Abstract

The majority of focus detection criteria reported is based on amplitude contrast. Due to phase wrapping, phase contrast was previously reported unsuitable for focus finding tasks. By taking the advantage of multi-wavelength digital holography, we propose a new focus detection criterion based on phase contrast. Experimental results are presented to prove the feasibility of the developed criterion. Possible applications of the developed technology include inspecting machined surfaces in the auto industry.

© 2011 OSA

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References

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2010 (2)

2009 (3)

2008 (2)

2007 (1)

2006 (4)

2005 (1)

2004 (2)

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(29), 5429–5437 (2004).
[CrossRef] [PubMed]

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).

2003 (1)

2000 (1)

1999 (2)

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(4), 1074–1079 (1996).
[CrossRef]

1989 (1)

J. Gillespie and R. A. King, “The use of self-entropy as a focus measure in digital holography,” Pattern Recognit. Lett. 9(1), 19–25 (1989).
[CrossRef]

Aleksoff, C. C.

C. C. Aleksoff, “Multi-wavelength digital holographic metrology,” Proc. SPIE 6311, 63111D, 63111D-7 (2006).
[CrossRef]

Alfieri, D.

Callens, N.

Carl, D.

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(4), 761–770 (2006).
[CrossRef]

Clark, R. L.

Colomb, T.

Coppola, G.

Cuche, E.

Dakoff, A.

De Nicola, S.

Depeursinge, C.

Dirksen, D.

Dubois, F.

Emery, Y.

Ferraro, P.

Finizio, A.

Fratz, M.

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,” Pattern Recognit. Lett. 9(1), 19–25 (1989).
[CrossRef]

Grilli, S.

Han, R.

J. Liu, X. Song, R. Han, and H. Wang, “Autofocus method in digital holographic microscopy,” Proc. SPIE 7283, 72833Q, 72833Q-6 (2009).
[CrossRef]

Herminjard, S.

Höfler, H.

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).

Joannes, L.

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(4), 761–770 (2006).
[CrossRef]

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,” Pattern Recognit. Lett. 9(1), 19–25 (1989).
[CrossRef]

Knoche, S.

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).

Liu, J.

J. Liu, X. Song, R. Han, and H. Wang, “Autofocus method in digital holographic microscopy,” Proc. SPIE 7283, 72833Q, 72833Q-6 (2009).
[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).

Marquet, P.

Montfort, F.

Moratal, C.

Ni, J.

Li Xu and J. Ni, “3D resolution enhancement in multi-wavelength interferometric imaging by digital refocusing,” (Submitted manuscript to Appl. Opt. ).
[PubMed]

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(4), 1074–1079 (1996).
[CrossRef]

Pfeifer, M.

Pierattini, G.

Rappaz, B.

Rinehart, M. T.

Schockaert, C.

Shaked, N. T.

Song, X.

J. Liu, X. Song, R. Han, and H. Wang, “Autofocus method in digital holographic microscopy,” Proc. SPIE 7283, 72833Q, 72833Q-6 (2009).
[CrossRef]

Striano, V.

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(4), 1074–1079 (1996).
[CrossRef]

von Bally, G.

Wang, H.

J. Liu, X. Song, R. Han, and H. Wang, “Autofocus method in digital holographic microscopy,” Proc. SPIE 7283, 72833Q, 72833Q-6 (2009).
[CrossRef]

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).

Wax, A.

Xu, Li

Li Xu and J. Ni, “3D resolution enhancement in multi-wavelength interferometric imaging by digital refocusing,” (Submitted manuscript to Appl. Opt. ).
[PubMed]

Yourassowsky, C.

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(4), 1074–1079 (1996).
[CrossRef]

Appl. Opt. (6)

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).

