Abstract

Three-dimensional (3D) shape reconstructions and metrology measurements are often limited by depth-of-field constraints. Current focus-detection-based techniques are insufficient to profile out-of-focus 3D objects with high axial accuracy. Extended-focus imaging (EFI) techniques can improve the range and precision of such measurements. By incorporating digital refocusing with multiwavelength interferometry, a holographic imaging solution is presented in this paper to accurately measure 3D objects over a large depth range. Accuracy and repeatability of the proposed EFI technique are validated by digital simulations and refocusing experiments. A reconstruction example demonstrates the feasibility of high-precision 3D measurements of objects deeper than the system’s classical depth of field.

© 2012 Optical Society of America

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2011 (2)

2010 (2)

2009 (3)

2008 (3)

2007 (1)

2006 (4)

F. Montfort, T. Colomb, F. Charrière, J. Kuhn, P. Marquet, E. Cuche, S. Herminjard, and C. Depeursinge, “Submicrometer optical tomography by multiple-wavelength digital holographic microscopy,” Appl. Opt. 45, 8209–8217 (2006).
[CrossRef]

Y. J. Choo and B. S. Kang, “The characteristics of the particle position along an optical axis in particle holography,” Meas. Sci. Technol. 17, 761–770 (2006).
[CrossRef]

C. C. Aleksoff, “Multi-wavelength digital holographic metrology,” Proc. SPIE 6311, 63111D (2006).
[CrossRef]

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14, 61–74 (2006).
[CrossRef]

2005 (1)

2004 (3)

2003 (1)

2002 (1)

2001 (1)

2000 (1)

1999 (2)

1998 (1)

1997 (1)

1996 (1)

Y. Zou, G. Pedrini, and H. Tiziani, “Surface contouring in a video frame by changing the wavelength of a diode laser,” Opt. Eng. 35, 1074–1079 (1996).
[CrossRef]

1994 (1)

S. K. Nayar and Y. Nakagawa, “Shape from focus,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 824–831 (1994).
[CrossRef]

1989 (1)

J. Gillespie and R. A. King, “The use of self-entropy as a focus measure in digital holography,” Patt. Recogn. Lett. 9, 19–25 (1989).
[CrossRef]

1980 (1)

1974 (1)

1966 (1)

P. Carré, “Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Aleksoff, C.

Aleksoff, C. C.

C. C. Aleksoff, “Multi-wavelength digital holographic metrology,” Proc. SPIE 6311, 63111D (2006).
[CrossRef]

Alfieri, D.

Bonsch, G.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Bothe, T.

Brangaccio, D. J.

Bruning, J. H.

Burke, J.

Callens, N.

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14, 61–74 (2006).
[CrossRef]

Carl, D.

Carré, P.

P. Carré, “Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Charrière, F.

Choo, Y. J.

Y. J. Choo and B. S. Kang, “The characteristics of the particle position along an optical axis in particle holography,” Meas. Sci. Technol. 17, 761–770 (2006).
[CrossRef]

Clark, R. L.

Colomb, T.

Coppola, G.

Cuche, E.

Dakoff, A.

De Nicola, S.

Depeursinge, C.

Dirksen, D.

Dubois, F.

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14, 61–74 (2006).
[CrossRef]

F. Dubois, L. Joannes, and J. C. Legros, “Improved three-dimensional imaging with a digital holography microscope with a source of partial spatial coherence,” Appl. Opt. 38, 7085–7094 (1999).
[CrossRef]

Emery, Y.

Falaggis, K.

Ferraro, P.

Finizio, A.

Fratz, M.

Gallagher, J. E.

Gass, J.

Giel, D. M.

Gillespie, J.

J. Gillespie and R. A. King, “The use of self-entropy as a focus measure in digital holography,” Patt. Recogn. Lett. 9, 19–25 (1989).
[CrossRef]

Grilli, S.

Helmers, H.

Herminjard, S.

Herriott, D. R.

Höfler, H.

Itoh, M.

Javidi, B.

Jenness, N. J.

Jin, H.

L. Ma, H. Wang, Y. Li, and H. Jin, “Numerical reconstruction of digital holograms for three-dimensional shape measurement,” J. Opt. Soc. Am. A 6, 396–400 (2004).
[CrossRef]

Joannes, L.

Jones, J. D. C.

Kandulla, J.

Kang, B. S.

Y. J. Choo and B. S. Kang, “The characteristics of the particle position along an optical axis in particle holography,” Meas. Sci. Technol. 17, 761–770 (2006).
[CrossRef]

Kato, J.

Kemper, B.

Khmaladze, A.

Kim, M.

Kim, M. K.

King, R. A.

J. Gillespie and R. A. King, “The use of self-entropy as a focus measure in digital holography,” Patt. Recogn. Lett. 9, 19–25 (1989).
[CrossRef]

Knoche, S.

Kuhn, J.

Kühn, J.

Langehanenberg, P.

Legros, J. C.

Li, Y.

