Abstract

An approach using a liquid-crystal spatial light modulator (LC-SLM) to enlarge the depth measuring range of the projected fringe profilometry is presented. This approach is especially applicable to detect dynamic objects with micro-scale sizes. Compared with a typical 2D image system, the LC-SLM provides a better performance for a 3D shape sensing system. The main advantages include (1) a much higher allowance to increase in the depth measuring range, (2) easiness to compensate perspective distortion and geometric distortion, (3) very high accuracy (in the micron-range) and (4) only one phase measurement needed for operation.

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References

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    [CrossRef]
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2008

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46(2), 106–116 (2008).
[CrossRef]

W. H. Su, C. Y. Kuo, C. C. Wang, and C. F. Tu, “Projected fringe profilometry with multiple measurements to form an entire shape,” Opt. Express 16(6), 4069–4077 (2008).
[CrossRef] [PubMed]

2007

2005

2003

K. Kubala, E. Dowski, and W. T. Cathey, “Reducing complexity in computational imaging systems,” Opt. Express 11(18), 2102–2108 (2003).
[CrossRef] [PubMed]

H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1-3), 65–80 (2003).
[CrossRef]

2001

K. Körner, R. Windecker, M. Fleischer, and H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40(8), 1653–1660 (2001).
[CrossRef]

R. Windecker, M. Fleischer, K. Körner, and H. J. Tiziani, “Testing micro devices with fringe projection and white-light interfeometry,” Opt. Lasers Eng. 36(2), 141–154 (2001).
[CrossRef]

1999

1997

1995

1990

J. Ojeda-Castaneda and L. R. Berriel-Valdos, “Zone plate for arbitrarily high focal depth,” Appl. Opt. 29(7), 994–997 (1990).
[CrossRef] [PubMed]

B. E. A. Saleh and K. Lu, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29(3), 240–245 (1990).
[CrossRef]

1983

1972

G. Ha¨usler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6(1), 38–42 (1972).
[CrossRef]

1971

Berriel-Valdos, L. R.

Bradburn, S.

Busca, G.

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46(2), 106–116 (2008).
[CrossRef]

Cathey, W. T.

Cho, H.

Dowski, E.

Dowski, E. R.

Fleischer, M.

K. Körner, R. Windecker, M. Fleischer, and H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40(8), 1653–1660 (2001).
[CrossRef]

R. Windecker, M. Fleischer, K. Körner, and H. J. Tiziani, “Testing micro devices with fringe projection and white-light interfeometry,” Opt. Lasers Eng. 36(2), 141–154 (2001).
[CrossRef]

Ha¨usler, G.

G. Ha¨usler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6(1), 38–42 (1972).
[CrossRef]

Hong, D.

Kim, M.

Körner, K.

K. Körner, R. Windecker, M. Fleischer, and H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40(8), 1653–1660 (2001).
[CrossRef]

R. Windecker, M. Fleischer, K. Körner, and H. J. Tiziani, “Testing micro devices with fringe projection and white-light interfeometry,” Opt. Lasers Eng. 36(2), 141–154 (2001).
[CrossRef]

Kubala, K.

Kuo, C. Y.

Liu, H.

H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1-3), 65–80 (2003).
[CrossRef]

Liu, Z.

Lu, K.

B. E. A. Saleh and K. Lu, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29(3), 240–245 (1990).
[CrossRef]

Mino, M.

Mutoh, K.

Ojeda-Castaneda, J.

Okano, Y.

Park, K.

Reichard, K.

W. H. Su, K. Shi, Z. Liu, B. Wang, K. Reichard, and S. Yin, “A large-depth-of-field projected fringe profilometry using supercontinuum light illumination,” Opt. Express 13(3), 1025–1032 (2005).
[CrossRef] [PubMed]

H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1-3), 65–80 (2003).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and K. Lu, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29(3), 240–245 (1990).
[CrossRef]

Shi, K.

Su, W. H.

Takeda, M.

Tiziani, H. J.

R. Windecker, M. Fleischer, K. Körner, and H. J. Tiziani, “Testing micro devices with fringe projection and white-light interfeometry,” Opt. Lasers Eng. 36(2), 141–154 (2001).
[CrossRef]

K. Körner, R. Windecker, M. Fleischer, and H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40(8), 1653–1660 (2001).
[CrossRef]

Tu, C. F.

Tucker, S. C.

Wang, B.

Wang, C. C.

Windecker, R.

R. Windecker, M. Fleischer, K. Körner, and H. J. Tiziani, “Testing micro devices with fringe projection and white-light interfeometry,” Opt. Lasers Eng. 36(2), 141–154 (2001).
[CrossRef]

K. Körner, R. Windecker, M. Fleischer, and H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40(8), 1653–1660 (2001).
[CrossRef]

Yin, S.

W. H. Su, K. Shi, Z. Liu, B. Wang, K. Reichard, and S. Yin, “A large-depth-of-field projected fringe profilometry using supercontinuum light illumination,” Opt. Express 13(3), 1025–1032 (2005).
[CrossRef] [PubMed]

H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1-3), 65–80 (2003).
[CrossRef]

Zappa, E.