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(4), 761–770 (2006).
[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(4), 1074–1079 (1996).
[CrossRef]

Opt. Express (5)

Opt. Lett. (5)

Pattern Recognit. Lett. (1)

J. Gillespie and R. A. King, “The use of self-entropy as a focus measure in digital holography,” Pattern Recognit. Lett. 9(1), 19–25 (1989).
[CrossRef]

Proc. SPIE (2)

C. C. Aleksoff, “Multi-wavelength digital holographic metrology,” Proc. SPIE 6311, 63111D, 63111D-7 (2006).
[CrossRef]

J. Liu, X. Song, R. Han, and H. Wang, “Autofocus method in digital holographic microscopy,” Proc. SPIE 7283, 72833Q, 72833Q-6 (2009).
[CrossRef]

Other (3)

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

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

J. W. Goodman, Introduction to Fourier Optics, 2nd ed (McGraw-Hill, 1996).

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Figures (11)

Fig. 1
Fig. 1

MWI imaging system.

Fig. 2
Fig. 2

Coordinate system for digital refocusing.

Fig. 3
Fig. 3

Experimental measurement of a 200mm out-of-focus penny.

Fig. 4
Fig. 4

Sequential height maps and focus detection curves.

Fig. 5
Fig. 5

Flow chart of the differential focus detection criterion.

Fig. 6
Fig. 6

height map before and after median filtering.

Fig. 7
Fig. 7

Feature enhancement: (a) h ¯ _ d i f f ( x , y ) { 0 m m , 150 m m } ; (b) histogram of (a); (c) histogram equalization without uncertainty elimination; (d) histogram of (c); (e) h ¯ _ d i f f ¯ e q ( x , y ) { 0 m m , 150 m m } feature enhancement after uncertainty elimination; (f) histogram of (e).

Fig. 8
Fig. 8

Focus detection curve η { d } for the out-of-focus penny in Fig. 3.

Fig. 9
Fig. 9

Result of other indicators: (a) entropy indicator; (b) variance indicator; (c) spectral indicator; (d) correlation coefficient indicator.

Fig. 10
Fig. 10

result of imaging a key 200mm out of focus.

Fig. 11
Fig. 11

result of “coherix” image. For clearance, in (d) the refocused height map is displayed within −60μm to + 35μm range after 3-by-3 median filtering.

Equations (15)

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I ( φ ) = I o b j + I r e f + 2 I o b j I r e f cos [ ( γ o b j γ r e f ) φ ]
γ o b j γ r e f = 2 π H λ = 2 n π + θ
θ = atan 2 ( I ( 3 π / 2 ) I ( π / 2 ) I ( 0 ) I ( π ) )
E ( x , y ) = 2 I o b j ( x , y ) I r e f · e i θ ( x , y )
S ( h ) = | 1 P p = 1 P exp [ j ( 4 π h λ p θ ( λ p ) ) ] |
E 2 ( x ' , y ' ) = F x ' , y ' 1 { exp [ j k d λ 2 2 ( u 2 + v 2 ) ] × [ F u , v + 1 E 1 ( x , y ) ] }
F η , ξ ± 1 f ( α , β ) = exp [ j 2 π ( α η + β ξ ) ] f ( α , β ) d α d β
E 2 ( X ' Δ M , Y ' Δ M ) = X , Y , U , V = 0 N 1 1 N 2 E 1 ( X Δ M , Y Δ M ) ×
× exp [ j π λ d M 2 N 2 Δ 2 ( U 2 + V 2 ) ] × exp { j 2 π N [ ( X X ' ) U + ( Y Y ' ) V ] }
h ¯ _ d i f f ( x , y ) { d , d l δ d } = h ¯ ( x , y ) { d } h ¯ ( x , y ) { d l δ d }
η { d } = V a r _ d i f f e q { d + l δ d , d } V a r _ d i f f e q { d , d l δ d } V a r _ d i f f e q { d , d l δ d } + V a r _ d i f f e q { d + l δ d , d }
E n t = x y { p ( x , y ) × log [ p ( x , y ) ] }
V a r = x y [ p ( x , y ) p m e a n ] 2
S p e c = u v log { 1 + | [ F x , y + 1 p ( x , y ) ] ( u , v ) | }
C C = x y [ p 1 ( x , y ) p 1 m e a n ] [ p 2 ( x , y ) p 2 m e a n ] { x y [ p 1 ( x , y ) p 1 m e a n ] 2 } { x y [ p 2 ( x , y ) p 2 m e a n ] 2 }

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