Abstract

In this paper we present several eight-frame algorithms for their use in phase shifting profilometry and their application for the analysis of semi-fossilized materials. All algorithms are obtained from a set of two-frame algorithms and designed to compensate common errors such as phase shift detuning and bias errors.

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References

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  1. J. F. Mosiño, D. M. Doblado, and D. M. Hernández, “A method to design tunable quadrature filters in phase shifting interferometry,” Opt. Express17(18), 15772–15777 (2009).
    [CrossRef] [PubMed]
  2. K. Larkin, “A self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns,” Opt. Express9(5), 236–253 (2001).
    [CrossRef] [PubMed]
  3. P. D. Ruiz, J. M. Huntley, and G. H. Kaufmann, “Adaptive phase-shifting algorithm for temporal phase evaluation,” J. Opt. Soc. Am. A20(2), 325–332 (2003).
    [CrossRef] [PubMed]
  4. H. Katterwe, “Modern approaches for the examination of toolmarks and other surface marks,” Forensic Sci. Rev.8, 45–72 (1996).
  5. T. M. Kaiser and H. Katterwe, “The application of 3D-microprofilometry as a tool in the surface diagnosis of fossil and sub-fossil vertebrate hard tissue. An example from the pliocene upper laetolil beds, Tanzania,” Int. J. Osteoarchaeol.11(5), 350–356 (2001).
    [CrossRef]
  6. Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt.35(1), 51–60 (1996).
    [CrossRef] [PubMed]
  7. D. W. Phillion, “General methods for generating phase-shifting interferometry algorithms,” Appl. Opt.36(31), 8098–8115 (1997).
    [CrossRef] [PubMed]
  8. J. Schmit and K. Creath, “Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry,” Appl. Opt.34(19), 3610–3619 (1995).
    [CrossRef] [PubMed]
  9. K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, 1993).
  10. J. M. Huntley, “Automated Analysis of Speckle Interferograms,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001).
  11. Y. Surrel, “Phase stepping: a new self-calibrating algorithm,” Appl. Opt.32(19), 3598–3600 (1993).
    [CrossRef] [PubMed]
  12. K. Creath and J. Schmit, “N-point spatial phase measurement techniques for nondestructive testing,” Opt. Lasers Eng.24(5-6), 365–379 (1996).
    [CrossRef]
  13. K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, “Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts,” J. Opt. Soc. Am. A14(4), 918–930 (1997).
    [CrossRef]
  14. C. Rathjen, “Statistical properties of phase-shift algorithms,” J. Opt. Soc. Am. A12(9), 1997–2008 (1995).
    [CrossRef]
  15. C. S. Guo, L. Zhang, H. T. Wang, J. Liao, and Y. Y. Zhu, “Phase-shifting error and its elimination in phase-shifting digital holography,” Opt. Lett.27(19), 1687–1689 (2002).
    [CrossRef] [PubMed]
  16. J. F. Mosiño, J. C. Gutiérrez-García, T. A. Gutiérrez-García, and J. M. Macías-Preza, “Two-frame algorithm to design quadrature filters in phase shifting interferometry,” Opt. Express18(24), 24405–24411 (2010).
    [CrossRef] [PubMed]
  17. P. D. Ruiz, J. M. Huntley, and G. H. Kaufmann, “Adaptive phase-shifting algorithm for temporal phase evaluation,” J. Opt. Soc. Am. A20(2), 325–332 (2003).
    [CrossRef] [PubMed]
  18. J. F. Mosiño, J. C. Gutiérrez-García, T. A. Gutiérrez-García, F. Castillo, M. A. García-González, and V. A. Gutiérrez-García, “Algorithm for phase extraction from a set of interferograms with arbitrary phase shifts,” Opt. Express19(6), 4908–4923 (2011).
    [CrossRef] [PubMed]
  19. P. Groot, “Derivation of algorithms for phase-shifting interferometry using the concept of a data-sampling window,” Appl. Opt.34(22), 4723–4730 (1995).
    [CrossRef] [PubMed]
  20. S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng.48(2), 133–140 (2010).
    [CrossRef]
  21. S. Ma, C. Quan, R. Zhu, and C. J. Tay, “Investigation of phase error correction for digital sinusoidal phase-shifting fringe projection profilometry,” Opt. Lasers Eng.50(8), 1107–1118 (2012).
    [CrossRef]
  22. J. A. N. Buytaert and J. J. J. Dirckx, “Study of the performance of 84 phase-shifting algorithms for interferometry,” J. Opt.40(3), 114–131 (2011).
    [CrossRef]

