Abstract

We propose a virtual interferogram-generation algorithm using two interferograms. This algorithm can measure a complex amplitude of a signal beam with high accuracy even when its intensity is greater than the intensity of a reference beam. Unlike the conventional algorithm that uses two interferograms, our algorithm can compute measurements when the phase shift of interferograms in not equal to π/2. Our method generates two phase-shifted holograms in a computer by capturing the intensities of two signal beams, two reference beams, and two interferograms. The complex amplitude of a signal beam is calculated by four interference patterns, two holograms, and two interferograms. The proposed algorithm can drastically suppress the calculation error caused by the smaller value between the intensity of the reference beam and can choose the most suitable phase shift.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Two-channel algorithm for single-shot, high-resolution measurement of optical wavefronts using two image sensors

Jin Nozawa, Atsushi Okamoto, Atsushi Shibukawa, Masanori Takabayashi, and Akihisa Tomita
Appl. Opt. 54(29) 8644-8652 (2015)

Reference-free holographic diversity interferometry via iterative measurements for high accuracy phase detection

Yuta Goto, Atsushi Okamoto, Yuta Wakayama, Kazuhisa Ogawa, Jin Nozawa, Akihisa Tomita, and Takehiro Tsuritani
Opt. Express 24(21) 24739-24749 (2016)

Optical vortex phase-shifting digital holography

Cheng-Shan Guo, Xin Cheng, Xiu-Yun Ren, Jian-Ping Ding, and Hui-Tian Wang
Opt. Express 12(21) 5166-5171 (2004)

References

  • View by:
  • |
  • |
  • |

  1. B. C. Platt and R. Shack, “History and Principles of Shack-Hartmann Wavefront Sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
    [PubMed]
  2. B. Kemper, P. Langehanenberg, and G. V. Bally, “Digital Holographic Microscopy,” WILEY-VCH, Optik&Photonik, 41–44 (2007).
    [Crossref]
  3. T. Tahara, K. Ito, T. Kakue, M. Fujii, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel phase-shifting digital holographic microscopy,” Biomed. Opt. Express 1(2), 610–616 (2010).
    [Crossref] [PubMed]
  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]
  5. Y. Kikuchi, D. Barada, T. Kiire, and T. Yatagai, “Doppler phase-shifting digital holography and its application to surface shape measurement,” Opt. Lett. 35(10), 1548–1550 (2010).
    [Crossref] [PubMed]
  6. E. Tajahuerce, O. Matoba, and B. Javidi, “Shift-invariant three-dimensional object recognition by means of digital holography,” Appl. Opt. 40(23), 3877–3886 (2001).
    [Crossref] [PubMed]
  7. B. Javidi and D. Kim, “Three-dimensional-object recognition by use of single-exposure on-axis digital holography,” Opt. Lett. 30(3), 236–238 (2005).
    [Crossref] [PubMed]
  8. A. Stadelmaier and J. H. Massig, “Compensation of lens aberrations in digital holography,” Opt. Lett. 25(22), 1630–1632 (2000).
    [Crossref] [PubMed]
  9. P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. 42(11), 1938–1946 (2003).
    [Crossref] [PubMed]
  10. A. Okamoto, T. Maeda, Y. Hirasaki, A. Shibukawa, and A. Tomita, “Progressive phase conjugation and its application in reconfigurable spatial-mode extraction and conversion,” Proc. SPIE 9130, 913012 (2014).
    [Crossref]
  11. S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32(7-8), 567–574 (2000).
    [Crossref]
  12. G. Pan and H. Meng, “Digital holography of particle fields: reconstruction by use of complex amplitude,” Appl. Opt. 42(5), 827–833 (2003).
    [Crossref] [PubMed]
  13. R. G. Lane and M. Tallon, “Wave-front reconstruction using a Shack-Hartmann sensor,” Appl. Opt. 31(32), 6902–6908 (1992).
    [Crossref] [PubMed]
  14. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
    [Crossref] [PubMed]
  15. G. Pedrini, P. Fröning, H. Fessler, and H. J. Tiziani, “In-line digital holographic interferometry,” Appl. Opt. 37(26), 6262–6269 (1998).
    [Crossref] [PubMed]
  16. K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24(18), 3053–3058 (1985).
    [Crossref] [PubMed]
  17. Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
    [Crossref]
  18. T. Nomura, S. Murata, E. Nitanai, and T. Numata, “Phase-shifting digital holography with a phase difference between orthogonal polarizations,” Appl. Opt. 45(20), 4873–4877 (2006).
    [Crossref] [PubMed]
  19. A. Okamoto, K. Kunori, M. Takabayashi, A. Tomita, and K. Sato, “Holographic Diversity interferometry for optical storage,” Opt. Express 19(14), 13436–13444 (2011).
    [Crossref] [PubMed]
  20. X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, “Two-step phase-shifting interferometry and its application in image encryption,” Opt. Lett. 31(10), 1414–1416 (2006).
    [Crossref] [PubMed]
  21. J. P. Liu and T. C. Poon, “Two-step-only quadrature phase-shifting digital holography,” Opt. Lett. 34(3), 250–252 (2009).
    [Crossref] [PubMed]
  22. J. Li, Y. Y. Pan, J. S. Li, R. Li, and T. Zheng, “Experimental Study of Two-step Phase-shifting Digital Holography based on the Calculated Intensity of a Reference Wave,” J. Opt. Soc. Korea 18(3), 230–235 (2014).
    [Crossref]
  23. J. Nozawa, A. Okamoto, A. Shibukawa, M. Takabayashi, and A. Tomita, “Two-channel algorithm for single-shot, high-resolution measurement of optical wavefronts using two image sensors,” Appl. Opt. 54(29), 8644–8652 (2015).
    [Crossref] [PubMed]
  24. D. Malacara, Optical Shop Testing II, 3rd ed. (Wiley, 2008) (2008), pp. 116–119.

