Abstract

This paper proposes quantitative phase imaging by using a high resolution holographic grating for generating a four-wave shearing interferogram. The high-resolution holographic grating is designed in a “kite” configuration so as to avoid parasitic mixing of diffraction orders. The selection of six diffraction orders in the Fourier spectrum of the interferogram allows reconstructing phase gradients along specific directions. The spectral analysis yields the useful parameters of the reconstruction process. The derivative axes are exactly determined whatever the experimental configurations of the holographic grating. The integration of the derivative yields the phase and the optical thickness. Demonstration of the proposed approach is carried out for the case of the analysis of the supersonic flow of a small vertical jet, 5.56mm in diameter. The experimental results compared with those obtained with digital holography exhibit a very good agreement.

© 2015 Optical Society of America

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References

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    [Crossref] [PubMed]
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  7. P. Girshovitz and N. T. Shaked, “Compact and portable low-coherence interferometer with off-axis geometry for quantitative phase microscopy and nanoscopy,” Opt. Express 21(5), 5701–5714 (2013).
    [Crossref] [PubMed]
  8. G. Rajshekhar, B. Bhaduri, C. Edwards, R. Zhou, L. L. Goddard, and G. Popescu, “Nanoscale topography and spatial light modulator characterization using wide-field quantitative phase imaging,” Opt. Express 22(3), 3432–3438 (2014).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  17. R. Doleček, P. Psota, V. Lédl, T. Vít, J. Václavík, and V. Kopecký, “General temperature field measurement by digital holography,” Appl. Opt. 52(1), A319–A325 (2013).
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    [Crossref] [PubMed]
  22. J. Chu and S. W. Kim, “Absolute distance measurement by lateral shearing interferometry of point-diffracted spherical waves,” Opt. Express 14(13), 5961–5967 (2006).
    [Crossref] [PubMed]
  23. Y. S. Ghim, H. G. Rhee, A. Davies, H. S. Yang, and Y. W. Lee, “3D surface mapping of freeform optics using wavelength scanning lateral shearing interferometry,” Opt. Express 22(5), 5098–5105 (2014).
    [Crossref] [PubMed]
  24. K. U. Hii and K. H. Kwek, “Wavefront reversal technique for self-referencing collimation testing,” Appl. Opt. 49(4), 668–672 (2010).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  26. C. Falldorf, “Measuring the complex amplitude of wave fields by means of shear interferometry,” J. Opt. Soc. Am. A 28(8), 1636–1647 (2011).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  30. J. Primot and N. Guérineau, “Extended Hartmann test based on the pseudoguiding property of a Hartmann mask completed by a phase chessboard,” Appl. Opt. 39(31), 5715–5720 (2000).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  42. J. Rizzi, T. Weitkamp, N. Guérineau, M. Idir, P. Mercère, G. Druart, G. Vincent, P. da Silva, and J. Primot, “Quadriwave lateral shearing interferometry in an achromatic and continuously self-imaging regime for future x-ray phase imaging,” Opt. Lett. 36(8), 1398–1400 (2011).
    [Crossref] [PubMed]
  43. http://www.ultimate-holography.com/
  44. Th. Kreis, Holographic Interferometry - Pinciples and Methods (Akademie Verlag series in Optical Metrology Vol. 1, Akademie Verlag Gmbh, Berlin, 1996).

2015 (2)

J. M. Desse and P. Picart, “Quasi-common path three-wavelength holographic interferometer based on Wollaston prisms,” Opt. Lasers Eng. 68, 188–193 (2015).
[Crossref]

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54(2), 024110 (2015).
[Crossref]

2014 (3)

2013 (3)

2012 (7)

2011 (4)

2010 (2)

2009 (1)

2008 (1)

2006 (2)

2005 (3)

2003 (1)

J. Primot, “Theoretical description of Shack-Hartmann wave-front sensor,” Opt. Commun. 222(1-6), 81–92 (2003).
[Crossref]

2000 (1)

1993 (1)

1986 (1)

1980 (2)

1979 (1)

1978 (1)

1977 (2)

1974 (1)

Agour, M.