2012

S. Ma, C. Quan, R. Zhu, and C. J. Tay, “Investigation of phase error correction for digital sinusoidal phase-shifting fringe projection profilometry,” Opt. Lasers Eng.50(8), 1107–1118 (2012).
[CrossRef]

2011

2010

2009

2003

2002

2001

K. Larkin, “A self-calibrating phase-shifting algorithm based on the natural demodulation of two-dimensional fringe patterns,” Opt. Express9(5), 236–253 (2001).
[CrossRef] [PubMed]

T. M. Kaiser and H. Katterwe, “The application of 3D-microprofilometry as a tool in the surface diagnosis of fossil and sub-fossil vertebrate hard tissue. An example from the pliocene upper laetolil beds, Tanzania,” Int. J. Osteoarchaeol.11(5), 350–356 (2001).
[CrossRef]

1997

1996

Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt.35(1), 51–60 (1996).
[CrossRef] [PubMed]

K. Creath and J. Schmit, “N-point spatial phase measurement techniques for nondestructive testing,” Opt. Lasers Eng.24(5-6), 365–379 (1996).
[CrossRef]

H. Katterwe, “Modern approaches for the examination of toolmarks and other surface marks,” Forensic Sci. Rev.8, 45–72 (1996).

1995

1993

Buytaert, J. A. N.

J. A. N. Buytaert and J. J. J. Dirckx, “Study of the performance of 84 phase-shifting algorithms for interferometry,” J. Opt.40(3), 114–131 (2011).
[CrossRef]

Castillo, F.

Creath, K.

K. Creath and J. Schmit, “N-point spatial phase measurement techniques for nondestructive testing,” Opt. Lasers Eng.24(5-6), 365–379 (1996).
[CrossRef]

J. Schmit and K. Creath, “Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry,” Appl. Opt.34(19), 3610–3619 (1995).
[CrossRef] [PubMed]

Dirckx, J. J. J.

J. A. N. Buytaert and J. J. J. Dirckx, “Study of the performance of 84 phase-shifting algorithms for interferometry,” J. Opt.40(3), 114–131 (2011).
[CrossRef]

Doblado, D. M.

Farrant, D. I.

García-González, M. A.

Gorthi, S. S.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng.48(2), 133–140 (2010).
[CrossRef]

Groot, P.

Guo, C. S.

Gutiérrez-García, J. C.

Gutiérrez-García, T. A.

Gutiérrez-García, V. A.

Hernández, D. M.

Hibino, K.

Huntley, J. M.

Kaiser, T. M.

T. M. Kaiser and H. Katterwe, “The application of 3D-microprofilometry as a tool in the surface diagnosis of fossil and sub-fossil vertebrate hard tissue. An example from the pliocene upper laetolil beds, Tanzania,” Int. J. Osteoarchaeol.11(5), 350–356 (2001).
[CrossRef]

Katterwe, H.

T. M. Kaiser and H. Katterwe, “The application of 3D-microprofilometry as a tool in the surface diagnosis of fossil and sub-fossil vertebrate hard tissue. An example from the pliocene upper laetolil beds, Tanzania,” Int. J. Osteoarchaeol.11(5), 350–356 (2001).
[CrossRef]

H. Katterwe, “Modern approaches for the examination of toolmarks and other surface marks,” Forensic Sci. Rev.8, 45–72 (1996).

Kaufmann, G. H.

Larkin, K.

Larkin, K. G.

Liao, J.

Ma, S.

S. Ma, C. Quan, R. Zhu, and C. J. Tay, “Investigation of phase error correction for digital sinusoidal phase-shifting fringe projection profilometry,” Opt. Lasers Eng.50(8), 1107–1118 (2012).
[CrossRef]

Macías-Preza, J. M.

Mosiño, J. F.

Oreb, B. F.

Phillion, D. W.

Quan, C.

S. Ma, C. Quan, R. Zhu, and C. J. Tay, “Investigation of phase error correction for digital sinusoidal phase-shifting fringe projection profilometry,” Opt. Lasers Eng.50(8), 1107–1118 (2012).
[CrossRef]

Rastogi, P.

