Abstract

To obtain a phase distribution without the use of an optical path besides an object beam, a reference-free holographic diversity interferometry (RF-HDI) has been proposed. Although the RF-HDI can generate an internal reference beam from the object beam, the method has a problem of measurement accuracy due to insufficient power of the internal reference beam. To solve the problem, we newly propose a RF-HDI via iterative measurements. Our method improves the measurement accuracy by utilizing iterative measurements and feedback of each obtained phase image to the measurement system. In the experiment, the phase image, which has a random pattern, can be measured as an object beam with a higher accuracy than in the conventional RF-HDI. To support this result, we also evaluated the wavefront accuracy and optical power efficiency of an internal reference beam in this method. As a result, we verified that our method enables us to generate an internal reference beam that has the wavefront of a near single plane wave and a higher power efficiency than the conventional RF-HDI. In addition, our method can be applied to measurement for the modal content in an optical fiber, atmosphere turbulence, etc., where it is difficult to prepare an external reference beam with a high coherency.

© 2016 Optical Society of America

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References

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    [Crossref] [PubMed]

2016 (2)

D. R. Gray, M. N. Petrovich, S. RezaSandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-Time Modal Analysis via Wavelength-Swept Spatial and Spectral (S2) Imaging,” IEEE Photon. Technol. Lett. 28(9), 1034–1037 (2016).

T. D. Bradley, N. V. Wheeler, G. T. Jasion, D. Gray, J. Hayes, M. AlonsoGouveia, S. R. Sandoghchi, Y. Chen, F. Poletti, D. Richardson, and M. Petrovich, “Modal content in hypocycloid Kagomé hollow core photonic crystal fibers,” Opt. Express 24(14), 15798–15812 (2016).
[Crossref] [PubMed]

2015 (1)

2014 (2)

R. Schubert, A. Vollmer, S. Ketelhut, and B. Kemper, “Enhanced quantitative phase imaging in self-interference digital holographic microscopy using an electrically focus tunable lens,” Biomed. Opt. Express 5(12), 4213–4222 (2014).
[Crossref]

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

2013 (1)

W. Liu, W. Shi, B. Wang, K. Yao, Y. Lv, and J. Wang, “Free space optical communication performance analysis with focal plane based wavefront measurement,” Opt. Commun. 309(15), 212–220 (2013).
[Crossref]

2012 (4)

2011 (3)

2010 (3)

2009 (2)

2008 (2)

2006 (3)

2004 (1)

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

2002 (2)

J. H. Massig, “Digital off-axis holography with a synthetic aperture,” Opt. Lett. 17(24), 2179–2181 (2002).
[Crossref]

M. K. Kim, “Adaptive optics by incoherent digital holography,” Appl. Opt. 37(13), 2694–2696 (2002).

2001 (1)

1998 (1)

1997 (1)

1989 (1)

1971 (1)

T. S. Huang, “Digital holography,” Proc. IEEE 59(9), 1335–1346 (1971).
[Crossref]

AlonsoGouveia, M.

Awatsuji, Y.

Baddela, N. K.

D. R. Gray, M. N. Petrovich, S. RezaSandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-Time Modal Analysis via Wavelength-Swept Spatial and Spectral (S2) Imaging,” IEEE Photon. Technol. Lett. 28(9), 1034–1037 (2016).

Bally, G.

B. Kemper, A. Vollmer, C. E. Rommel, J. Schnekenburger, and G. Bally, “Simplified approach for quantitative digital holographic phase contrast imaging of living cells,” J. Biomed. Opt. 16(2), 026014 (2011).
[Crossref] [PubMed]

Bally, G. V.

Barada, D.

Bon, P.

Bradley, T.

D. R. Gray, M. N. Petrovich, S. RezaSandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-Time Modal Analysis via Wavelength-Swept Spatial and Spectral (S2) Imaging,” IEEE Photon. Technol. Lett. 28(9), 1034–1037 (2016).

Bradley, T. D.

Bunsen, M.

T. Maeda, A. Okamoto, A. Tomita, Y. Hirasaki, Y. Wakayama, and M. Bunsen, “Holographic-Diversity Interferometry for Reference-Free Phase Detection,” in 2013 Conference on Lasers and Electro-Optics Pacific Rim, (Optical Society of America, 2013), paper WF4_4 (2013).

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Chen, Y.

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De Nicola, S.

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Ding, H.

Druon, F.

Farahi, S.

Feld, M. S.

Ferraro, P.

Finizio, A.

Fujii, M.

Georges, P.

Gillette, M. U.

Gray, D.

Gray, D. R.

D. R. Gray, M. N. Petrovich, S. RezaSandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-Time Modal Analysis via Wavelength-Swept Spatial and Spectral (S2) Imaging,” IEEE Photon. Technol. Lett. 28(9), 1034–1037 (2016).