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54(2), 024110 (2015).
[Crossref]

Alferi, D.

Anand, A.

Awatsuji, Y.

Bergmann, R. B.

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54(2), 024110 (2015).
[Crossref]

Bhaduri, B.

Bon, P.

Chanteloup, J. C.

Chhaniwal, V.

Chu, J.

Chu, K. K.

Cohen, M.

Cubalchini, R.

da Silva, P.

Dasari, R. R.

N. Lue, J. W. Kang, T. R. Hillman, R. R. Dasari, and Z. Yaqoob, “Single-shot quantitative dispersion phase microscopy,” Appl. Phys. Lett. 101(8), 084101 (2012).
[Crossref] [PubMed]

Davies, A.

De Nicola, S.

De Petrocellis, L.

Depeursinge, C.

Desse, J. M.

J. M. Desse and P. Picart, “Quasi-common path three-wavelength holographic interferometer based on Wollaston prisms,” Opt. Lasers Eng. 68, 188–193 (2015).
[Crossref]

Desse, J.-M.

Ding, H.

Dolecek, R.

Druart, G.

Edwards, C.

Falldorf, C.

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54(2), 024110 (2015).
[Crossref]

C. Falldorf, “Measuring the complex amplitude of wave fields by means of shear interferometry,” J. Opt. Soc. Am. A 28(8), 1636–1647 (2011).
[Crossref] [PubMed]

Ferraro, P.

Finizio, A.

Ford, T. N.

Freischlad, K. R.

Fried, D. L.

Gabai, H.

Ganti, R.

Ghim, Y. S.

Girshovitz, P.

Goddard, L. L.

Guérineau, N.

Herrmann, J.

Hii, K. U.

Hillman, T. R.

N. Lue, J. W. Kang, T. R. Hillman, R. R. Dasari, and Z. Yaqoob, “Single-shot quantitative dispersion phase microscopy,” Appl. Phys. Lett. 101(8), 084101 (2012).
[Crossref] [PubMed]

Hudgin, R. H.

Hwang, S.-W.

Idir, M.

Javidi, B.

Kakue, T.

Kang, J. W.

N. Lue, J. W. Kang, T. R. Hillman, R. R. Dasari, and Z. Yaqoob, “Single-shot quantitative dispersion phase microscopy,” Appl. Phys. Lett. 101(8), 084101 (2012).
[Crossref] [PubMed]

Kim, M.

Kim, S. W.

Koliopoulos, C. L.

Kopecký, V.

Kubota, T.

Kwek, K. H.

Lédl, V.

Lee, Y. W.

Leitgeb, R. A.

Lo, C.-M.

Lue, N.

N. Lue, J. W. Kang, T. R. Hillman, R. R. Dasari, and Z. Yaqoob, “Single-shot quantitative dispersion phase microscopy,” Appl. Phys. Lett. 101(8), 084101 (2012).
[Crossref] [PubMed]

Lv, W.

Magistretti, P.

Malek, M.

Mann, C.

Marquet, P.

Matoba, O.

Maucort, G.

McKeown, S. J.

Mercère, P.

Mertz, J.

Mir, M.

Monneret, S.

Moratal, C.

Nishio, K.

Noll, J. R.

Parthasarathy, A. B.

Pham, H.

Picart, P.

Pierattini, G.

Popescu, G.

Primot, J.

Psota, P.

Rajshekhar, G.

Rhee, H. G.

Rimmer, M. P.

Rizzi, J.

Rogers, J. A.

Shaffer, E.

Shaked, N. T.

Shakher, C.

S. Sharma, G. Sheoran, and C. Shakher, “Investigation of temperature and temperature profile in axi-symmetric flame of butane torch burner using digital holographic interferometry,” Opt. Lasers Eng. 50, 1436–1444 (2012).
[Crossref]

Sharma, S.

S. Sharma, G. Sheoran, and C. Shakher, “Investigation of temperature and temperature profile in axi-symmetric flame of butane torch burner using digital holographic interferometry,” Opt. Lasers Eng. 50, 1436–1444 (2012).
[Crossref]

Sheoran, G.

