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Multi-frequency and multiple phase-shift sinusoidal fringe projection for 3D profilometry

E. B. Li, X. Peng, J. Xi, J. F. Chicharo, J. Q. Yao, and D. W. Zhang

Open Access Open Access

Abstract

In this paper, we report on a laser fringe projection set-up, which can generate fringe patterns with multiple frequencies and phase shifts. Stationary fringe patterns with sinusoidal intensity distributions are produced by the interference of two laser beams, which are frequency modulated by a pair of acousto-optic modulators (AOMs). The AOMs are driven by two RF signals with the same frequency but a phase delay between them. By changing the RF frequency and the phase delay, the fringe spatial frequency and phase shift can be electronically controlled, which allows high-speed switching from one frequency or phase to another thus makes a dynamic 3D profiling possible.

©2005 Optical Society of America

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Figures (7)
Fig. 1.
Fig. 1. Schematic diagram of the proposed fringe projector. BS - beam splitter; AOM - acousto-optic modulator; WP- wedge prism, PH - pinholes; BC - beam combiner; MO - microscope objective.

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Fig. 2.
Fig. 2. Simulated fringe pattern projected on a convex surface with a plane as reference.

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Fig. 3.
Fig. 3. Schematic diagram of the electronics developed for driving the AOMs, and for controlling the fringe spacing and the phase shift.

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Fig. 4.
Fig. 4. Image recorded by a CCD camera when the fringe pattern was projected on a dome-shaped object with a reference plane.

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Fig. 5.
Fig. 5. Fringes recorded with a nominal phase shift of 180 degrees.

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Fig. 6.
Fig. 6. Recorded fringe patterns with three different periods projected on a rectangle block

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Fig. 7.
Fig. 7. Reconstructed 3D surface plot of the rectangle block

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Equations (12)

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E ( x , y , z , t ) = E 0 w o w ( z ) exp { − x 2 + y 2 w 2 ( z ) } exp { − i [ k z − ω t − tan − 1 ( z z 0 ) + k x 2 + y 2 2 R ( z ) ] } ,
z 0 = π w 0 2 ⁄ λ ,
w ( z ) = w 0 [ 1 + ( z ⁄ z 0 ) 2 ] 1 ⁄ 2 ,
R ( z ) = z [ 1 + ( z 0 + z ) 2 ] .
E ( x , y , z , t ) = E 0 exp { − x 2 + y 2 w 0 2 } exp { − i [ k z − ω t ] } .
A 1 = A 10 exp [ − i ( K 1 X 1 − Ω t + Φ 1 ) ] ,
A 2 = A 20 exp [ − i ( K 2 X 2 − Ω t + Φ 2 ) ] .
E ′ 1 ( x 1 , y 1 , z 1 , t ) = E 10 exp { − x 1 2 + y 1 2 w 0 2 } exp { − i [ k 1 z 1 − ( ω 0 + Ω ) t + Φ 1 ] } ,
E 2 ′ ( x 2 , y 2 , z 2 , t ) = E 20 exp { − x 2 2 + y 2 2 w 0 2 } exp { − i [ k 2 z 2 − ( ω 0 + Ω ) t + Φ 2 ] } ,
E ( x , y , z , t ) = E ′ 10 w ′ 0 w ′ ( z ) exp { − r 2 w ′ 2 ( z ) } exp { − i [ k z + r 2 2 R 1 − ( ω 0 + Ω ) t + Φ 1 ] }
+ E ′ 20 w ′ 0 w ′ ( z ) exp { − r 2 w ′ 2 ( z ) } exp { − i [ k z + r 2 2 R 2 − ( ω 0 + Ω ) t + Φ 2 ] } ,
I ( x , y , z ) = [ E ( x , y , z , t ) · E ( x , y , z , t ) * ] .
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