Abstract

Recent development of parallel phase-shifting interferometry (PPSI) enables accurate measurement of time-varying phase maps. By combining a high-speed camera with PPSI, it became possible to observe not only time-varying but also fast phenomena including fluid flow and sound in air. In such observation, one has to remove static phase (time-invariant or slowly-varying phase unrelated to the phenomena of interest) from the observed phase maps. Ordinarily, a signal processing method for eliminating the static phase is utilized after phase unwrapping to avoid the 2π discontinuity which can be a source of error. In this paper, it is shown that such phase unwrapping is not necessary for the high-speed observation, and a time-directional filtering method is proposed for removing the static phase directly from the wrapped phase without performing phase unwrapping. In addition, experimental results of simultaneously visualizing flow and sound with 42 000 fps are shown to illustrate how the time-directional filtering changes the appearance. A MATLAB code is included within the paper (also in https://goo.gl/N4wzdp) for aiding the understanding of the proposed method.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (2)

B.-C. Cui, J.-L. Wang, K.-N. Yao, and T. Chen, “Measurement of high-dynamic temperature field using high-speed quadriwave lateral shearing interferometer,” Optoelectron. Lett. 14, 124–128 (2018).
[Crossref]

K. Ishikawa, R. Tanigawa, K. Yatabe, Y. Oikawa, T. Onuma, and H. Niwa, “Simultaneous imaging of flow and sound using high-speed parallel phase-shifting interferometry,” Opt. Lett. 43, 991–994 (2018).
[Crossref] [PubMed]

2017 (9)

K. Yatabe, K. Ishikawa, and Y. Oikawa, “Simple, flexible, and accurate phase retrieval method for generalized phase-shifting interferometry,” J. Opt. Soc. Am. A 34, 87–96 (2017).
[Crossref]

M. Ney, A. Safrani, and I. Abdulhalim, “Three wavelengths parallel phase-shift interferometry for real-time focus tracking and vibration measurement,” Opt. Lett. 42, 719–722 (2017).
[Crossref] [PubMed]

J. S. Pérez-Huerta, T. Saucedo-Anaya, I. Moreno, D. Ariza-Flores, and B. Saucedo-Orozco, “Digital holographic interferometry applied to the investigation of ignition process,” Opt. Express 25, 13190–13198 (2017).
[Crossref] [PubMed]

T. Fukuda, Y. Wang, P. Xia, Y. Awatsuji, T. Kakue, K. Nishio, and O. Matoba, “Three-dimensional imaging of distribution of refractive index by parallel phase-shifting digital holography using Abel inversion,” Opt. Express 25, 18066–18071 (2017).
[Crossref] [PubMed]

K. Yatabe, K. Ishikawa, and Y. Oikawa, “Hyper ellipse fitting in subspace method for phase-shifting interferometry: practical implementation with automatic pixel selection,” Opt. Express 25, 29401–29416 (2017).
[Crossref]

T. Kakue, Y. Endo, T. Nishitsuji, T. Shimobaba, N. Masuda, and T. Ito, “Digital holographic high-speed 3D imaging for the vibrometry of fast-occurring phenomena,” Sci. Rep. 7, 10413 (2017).
[Crossref] [PubMed]

K. Ishikawa, K. Yatabe, Y. Ikeda, Y. Oikawa, T. Onuma, H. Niwa, and M. Yoshii, “Interferometric imaging of acoustical phenomena using high-speed polarization camera and 4-step parallel phase-shifting technique,” Proc. SPIE 10328, 103280I (2017).

N. Chitanont, K. Yatabe, K. Ishikawa, and Y. Oikawa, “Spatio-temporal filter bank for visualizing audible sound field by schlieren method,” Appl. Acoust. 115, 109–120 (2017).
[Crossref]

K. Yatabe, K. Ishikawa, and Y. Oikawa, “Acousto-optic back-projection: Physical-model-based sound field reconstruction from optical projections,” J. Sound Vib. 394, 171–184 (2017).
[Crossref]

2016 (4)

2015 (5)

T. Yatagai, B. J. Jackin, A. Ono, K. Kiyohara, M. Noguchi, M. Yoshii, M. Kiyohara, H. Niwa, K. Ikuo, and T. Onuma, “Instantaneous phase-shifting fizeau interferometry with high-speed pixelated phase-mask camera,” Proc. SPIE 9660, 966018 (2015).

A. Safrani and I. Abdulhalim, “Full-field parallel interferometry coherence probe microscope for high-speed optical metrology,” Appl. Opt. 54, 5083–5087 (2015).
[Crossref] [PubMed]

E. Shoji, A. Komiya, J. Okajima, H. Kawamura, and S. Maruyama, “High-speed phase-shifting interferometry using triangular prism for time-resolved temperature measurement,” Appl. Opt. 54, 6297–6304 (2015).
[Crossref] [PubMed]

K. Yatabe and Y. Oikawa, “Optically visualized sound field reconstruction using Kirchhoff–Helmholtz equation,” Acoust. Sci. Tech. 36, 351–354 (2015).
[Crossref]

E. Shoji, R. Nakaoku, A. Komiya, J. Okajima, and S. Maruyama, “Quantitative visualization of boundary layers by developing quasi-common-path phase-shifting interferometer,” Exp. Therm. Fluid Sci. 60, 231–240 (2015).
[Crossref]