Grilli, S.

Hanna, M.

Hayes, J.

Hirasaki, Y.

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

T. Maeda, A. Okamoto, A. Tomita, Y. Hirasaki, Y. Wakayama, and M. Bunsen, “Holographic-Diversity Interferometry for Reference-Free Phase Detection,” in 2013 Conference on Lasers and Electro-Optics Pacific Rim, (Optical Society of America, 2013), paper WF4_4 (2013).

Huang, T. S.

T. S. Huang, “Digital holography,” Proc. IEEE 59(9), 1335–1346 (1971).
[Crossref]

Ida, T.

Ikeda, T.

Ito, K.

Jasion, G. T.

T. D. Bradley, N. V. Wheeler, G. T. Jasion, D. Gray, J. Hayes, M. AlonsoGouveia, S. R. Sandoghchi, Y. Chen, F. Poletti, D. Richardson, and M. Petrovich, “Modal content in hypocycloid Kagomé hollow core photonic crystal fibers,” Opt. Express 24(14), 15798–15812 (2016).
[Crossref] [PubMed]

D. R. Gray, M. N. Petrovich, S. RezaSandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-Time Modal Analysis via Wavelength-Swept Spatial and Spectral (S2) Imaging,” IEEE Photon. Technol. Lett. 28(9), 1034–1037 (2016).

Kakue, T.

Kaneko, A.

Kemper, B.

Ketelhut, S.

Kiire, T.

Kikuchi, Y.

Kim, M. K.

M. K. Kim, “Adaptive optics by incoherent digital holography,” Appl. Opt. 37(13), 2694–2696 (2002).

M. K. Kim, Digital Holographic Microscopy Principles, Techniques, and Applications(Springer, 2011), Chap. 8.
[Crossref]

Koyama, T.

Kubota, T.

Kunori, K.

Lévèque, L.

Lin, M.

Liu, J. P.

Liu, W.

W. Liu, W. Shi, B. Wang, K. Yao, Y. Lv, and J. Wang, “Free space optical communication performance analysis with focal plane based wavefront measurement,” Opt. Commun. 309(15), 212–220 (2013).
[Crossref]

Lv, Y.

W. Liu, W. Shi, B. Wang, K. Yao, Y. Lv, and J. Wang, “Free space optical communication performance analysis with focal plane based wavefront measurement,” Opt. Commun. 309(15), 212–220 (2013).
[Crossref]

Maeda, T.

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

T. Maeda, A. Okamoto, A. Tomita, Y. Hirasaki, Y. Wakayama, and M. Bunsen, “Holographic-Diversity Interferometry for Reference-Free Phase Detection,” in 2013 Conference on Lasers and Electro-Optics Pacific Rim, (Optical Society of America, 2013), paper WF4_4 (2013).

Massig, J. H.

J. H. Massig, “Digital off-axis holography with a synthetic aperture,” Opt. Lett. 17(24), 2179–2181 (2002).
[Crossref]

Matoba, O.

Maucort, G.

Meucci, R.

Millet, L.

Mir, M.

Monneret, S.

Moser, C.

Murata, S.

Murphy, K.

Nishio, K.

Nitanai, E.

Nitta, K.

Nomura, T.

Nozawa, J.

Numata, T.

Okamoto, 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. Tomita, and K. Sato, “Progressive phase conjugation and its application in reconfigurable spatial-mode extraction and conversion,” Proc. SPIE 9130, 913012 (2014).
[Crossref]

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]

T. Maeda, A. Okamoto, A. Tomita, Y. Hirasaki, Y. Wakayama, and M. Bunsen, “Holographic-Diversity Interferometry for Reference-Free Phase Detection,” in 2013 Conference on Lasers and Electro-Optics Pacific Rim, (Optical Society of America, 2013), paper WF4_4 (2013).

Papadopoulos, I. N.

Paurisse, M.

Petrovich, M.

Petrovich, M. N.

D. R. Gray, M. N. Petrovich, S. RezaSandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-Time Modal Analysis via Wavelength-Swept Spatial and Spectral (S2) Imaging,” IEEE Photon. Technol. Lett. 28(9), 1034–1037 (2016).

Pierattini, G.

Poletti, F.

D. R. Gray, M. N. Petrovich, S. RezaSandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-Time Modal Analysis via Wavelength-Swept Spatial and Spectral (S2) Imaging,” IEEE Photon. Technol. Lett. 28(9), 1034–1037 (2016).