2015 (1)

2014 (2)

J. Li, Y. Y. Pan, J. S. Li, R. Li, and T. Zheng, “Experimental Study of Two-step Phase-shifting Digital Holography based on the Calculated Intensity of a Reference Wave,” J. Opt. Soc. Korea 18(3), 230–235 (2014).
[Crossref]

A. Okamoto, T. Maeda, Y. Hirasaki, A. Shibukawa, and A. Tomita, “Progressive phase conjugation and its application in reconfigurable spatial-mode extraction and conversion,” Proc. SPIE 9130, 913012 (2014).
[Crossref]

2011 (1)

2010 (2)

2009 (1)

2006 (3)

2005 (1)

2004 (1)

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

2003 (2)

2001 (2)

B. C. Platt and R. Shack, “History and Principles of Shack-Hartmann Wavefront Sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

E. Tajahuerce, O. Matoba, and B. Javidi, “Shift-invariant three-dimensional object recognition by means of digital holography,” Appl. Opt. 40(23), 3877–3886 (2001).
[Crossref] [PubMed]

2000 (2)

A. Stadelmaier and J. H. Massig, “Compensation of lens aberrations in digital holography,” Opt. Lett. 25(22), 1630–1632 (2000).
[Crossref] [PubMed]

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32(7-8), 567–574 (2000).
[Crossref]

1998 (1)

1997 (1)

1992 (1)

1985 (1)

Awatsuji, Y.

Barada, D.

Cai, L. Z.

Coppola, G.

Creath, K.

De Nicola, S.

Dong, G. Y.

Ferraro, P.

Fessler, H.

Finizio, A.

Fröning, P.

Fujii, M.

Grilli, S.

Hirasaki, Y.

A. Okamoto, T. Maeda, Y. Hirasaki, A. Shibukawa, and A. Tomita, “Progressive phase conjugation and its application in reconfigurable spatial-mode extraction and conversion,” Proc. SPIE 9130, 913012 (2014).
[Crossref]

Ida, T.

Ito, K.

Javidi, B.

Kakue, T.

Kiire, T.

Kikuchi, Y.

Kim, D.

Kubota, T.

Kunori, K.

Lane, R. G.

Li, J.

Li, J. S.

Li, R.

Liu, J. P.

Maeda, T.

A. Okamoto, T. Maeda, Y. Hirasaki, A. Shibukawa, and A. Tomita, “Progressive phase conjugation and its application in reconfigurable spatial-mode extraction and conversion,” Proc. SPIE 9130, 913012 (2014).
[Crossref]

Magro, C.

Massig, J. H.

Matoba, O.

Meng, H.

Meng, X. F.

Murata, S.

Nishio, K.

Nitanai, E.

Nomura, T.

Nozawa, J.

Numata, T.

Okamoto, A.

Pan, G.

Pan, Y. Y.

Pedrini, G.

Pierattini, G.

Platt, B. C.

B. C. Platt and R. Shack, “History and Principles of Shack-Hartmann Wavefront Sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

Poon, T. C.

Sasada, M.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

Sato, K.

Shack, R.

B. C. Platt and R. Shack, “History and Principles of Shack-Hartmann Wavefront Sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

Shen, X. X.

Shibukawa, A.

J. Nozawa, A. Okamoto, A. Shibukawa, M. Takabayashi, and A. Tomita, “Two-channel algorithm for single-shot, high-resolution measurement of optical wavefronts using two image sensors,” Appl. Opt. 54(29), 8644–8652 (2015).
[Crossref] [PubMed]

A. Okamoto, T. Maeda, Y. Hirasaki, A. Shibukawa, and A. Tomita, “Progressive phase conjugation and its application in reconfigurable spatial-mode extraction and conversion,” Proc. SPIE 9130, 913012 (2014).
[Crossref]

Shimozato, Y.