2014 (4)

P. Xia, Y. Awatsuji, K. Nishio, and O. Matoba, “One million fps digital holography,” Electron. Lett. 50, 1693–1695 (2014).
[Crossref]

D. I. Serrano-García, A. Martínez-García, N.-I. Toto-Arellano, and Y. Otani, “Dynamic temperature field measurements using a polarization phase-shifting technique,” Opt. Eng. 53, 112202 (2014).
[Crossref]

T. Onuma and Y. Otani, “A development of two-dimensional birefringence distribution measurement system with a sampling rate of 1.3 MHz,” Opt. Commun. 315, 69–73 (2014).
[Crossref]

O. Matoba, H. Inokuchi, K. Nitta, and Y. Awatsuji, “Optical voice recorder by off-axis digital holography,” Opt. Lett. 39, 6549–6552 (2014).
[Crossref] [PubMed]

2013 (1)

T. Aratani, T. Inage, Y. Miwa, M. Ota, and K. Maeno, “Application of high-speed camera to 4D-CT density measurement of unsteady shock-vortex flow discharged from two inclined and cylindrical holes,” J. JSEM 13, s64–s68 (2013).

2012 (1)

2011 (1)

2010 (2)

2009 (2)

2008 (2)

2007 (1)

S. Suzuki, K. Sakaue, and K. Iwanaga, “Measurement of energy release rate and energy flux of rapidly bifurcating crack in homalite 100 and Araldite B by high-speed holographic microscopy,” J. Mech. Phys. Solids 55, 1487–1512 (2007).
[Crossref]

2006 (2)

J.-M. Desse, “Recent contribution in color interferometry and applications to high-speed flows,” Opt. Lasers Eng. 44, 304–320 (2006).
[Crossref]

G. Pedrini, W. Osten, and M. E. Gusev, “High-speed digital holographic interferometry for vibration measurement,” Appl. Opt. 45, 3456–3462 (2006).
[Crossref] [PubMed]

2005 (2)

M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Appl. Opt. 44, 6861–6868 (2005).
[Crossref] [PubMed]

Q. Kemao, S. H. Soon, and A. Asundi, “A simple phase unwrapping approach based on filtering by windowed fourier transform,” Opt. Laser Technol. 37, 458–462 (2005).
[Crossref]

2004 (2)

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

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

2003 (1)

2001 (1)

H. S. Ko, K. Okamoto, and H. Madarame, “Reconstruction of transient three-dimensional density distributions using digital speckle tomography,” Meas. Sci. Technol. 12, 1219 (2001).
[Crossref]

2000 (2)

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng. 39, 960–966 (2000).
[Crossref]

S.-H. Baik, S.-K. Park, C.-J. Kim, and S.-Y. Kim, “Shockwave visualization using holographic interferometer,” Opt. Rev. 7, 535–542 (2000).
[Crossref]

1982 (1)

Abdulhalim, I.

Aguayo, D. D.

Alessio, S. M.

S. M. Alessio, Digital Signal Processing and Spectral Analysis for Scientists: Concepts and Applications (Springer, 2016).

Alexeenko, I.

Aratani, T.

T. Aratani, T. Inage, Y. Miwa, M. Ota, and K. Maeno, “Application of high-speed camera to 4D-CT density measurement of unsteady shock-vortex flow discharged from two inclined and cylindrical holes,” J. JSEM 13, s64–s68 (2013).

Ariza-Flores, D.

Asundi, A.

Q. Kemao, S. H. Soon, and A. Asundi, “A simple phase unwrapping approach based on filtering by windowed fourier transform,” Opt. Laser Technol. 37, 458–462 (2005).
[Crossref]

Awatsuji, Y.

Baik, S.-H.

S.-H. Baik, S.-K. Park, C.-J. Kim, and S.-Y. Kim, “Shockwave visualization using holographic interferometer,” Opt. Rev. 7, 535–542 (2000).
[Crossref]

Bon, P.

Brock, N.

Brock, N. J.

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

Caloca-Mendez, C.

Chen, T.

B.-C. Cui, J.-L. Wang, K.-N. Yao, and T. Chen, “Measurement of high-dynamic temperature field using high-speed quadriwave lateral shearing interferometer,” Optoelectron. Lett. 14, 124–128 (2018).
[Crossref]

Chitanont, N.

N. Chitanont, K. Yatabe, K. Ishikawa, and Y. Oikawa, “Spatio-temporal filter bank for visualizing audible sound field by schlieren method,” Appl. Acoust. 115, 109–120 (2017).
[Crossref]

K. Ishikawa, K. Yatabe, N. Chitanont, Y. Ikeda, Y. Oikawa, T. Onuma, H. Niwa, and M. Yoshii, “High-speed imaging of sound using parallel phase-shifting interferometry,” Opt. Express 24, 12922–12932 (2016).
[Crossref] [PubMed]

N. Chitanont, K. Yaginuma, K. Yatabe, and Y. Oikawa, “Visualization of sound field by means of Schlieren method with spatio-temporal filtering,” in “IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP),” (2015), pp. 509–513.

Cui, B.-C.

