiframe full-field heterodyne digital holographic microscopy,” Chin. Opt. Lett. 14, 050901 (2016).
  17. D. Barada, Y. Kikuchi, and T. Yatagai, “Doppler phase-shifting digital holography,” in Advances in Imaging (Optical Society of America, 2009), paper DWD4.
  18. Y. Kikuchi, D. Barada, T. Kiire, and T. Yatagai, “Doppler phase-shifting digital holography and its application to surface shape measurement,” Opt. Lett. 35, 1548–1550 (2010).
    [Crossref]
  19. D. Barada, T. Kiire, J. I. Sugisaka, S. Kawata, and T. Yatagai, “Simultaneous two-wavelength Doppler phase-shifting digital holography,” Appl. Opt. 50, H237–H244 (2011).
    [Crossref]
  20. T. Kiire, D. Barada, J. I. Sugisaka, Y. Hayasaki, and T. Yatagai, “Color digital holography using a single monochromatic imaging sensor,” Opt. Lett. 37, 3153–3155 (2012).
    [Crossref]
  21. S. G. Kalenkov, G. S. Kalenkov, and A. E. Shtanko, “The Fourier spectrometer as a holographic micro-object imaging system in low-coherence light,” Meas. Tech. 55, 1256–1262 (2013).
    [Crossref]
  22. S. G. Kalenkov, G. S. Kalenkov, and A. E. Shtanko, “Spectrally-spatial Fourier-holography,” Opt. Express 21, 24985–24990 (2013).
    [Crossref]
  23. S. G. Kalenkov, G. S. Kalenkov, and A. E. Shtanko, “Hyperspectral holography: an alternative application of the Fourier transform spectrometer,” J. Opt. Soc. Am. B 34, B49–B55 (2017).
    [Crossref]
  24. S. G. Kalenkov, G. S. Kalenkov, and A. E. Shtanko, “Self-reference hyperspectral holographic microscopy,” J. Opt. Soc. Am. A 36, A34–A38 (2019).
    [Crossref]
  25. R. Bell, Introductory Fourier Transform Spectroscopy (Academic, 1972).
  26. N. G. Vlasov, S. G. Kalenkov, D. V. Krilov, and A. E. Shtanko, “Non-lens digital microscopy,” Proc. SPIE 5821, 158–162 (2005).
    [Crossref]
  27. P. S. Huang and S. Zhang, “Fast three-step phase-shifting algorithm,” Appl. Opt. 45, 5086–5091 (2006).
    [Crossref]
  28. S. Kalenkov and G. S. Kalenkov, “Hyperspectral holography and volume Denisyuk holograms,” Proc. SPIE 11030, 1103004 (2019).
    [Crossref]

2019 (2)

S. G. Kalenkov, G. S. Kalenkov, and A. E. Shtanko, “Self-reference hyperspectral holographic microscopy,” J. Opt. Soc. Am. A 36, A34–A38 (2019).
[Crossref]

S. Kalenkov and G. S. Kalenkov, “Hyperspectral holography and volume Denisyuk holograms,” Proc. SPIE 11030, 1103004 (2019).
[Crossref]

2017 (1)

2016 (2)

2013 (2)

S. G. Kalenkov, G. S. Kalenkov, and A. E. Shtanko, “The Fourier spectrometer as a holographic micro-object imaging system in low-coherence light,” Meas. Tech. 55, 1256–1262 (2013).
[Crossref]

S. G. Kalenkov, G. S. Kalenkov, and A. E. Shtanko, “Spectrally-spatial Fourier-holography,” Opt. Express 21, 24985–24990 (2013).
[Crossref]

2012 (1)

2011 (3)

2010 (1)

2009 (3)

2007 (1)

2006 (1)

2005 (1)

N. G. Vlasov, S. G. Kalenkov, D. V. Krilov, and A. E. Shtanko, “Non-lens digital microscopy,” Proc. SPIE 5821, 158–162 (2005).
[Crossref]

2001 (1)

2000 (1)

1997 (2)

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
[Crossref]

P. J. de Groot, “101-frame algorithm for phase-shifting interferometry,” Proc. SPIE 3098, 283–292 (1997).
[Crossref]

1996 (1)

1991 (1)

1987 (1)

1984 (1)

Atlan, M.

