Abstract

We propose a new method for signal separation from a multicomponent interference field recorded in a digital holographic interferometry setup. The setup consisting of multiple object illuminating beams results in an interference field containing multiple signal components. The proposed method utilizes an amplitude discrimination criteria established by setting different intensities to the object illuminating beams in order to separate the signal components iteratively. The signal separation is performed in a small block of the interference field at a time. The augmentation of the block matrix with its own rows and columns is performed which has an effect of noise subspace inflation. This operation offers an improved noise robustness to the signal separation capability of the proposed method. The simulation and experimental results are provided to substantiate the applicability of the proposed method in multidimensional deformation measurement.

© 2015 Optical Society of America

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References

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  1. P. Picart, E. Moisson, and D. Mounier, “Twin-sensitivity measurement by spatial multiplexing of digitally recorded holograms,” App. Opt. 42 (11), 1947–1957 (2003).
    [Crossref]
  2. S. Okazawa, M. Fujigaki, Y. Morimoto, and T. Matui, “Simultaneous measurement of out-of-plane and in-plane displacements by phase-shifting digital holographic interferometry,” App. Mech. Mat. 3–4, 223–228 (2005).
    [Crossref]
  3. P. Picart, D. Mounier, and J. M. Desse, “High-resolution digital two-color holographic metrology,” Opt. Lett. 33(3), 276–278 (2008).
    [Crossref] [PubMed]
  4. C. Kohler, M. R. Viotti, and A. G. Albertazzi, “Measurement of three-dimensional deformations using digital holography with radial sensitivity,” App. Opt. 49(20), 4004–4009 (2010).
    [Crossref]
  5. G. Rajshekhar, S. S. Gorthi, and P. Rastogi, “Estimation of multiple phases from a single fringe pattern in digital holographic interferometry,” Opt. Exp. 20(2), 1281–1291 (2012).
    [Crossref]
  6. R. Kulkarni, S. S. Gorthi, and P. Rastogi, “Measurement of in-plane and out-of-plane displacements and strains using digital holographic moiré,” J. Mod. Opt. 61(9), 755–762 (2014).
    [Crossref]
  7. R. Kulkarni and P. Rastogi, “Simultaneous measurement of in-plane and out-of-plane displacements using pseudo-wigner-hough transform,” Opt. Exp. 22(7), 8703–8711 (2014).
    [Crossref]
  8. R. Kulkarni and P. Rastogi, “Three-dimensional displacement measurement from phase signals embedded in a frame in digital holographic interferometry,” App. Opt. 54(11), 3393–3397 (2015).
    [Crossref]
  9. R. Kulkarni and P. Rastogi, “Digital holographic moiré for the direct and simultaneous estimation of strain and slope fields,” Opt. Exp. 22(19), 23192–23201 (2014).
    [Crossref]
  10. G. Rajshekhar, S. SivaGorthi, and P. Rastogi, “Simultaneous multidimensional deformation measurements using digital holographic moiré,” App. Opt. 50(21), 4189–4197 (2011).
    [Crossref]
  11. R. Kulkarni and P. Rastogi, “Multiple phase estimation via signal separation using a windowed fourier transform in digital holographic interferometry,” Meas. Sci. Tech. 26(7) 075204 (2015).
    [Crossref]
  12. Y. Hua, “Estimating two-dimensional frequencies by matrix enhancement and matrix pencil,” IEEE Trans. on Sig. Proc. 40(9), 2267–2280 (1992).
    [Crossref]

2015 (2)

R. Kulkarni and P. Rastogi, “Three-dimensional displacement measurement from phase signals embedded in a frame in digital holographic interferometry,” App. Opt. 54(11), 3393–3397 (2015).
[Crossref]

R. Kulkarni and P. Rastogi, “Multiple phase estimation via signal separation using a windowed fourier transform in digital holographic interferometry,” Meas. Sci. Tech. 26(7) 075204 (2015).
[Crossref]

2014 (3)

R. Kulkarni and P. Rastogi, “Digital holographic moiré for the direct and simultaneous estimation of strain and slope fields,” Opt. Exp. 22(19), 23192–23201 (2014).
[Crossref]

R. Kulkarni, S. S. Gorthi, and P. Rastogi, “Measurement of in-plane and out-of-plane displacements and strains using digital holographic moiré,” J. Mod. Opt. 61(9), 755–762 (2014).
[Crossref]

R. Kulkarni and P. Rastogi, “Simultaneous measurement of in-plane and out-of-plane displacements using pseudo-wigner-hough transform,” Opt. Exp. 22(7), 8703–8711 (2014).
[Crossref]

2012 (1)