S. Sharma, G. Sheoran, and C. Shakher, “Investigation of temperature and temperature profile in axi-symmetric flame of butane torch burner using digital holographic interferometry,” Opt. Lasers Eng. 50, 1436–1444 (2012).
[Crossref]

Singh, A. S. G.

Southwell, W. H.

Tahara, T.

Tankam, P.

Ura, S.

Václavík, J.

Velghe, S.

Vincent, G.

Vít, T.

Wang, K.

Wattellier, B.

Weitkamp, T.

Yang, H. S.

Yaqoob, Z.

N. Lue, J. W. Kang, T. R. Hillman, R. R. Dasari, and Z. Yaqoob, “Single-shot quantitative dispersion phase microscopy,” Appl. Phys. Lett. 101(8), 084101 (2012).
[Crossref] [PubMed]

Yodh, A. G.

Yonesaka, R.

Yu, L.

Yunker, P. J.

Zhou, H. C.

Zhou, R.

Zhu, J. R.

Appl. Opt. (8)

C. Edwards, R. Zhou, S.-W. Hwang, S. J. McKeown, K. Wang, B. Bhaduri, R. Ganti, P. J. Yunker, A. G. Yodh, J. A. Rogers, L. L. Goddard, and G. Popescu, “Diffraction phase microscopy: monitoring nanoscale dynamics in materials science [invited],” Appl. Opt. 53(27), G33–G43 (2014).
[Crossref] [PubMed]

J. Primot, “Three-wave lateral shearing interferometer,” Appl. Opt. 32(31), 6242–6249 (1993).
[Crossref] [PubMed]

J. C. Chanteloup, “Multiple-wave lateral shearing interferometry for wave-front sensing,” Appl. Opt. 44(9), 1559–1571 (2005).
[Crossref] [PubMed]

K. U. Hii and K. H. Kwek, “Wavefront reversal technique for self-referencing collimation testing,” Appl. Opt. 49(4), 668–672 (2010).
[Crossref] [PubMed]

W. Lv, H. C. Zhou, and J. R. Zhu, “Implementation of tridirectional large lateral shearing displacement interferometry in temperature measurement of a diffused ethylene flame,” Appl. Opt. 50(21), 3924–3936 (2011).
[Crossref] [PubMed]

R. Doleček, P. Psota, V. Lédl, T. Vít, J. Václavík, and V. Kopecký, “General temperature field measurement by digital holography,” Appl. Opt. 52(1), A319–A325 (2013).
[Crossref] [PubMed]

M. P. Rimmer, “Method for evaluating lateral shearing interferograms,” Appl. Opt. 13(3), 623–629 (1974).
[Crossref] [PubMed]

J. Primot and N. Guérineau, “Extended Hartmann test based on the pseudoguiding property of a Hartmann mask completed by a phase chessboard,” Appl. Opt. 39(31), 5715–5720 (2000).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

N. Lue, J. W. Kang, T. R. Hillman, R. R. Dasari, and Z. Yaqoob, “Single-shot quantitative dispersion phase microscopy,” Appl. Phys. Lett. 101(8), 084101 (2012).
[Crossref] [PubMed]

J. Opt. Soc. Am. (6)

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

Opt. Commun. (1)

J. Primot, “Theoretical description of Shack-Hartmann wave-front sensor,” Opt. Commun. 222(1-6), 81–92 (2003).
[Crossref]

Opt. Eng. (1)

C. Falldorf, M. Agour, and R. B. Bergmann, “Digital holography and quantitative phase contrast imaging using computational shear interferometry,” Opt. Eng. 54(2), 024110 (2015).
[Crossref]

Opt. Express (8)

C. Mann, L. Yu, C.-M. Lo, and M. Kim, “High-resolution quantitative phase-contrast microscopy by digital holography,” Opt. Express 13(22), 8693–8698 (2005).
[Crossref] [PubMed]

P. Girshovitz and N. T. Shaked, “Compact and portable low-coherence interferometer with off-axis geometry for quantitative phase microscopy and nanoscopy,” Opt. Express 21(5), 5701–5714 (2013).
[Crossref] [PubMed]