B.-C. Cui, J.-L. Wang, K.-N. Yao, and T. Chen, “Measurement of high-dynamic temperature field using high-speed quadriwave lateral shearing interferometer,” Optoelectron. Lett. 14, 124–128 (2018).
[Crossref]

del Socorro Hernández-Montes, M.

Desse, J.-M.

J.-M. Desse, “Recent contribution in color interferometry and applications to high-speed flows,” Opt. Lasers Eng. 44, 304–320 (2006).
[Crossref]

Di, J.

Endo, Y.

T. Kakue, Y. Endo, T. Nishitsuji, T. Shimobaba, N. Masuda, and T. Ito, “Digital holographic high-speed 3D imaging for the vibrometry of fast-occurring phenomena,” Sci. Rep. 7, 10413 (2017).
[Crossref] [PubMed]

Fujii, M.

Fukuda, T.

Gao, W.

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (Wiley, 1998).

Gusev, M. E.

Hayes, J.

Hayes, J. B.

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

Hernandez, D. A. G.

Hettwer, A.

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng. 39, 960–966 (2000).
[Crossref]

Hruschka, R.

Hussain, Z. M.

P. O’Shea, A. Z. Sadik, and Z. M. Hussain, Digital Signal Processing: An Introduction with MATLAB and Applications (Springer, 2011).
[Crossref]

Ikeda, Y.

K. Ishikawa, K. Yatabe, Y. Ikeda, Y. Oikawa, T. Onuma, H. Niwa, and M. Yoshii, “Interferometric imaging of acoustical phenomena using high-speed polarization camera and 4-step parallel phase-shifting technique,” Proc. SPIE 10328, 103280I (2017).

K. Ishikawa, K. Yatabe, N. Chitanont, Y. Ikeda, Y. Oikawa, T. Onuma, H. Niwa, and M. Yoshii, “High-speed imaging of sound using parallel phase-shifting interferometry,” Opt. Express 24, 12922–12932 (2016).
[Crossref] [PubMed]

Y. Oikawa, K. Yatabe, K. Ishikawa, and Y. Ikeda, “Optical sound field measurement and imaging using laser and high-speed camera,” in “Proc. 45th Int. Congr. Noise Control Eng. (INTER-NOISE 2016),” (2016), pp. 258–266.

Ikuo, K.

T. Yatagai, B. J. Jackin, A. Ono, K. Kiyohara, M. Noguchi, M. Yoshii, M. Kiyohara, H. Niwa, K. Ikuo, and T. Onuma, “Instantaneous phase-shifting fizeau interferometry with high-speed pixelated phase-mask camera,” Proc. SPIE 9660, 966018 (2015).

Inage, T.

T. Aratani, T. Inage, Y. Miwa, M. Ota, and K. Maeno, “Application of high-speed camera to 4D-CT density measurement of unsteady shock-vortex flow discharged from two inclined and cylindrical holes,” J. JSEM 13, s64–s68 (2013).

Inokuchi, H.

Ishikawa, K.

K. Ishikawa, R. Tanigawa, K. Yatabe, Y. Oikawa, T. Onuma, and H. Niwa, “Simultaneous imaging of flow and sound using high-speed parallel phase-shifting interferometry,” Opt. Lett. 43, 991–994 (2018).
[Crossref] [PubMed]

K. Yatabe, K. Ishikawa, and Y. Oikawa, “Hyper ellipse fitting in subspace method for phase-shifting interferometry: practical implementation with automatic pixel selection,” Opt. Express 25, 29401–29416 (2017).
[Crossref]

K. Yatabe, K. Ishikawa, and Y. Oikawa, “Simple, flexible, and accurate phase retrieval method for generalized phase-shifting interferometry,” J. Opt. Soc. Am. A 34, 87–96 (2017).
[Crossref]

K. Ishikawa, K. Yatabe, Y. Ikeda, Y. Oikawa, T. Onuma, H. Niwa, and M. Yoshii, “Interferometric imaging of acoustical phenomena using high-speed polarization camera and 4-step parallel phase-shifting technique,” Proc. SPIE 10328, 103280I (2017).

N. Chitanont, K. Yatabe, K. Ishikawa, and Y. Oikawa, “Spatio-temporal filter bank for visualizing audible sound field by schlieren method,” Appl. Acoust. 115, 109–120 (2017).
[Crossref]

K. Yatabe, K. Ishikawa, and Y. Oikawa, “Acousto-optic back-projection: Physical-model-based sound field reconstruction from optical projections,” J. Sound Vib. 394, 171–184 (2017).
[Crossref]

K. Yatabe, K. Ishikawa, and Y. Oikawa, “Compensation of fringe distortion for phase-shifting three-dimensional shape measurement by inverse map estimation,” Appl. Opt. 55, 6017–6024 (2016).
[Crossref] [PubMed]

K. Yatabe, K. Ishikawa, and Y. Oikawa, “Improving principal component analysis based phase extraction method for phase-shifting interferometry by integrating spatial information,” Opt. Express 24, 22881–22891 (2016).
[Crossref] [PubMed]

K. Ishikawa, K. Yatabe, N. Chitanont, Y. Ikeda, Y. Oikawa, T. Onuma, H. Niwa, and M. Yoshii, “High-speed imaging of sound using parallel phase-shifting interferometry,” Opt. Express 24, 12922–12932 (2016).
[Crossref] [PubMed]

Y. Oikawa, K. Yatabe, K. Ishikawa, and Y. Ikeda, “Optical sound field measurement and imaging using laser and high-speed camera,” in “Proc. 45th Int. Congr. Noise Control Eng. (INTER-NOISE 2016),” (2016), pp. 258–266.