G. Rajshekhar, S. S. Gorthi, and P. Rastogi, “Estimation of multiple phases from a single fringe pattern in digital holographic interferometry,” Opt. Exp. 20(2), 1281–1291 (2012).
[Crossref]

2011 (1)

G. Rajshekhar, S. SivaGorthi, and P. Rastogi, “Simultaneous multidimensional deformation measurements using digital holographic moiré,” App. Opt. 50(21), 4189–4197 (2011).
[Crossref]

2010 (1)

C. Kohler, M. R. Viotti, and A. G. Albertazzi, “Measurement of three-dimensional deformations using digital holography with radial sensitivity,” App. Opt. 49(20), 4004–4009 (2010).
[Crossref]

2008 (1)

2005 (1)

S. Okazawa, M. Fujigaki, Y. Morimoto, and T. Matui, “Simultaneous measurement of out-of-plane and in-plane displacements by phase-shifting digital holographic interferometry,” App. Mech. Mat. 3–4, 223–228 (2005).
[Crossref]

2003 (1)

P. Picart, E. Moisson, and D. Mounier, “Twin-sensitivity measurement by spatial multiplexing of digitally recorded holograms,” App. Opt. 42 (11), 1947–1957 (2003).
[Crossref]

1992 (1)

Y. Hua, “Estimating two-dimensional frequencies by matrix enhancement and matrix pencil,” IEEE Trans. on Sig. Proc. 40(9), 2267–2280 (1992).
[Crossref]

Albertazzi, A. G.

C. Kohler, M. R. Viotti, and A. G. Albertazzi, “Measurement of three-dimensional deformations using digital holography with radial sensitivity,” App. Opt. 49(20), 4004–4009 (2010).
[Crossref]

Desse, J. M.

Fujigaki, M.

S. Okazawa, M. Fujigaki, Y. Morimoto, and T. Matui, “Simultaneous measurement of out-of-plane and in-plane displacements by phase-shifting digital holographic interferometry,” App. Mech. Mat. 3–4, 223–228 (2005).
[Crossref]

Gorthi, S. S.

R. Kulkarni, S. S. Gorthi, and P. Rastogi, “Measurement of in-plane and out-of-plane displacements and strains using digital holographic moiré,” J. Mod. Opt. 61(9), 755–762 (2014).
[Crossref]

G. Rajshekhar, S. S. Gorthi, and P. Rastogi, “Estimation of multiple phases from a single fringe pattern in digital holographic interferometry,” Opt. Exp. 20(2), 1281–1291 (2012).
[Crossref]

Hua, Y.

Y. Hua, “Estimating two-dimensional frequencies by matrix enhancement and matrix pencil,” IEEE Trans. on Sig. Proc. 40(9), 2267–2280 (1992).
[Crossref]

Kohler, C.

C. Kohler, M. R. Viotti, and A. G. Albertazzi, “Measurement of three-dimensional deformations using digital holography with radial sensitivity,” App. Opt. 49(20), 4004–4009 (2010).
[Crossref]

Kulkarni, R.

R. Kulkarni and P. Rastogi, “Multiple phase estimation via signal separation using a windowed fourier transform in digital holographic interferometry,” Meas. Sci. Tech. 26(7) 075204 (2015).
[Crossref]

R. Kulkarni and P. Rastogi, “Three-dimensional displacement measurement from phase signals embedded in a frame in digital holographic interferometry,” App. Opt. 54(11), 3393–3397 (2015).
[Crossref]

R. Kulkarni and P. Rastogi, “Simultaneous measurement of in-plane and out-of-plane displacements using pseudo-wigner-hough transform,” Opt. Exp. 22(7), 8703–8711 (2014).
[Crossref]

R. Kulkarni and P. Rastogi, “Digital holographic moiré for the direct and simultaneous estimation of strain and slope fields,” Opt. Exp. 22(19), 23192–23201 (2014).
[Crossref]

R. Kulkarni, S. S. Gorthi, and P. Rastogi, “Measurement of in-plane and out-of-plane displacements and strains using digital holographic moiré,” J. Mod. Opt. 61(9), 755–762 (2014).
[Crossref]

Matui, T.

S. Okazawa, M. Fujigaki, Y. Morimoto, and T. Matui, “Simultaneous measurement of out-of-plane and in-plane displacements by phase-shifting digital holographic interferometry,” App. Mech. Mat. 3–4, 223–228 (2005).
[Crossref]

Moisson, E.

P. Picart, E. Moisson, and D. Mounier, “Twin-sensitivity measurement by spatial multiplexing of digitally recorded holograms,” App. Opt. 42 (11), 1947–1957 (2003).
[Crossref]

Morimoto, Y.