T. D. Bradley, N. V. Wheeler, G. T. Jasion, D. Gray, J. Hayes, M. AlonsoGouveia, S. R. Sandoghchi, Y. Chen, F. Poletti, D. Richardson, and M. Petrovich, “Modal content in hypocycloid Kagomé hollow core photonic crystal fibers,” Opt. Express 24(14), 15798–15812 (2016).
[Crossref] [PubMed]

Poon, T. C.

Popescu, G.

Psaltis, D.

RezaSandoghchi, S.

D. R. Gray, M. N. Petrovich, S. RezaSandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-Time Modal Analysis via Wavelength-Swept Spatial and Spectral (S2) Imaging,” IEEE Photon. Technol. Lett. 28(9), 1034–1037 (2016).

Richardson, D.

Richardson, D. J.

D. R. Gray, M. N. Petrovich, S. RezaSandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-Time Modal Analysis via Wavelength-Swept Spatial and Spectral (S2) Imaging,” IEEE Photon. Technol. Lett. 28(9), 1034–1037 (2016).

Rogers, J.

Rommel, C. E.

B. Kemper, A. Vollmer, C. E. Rommel, J. Schnekenburger, and G. Bally, “Simplified approach for quantitative digital holographic phase contrast imaging of living cells,” J. Biomed. Opt. 16(2), 026014 (2011).
[Crossref] [PubMed]

Sandoghchi, S. R.

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.

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

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]

Schnekenburger, J.

B. Kemper, A. Vollmer, C. E. Rommel, J. Schnekenburger, and G. Bally, “Simplified approach for quantitative digital holographic phase contrast imaging of living cells,” J. Biomed. Opt. 16(2), 026014 (2011).
[Crossref] [PubMed]

Schubert, R.

Schwider, J.

Shaked, N. T.

Shi, W.

W. Liu, W. Shi, B. Wang, K. Yao, Y. Lv, and J. Wang, “Free space optical communication performance analysis with focal plane based wavefront measurement,” Opt. Commun. 309(15), 212–220 (2013).
[Crossref]

Shibukawa, A.

Shimozato, Y.

Tahara, T.

Takabayashi, M.

Tomita, 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. Tomita, and K. Sato, “Progressive phase conjugation and its application in reconfigurable spatial-mode extraction and conversion,” Proc. SPIE 9130, 913012 (2014).
[Crossref]

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]

T. Maeda, A. Okamoto, A. Tomita, Y. Hirasaki, Y. Wakayama, and M. Bunsen, “Holographic-Diversity Interferometry for Reference-Free Phase Detection,” in 2013 Conference on Lasers and Electro-Optics Pacific Rim, (Optical Society of America, 2013), paper WF4_4 (2013).

Unarunotai, S.

Ura, S.

Vollmer, A.

R. Schubert, A. Vollmer, S. Ketelhut, and B. Kemper, “Enhanced quantitative phase imaging in self-interference digital holographic microscopy using an electrically focus tunable lens,” Biomed. Opt. Express 5(12), 4213–4222 (2014).
[Crossref]

B. Kemper, A. Vollmer, C. E. Rommel, J. Schnekenburger, and G. Bally, “Simplified approach for quantitative digital holographic phase contrast imaging of living cells,” J. Biomed. Opt. 16(2), 026014 (2011).
[Crossref] [PubMed]

Wakayama, Y.

T. Maeda, A. Okamoto, A. Tomita, Y. Hirasaki, Y. Wakayama, and M. Bunsen, “Holographic-Diversity Interferometry for Reference-Free Phase Detection,” in 2013 Conference on Lasers and Electro-Optics Pacific Rim, (Optical Society of America, 2013), paper WF4_4 (2013).

Wang, B.

W. Liu, W. Shi, B. Wang, K. Yao, Y. Lv, and J. Wang, “Free space optical communication performance analysis with focal plane based wavefront measurement,” Opt. Commun. 309(15), 212–220 (2013).
[Crossref]

Wang, J.

W. Liu, W. Shi, B. Wang, K. Yao, Y. Lv, and J. Wang, “Free space optical communication performance analysis with focal plane based wavefront measurement,” Opt. Commun. 309(15), 212–220 (2013).
[Crossref]

Wang, Z.

Wattellier, B.

Wheeler, N. V.

T. D. Bradley, N. V. Wheeler, G. T. Jasion, D. Gray, J. Hayes, M. AlonsoGouveia, S. R. Sandoghchi, Y. Chen, F. Poletti, D. Richardson, and M. Petrovich, “Modal content in hypocycloid Kagomé hollow core photonic crystal fibers,” Opt. Express 24(14), 15798–15812 (2016).
[Crossref] [PubMed]

D. R. Gray, M. N. Petrovich, S. RezaSandoghchi, N. V. Wheeler, N. K. Baddela, G. T. Jasion, T. Bradley, D. J. Richardson, and F. Poletti, “Real-Time Modal Analysis via Wavelength-Swept Spatial and Spectral (S2) Imaging,” IEEE Photon. Technol. Lett. 28(9), 1034–1037 (2016).