Ito, K.

Ito, T.

T. Kakue, Y. Endo, T. Nishitsuji, T. Shimobaba, N. Masuda, and T. Ito, “Digital holographic high-speed 3D imaging for the vibrometry of fast-occurring phenomena,” Sci. Rep. 7, 10413 (2017).
[Crossref] [PubMed]

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Iwanaga, K.

S. Suzuki, K. Sakaue, and K. Iwanaga, “Measurement of energy release rate and energy flux of rapidly bifurcating crack in homalite 100 and Araldite B by high-speed holographic microscopy,” J. Mech. Phys. Solids 55, 1487–1512 (2007).
[Crossref]

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T. Yatagai, B. J. Jackin, A. Ono, K. Kiyohara, M. Noguchi, M. Yoshii, M. Kiyohara, H. Niwa, K. Ikuo, and T. Onuma, “Instantaneous phase-shifting fizeau interferometry with high-speed pixelated phase-mask camera,” Proc. SPIE 9660, 966018 (2015).

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Q. Kemao, S. H. Soon, and A. Asundi, “A simple phase unwrapping approach based on filtering by windowed fourier transform,” Opt. Laser Technol. 37, 458–462 (2005).
[Crossref]

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S.-H. Baik, S.-K. Park, C.-J. Kim, and S.-Y. Kim, “Shockwave visualization using holographic interferometer,” Opt. Rev. 7, 535–542 (2000).
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S.-H. Baik, S.-K. Park, C.-J. Kim, and S.-Y. Kim, “Shockwave visualization using holographic interferometer,” Opt. Rev. 7, 535–542 (2000).
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Kiyohara, M.

T. Yatagai, B. J. Jackin, A. Ono, K. Kiyohara, M. Noguchi, M. Yoshii, M. Kiyohara, H. Niwa, K. Ikuo, and T. Onuma, “Instantaneous phase-shifting fizeau interferometry with high-speed pixelated phase-mask camera,” Proc. SPIE 9660, 966018 (2015).

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E. Shoji, A. Komiya, J. Okajima, H. Kawamura, and S. Maruyama, “High-speed phase-shifting interferometry using triangular prism for time-resolved temperature measurement,” Appl. Opt. 54, 6297–6304 (2015).
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A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng. 39, 960–966 (2000).
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T. Aratani, T. Inage, Y. Miwa, M. Ota, and K. Maeno, “Application of high-speed camera to 4D-CT density measurement of unsteady shock-vortex flow discharged from two inclined and cylindrical holes,” J. JSEM 13, s64–s68 (2013).

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D. I. Serrano-García, A. Martínez-García, N.-I. Toto-Arellano, and Y. Otani, “Dynamic temperature field measurements using a polarization phase-shifting technique,” Opt. Eng. 53, 112202 (2014).
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E. Shoji, R. Nakaoku, A. Komiya, J. Okajima, and S. Maruyama, “Quantitative visualization of boundary layers by developing quasi-common-path phase-shifting interferometer,” Exp. Therm. Fluid Sci. 60, 231–240 (2015).
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E. Shoji, A. Komiya, J. Okajima, H. Kawamura, and S. Maruyama, “High-speed phase-shifting interferometry using triangular prism for time-resolved temperature measurement,” Appl. Opt. 54, 6297–6304 (2015).
[Crossref] [PubMed]

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T. Kakue, Y. Endo, T. Nishitsuji, T. Shimobaba, N. Masuda, and T. Ito, “Digital holographic high-speed 3D imaging for the vibrometry of fast-occurring phenomena,” Sci. Rep. 7, 10413 (2017).
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T. Aratani, T. Inage, Y. Miwa, M. Ota, and K. Maeno, “Application of high-speed camera to 4D-CT density measurement of unsteady shock-vortex flow discharged from two inclined and cylindrical holes,” J. JSEM 13, s64–s68 (2013).

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E. Shoji, R. Nakaoku, A. Komiya, J. Okajima, and S. Maruyama, “Quantitative visualization of boundary layers by developing quasi-common-path phase-shifting interferometer,” Exp. Therm. Fluid Sci. 60, 231–240 (2015).
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T. Kakue, Y. Endo, T. Nishitsuji, T. Shimobaba, N. Masuda, and T. Ito, “Digital holographic high-speed 3D imaging for the vibrometry of fast-occurring phenomena,” Sci. Rep. 7, 10413 (2017).
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Niwa, H.

K. Ishikawa, R. Tanigawa, K. Yatabe, Y. Oikawa, T. Onuma, and H. Niwa, “Simultaneous imaging of flow and sound using high-speed parallel phase-shifting interferometry,” Opt. Lett. 43, 991–994 (2018).
[Crossref] [PubMed]

K. Ishikawa, K. Yatabe, Y. Ikeda, Y. Oikawa, T. Onuma, H. Niwa, and M. Yoshii, “Interferometric imaging of acoustical phenomena using high-speed polarization camera and 4-step parallel phase-shifting technique,” Proc. SPIE 10328, 103280I (2017).