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng.48(2), 133–140 (2010).
[CrossRef]

Rathjen, C.

Ruiz, P. D.

Schmit, J.

K. Creath and J. Schmit, “N-point spatial phase measurement techniques for nondestructive testing,” Opt. Lasers Eng.24(5-6), 365–379 (1996).
[CrossRef]

J. Schmit and K. Creath, “Extended averaging technique for derivation of error-compensating algorithms in phase-shifting interferometry,” Appl. Opt.34(19), 3610–3619 (1995).
[CrossRef] [PubMed]

Surrel, Y.

Tay, C. J.

S. Ma, C. Quan, R. Zhu, and C. J. Tay, “Investigation of phase error correction for digital sinusoidal phase-shifting fringe projection profilometry,” Opt. Lasers Eng.50(8), 1107–1118 (2012).
[CrossRef]

Wang, H. T.

Zhang, L.

Zhu, R.

S. Ma, C. Quan, R. Zhu, and C. J. Tay, “Investigation of phase error correction for digital sinusoidal phase-shifting fringe projection profilometry,” Opt. Lasers Eng.50(8), 1107–1118 (2012).
[CrossRef]

Zhu, Y. Y.

Appl. Opt.

Forensic Sci. Rev.

H. Katterwe, “Modern approaches for the examination of toolmarks and other surface marks,” Forensic Sci. Rev.8, 45–72 (1996).

Int. J. Osteoarchaeol.

T. M. Kaiser and H. Katterwe, “The application of 3D-microprofilometry as a tool in the surface diagnosis of fossil and sub-fossil vertebrate hard tissue. An example from the pliocene upper laetolil beds, Tanzania,” Int. J. Osteoarchaeol.11(5), 350–356 (2001).
[CrossRef]

J. Opt.

J. A. N. Buytaert and J. J. J. Dirckx, “Study of the performance of 84 phase-shifting algorithms for interferometry,” J. Opt.40(3), 114–131 (2011).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lasers Eng.

K. Creath and J. Schmit, “N-point spatial phase measurement techniques for nondestructive testing,” Opt. Lasers Eng.24(5-6), 365–379 (1996).
[CrossRef]

S. S. Gorthi and P. Rastogi, “Fringe projection techniques: whither we are?” Opt. Lasers Eng.48(2), 133–140 (2010).
[CrossRef]

S. Ma, C. Quan, R. Zhu, and C. J. Tay, “Investigation of phase error correction for digital sinusoidal phase-shifting fringe projection profilometry,” Opt. Lasers Eng.50(8), 1107–1118 (2012).
[CrossRef]

Opt. Lett.

Other

K. Creath, “Temporal phase measurement methods,” in Interferogram Analysis, D. W. Robinson and G. T. Reid, eds. (Institute of Physics, 1993).

J. M. Huntley, “Automated Analysis of Speckle Interferograms,” in Digital Speckle Pattern Interferometry and Related Techniques, P. K. Rastogi, ed. (Wiley, 2001).

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Figures (12)

Fig. 1
Fig. 1

Plot of the polynomial characteristic of an harmonics suppress filter (a), an insensible to linear detuning filter (b), a mainly bias error filter (c) and a detuning + bias compensating filter (d). All were obtained with the two-frame filter method [16,18].

Fig. 2
Fig. 2

Normalized Fourier response of the four algorithms calculated with two-frame algorithm method.

Fig. 3
Fig. 3

Response of the filters proposed to detuning error, bias error and harmonics.

Fig. 4
Fig. 4

Phase shift detuning error of the filters in Fig. 1.

Fig. 5
Fig. 5

(a) Simulation of algorithms and their errors. (b) Detailed view of the red square region.

Fig. 6
Fig. 6

Simulated reconstruction of function “peaks” with the (a) MDE filter and the (c) Least-squares filter. Average errors are shown in (b) and (d) respectively.

Fig. 7
Fig. 7

Intensity patterns acquired from a FPP system. Phase shift values of the projected fringes are 0 (a), π/4 (b), π/2 (c), 3π/4 (d), π (e), 5π/4 (f), 3π/2 (g) and 7π/4 (h).

Fig. 8
Fig. 8

Phase estimator of images achieved from semi-fossilized samples. The ideal phase step is π/4.