Barada, D.

Belenguer, T.

Bell, R.

R. Bell, Introductory Fourier Transform Spectroscopy (Academic, 1972).

Chen, P.-J.

Cheng, Y.-Y.

Clerc, F. L.

Collot, L.

de Groot, P. J.

P. J. de Groot, “101-frame algorithm for phase-shifting interferometry,” Proc. SPIE 3098, 283–292 (1997).
[Crossref]

Eiju, T.

Estrada, J. C.

García, J.

Gross, M.

Hariharan, P.

Hayasaki, Y.

Huang, P. S.

Javidi, B.

Jhou, G.-S.

Kalenkov, G. S.

Kalenkov, S.

S. Kalenkov and G. S. Kalenkov, “Hyperspectral holography and volume Denisyuk holograms,” Proc. SPIE 11030, 1103004 (2019).
[Crossref]

Kalenkov, S. G.

Kawata, S.

Kiire, T.

Kikuchi, Y.

Y. Kikuchi, D. Barada, T. Kiire, and T. Yatagai, “Doppler phase-shifting digital holography and its application to surface shape measurement,” Opt. Lett. 35, 1548–1550 (2010).
[Crossref]

D. Barada, Y. Kikuchi, and T. Yatagai, “Doppler phase-shifting digital holography,” in Advances in Imaging (Optical Society of America, 2009), paper DWD4.

Kong, X.

Krilov, D. V.

N. G. Vlasov, S. G. Kalenkov, D. V. Krilov, and A. E. Shtanko, “Non-lens digital microscopy,” Proc. SPIE 5821, 158–162 (2005).
[Crossref]

Lai, G.

Larkin, K. G.

Li, Y.

Liu, J.-P.

Lv, X.

Micó, V.

Oreb, B. F.

Poon, T.-C.

Quiroga, J. A.

Rinehart, M. T.

Servín, M.

Shaked, N. T.

Shtanko, A. E.

Sugisaka, J. I.

Surrel, Y.

Vargas, J.

Vlasov, N. G.

N. G. Vlasov, S. G. Kalenkov, D. V. Krilov, and A. E. Shtanko, “Non-lens digital microscopy,” Proc. SPIE 5821, 158–162 (2005).
[Crossref]

Wax, A.

Wu, Z.

Wyant, J. C.

Xiangli, B.

Yamaguchi, I.

Yatagai, T.

Zalevsky, Z.

Zhang, S.

Zhang, T.

Zhang, W.

Zhou, Z.

Zhu, Y.

Appl. Opt. (7)

Chin. Opt. Lett. (1)

J. Opt. Soc. Am. A (2)

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

Meas. Tech. (1)

S. G. Kalenkov, G. S. Kalenkov, and A. E. Shtanko, “The Fourier spectrometer as a holographic micro-object imaging system in low-coherence light,” Meas. Tech. 55, 1256–1262 (2013).
[Crossref]

Opt. Express (4)

Opt. Lett. (7)

Proc. SPIE (3)

P. J. de Groot, “101-frame algorithm for phase-shifting interferometry,” Proc. SPIE 3098, 283–292 (1997).
[Crossref]

N. G. Vlasov, S. G. Kalenkov, D. V. Krilov, and A. E. Shtanko, “Non-lens digital microscopy,” Proc. SPIE 5821, 158–162 (2005).
[Crossref]

S. Kalenkov and G. S. Kalenkov, “Hyperspectral holography and volume Denisyuk holograms,” Proc. SPIE 11030, 1103004 (2019).
[Crossref]

Other (2)

R. Bell, Introductory Fourier Transform Spectroscopy (Academic, 1972).

D. Barada, Y. Kikuchi, and T. Yatagai, “Doppler phase-shifting digital holography,” in Advances in Imaging (Optical Society of America, 2009), paper DWD4.

Supplementary Material (2)

NameDescription
» Visualization 1       A set of digital holograms registered in the intererometer during continuous mirror displacement.
» Visualization 2       Phase profile of the object.