S. Okazawa, M. Fujigaki, Y. Morimoto, and T. Matui, “Simultaneous measurement of out-of-plane and in-plane displacements by phase-shifting digital holographic interferometry,” App. Mech. Mat. 3–4, 223–228 (2005).
[Crossref]

Mounier, D.

P. Picart, D. Mounier, and J. M. Desse, “High-resolution digital two-color holographic metrology,” Opt. Lett. 33(3), 276–278 (2008).
[Crossref] [PubMed]

P. Picart, E. Moisson, and D. Mounier, “Twin-sensitivity measurement by spatial multiplexing of digitally recorded holograms,” App. Opt. 42 (11), 1947–1957 (2003).
[Crossref]

Okazawa, S.

S. Okazawa, M. Fujigaki, Y. Morimoto, and T. Matui, “Simultaneous measurement of out-of-plane and in-plane displacements by phase-shifting digital holographic interferometry,” App. Mech. Mat. 3–4, 223–228 (2005).
[Crossref]

Picart, P.

P. Picart, D. Mounier, and J. M. Desse, “High-resolution digital two-color holographic metrology,” Opt. Lett. 33(3), 276–278 (2008).
[Crossref] [PubMed]

P. Picart, E. Moisson, and D. Mounier, “Twin-sensitivity measurement by spatial multiplexing of digitally recorded holograms,” App. Opt. 42 (11), 1947–1957 (2003).
[Crossref]

Rajshekhar, G.

G. Rajshekhar, S. S. Gorthi, and P. Rastogi, “Estimation of multiple phases from a single fringe pattern in digital holographic interferometry,” Opt. Exp. 20(2), 1281–1291 (2012).
[Crossref]

G. Rajshekhar, S. SivaGorthi, and P. Rastogi, “Simultaneous multidimensional deformation measurements using digital holographic moiré,” App. Opt. 50(21), 4189–4197 (2011).
[Crossref]

Rastogi, P.

R. Kulkarni and P. Rastogi, “Three-dimensional displacement measurement from phase signals embedded in a frame in digital holographic interferometry,” App. Opt. 54(11), 3393–3397 (2015).
[Crossref]

R. Kulkarni and P. Rastogi, “Multiple phase estimation via signal separation using a windowed fourier transform in digital holographic interferometry,” Meas. Sci. Tech. 26(7) 075204 (2015).
[Crossref]

R. Kulkarni and P. Rastogi, “Simultaneous measurement of in-plane and out-of-plane displacements using pseudo-wigner-hough transform,” Opt. Exp. 22(7), 8703–8711 (2014).
[Crossref]

R. Kulkarni and P. Rastogi, “Digital holographic moiré for the direct and simultaneous estimation of strain and slope fields,” Opt. Exp. 22(19), 23192–23201 (2014).
[Crossref]

R. Kulkarni, S. S. Gorthi, and P. Rastogi, “Measurement of in-plane and out-of-plane displacements and strains using digital holographic moiré,” J. Mod. Opt. 61(9), 755–762 (2014).
[Crossref]

G. Rajshekhar, S. S. Gorthi, and P. Rastogi, “Estimation of multiple phases from a single fringe pattern in digital holographic interferometry,” Opt. Exp. 20(2), 1281–1291 (2012).
[Crossref]

G. Rajshekhar, S. SivaGorthi, and P. Rastogi, “Simultaneous multidimensional deformation measurements using digital holographic moiré,” App. Opt. 50(21), 4189–4197 (2011).
[Crossref]

SivaGorthi, S.

G. Rajshekhar, S. SivaGorthi, and P. Rastogi, “Simultaneous multidimensional deformation measurements using digital holographic moiré,” App. Opt. 50(21), 4189–4197 (2011).
[Crossref]

Viotti, M. R.

C. Kohler, M. R. Viotti, and A. G. Albertazzi, “Measurement of three-dimensional deformations using digital holography with radial sensitivity,” App. Opt. 49(20), 4004–4009 (2010).
[Crossref]

App. Mech. Mat. (1)

S. Okazawa, M. Fujigaki, Y. Morimoto, and T. Matui, “Simultaneous measurement of out-of-plane and in-plane displacements by phase-shifting digital holographic interferometry,” App. Mech. Mat. 3–4, 223–228 (2005).
[Crossref]

App. Opt. (4)

P. Picart, E. Moisson, and D. Mounier, “Twin-sensitivity measurement by spatial multiplexing of digitally recorded holograms,” App. Opt. 42 (11), 1947–1957 (2003).
[Crossref]

C. Kohler, M. R. Viotti, and A. G. Albertazzi, “Measurement of three-dimensional deformations using digital holography with radial sensitivity,” App. Opt. 49(20), 4004–4009 (2010).
[Crossref]