G. Rajshekhar, B. Bhaduri, C. Edwards, R. Zhou, L. L. Goddard, and G. Popescu, “Nanoscale topography and spatial light modulator characterization using wide-field quantitative phase imaging,” Opt. Express 22(3), 3432–3438 (2014).
[Crossref] [PubMed]

P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17(15), 13080–13094 (2009).
[Crossref] [PubMed]

J. Chu and S. W. Kim, “Absolute distance measurement by lateral shearing interferometry of point-diffracted spherical waves,” Opt. Express 14(13), 5961–5967 (2006).
[Crossref] [PubMed]

Y. S. Ghim, H. G. Rhee, A. Davies, H. S. Yang, and Y. W. Lee, “3D surface mapping of freeform optics using wavelength scanning lateral shearing interferometry,” Opt. Express 22(5), 5098–5105 (2014).
[Crossref] [PubMed]

H. Gabai and N. T. Shaked, “Dual-channel low-coherence interferometry and its application to quantitative phase imaging of fingerprints,” Opt. Express 20(24), 26906–26912 (2012).
[Crossref] [PubMed]

J.-M. Desse, P. Picart, and P. Tankam, “Digital three-color holographic interferometry for flow analysis,” Opt. Express 16(8), 5471–5480 (2008).
[Crossref] [PubMed]

Opt. Lasers Eng. (2)

S. Sharma, G. Sheoran, and C. Shakher, “Investigation of temperature and temperature profile in axi-symmetric flame of butane torch burner using digital holographic interferometry,” Opt. Lasers Eng. 50, 1436–1444 (2012).
[Crossref]

J. M. Desse and P. Picart, “Quasi-common path three-wavelength holographic interferometer based on Wollaston prisms,” Opt. Lasers Eng. 68, 188–193 (2015).
[Crossref]

Opt. Lett. (10)

T. Kakue, R. Yonesaka, T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “High-speed phase imaging by parallel phase-shifting digital holography,” Opt. Lett. 36(21), 4131–4133 (2011).
[Crossref] [PubMed]

A. B. Parthasarathy, K. K. Chu, T. N. Ford, and J. Mertz, “Quantitative phase imaging using a partitioned detection aperture,” Opt. Lett. 37(19), 4062–4064 (2012).
[Crossref] [PubMed]

P. Picart and M. Malek, “Complex field recovering from in-line digital holography,” Opt. Lett. 38(17), 3230–3232 (2013).
[Crossref] [PubMed]

P. Ferraro, D. Alferi, S. De Nicola, L. De Petrocellis, A. Finizio, and G. Pierattini, “Quantitative phase-contrast microscopy by a lateral shear approach to digital holographic image reconstruction,” Opt. Lett. 31(10), 1405–1407 (2006).
[Crossref] [PubMed]

E. Shaffer, C. Moratal, P. Magistretti, P. Marquet, and C. Depeursinge, “Label-free second-harmonic phase imaging of biological specimen by digital holographic microscopy,” Opt. Lett. 35(24), 4102–4104 (2010).
[Crossref] [PubMed]

B. Bhaduri, H. Pham, M. Mir, and G. Popescu, “Diffraction phase microscopy with white light,” Opt. Lett. 37(6), 1094–1096 (2012).
[Crossref] [PubMed]

V. Chhaniwal, A. S. G. Singh, R. A. Leitgeb, B. Javidi, and A. Anand, “Quantitative phase-contrast imaging with compact digital holographic microscope employing Lloyd’s mirror,” Opt. Lett. 37(24), 5127–5129 (2012).
[Crossref] [PubMed]

H. Pham, B. Bhaduri, H. Ding, and G. Popescu, “Spectroscopic diffraction phase microscopy,” Opt. Lett. 37(16), 3438–3440 (2012).
[Crossref] [PubMed]

S. Velghe, J. Primot, N. Guérineau, M. Cohen, and B. Wattellier, “Wave-front reconstruction from multidirectional phase derivatives generated by multilateral shearing interferometers,” Opt. Lett. 30(3), 245–247 (2005).
[Crossref] [PubMed]

J. Rizzi, T. Weitkamp, N. Guérineau, M. Idir, P. Mercère, G. Druart, G. Vincent, P. da Silva, and J. Primot, “Quadriwave lateral shearing interferometry in an achromatic and continuously self-imaging regime for future x-ray phase imaging,” Opt. Lett. 36(8), 1398–1400 (2011).
[Crossref] [PubMed]

Other (5)

http://www.ultimate-holography.com/

Th. Kreis, Holographic Interferometry - Pinciples and Methods (Akademie Verlag series in Optical Metrology Vol. 1, Akademie Verlag Gmbh, Berlin, 1996).