K. Ishikawa, K. Yatabe, N. Chitanont, Y. Ikeda, Y. Oikawa, T. Onuma, H. Niwa, and M. Yoshii, “High-speed imaging of sound using parallel phase-shifting interferometry,” Opt. Express 24, 12922–12932 (2016).
[Crossref] [PubMed]

T. Yatagai, B. J. Jackin, A. Ono, K. Kiyohara, M. Noguchi, M. Yoshii, M. Kiyohara, H. Niwa, K. Ikuo, and T. Onuma, “Instantaneous phase-shifting fizeau interferometry with high-speed pixelated phase-mask camera,” Proc. SPIE 9660, 966018 (2015).

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T. Yatagai, B. J. Jackin, A. Ono, K. Kiyohara, M. Noguchi, M. Yoshii, M. Kiyohara, H. Niwa, K. Ikuo, and T. Onuma, “Instantaneous phase-shifting fizeau interferometry with high-speed pixelated phase-mask camera,” Proc. SPIE 9660, 966018 (2015).

North-Morris, M.

North-Morris, M. B.

J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
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J. E. Millerd, N. J. Brock, J. B. Hayes, M. B. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
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K. Ishikawa, R. Tanigawa, K. Yatabe, Y. Oikawa, T. Onuma, and H. Niwa, “Simultaneous imaging of flow and sound using high-speed parallel phase-shifting interferometry,” Opt. Lett. 43, 991–994 (2018).
[Crossref] [PubMed]

K. Yatabe, K. Ishikawa, and Y. Oikawa, “Hyper ellipse fitting in subspace method for phase-shifting interferometry: practical implementation with automatic pixel selection,” Opt. Express 25, 29401–29416 (2017).
[Crossref]

K. Yatabe, K. Ishikawa, and Y. Oikawa, “Simple, flexible, and accurate phase retrieval method for generalized phase-shifting interferometry,” J. Opt. Soc. Am. A 34, 87–96 (2017).
[Crossref]

K. Yatabe, K. Ishikawa, and Y. Oikawa, “Acousto-optic back-projection: Physical-model-based sound field reconstruction from optical projections,” J. Sound Vib. 394, 171–184 (2017).
[Crossref]

N. Chitanont, K. Yatabe, K. Ishikawa, and Y. Oikawa, “Spatio-temporal filter bank for visualizing audible sound field by schlieren method,” Appl. Acoust. 115, 109–120 (2017).
[Crossref]

K. Ishikawa, K. Yatabe, Y. Ikeda, Y. Oikawa, T. Onuma, H. Niwa, and M. Yoshii, “Interferometric imaging of acoustical phenomena using high-speed polarization camera and 4-step parallel phase-shifting technique,” Proc. SPIE 10328, 103280I (2017).

K. Yatabe, K. Ishikawa, and Y. Oikawa, “Improving principal component analysis based phase extraction method for phase-shifting interferometry by integrating spatial information,” Opt. Express 24, 22881–22891 (2016).
[Crossref] [PubMed]

K. Yatabe, K. Ishikawa, and Y. Oikawa, “Compensation of fringe distortion for phase-shifting three-dimensional shape measurement by inverse map estimation,” Appl. Opt. 55, 6017–6024 (2016).
[Crossref] [PubMed]

K. Yatabe and Y. Oikawa, “Convex optimization based windowed Fourier filtering with multiple windows for wrapped phase denoising,” Appl. Opt.,  55, 4632–4641 (2016).
[Crossref] [PubMed]

K. Ishikawa, K. Yatabe, N. Chitanont, Y. Ikeda, Y. Oikawa, T. Onuma, H. Niwa, and M. Yoshii, “High-speed imaging of sound using parallel phase-shifting interferometry,” Opt. Express 24, 12922–12932 (2016).
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K. Yatabe and Y. Oikawa, “Optically visualized sound field reconstruction using Kirchhoff–Helmholtz equation,” Acoust. Sci. Tech. 36, 351–354 (2015).
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N. Chitanont, K. Yaginuma, K. Yatabe, and Y. Oikawa, “Visualization of sound field by means of Schlieren method with spatio-temporal filtering,” in “IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP),” (2015), pp. 509–513.

K. Yatabe and Y. Oikawa, “PDE-based interpolation method for optically visualized sound field,” in “IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP),” (2014), pp. 4738–4742.

K. Yatabe and Y. Oikawa, “Optically visualized sound field reconstruction based on sparse selection of point sound sources,” in “IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP),” (2015), pp. 504–508.

Y. Oikawa, K. Yatabe, K. Ishikawa, and Y. Ikeda, “Optical sound field measurement and imaging using laser and high-speed camera,” in “Proc. 45th Int. Congr. Noise Control Eng. (INTER-NOISE 2016),” (2016), pp. 258–266.

Okajima, J.

