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Superfast multifrequency phase-shifting technique with optimal pulse width modulation

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Abstract

The technique of generating sinusoidal fringe patterns by defocusing squared binary structured ones has numerous merits for high-speed three-dimensional (3D) shape measurement. However, it is challenging for this method to realize a multifrequency phase-shifting (MFPS) algorithm because it is difficult to simultaneously generate high-quality sinusoidal fringe patterns with different periods. This paper proposes to realize an MFPS algorithm utilizing an optimal pulse width modulation (OPWM) technique that can selectively eliminate high-order harmonics of squared binary patterns. We successfully develop a 556 Hz system utilizing a three-frequency algorithm for simultaneously measuring multiple objects.

© 2011 Optical Society of America

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Supplementary Material (2)

Media 1: MOV (113 KB)     
Media 2: MOV (1056 KB)     

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Figures (3)

Fig. 1
Fig. 1 Quarter-wave symmetric OPWM waveform.
Fig. 2
Fig. 2 (a) Photograph of the captured scene; (b) One fringe pattern (λ1 = 60 pixels); (c) One fringe pattern (λ2 = 90 pixels); (d) One fringe pattern(λ3 = 102 pixels); (e) Wrapped phase ϕ1; (f) Wrapped phase ϕ2; (g) Wrapped phase ϕ3; (h) Equivalent phase difference Δϕ12; (i) Equivalent phase difference Δϕ13; (j) Resultant phase Δϕ123.
Fig. 3
Fig. 3 (a) Averaged image of the object ( Media 1); (b) 3-D result ( Media 2).

Equations (11)

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I 1 ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ 2 π / 3 ) ,
I 2 ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ ) ,
I 3 ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ + 2 π / 3 ) .
ϕ ( x , y ) = tan 1 [ 3 ( I 1 I 3 ) / ( 2 I 2 I 1 I 3 ) ] ,
I ( x , y ) = ( I 1 + I 2 + I 3 ) / 3 .
Φ = [ C h ( x , y ) / λ ] 2 π .
Δ Φ 12 = Φ 1 Φ 2 = [ C h ( x , y ) / λ 12 eq ] 2 π .
Δ ϕ 12 = [ Φ 1 Φ 2 ] ( mod 2 π ) = [ ϕ 1 ϕ 2 ] ( mod 2 π ) .
Δ ϕ 13 = [ ϕ 1 ϕ 3 ] ( mod 2 π ) = { [ C h ( x , y ) / λ 13 eq ] 2 π } ( mod 2 π ) ,
Δ ϕ 123 = ( Δ ϕ 13 Δ ϕ 12 ) ( mod 2 π ) = { [ C h ( x , y ) / λ 123 eq ] 2 π } ( mod 2 π ) .
b k = 4 π θ = 0 π / 2 f ( θ ) sin ( k θ ) d θ .
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