Abstract

We describe a novel method of processing complex phasors in digital holographic interferometry (DHI). Unlike the commonly used digital phase subtraction method that operates on the phase itself, the proposed method operates on the complex phasor instead. Two temporal phase retrieval algorithms are developed in which the complex phasor of each pixel is measured and analyzed as a function of time. The developed algorithms are demonstrated in profile measurement of step heights. Experimental results show that the proposed phase retrieval algorithms for DHI perform well compared with conventional methods.

© 2007 Optical Society of America

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References

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  1. U. Schnars, J. Opt. Soc. Am. A 11, 2011 (1994).
    [CrossRef]
  2. J. M. Huntley and H. Saldner, Appl. Opt. 32, 3047 (1993).
    [CrossRef] [PubMed]
  3. J. M. Huntley and H. O. Saldner, J. Opt. Soc. Am. A 14, 3188 (1997).
    [CrossRef]
  4. S. Bernhard, Appl. Opt. 35, 2192 (1996).
    [CrossRef]
  5. Q. K. Mao, Opt. Eng. 42, 2792 (2003).
    [CrossRef]
  6. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
  7. J. M. Huntley, J. Phys. E 19, 43 (1986).
    [CrossRef]
  8. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: the Arts of Scientific Computing, 2nd ed (Cambridge U. Press, 2002).
  9. S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed (Academic, 1999).
  10. U. Schnars and W. Jueptner, Digital holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).
  11. I. Yamaguchi, J. Kato, and S. Ohta, Opt. Rev. 8, 85 (2001).
    [CrossRef]
  12. T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2005).

2003

Q. K. Mao, Opt. Eng. 42, 2792 (2003).
[CrossRef]

2001

I. Yamaguchi, J. Kato, and S. Ohta, Opt. Rev. 8, 85 (2001).
[CrossRef]

1997

1996

1994

1993

1986

J. M. Huntley, J. Phys. E 19, 43 (1986).
[CrossRef]

Bernhard, S.

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: the Arts of Scientific Computing, 2nd ed (Cambridge U. Press, 2002).

Ghiglia, D. C.

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

Huntley, J. M.

Jueptner, W.

U. Schnars and W. Jueptner, Digital holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).

Kato, J.

I. Yamaguchi, J. Kato, and S. Ohta, Opt. Rev. 8, 85 (2001).
[CrossRef]

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2005).

Mallat, S.

S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed (Academic, 1999).

Mao, Q. K.

Q. K. Mao, Opt. Eng. 42, 2792 (2003).
[CrossRef]

Ohta, S.

I. Yamaguchi, J. Kato, and S. Ohta, Opt. Rev. 8, 85 (2001).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: the Arts of Scientific Computing, 2nd ed (Cambridge U. Press, 2002).

Pritt, M. D.

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

Saldner, H.

Saldner, H. O.

Schnars, U.

U. Schnars, J. Opt. Soc. Am. A 11, 2011 (1994).
[CrossRef]

U. Schnars and W. Jueptner, Digital holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: the Arts of Scientific Computing, 2nd ed (Cambridge U. Press, 2002).

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: the Arts of Scientific Computing, 2nd ed (Cambridge U. Press, 2002).

Yamaguchi, I.

I. Yamaguchi, J. Kato, and S. Ohta, Opt. Rev. 8, 85 (2001).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

J. Phys. E

J. M. Huntley, J. Phys. E 19, 43 (1986).
[CrossRef]

Opt. Eng.

Q. K. Mao, Opt. Eng. 42, 2792 (2003).
[CrossRef]

Opt. Rev.

I. Yamaguchi, J. Kato, and S. Ohta, Opt. Rev. 8, 85 (2001).
[CrossRef]

Other

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2005).

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

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++: the Arts of Scientific Computing, 2nd ed (Cambridge U. Press, 2002).

S. Mallat, A Wavelet Tour of Signal Processing, 2nd ed (Academic, 1999).

U. Schnars and W. Jueptner, Digital holography: Digital Hologram Recording, Numerical Reconstruction, and Related Techniques (Springer, 2005).

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Figures (3)

Fig. 1
Fig. 1

Optical arrangement for profile measurement using a multiple-illumination-point method.

Fig. 2
Fig. 2

3D plot of unwrapped phase obtained by temporal phase unwrapping.

Fig. 3
Fig. 3

3D plots of unwrapped phase obtained by (a) temporal Fourier transform and (b) WFT.

Equations (10)

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Δ φ w = { φ w ( 1 ) φ w ( 2 ) if φ w ( 1 ) φ w ( 2 ) φ w ( 1 ) φ w ( 2 ) + 2 π if φ w ( 1 ) < φ w ( 2 ) } .
Γ ( ξ , η , n ) = a ( ξ , η , n ) exp [ i φ ( ξ , η , n ) ] ( n = 0 , 1 , , N ) ,
A ( n ) = Γ ( n ) Γ * ( 0 ) = a ( n ) a ( 0 ) exp { i [ φ ( n ) φ ( 0 ) ] } = A ( n ) exp [ i Δ φ ( n , 0 ) ] ,
Δ φ w ( n , 0 ) = arctan Im [ A ( n ) ] Re [ A ( n ) ] .
I ( k ) = n = 1 N ( a n + i b n ) { cos [ 2 π k ( n 1 ) N ] + i sin [ 2 π k ( n 1 ) N ] } = n = 1 N ( a n cos α n 1 + b n sin α n 1 ) + i n = 1 N ( b n cos α n 1 a n sin α n 1 ) = Re [ I ( k ) ] + i Im [ I ( k ) ] ,
I ( k ) 2 = Re 2 [ I ( k ) ] + Im 2 [ I ( k ) ] ,
k I ( k ) 2 = 2 { Re [ I ( k ) ] d Re [ I ( k ) ] + Im [ I ( k ) ] d Im [ I ( k ) ] } ,
w = 2 π k p N .
S f ( u , v ) = + f ( t ) g ( t u ) exp ( i v t ) d t ,
f ( t ) = 1 2 π + L U S f ( u , v ) g ( t u ) exp ( i v t ) d v d u ,

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