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Figures (11)

Fig. 1.
Fig. 1. Computer simulation of the registration and restoration procedure of the amplitude-phase object. An interferogram $ G({\xi _0},\delta ) $ formed in a certain pixel of the matrix. Charlie Chaplin images are derivatives of “Charlie Chaplin” by Insomnia Cured Here, used under CC BY-SA, and licensed under CC BY-SA by Georgy Kalenkov.
Fig. 2.
Fig. 2. Interferogram, its power spectrum, and the reconstructed images of the object, when $ | \Delta | \le {\varphi _n}/2 $. Charlie Chaplin images are derivatives of “Charlie Chaplin” by Insomnia Cured Here, used under CC BY-SA, and licensed under CC BY-SA by Georgy Kalenkov.
Fig. 3.
Fig. 3. Interferogram, its power spectrum, and the reconstructed images of the object, when $ | \Delta | \le 2{\varphi _n} $. Charlie Chaplin images are derivatives of “Charlie Chaplin” by Insomnia Cured Here, used under CC BY-SA, and licensed under CC BY-SA by Georgy Kalenkov.
Fig. 4.
Fig. 4. Pairs of reconstructed amplitude-phase images of the object at symmetrical spectral frequencies. Top row, noise free; bottom row, phase noise at $ \vert \Delta \vert \le 2{\varphi _n} $ is introduced. Charlie Chaplin images are derivatives of “Charlie Chaplin” by Insomnia Cured Here, used under CC BY-SA, and licensed under CC BY-SA by Georgy Kalenkov.
Fig. 5.
Fig. 5. Dependence of $ {I_{\rm res}}/{I_{\rm obj}}(\Delta ) $ at a random phase error of $ \vert \Delta \vert \le 2{\varphi _n} $. Dashed line, experimental data; solid line, smoothed spline curve.
Fig. 6.
Fig. 6. Difference between the reconstructed and initial phase profiles when $ \vert \Delta \vert \le {\varphi _n}/2 $.
Fig. 7.
Fig. 7. Optical scheme. M, mirror; BS, beam splitter; $ \delta $, optical path difference.
Fig. 8.
Fig. 8. Reconstructed image of target.
Fig. 9.
Fig. 9. (a) Hologram of the amplitude-phase object, (b) the reconstructed amplitude image, (c) the wrapped phase of the reconstructed image in the range $ [ - \pi /2;\pi /2] $, and (d) the unwrapped phase of the image after subtracting of the parabolic wavefront carrier. Charlie Chaplin images are derivatives of “Charlie Chaplin” by Insomnia Cured Here, used under CC BY-SA, and licensed under CC BY-SA by Georgy Kalenkov.
Fig. 10.
Fig. 10. Comparisons between the reconstructed images. Images reconstructed from 3 holograms registered by means of a three-phase-shifting algorithm, ${2}\pi /{3}$. (a) The zero spectral component ${S_0}$ holds the reference and noise; (b) a direct image of the object, ${S_1}$; (c) a twin image, ${S_2}$; (d) an image reconstructed from the same holograms using the original method.
Fig. 11.
Fig. 11. Estimation of the signal-to-noise ratio. (a) The suggested approach. (b) Three-phase-step algorithm.

Equations (5)

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G i n t ( ξ , δ ) = S ( σ ) [ A ( σ , ξ ) r exp ( 2 π i σ δ ) + A ( σ , ξ ) r exp ( 2 π i σ δ ) ] d σ ,
G i n t ( ξ , δ ) = Δ σ S ( σ 0 ) [ A ( σ 0 , ξ ) r exp ( 2 π i σ 0 δ ) + A ( σ 0 , ξ ) r exp ( 2 π i σ 0 δ ) ] ,
1 / ( Δ σ S ( σ 0 ) ) L / 2 L / 2 G i n t ( ξ , δ ) exp ( 2 π i σ δ ) d δ = L A ( σ 0 , ξ ) r + A ( σ 0 , ξ ) r L / 2 L / 2 exp ( 4 π i σ 0 δ ) d δ = L r [ A ( σ 0 , ξ ) + A ( σ 0 , ξ ) s i n c ( σ 0 L ) ] .
A ( σ 0 , ξ ) = 1 / L r Δ σ S ( σ 0 ) L / 2 L / 2 G i n t ( ξ , δ ) exp ( 2 π i σ δ ) d δ .
G n = | A ( ξ ) exp [ 2 π i φ o b j ( ξ ) ] + exp [ 2 π i ( φ n ± Δ ) ] | 2 .

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