D. C. Ghiglia and M. D. Pritt, Two-dimensional phase unwrapping: theory, algorithms, and software, (Wiley, 1998).

P. Picart and M. Malek, “Digital holographic imaging based on shearing interferometry,” FRINGE 2013, The 7th International Workshop on Automatic Processing of Fringe Pattern, Nürtingen, Germany, September 9–11, 2013, pp 745–750.

R. T. Frankot and R. Chellappa, “A method for enforcing integrability in shape from shading algorithms,” in Shape from Shading, B.K.P. Horn and M.J. Brooks, ed, 89–122 (1989).

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Figures (7)

Fig. 1
Fig. 1 Principle of wave mixing using a high-resolution reflection hologram.
Fig. 2
Fig. 2 Optical setup for recording the high-resolution holographic grating in reflection mode (SF1 and SF2: spatial filter, M1 to M7 and MP1 to MP4: flat mirrors, PBS: polarizing beam splitter, BS1 to BS3: 50% beam splitter cube).
Fig. 3
Fig. 3 Set-up for quantitative phase imaging of flows with the holographic grating (SF: spatial filter, L1 to L5: lenses, M1: flat mirror, BS: 50% beam splitter cube; HRHG: high resolution holographic grating).
Fig. 4
Fig. 4 (a) square configuration with interference labeling, (b) same as (a) for the kite configuration, (c) spatial spectrum for the square configuration, (d) spatial spectrum for the kite configuration with axis increased with reduced spatial frequencies, (e) zoom on the 1,1’ spectral order of the square configuration, (c) zoom on the 1 spectral order of the kite configuration.
Fig. 5
Fig. 5 Derivatives axis in the Fourier domain, each color is related to axis that are numbered 1 to 6; illustration of the angle γq with order n°3 and angle γ3.
Fig. 6
Fig. 6 Recorded interferograms, and maps of modulo 2π phase gradients obtained for the six interference orders, (a) reference interferogram recorded without flow in the test section, (b) interferogram recorded with the micro jet the test section, (c) zoom of the measurement interferogram exhibiting the structure of the microscopic fringes, (d) phase gradient along q = 1 (order 1 in Fig. 4(d)), (e) phase gradient along q = 2 (order 2 in Fig. 4(d)), (f) phase gradient along q = 3 (order 3 in Fig. 4(d)), (g) phase gradient along q = 4 (order 4 in Fig. 4(d)), (h) phase gradient along q = 5 (order 1’ in Fig. 4(d)), (i) phase gradient along q = 6 (order 2’ in Fig. 4(d)); the gray scale refers to the phase maps.
Fig. 7
Fig. 7 Comparison of experimental results obtained for three different interferometric techniques for a pressure at P = 5 bars, (a) proposed method, (b) Michelson set-up, (c) “Z” architecture.

Tables (1)

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Table 1 Parameters of the useful parameters for the “kite” configuration

Equations (5)

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O ( r , k n ) = A 0 ( r r n ) exp ( i k n . r + i φ 0 ( r r n ) ) .
H ( r ) = n = 1 n = P A O 2 ( r r n ) + 2 { n = 1 P 1 m = n + 1 P O ( r , k n ) O * ( r , k m ) } .
Δ φ n m ( r ) = ( k n k m ) . r + φ O ( r r n ) φ O ( r r m ) .
Δ φ n m ( r ) ( k n k m ) . r + | s n m | φ O ( r ) r . e n m .
Ψ = 1 2 i π F T 1 [ q = 1 Q u q D ˜ q q = 1 Q u q 2 ] .

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