E. Shoji, R. Nakaoku, A. Komiya, J. Okajima, and S. Maruyama, “Quantitative visualization of boundary layers by developing quasi-common-path phase-shifting interferometer,” Exp. Therm. Fluid Sci. 60, 231–240 (2015).
[Crossref]

E. Shoji, A. Komiya, J. Okajima, H. Kawamura, and S. Maruyama, “High-speed phase-shifting interferometry using triangular prism for time-resolved temperature measurement,” Appl. Opt. 54, 6297–6304 (2015).
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H. S. Ko, K. Okamoto, and H. Madarame, “Reconstruction of transient three-dimensional density distributions using digital speckle tomography,” Meas. Sci. Technol. 12, 1219 (2001).
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Onuma, T.

K. Ishikawa, R. Tanigawa, K. Yatabe, Y. Oikawa, T. Onuma, and H. Niwa, “Simultaneous imaging of flow and sound using high-speed parallel phase-shifting interferometry,” Opt. Lett. 43, 991–994 (2018).
[Crossref] [PubMed]

K. Ishikawa, K. Yatabe, Y. Ikeda, Y. Oikawa, T. Onuma, H. Niwa, and M. Yoshii, “Interferometric imaging of acoustical phenomena using high-speed polarization camera and 4-step parallel phase-shifting technique,” Proc. SPIE 10328, 103280I (2017).

K. Ishikawa, K. Yatabe, N. Chitanont, Y. Ikeda, Y. Oikawa, T. Onuma, H. Niwa, and M. Yoshii, “High-speed imaging of sound using parallel phase-shifting interferometry,” Opt. Express 24, 12922–12932 (2016).
[Crossref] [PubMed]

T. Yatagai, B. J. Jackin, A. Ono, K. Kiyohara, M. Noguchi, M. Yoshii, M. Kiyohara, H. Niwa, K. Ikuo, and T. Onuma, “Instantaneous phase-shifting fizeau interferometry with high-speed pixelated phase-mask camera,” Proc. SPIE 9660, 966018 (2015).

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S. Suzuki, K. Sakaue, and K. Iwanaga, “Measurement of energy release rate and energy flux of rapidly bifurcating crack in homalite 100 and Araldite B by high-speed holographic microscopy,” J. Mech. Phys. Solids 55, 1487–1512 (2007).
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D. I. Serrano-García, A. Martínez-García, N.-I. Toto-Arellano, and Y. Otani, “Dynamic temperature field measurements using a polarization phase-shifting technique,” Opt. Eng. 53, 112202 (2014).
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T. Kakue, Y. Endo, T. Nishitsuji, T. Shimobaba, N. Masuda, and T. Ito, “Digital holographic high-speed 3D imaging for the vibrometry of fast-occurring phenomena,” Sci. Rep. 7, 10413 (2017).
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E. Shoji, R. Nakaoku, A. Komiya, J. Okajima, and S. Maruyama, “Quantitative visualization of boundary layers by developing quasi-common-path phase-shifting interferometer,” Exp. Therm. Fluid Sci. 60, 231–240 (2015).
[Crossref]

E. Shoji, A. Komiya, J. Okajima, H. Kawamura, and S. Maruyama, “High-speed phase-shifting interferometry using triangular prism for time-resolved temperature measurement,” Appl. Opt. 54, 6297–6304 (2015).
[Crossref] [PubMed]

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Q. Kemao, S. H. Soon, and A. Asundi, “A simple phase unwrapping approach based on filtering by windowed fourier transform,” Opt. Laser Technol. 37, 458–462 (2005).
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S. Suzuki, K. Sakaue, and K. Iwanaga, “Measurement of energy release rate and energy flux of rapidly bifurcating crack in homalite 100 and Araldite B by high-speed holographic microscopy,” J. Mech. Phys. Solids 55, 1487–1512 (2007).
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D. I. Serrano-García, A. Martínez-García, N.-I. Toto-Arellano, and Y. Otani, “Dynamic temperature field measurements using a polarization phase-shifting technique,” Opt. Eng. 53, 112202 (2014).
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N. Chitanont, K. Yaginuma, K. Yatabe, and Y. Oikawa, “Visualization of sound field by means of Schlieren method with spatio-temporal filtering,” in “IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP),” (2015), pp. 509–513.

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K. Ishikawa, R. Tanigawa, K. Yatabe, Y. Oikawa, T. Onuma, and H. Niwa, “Simultaneous imaging of flow and sound using high-speed parallel phase-shifting interferometry,” Opt. Lett. 43, 991–994 (2018).
[Crossref] [PubMed]

K. Yatabe, K. Ishikawa, and Y. Oikawa, “Hyper ellipse fitting in subspace method for phase-shifting interferometry: practical implementation with automatic pixel selection,” Opt. Express 25, 29401–29416 (2017).
[Crossref]

K. Yatabe, K. Ishikawa, and Y. Oikawa, “Simple, flexible, and accurate phase retrieval method for generalized phase-shifting interferometry,” J. Opt. Soc. Am. A 34, 87–96 (2017).
[Crossref]

K. Ishikawa, K. Yatabe, Y. Ikeda, Y. Oikawa, T. Onuma, H. Niwa, and M. Yoshii, “Interferometric imaging of acoustical phenomena using high-speed polarization camera and 4-step parallel phase-shifting technique,” Proc. SPIE 10328, 103280I (2017).