Stadelmaier, A.

Tahara, T.

Tajahuerce, E.

Takabayashi, M.

Tallon, M.

Tiziani, H. J.

Tomita, A.

Ura, S.

Wang, Y. R.

Xu, X. F.

Yamaguchi, I.

Yamashita, K.

Yang, X. L.

Yasuda, N.

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32(7-8), 567–574 (2000).
[Crossref]

Yatagai, T.

Yokota, M.

Zhang, T.

Zheng, T.

Appl. Opt. (9)

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]

E. Tajahuerce, O. Matoba, and B. Javidi, “Shift-invariant three-dimensional object recognition by means of digital holography,” Appl. Opt. 40(23), 3877–3886 (2001).
[Crossref] [PubMed]

P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini, “Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging,” Appl. Opt. 42(11), 1938–1946 (2003).
[Crossref] [PubMed]

G. Pan and H. Meng, “Digital holography of particle fields: reconstruction by use of complex amplitude,” Appl. Opt. 42(5), 827–833 (2003).
[Crossref] [PubMed]

R. G. Lane and M. Tallon, “Wave-front reconstruction using a Shack-Hartmann sensor,” Appl. Opt. 31(32), 6902–6908 (1992).
[Crossref] [PubMed]

T. Nomura, S. Murata, E. Nitanai, and T. Numata, “Phase-shifting digital holography with a phase difference between orthogonal polarizations,” Appl. Opt. 45(20), 4873–4877 (2006).
[Crossref] [PubMed]

G. Pedrini, P. Fröning, H. Fessler, and H. J. Tiziani, “In-line digital holographic interferometry,” Appl. Opt. 37(26), 6262–6269 (1998).
[Crossref] [PubMed]

K. Creath, “Phase-shifting speckle interferometry,” Appl. Opt. 24(18), 3053–3058 (1985).
[Crossref] [PubMed]

J. Nozawa, A. Okamoto, A. Shibukawa, M. Takabayashi, and A. Tomita, “Two-channel algorithm for single-shot, high-resolution measurement of optical wavefronts using two image sensors,” Appl. Opt. 54(29), 8644–8652 (2015).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[Crossref]

Biomed. Opt. Express (1)

J. Opt. Soc. Korea (1)

J. Refract. Surg. (1)

B. C. Platt and R. Shack, “History and Principles of Shack-Hartmann Wavefront Sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

Opt. Express (1)

Opt. Laser Technol. (1)

S. Murata and N. Yasuda, “Potential of digital holography in particle measurement,” Opt. Laser Technol. 32(7-8), 567–574 (2000).
[Crossref]

Opt. Lett. (6)

Proc. SPIE (1)

A. Okamoto, T. Maeda, Y. Hirasaki, A. Shibukawa, and A. Tomita, “Progressive phase conjugation and its application in reconfigurable spatial-mode extraction and conversion,” Proc. SPIE 9130, 913012 (2014).
[Crossref]

Other (2)

B. Kemper, P. Langehanenberg, and G. V. Bally, “Digital Holographic Microscopy,” WILEY-VCH, Optik&Photonik, 41–44 (2007).
[Crossref]

D. Malacara, Optical Shop Testing II, 3rd ed. (Wiley, 2008) (2008), pp. 116–119.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (17)