R. Kulkarni and P. Rastogi, “Three-dimensional displacement measurement from phase signals embedded in a frame in digital holographic interferometry,” App. Opt. 54(11), 3393–3397 (2015).
[Crossref]

G. Rajshekhar, S. SivaGorthi, and P. Rastogi, “Simultaneous multidimensional deformation measurements using digital holographic moiré,” App. Opt. 50(21), 4189–4197 (2011).
[Crossref]

IEEE Trans. on Sig. Proc. (1)

Y. Hua, “Estimating two-dimensional frequencies by matrix enhancement and matrix pencil,” IEEE Trans. on Sig. Proc. 40(9), 2267–2280 (1992).
[Crossref]

J. Mod. Opt. (1)

R. Kulkarni, S. S. Gorthi, and P. Rastogi, “Measurement of in-plane and out-of-plane displacements and strains using digital holographic moiré,” J. Mod. Opt. 61(9), 755–762 (2014).
[Crossref]

Meas. Sci. Tech. (1)

R. Kulkarni and P. Rastogi, “Multiple phase estimation via signal separation using a windowed fourier transform in digital holographic interferometry,” Meas. Sci. Tech. 26(7) 075204 (2015).
[Crossref]

Opt. Exp. (3)

R. Kulkarni and P. Rastogi, “Digital holographic moiré for the direct and simultaneous estimation of strain and slope fields,” Opt. Exp. 22(19), 23192–23201 (2014).
[Crossref]

R. Kulkarni and P. Rastogi, “Simultaneous measurement of in-plane and out-of-plane displacements using pseudo-wigner-hough transform,” Opt. Exp. 22(7), 8703–8711 (2014).
[Crossref]

G. Rajshekhar, S. S. Gorthi, and P. Rastogi, “Estimation of multiple phases from a single fringe pattern in digital holographic interferometry,” Opt. Exp. 20(2), 1281–1291 (2012).
[Crossref]

Opt. Lett. (1)

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Figures (7)

Fig. 1
Fig. 1 (a) A schematic diagram of the digital holographic interferometry setup with two object illuminating beams (b) N × N sized two dimensional block representation of an interference field of size K × L.
Fig. 2
Fig. 2 (a) Noisy phase fringe pattern. Filtered phase fringe pattern using the SVD of (b) Ib and (c) Ia.
Fig. 3
Fig. 3 (a) Noisy phase fringe pattern. Phase fringe patterns corresponding to (b) first signal component and (c) second signal component.
Fig. 4
Fig. 4 (a) Noisy fringe pattern associated with an interferogram containing two signal components (b) Fourier spectrum of the interferogram. Phase fringe patterns of (c) first signal component and (d) second signal component after first iteration. Phase fringe patterns of (c) first signal component and (d) second signal component after eight iterations.
Fig. 5
Fig. 5 RMSEs in the computation of phase of (a) first signal component and (b) second signal component in function of block size and SNR. RMSEs in the computation of phase of (a) first signal component and (b) second signal component in function of amplitude ratio and SNR.
Fig. 6
Fig. 6 (a) Experimentally recorded fringe pattern. Phase fringe pattern of separated (b) first signal component and (c) second signal component. Unwrapped phases associated with (d) first signal component and (e) second signal component.
Fig. 7
Fig. 7 Unwrapped form of (a) sum of phases (b) difference of phases. Wrapped form of (c) sum of phases (d) difference of phases.

Equations (8)

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I [ k , l ] = A 1 [ k , l ] exp ( j φ 1 [ k , l ] ) + A 2 [ k , l ] exp ( j φ 2 [ k , l ] ) + ε [ k , l ] ,
I b = [ I b [ 0 , 0 ] I b [ 0 , 1 ] I b [ 0 , N 1 ] I b [ 1 , 0 ] I b [ 1 , 1 ] I b [ 1 , N 1 ] I b [ N 1 , 0 ] I b [ N 1 , 1 ] I b [ N 1 , N 1 ] ] .
I b = U b Λ b V b * ,
I a = [ I 0 I 1 I N P I 1 I 2 I N P + 1 I P 1 I P I N 1 , ]
I n = [ I b ( n , 0 ) I b ( n , 1 ) I b ( n , N Q ) I b ( n , 1 ) I b ( n , 2 ) I b ( n , N Q + 1 ) I b ( n , Q 1 ) I b ( n , Q ) I b ( n , N 1 ) ] ,
I a = U a Λ a V a * .
i + 1 P , Q 1 2 ( N + 1 ) .
I ( 2 ) = I b I ( 1 ) .

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