N. Chitanont, K. Yatabe, K. Ishikawa, and Y. Oikawa, “Spatio-temporal filter bank for visualizing audible sound field by schlieren method,” Appl. Acoust. 115, 109–120 (2017).
[Crossref]

K. Yatabe, K. Ishikawa, and Y. Oikawa, “Acousto-optic back-projection: Physical-model-based sound field reconstruction from optical projections,” J. Sound Vib. 394, 171–184 (2017).
[Crossref]

K. Yatabe, K. Ishikawa, and Y. Oikawa, “Improving principal component analysis based phase extraction method for phase-shifting interferometry by integrating spatial information,” Opt. Express 24, 22881–22891 (2016).
[Crossref] [PubMed]

K. Yatabe and Y. Oikawa, “Convex optimization based windowed Fourier filtering with multiple windows for wrapped phase denoising,” Appl. Opt.,  55, 4632–4641 (2016).
[Crossref] [PubMed]

K. Yatabe, K. Ishikawa, and Y. Oikawa, “Compensation of fringe distortion for phase-shifting three-dimensional shape measurement by inverse map estimation,” Appl. Opt. 55, 6017–6024 (2016).
[Crossref] [PubMed]

K. Ishikawa, K. Yatabe, N. Chitanont, Y. Ikeda, Y. Oikawa, T. Onuma, H. Niwa, and M. Yoshii, “High-speed imaging of sound using parallel phase-shifting interferometry,” Opt. Express 24, 12922–12932 (2016).
[Crossref] [PubMed]

K. Yatabe and Y. Oikawa, “Optically visualized sound field reconstruction using Kirchhoff–Helmholtz equation,” Acoust. Sci. Tech. 36, 351–354 (2015).
[Crossref]

K. Yatabe and Y. Oikawa, “Optically visualized sound field reconstruction based on sparse selection of point sound sources,” in “IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP),” (2015), pp. 504–508.

K. Yatabe and Y. Oikawa, “PDE-based interpolation method for optically visualized sound field,” in “IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP),” (2014), pp. 4738–4742.

N. Chitanont, K. Yaginuma, K. Yatabe, and Y. Oikawa, “Visualization of sound field by means of Schlieren method with spatio-temporal filtering,” in “IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP),” (2015), pp. 509–513.

Y. Oikawa, K. Yatabe, K. Ishikawa, and Y. Ikeda, “Optical sound field measurement and imaging using laser and high-speed camera,” in “Proc. 45th Int. Congr. Noise Control Eng. (INTER-NOISE 2016),” (2016), pp. 258–266.

Yatagai, T.

T. Yatagai, B. J. Jackin, A. Ono, K. Kiyohara, M. Noguchi, M. Yoshii, M. Kiyohara, H. Niwa, K. Ikuo, and T. Onuma, “Instantaneous phase-shifting fizeau interferometry with high-speed pixelated phase-mask camera,” Proc. SPIE 9660, 966018 (2015).

Yonesaka, R.

Yoshii, M.

K. Ishikawa, K. Yatabe, Y. Ikeda, Y. Oikawa, T. Onuma, H. Niwa, and M. Yoshii, “Interferometric imaging of acoustical phenomena using high-speed polarization camera and 4-step parallel phase-shifting technique,” Proc. SPIE 10328, 103280I (2017).

K. Ishikawa, K. Yatabe, N. Chitanont, Y. Ikeda, Y. Oikawa, T. Onuma, H. Niwa, and M. Yoshii, “High-speed imaging of sound using parallel phase-shifting interferometry,” Opt. Express 24, 12922–12932 (2016).
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T. Yatagai, B. J. Jackin, A. Ono, K. Kiyohara, M. Noguchi, M. Yoshii, M. Kiyohara, H. Niwa, K. Ikuo, and T. Onuma, “Instantaneous phase-shifting fizeau interferometry with high-speed pixelated phase-mask camera,” Proc. SPIE 9660, 966018 (2015).

Zhao, J.

Acoust. Sci. Tech. (1)

K. Yatabe and Y. Oikawa, “Optically visualized sound field reconstruction using Kirchhoff–Helmholtz equation,” Acoust. Sci. Tech. 36, 351–354 (2015).
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Y. Oikawa, K. Yatabe, K. Ishikawa, and Y. Ikeda, “Optical sound field measurement and imaging using laser and high-speed camera,” in “Proc. 45th Int. Congr. Noise Control Eng. (INTER-NOISE 2016),” (2016), pp. 258–266.

K. Yatabe and Y. Oikawa, “PDE-based interpolation method for optically visualized sound field,” in “IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP),” (2014), pp. 4738–4742.

K. Yatabe and Y. Oikawa, “Optically visualized sound field reconstruction based on sparse selection of point sound sources,” in “IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP),” (2015), pp. 504–508.

P. K. Panigrahi and K. Muralidhar, Schlieren and Shadowgraph Methods in Heat and Mass Transfer (Springer, 2012).
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S. M. Alessio, Digital Signal Processing and Spectral Analysis for Scientists: Concepts and Applications (Springer, 2016).

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software (Wiley, 1998).