Fig. 1
Fig. 1 Conceptual diagram of the VIGA.
Fig. 2
Fig. 2 Comparison of the ideal hologram and the calculated virtual hologram. (A) the signal intensity image (B) the reference intensity image. (C) the interferogram image. (D) the virtual hologram calculated by VIGA. (E) the ideal hologram, with phase shift of π.
Fig. 3
Fig. 3 Reconstructed complex amplitude when the intensity of a reference beam was less than that of a signal beam. (A) the original intensity image (B) the original phase image. (C) the intensity image calculated by the two-channel algorithm. (D) the phase image calculated by the two-channel algorithm. (E) the intensity image calculated by VIGA. (F) the phase image calculated by VIGA.
Fig. 4
Fig. 4 RMSE between the original phase image and the calculated phase image when the intensity of the reference beam was changed from 1 μW to 20 μW. The intensity of signal beam was 10 μW.
Fig. 5
Fig. 5 Reconstructed complex amplitude when the phase shift of interferograms was π/4. (A) The original intensity image. (B) The original phase image. (C) the intensity image calculated by the two-channel algorithm (D) the phase image calculated by the two-channel algorithm. (E) the intensity image calculated by VIGA. (F) the phase image calculated by VIGA
Fig. 6
Fig. 6 RMSE between the original phase image and the calculated phase image when phase shift of interferograms was changed from –π to π Calculation error points were denoted as RMSE = −1.0.
Fig. 7
Fig. 7 Reconstructed complex amplitude when the grayscale of the image sensor is 8 bit. (A) Original intensity image. (B) Original phase image. (C) Intensity image calculated by four-step algorithm. (D) Phase image calculated by four-step algorithm. (E) Intensity image calculated by VIGA. (F) Phase image calculated by VIGA
Fig. 8
Fig. 8 RMSE between original phase image and calculated phase image when gray level of image sensor is changed from 8 bit to 16 bit.
Fig. 9
Fig. 9 Experimental setup for complex amplitude measurements. A LCOS-SLM (Hamamatsu, X10468-01) was used as the measuring object. The signal beam is delivered to two CCDs using relay lens constructed from Lens2 to Lens5. HWP(Sigma Koki, WPQ-5320-4M). QWP(Sigma Koki, WPQ-5320-4M), BS(Sigma Koki, NPCH-20-5320), SF(Sigma Koki, SFB-16RO-OBL10-25), PBS(Sigma Koki, PBS-20-5320).
Fig. 10
Fig. 10 Phase image displayed on the SLM and intensity distributions captured by two image sensors in first experiment. (A)Phase image displayed on the SLM (B) Signal intensity captured by CCD1. (C) Signal intensity captured by CCD2. (D) Reference intensity captured by CCD1. (E) Reference intensity captured by CCD2. (F) Interference pattern captured by CCD1. (G) Interference pattern captured by CCD2. (H) virtual hologram calculated by Fig. 10(f). (I) virtual hologram calculated by Fig. 10(g).
Fig. 11
Fig. 11 measured complex amplitudes and calculation error maps when the reference intensity was 0.96 μW and the signal intensity was 3.21 μW. (A) intensity image measured by two-channel algorithm. (B) Phase image measured by two-channel algorithm. (C) Intensity image measured by VIGA. (D) Phase image measured by VIGA. (E) Calculation error map of two-channel algorithm (F) Calculation error map of VIGA
Fig. 12
Fig. 12 RMSE between phase image displayed on SLM and measured phase image when intensity of reference beam is changed and intensity of signal beam is 3.21 μW.
Fig. 13
Fig. 13 Measured intensity ratios and influence of intensity ratios. (A) Calculated signal intensity ratio α. (B) Calculated reference intensity ratio β. (C) Calculated phase image with intensity ratios. (D) Calculated phase image without intensity ratios
Fig. 14
Fig. 14 Experimental setup for compensation of phase shift error. The wavelength of laser was changed from 532nm to 593nm for providing the given phase shift error. HWP(Sigma Koki, WPQ-5320-2M). QWP(Sigma Koki, WPQ-5320-4M), BS(Sigma Koki, HBCH-20-550), SF(Sigma Koki, SFB-16RO-OBL10-25), PBS(Sigma Koki, PBSW-20-550)
Fig. 15
Fig. 15 Phase image displayed on the SLM and intensity distributions captured by two image sensors in first experiment. (A)Phase image displayed on the SLM (B) Signal intensity captured by CCD1. (C) Signal intensity captured by CCD2. (D) Reference intensity captured by CCD1. (E) Reference intensity captured by CCD2. (F) Interference pattern captured by CCD1. (G) Interference pattern captured by CCD2. (H) virtual hologram calculated by Fig. 15(f). (I) virtual hologram calculated by Fig. 15(g).
Fig. 16
Fig. 16 measured complex amplitudes when the phase shift of interferograms is not π/2. (A) intensity image measured by two-channel algorithm. (B) Intensity image measured by VIGA. (C) Phase image measured by two-channel algorithm. (D) Phase image measured by VIGA.
Fig. 17
Fig. 17 Phase values along the horizontal yellow line of Fig. 16. The phase contrast of VIGA was greater than that of two-channel algorithm.

Equations (9)

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

H 1 = A o 2 + A r 2 +2 A o A r cosφ
H 2 =α A o 2 +β A r 2 +2 αβ A o A r cos(φγ)
2 A o A r cosφ= H 1 ( A o 2 + A r 2 )
2 αβ A o A r cos(φγ)= H 2 (α A o 2 +β A r 2 )
H v1 = A o 2 + A r 2 2 A o A r cosϕ=2( A o 2 + A r 2 ) H 1
H v2 =α A o 2 +β A r 2 2 αβ A o A r cos(ϕγ)=2(α A o 2 +β A r 2 ) H 2
A o exp(iϕ)= A o cosϕ+i A o sinϕ = H 1 H v1 4 A r +i ( H 2 H v2 ) αβ cosγ( H 1 H v1 ) 4 αβ A r sinγ
RMSE= 1 N x N y i=0 N x 1 j=0 N y 1 ( ϕ ij ϕ ^ ij ) 2
δ= 2π λ λ s 2 2π λ λ s 4 = λ s λ π 2

Metrics