Fig. 9
Fig. 9

A section of the wrapped phase achieved from experimental images. (a) Schmit’s filter. (b) Carré’s filter. (c) Hibino’s filter. (d) Surrel (N + 1) bucket filter.

Fig. 10
Fig. 10

A section of the wrapped phase achieved from experimental images. (a) Least-square filter. (b) MDE filter, cut off frequencies in 0, π/4, π/4, π/2, 3π/4, 3π/4, π. (c) MBE filter, cut off in 0, 0, π/4, π/2, π, π, 3π/4. (d) DBE filter, cut off in 0, 0, π/4, π/4, π/2, 3π/4, π.

Fig. 11
Fig. 11

A horizontal line of each image shown in Fig. 10.

Fig. 12
Fig. 12

Texture mapping onto the calculated 3D shape distribution.

Tables (2)

Tables Icon

Table 1 Errors of the filters according simulations.

Tables Icon

Table 2 Errors of the filters according the simulation of the “peaks” function in MATLAB.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

φ= tan 1 ( I 2 I 4 + I 6 I 8 I 1 I 3 + I 5 I 7 ).
tan( φ )= k=1 M b k I k k=1 M a k I k = [ b 1 b 2 ... b M ] I [ a 1 a 2 ... a M ] I = N I D I .
H( ω )= (2) M k=1 M sin[ ( ω α k )/2 ] .
tan( φ )= N I D I = b 1 I 1 + b 2 I 2 + b 3 I 3 + b 4 I 4 + b 5 I 5 + b 6 I 6 + b 7 I 7 + b 8 I 8 a 1 I 1 + a 2 I 2 + a 3 I 3 + a 4 I 4 + a 5 I 5 + a 6 I 6 + a 7 I 7 + a 8 I 8 .
N D = Ω k=1 M1 { cos( α k /2)[ 1, 1 ] sin( α k /2 )[ 1, 1 ] }.
N D = Ω k=1 7 { cos( α k /2)[ 1, 1 ] sin( α k /2 )[ 1, 1 ] }.
tan( ϕ )= [ 1, 1 2 , 1 2 , 1, 1, 1+ 2 , 1+ 2 , 1 ] I [ 1+ 2 , 1, 1, 1 2 , 1 2 , 1, 1, 1+ 2 ] I .
N r D r = Ω k=1 M1 { [ cos α k , 1 ] [ sin α k , 0 ] }.
N r D r = Ω k=1 7 { [ cos α k , 1 ] [ sin α k , 0 ] }.
tan( ϕ )= [ 2 , 2, 2 , 0, 2 , 2, 2 , 0 ] I [ 2, 0, 2 , 2, 2 , 0, 2 , 2 ] I .
tan( φ )= [ 1, 12 2 , 5+2 2 , 5+4 2 , 54 2 , 52 2 , 1+2 2 , 1 ] I [ 1, 12 2 , 52 2 , 5+4 2 , 5+4 2 , 52 2 , 12 2 , 1 ] I .
tan( ϕ )= [ 0, 12 2 , 0, 4 2 +5, 0, 52 2 , 0, 1 ] I [ 1, 0, 52 2 , 0, 4 2 +5, 0, 12 2 , 0 ] I .
tan( φ )= [ 1, 1 2 , 3+ 2 , 3+2 2 , 32 2 , 3 2 , 1+ 2 , 1 ] I [ 1, 1 2 , 3 2 , 3+2 2 , 3+2 2 , 3 2 , 1 2 , 1 ] I .
tan( φ )= [ 0, 1 2 , 0, 3+2 2 , 0, 3 2 , 0, 1 ] I [ 1, 0, 3 2 , 0, 3+2 2 , 0, 1 2 , 0 ] I .
tan( ϕ )= [ 1, 5+3 2 , 3 2 3, 96 2 , 9+6 2 , 3 2 +3, 3 2 5, 1 ] I [ 1 2 , 1, 6 2 +7, 75 2 , 75 2 , 6 2 +7, 1, 1 2 ] I .
tan( φ )= [ 1, 22 2 , 1+ 2 , 6+4 2 , 32 2 , 42 2 , 3+ 2 , 0 ] I [ 1, 2 , 5+3 2 , 2 2 , 54 2 , 2+3 2 , 1+ 2 , 2 ] I .

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