L. Ma, H. Wang, Y. Li, and H. Jin, “Numerical reconstruction of digital holograms for three-dimensional shape measurement,” J. Opt. Soc. Am. A 6, 396–400 (2004).
[CrossRef]

Lo, C. M.

Ma, L.

L. Ma, H. Wang, Y. Li, and H. Jin, “Numerical reconstruction of digital holograms for three-dimensional shape measurement,” J. Opt. Soc. Am. A 6, 396–400 (2004).
[CrossRef]

Marquet, P.

Mater, M.

Mizuno, J.

Montfort, F.

Moratal, C.

Nakagawa, Y.

S. K. Nayar and Y. Nakagawa, “Shape from focus,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 824–831 (1994).
[CrossRef]

Nayar, S. K.

S. K. Nayar and Y. Nakagawa, “Shape from focus,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 824–831 (1994).
[CrossRef]

Nazarathy, M.

Ni, J.

Nicolaus, A.

Ohta, S.

Pavillon, N.

Pedrini, G.

Y. Zou, G. Pedrini, and H. Tiziani, “Surface contouring in a video frame by changing the wavelength of a diode laser,” Opt. Eng. 35, 1074–1079 (1996).
[CrossRef]

Pfeifer, M.

Pierattini, G.

Rappaz, B.

Rinehart, M. T.

Rosenfeld, D. P.

Schockaert, C.

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14, 61–74 (2006).
[CrossRef]

Schodel, R.

Shaked, N. T.

Shamir, J.

Striano, V.

Tachiki, M. L.

Tiziani, H.

Y. Zou, G. Pedrini, and H. Tiziani, “Surface contouring in a video frame by changing the wavelength of a diode laser,” Opt. Eng. 35, 1074–1079 (1996).
[CrossRef]

Towers, C. E.

Towers, D. P.

von Bally, G.

Wang, H.

L. Ma, H. Wang, Y. Li, and H. Jin, “Numerical reconstruction of digital holograms for three-dimensional shape measurement,” J. Opt. Soc. Am. A 6, 396–400 (2004).
[CrossRef]

Wax, A.

White, A. D.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Xu, L.

Yamaguchi, I.

Yatagai, T.

Yourassowsky, C.

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14, 61–74 (2006).
[CrossRef]

Yu, H.

Zhang, T.

Zou, Y.

Y. Zou, G. Pedrini, and H. Tiziani, “Surface contouring in a video frame by changing the wavelength of a diode laser,” Opt. Eng. 35, 1074–1079 (1996).
[CrossRef]

Appl. Opt. (10)

T. Bothe, J. Burke, and H. Helmers, “Spatial phase shifting in electronic speckle pattern interferometry: minimization of phase reconstruction errors,” Appl. Opt. 36, 5310–5316 (1997).
[CrossRef]

F. Dubois, L. Joannes, and J. C. Legros, “Improved three-dimensional imaging with a digital holography microscope with a source of partial spatial coherence,” Appl. Opt. 38, 7085–7094 (1999).
[CrossRef]

I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, “Image formation in phase-shifting digital holography and applications to microscopy,” Appl. Opt. 40, 6177–6186 (2001).
[CrossRef]

R. Schodel, A. Nicolaus, and G. Bonsch, “Phase-stepping interferometry: methods for reducing errors caused by camera nonlinearities,” Appl. Opt. 41, 55–63 (2002).
[CrossRef]

J. H. Bruning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974).
[CrossRef]

J. Kandulla, B. Kemper, S. Knoche, and G. von Bally, “Two-wavelength method for endoscopic shape measurement by spatial phase-shifting speckle-interferometry,” Appl. Opt. 43, 5429–5437 (2004).
[CrossRef]

M. L. Tachiki, M. Itoh, and T. Yatagai, “Simultaneous depth determination of multiple objects by focus analysis in digital holography,” Appl. Opt. 47, D144–D153 (2008).
[CrossRef]

P. Langehanenberg, B. Kemper, D. Dirksen, and G. von Bally, “Autofocusing in digital holographic phase contrast microscopy on pure phase objects for live cell imaging,” Appl. Opt. 47, D176–D182 (2008).
[CrossRef]

F. Montfort, T. Colomb, F. Charrière, J. Kuhn, P. Marquet, E. Cuche, S. Herminjard, and C. Depeursinge, “Submicrometer optical tomography by multiple-wavelength digital holographic microscopy,” Appl. Opt. 45, 8209–8217 (2006).
[CrossRef]

D. Carl, M. Fratz, M. Pfeifer, D. M. Giel, and H. Höfler, “Multiwavelength digital holography with autocalibration of phase shifts and artificial wavelengths,” Appl. Opt. 48, H1–H8 (2009).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

S. K. Nayar and Y. Nakagawa, “Shape from focus,” IEEE Trans. Pattern Anal. Mach. Intell. 16, 824–831 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

L. Ma, H. Wang, Y. Li, and H. Jin, “Numerical reconstruction of digital holograms for three-dimensional shape measurement,” J. Opt. Soc. Am. A 6, 396–400 (2004).
[CrossRef]