N. Chitanont, K. Yaginuma, K. Yatabe, and Y. Oikawa, “Visualization of sound field by means of Schlieren method with spatio-temporal filtering,” in “IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP),” (2015), pp. 509–513.

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Figures (10)

Fig. 1
Fig. 1 Illustration of the ordinary observation process of sound using PPSI. Time-directional filtering is utilized after phase unwrapping in order to extract the time-varying phenomenon from static phase (color of each figure is adjusted independently for better visibility).
Fig. 2
Fig. 2 (a) Schematic of the experimental setup. A polarized interferometer is combined with a polarized high-speed camera for realizing PPSI. A whistle is placed between the interferometer and a mirror which reflects the object light. (b) Positional relation between the whistle and observed phase which contains the static phase related to setup of the mirror.
Fig. 3
Fig. 3 Temporal variation of the measured phase at three pixels. The phase variation in time at each position are shown on the right, while the positions of the pixels are illustrated on the left. The amount of the static phase depends on the position of the pixel.
Fig. 4
Fig. 4 Effect of taking difference of successive phase maps in time direction. The observed phase maps obtained by PPSI are shown in the top row, where one step of the time index n of φn corresponds to 23.81 µs since the frame rate was 42 000 fps. Each pair of successive frames generates a single phase map shown in the bottom row by the subtraction. The color of the bottom figures were adjusted so that the sound wave becomes visible.
Fig. 5
Fig. 5 Schematic illustration of filtering for extracting fast varying component from mixed signal. (a) Each component in time domain before mixing. (b) Mixed signal consisting of three components in (a). (c) Frequency domain representation of (b) and transfer functions to be applied. (d) Filtered signal in time domain obtained by the filters in (c).
Fig. 6
Fig. 6 MATLAB implementation of the proposed filtering method, where the 19th line corresponds to Eq. (19). The inputted wrapped phase must be a three-dimensional array where the third dimension represents time. b and a are one-dimensional vectors of filter coefficients corresponding to the numerator and denominator of the transfer function, respectively. For running this code, Signal Processing Toolbox is required. In addition, because of using the implicit expansion, MATLAB version 2016b or later is required. For 2016a or earlier, 18th line must be rewritten by using bsxfun with @minus option.
Fig. 7
Fig. 7 Magnitude responses of the utilized filters (top) and spectra of filtered results obtained by the Fourier transform applied in time direction (bottom). The colored lines correspond to the third-order maximally flat magnitude filter, while the gray and black lines represent the time difference and no filtering, respectively. The vertical axis of the bottom figure is normalized to the maximum value of the black line (unwrapped phase without filtering). The single peak around 8700 Hz corresponds to the sound, and the other components corresponds to the static phase, gas flow and measurement noise (see Figs. 2, 4 and 8).
Fig. 8
Fig. 8 Filtered results of the observed wrapped phase by the proposed method. Time evolves from left to right at 23.81 µs interval. Each row corresponds to each filter shown in Fig. 7. The color ranges were adjusted automatically based on RMS values of each video.
Fig. 9
Fig. 9 Filtered results of the observed wrapped phase by the proposed method. All settings are the same as Fig. 8 except for the range of the color which was fixed to ±0.2 rad. The appearances of sound are similar except for the case fc = 200 Hz because some slowly varying components remained in that case.
Fig. 10
Fig. 10 Band-pass filtered results obtained by the proposed method and the ordinary time-directional filtering method in Fig. 1. The ordinary method requires phase unwrapping which is usually time-consuming, while the proposed method does not require it.

Equations (19)

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I [ m ] ( x , y ) = B ( x , y ) + A ( x , y ) cos ( φ ( x , y ) + δ [ m ] ) ,
I n [ m ] ( x , y ) = B ( x , y ) + A ( x , y ) cos ( φ n ( x , y ) + δ [ m ] ) ,
I n [ m ] ( x , y ) = B ( x , y ) + A ( x , y ) cos ( φ n ( x , y ) + σ ( x , y ) + δ [ m ] ) .
D ( φ n + σ ) = ( φ n + σ ) ( φ n 1 + σ ) = φ n φ n 1 ,
Ψ ˜ ( z ) = Λ ( z ) Ψ ( z ) ,
Ψ ( z ) = n ψ n z n .
( λ * ψ ) n = m λ m ψ n m ,
D φ n = φ n φ n 1 = ( + 1 ) φ n 0 + ( 1 ) φ n 1 = m = 0 1 h m φ n m = h * φ n ,
H ( z ) = 1 z 1
| H ( e I ˙ ω ) | = 2 | sin ( ω / 2 ) | ,
W [ φ n ] = [ φ n + π ] mod 2 π π
D φ n = W [ D W [ φ n ] ] ( = W [ h * W [ φ n ] ] = h * φ n ) ,
[ ] = h ˜ * h 1 * W [ h * ] ,
H 1 ( z ) = 1 1 z 1 .
[ W [ φ n ] ] = h ˜ * h 1 * W [ h * W [ φ n ] ] = h ˜ * h 1 * h * φ n = h ˜ * φ n ,
H 1 ( z ) H ( z ) = 1 z 1 1 z 1 = 1 .
h ˜ = h * h
h ˜ * h 1 = h * h * h 1 = h ,
[ ] = h * W [ h * ] ,

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