Yamaguchi, I.

Yamashita, K.

Yao, K.

W. Liu, W. Shi, B. Wang, K. Yao, Y. Lv, and J. Wang, “Free space optical communication performance analysis with focal plane based wavefront measurement,” Opt. Commun. 309(15), 212–220 (2013).
[Crossref]

Yatagai, T.

Yokota, M.

Zhang, T.

Appl. Opt. (8)

J. Schwider, “Phase shifting interferometry: reference phase error reduction,” Appl. Opt. 28(18), 3889–3892 (1989).
[Crossref] [PubMed]

M. Lin, K. Nitta, O. Matoba, and Y. Awatsuji, “Parallel phase-shifting digital holography with adaptive function using phase-mode spatial light modulator,” Appl. Opt. 51(14), 2633–2637 (2012).
[Crossref] [PubMed]

M. K. Kim, “Adaptive optics by incoherent digital holography,” Appl. Opt. 37(13), 2694–2696 (2002).

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]

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Figures (7)

Fig. 1
Fig. 1 Schematic diagram of our method; PSLM: phase-type spatial light modulator, and HDI: holographic diversity interferometry, which is a phase-shifting digital holography technique developed in our laboratory. A beam to be measured is divided into two optical paths using a beam splitter; one is used for the object beam, and the other is used for the internal reference beam. In the path of the internal reference beam, a component of a single plane wave (DC-component) is extracted using a spatial filter and a PSLM. Then, by iterative measurements and feedback of each measured image to the internal reference beam through the PSLM, our method obtains a phase image with a high power efficiency and high measurement accuracy without an additional optical path for the reference beam.
Fig. 2
Fig. 2 Experimental setup. L1–L9: lens, BS1, BS2: beam splitter, PBS1–PBS3: polarizing BS, HWP1, HWP2: half wave plate, QWP: quarter wave plate, PSLM: phase-type LCOS SLM (Hamamatsu, x12222-01, 800×600 pixels, pixel size 20μm×20μm and the gray-level for the 2π modulation is 157), OPM: optical power meter (Advantest, TQ8210, Sensor size 10mm × 10mm), ISLM: intensity-type LCOS SLM (HOLOEYE, LC-R 1080, 1920 × 1200 pixels, pixel size 8.1μm × 8.1μm), CCD1, CCD2: charge coupled device (Allied Vision Technology, Stingray, F125B, 1280 × 960 pixels, pixel size 3.75μm × 3.75μm).
Fig. 3
Fig. 3 Original phase distribution of the input object beam: (a) a random phase distribution, including 0 and π; (b) the Lenna image.
Fig. 4
Fig. 4 SNRs for each iterative measurement when the (a) random phase and (b) Lenna image are measured.
Fig. 5
Fig. 5 Histograms of the internal reference beam: (a) conventional RF-HDI; (b) our method for 5 iterations.
Fig. 6
Fig. 6 Intensity distribution at the pinhole plane (measured by CCD3): (a) without feedback, (b) 1st feedback, (c) 2nd feedback, (d) 3rd feedback, (e) 4th feedback, (f) 5th feedback, (g) absolute DC-component, and (h) the intensity profile at y = 0.0 μm when the absolute DC-component and 5th feedback image are displayed on the PSLM.
Fig. 7
Fig. 7 Optical power of the internal reference beam passing through the pinhole when each feedback image is displayed on PSLM.

Tables (3)

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Table 1 Feedback images displayed on PSLM, and phase images obtained by 2ch-HDI for each iterative measurement when a random phase distribution as shown in Fig 3(a) is measured.

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Table 2 Feedback and obtained images for each iterative measurement when the Lenna image as shown in Fig 3(b) is measured.

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Table 3 Intensity distribution captured by CCD1 and the phase distribution calculated from the intensity distributions.

Equations (6)

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E ( r ) = A ( r ) exp [ i ϕ ( r ) ] .
R ( r ) E ( r ) = A ( r ) exp [ i ϕ ( r ) ] .
R ν ( r ) = A ν ( r ) exp [ i ϕ ν ( r ) ] ,
U ( r ) A ( r ) exp [ i { ϕ ( r ) ϕ ν ( r ) } ] .
R ( r ) = A ( r ) exp [ i { ϕ ( r ) ϕ ( r ) + ϕ ν ( r ) } ] = A ( r ) exp [ i ϕ ν ( r ) ] .
S N R ( dB ) = 10 × log 10 i = 1 N x j = 1 N y S ( i , j ) 2 i = 1 N x j = 1 N y { S ( i , j ) R ( i , j ) } 2 ,

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