Meas. Sci. Technol. (1)

Y. J. Choo and B. S. Kang, “The characteristics of the particle position along an optical axis in particle holography,” Meas. Sci. Technol. 17, 761–770 (2006).
[CrossRef]

Metrologia (1)

P. Carré, “Installation et utilisation du comparateur photoélectrique et interférentiel du Bureau International des Poids et Mesures,” Metrologia 2, 13–23 (1966).
[CrossRef]

Opt. Eng. (1)

Y. Zou, G. Pedrini, and H. Tiziani, “Surface contouring in a video frame by changing the wavelength of a diode laser,” Opt. Eng. 35, 1074–1079 (1996).
[CrossRef]

Opt. Express (7)

Opt. Lett. (8)

Patt. Recogn. Lett. (1)

J. Gillespie and R. A. King, “The use of self-entropy as a focus measure in digital holography,” Patt. Recogn. Lett. 9, 19–25 (1989).
[CrossRef]

Proc. SPIE (1)

C. C. Aleksoff, “Multi-wavelength digital holographic metrology,” Proc. SPIE 6311, 63111D (2006).
[CrossRef]

Other (5)

http://www.coherix.com/automotive .

National Institute of Standards and Technology ATP project: “High definition metrology and processes—-2 micron manufacturing,” www.atp.nist.gov .

Howard W. Sams & Co. Engineers, Reference Data for Radio Engineers, 6th ed. (Sams, 1975), Chap. 46, p. 7.

MATLAB, by Mathworks, http://www.Mathworks.com .

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

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Figures (9)

Fig. 1.
Fig. 1.

Optical arrangement of a typical MWI imaging system.

Fig. 2.
Fig. 2.

Coordinate system for digital refocusing.

Fig. 3.
Fig. 3.

Maximum refocusing distance dmax and magnification (N=2048, Δ=7.5μm, λ=850nm).

Fig. 4.
Fig. 4.

Simulation “UMICH” (a) original test plate, (b) ideal in-focus phase map, (c) out-of-focus noisy phase map, (d) blurred out-of-focus 3D map, (e) refocused 3D map using Eq. (14), (f) refocused 3D map using Eq. (9).

Fig. 5.
Fig. 5.

Experimental measurement of a penny: (a) in-focus measurement, (b) out-of-focus measurement, (c) refocused measurement using Eq. (14), (d) refocused measurement using Eq. (9). In every subpicture: left, rearranged 3D map to show penny patterns; upper-right: original 3D map scaled from 1mm to 3 mm; lower-right: hologram example.

Fig. 6.
Fig. 6.

Height measurement result.

Fig. 7.
Fig. 7.

Test part with tooling marks.

Fig. 8.
Fig. 8.

3D shape reconstructed via (a) MWI refocusing approach, (b) plateau-by-plateau sharpness focus detection and refocusing approach.

Fig. 9.
Fig. 9.

Zoomed views of plateau D (penny and tooling mark).

Tables (2)

Tables Icon

Table 1. Experimental Parameters

Tables Icon

Table 2. Refocusing Distances of Plateaus (/mm)

Equations (17)

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

I(φ)=Iobj+Iref+2IobjIrefcos[(γobjγref)φ],
γobjγref=2πHλ=2nπ+θ,
θ=atan2(q=1QI(φq)sin(2(q1)π/Q)q=1QI(φq)cos(2(q1)π/Q)),
θ=atan2(I(3π/2)I(π/2)I(0)I(π)),
E(x,y)=2Iobj(x,y)Irefeiθ(x,y),
S(h)=|1Pp=1Pexp[j(4πhλpθ(λp))]|,
E2(x,y)=exp(jkd)Fx,y1{exp[jkdλ22(u2+v2)]×[Fu,v+1E1(x,y)]},
Fη,ξ±1f(α,β)=exp[j2π(αη+βξ)]f(α,β)dαdβ.
x=XΔM,y=YΔM,x=XΔM,y=YΔM,u=UMNΔ,v=VMNΔ,
E2(XΔM,YΔM)=exp(j2πdλ)X,Y,U,V=0N11N2E1(XΔM,YΔM)×exp[jπλdM2N2Δ2(U2+V2)]×exp{j2πN[(XX)U+(YY)V]}.
πλdM2N2Δ2[Umax2(Umax1)2]π.
dNΔ22λM2=dmax.
exp(j2πdλ),
exp[jπλdM2N2Δ2(U2+V2)].
|(2πdλ)λ|=|2πdλ2|,
|[πλdM2N2Δ2(U2+V2)]λ|=|πdM2N2Δ2(U2+V2)|<|2πdM2Δ2|(sinceU,V<N),
E2(XΔM,YΔM)=X,Y,U,V=0N11N2E1(XΔM,YΔM)×exp[jπλdM2N2Δ2(U2+V2)]×exp{j2πN[(XX)U+(YY)V]}

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