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46(2), 106–116 (2008).
[CrossRef]

Appl. Opt.

Opt. Commun.

H. Liu, W. H. Su, K. Reichard, and S. Yin, “Calibration-based phase-shifting projected fringe profilometry for accurate absolute 3D surface profile measurement,” Opt. Commun. 216(1-3), 65–80 (2003).
[CrossRef]

G. Ha¨usler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6(1), 38–42 (1972).
[CrossRef]

Opt. Eng.

K. Körner, R. Windecker, M. Fleischer, and H. J. Tiziani, “One-grating projection for absolute three-dimensional profiling,” Opt. Eng. 40(8), 1653–1660 (2001).
[CrossRef]

B. E. A. Saleh and K. Lu, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29(3), 240–245 (1990).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

R. Windecker, M. Fleischer, K. Körner, and H. J. Tiziani, “Testing micro devices with fringe projection and white-light interfeometry,” Opt. Lasers Eng. 36(2), 141–154 (2001).
[CrossRef]

E. Zappa and G. Busca, “Comparison of eight unwrapping algorithms applied to Fourier-transform profilometry,” Opt. Lasers Eng. 46(2), 106–116 (2008).
[CrossRef]

Other

L. B. Jackson, Digital Filters and Signal Processing (Toppan, 1996), Chap. 6.

J. W. Goodman, Introduction to Fourier Optics (Roberts & Company, Englewood, Colorado, USA, 2005), Chap. 5.

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Figures (17)

Fig. 1
Fig. 1

Configuration of an incoherent system.

Fig. 2
Fig. 2

Phase profile of the pupil function.

Fig. 3
Fig. 3

Magnitude of the optical transfer functions: (a) ψ = 10, (b) ψ = 15, and (c) ψ = 40.

Fig. 4
Fig. 4

Phase modulation using the LC-SLM.

Fig. 5
Fig. 5

Response of the LC-SLM when θp = 170° and θa = −150: (a) Phase modulation, and (b) intensity variation.

Fig. 6
Fig. 6

Distribution of the input signals ranging from level 50 to 190: the brighter one represents the stronger input signal.

Fig. 7
Fig. 7

(a) Extended DOF system using a LC-SLM as the phase mask. (b) Optical configuration to observe the impulse response of the extended DOF system.

Fig. 8
Fig. 8

Schematic setup of a projected fringe profilometric system using the phase mask.

Fig. 9
Fig. 9

Systematic calibration: (a) depth calibration, and (b) lateral calibration.

Fig. 10
Fig. 10

Schematic setup for the inspected surface.

Fig. 11
Fig. 11

Appearance of the recorded images at (a) z = −750μm, (b) z = 30μm, and (c) z = 700μm.

Fig. 12
Fig. 12

Retrieved images at (a) z = −750μm, (b) z = 30μm, and (c) z = 700μm.

Fig. 13
Fig. 13

Phase distributions at (a) z = −750μm, (b) z = 30μm, and (c) z = 700μm.

Fig. 14
Fig. 14

Retrieved 3D profiles at (a) z = −750μm, (b) z = 30μm, and (c) z = 700μm.

Fig. 15
Fig. 15

(a) Appearance of the projected fringes on the tilted object. (b) Retrieved image.

Fig. 16
Fig. 16

Retrieved 3D profile of the tilted object.

Fig. 17
Fig. 17

(a) Appearance of an in-focused image through a microscope. (b) Retrieved image with a proper mask strength when the object was shifted with a displacement of 300μm behind the object plane.

Equations (12)

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

I i ( x i , y i , ψ ) = | h ( x i , y i , ψ ; x o , y o ) | 2 I o ( x o , y o ) d x o d y o ,
ψ = π λ ( 1 d o + 1 d i 1 f ) .
h ( x i , y i , ψ ; x o , y o ) = h ( x i M x o , y i M y o , ψ ) = A λ 2 d i d o P ( x , y ) exp [ j ψ ( x 2 + y 2 ) ] exp { j 2 π λ d i [ ( x i M x o ) x + ( y i M y o ) y ] } d x d y ,
H ( f x , f y , ψ ) = [ P ( τ x + f x / 2 , τ y + f y / 2 ) e j k 2 [ ( τ x + f x / 2 ) 2 + ( τ y + f y / 2 ) 2 ] ψ × P * ( τ x f x / 2 , τ y f y / 2 ) e j k 2 [ ( τ x f x / 2 ) 2 + ( τ y f y / 2 ) 2 ] ψ ] d τ x d τ y ,
{ I i ( x i , y i , ψ ) } = H ( f x , f y , ψ ) { I o ( x o , y o ) } ,
H ( f x , f y , ψ ) H ( f x , f y , 0 ) .
I o ( x o , y o ) = 1 { { I i ( x i , y i , ψ ) } H ( f x , f y , ψ ) } 1 { { I i ( x i , y i , ψ ) } H ( f x , f y , 0 ) } ,
P ( x , y ) = { 1 2 exp [ j α ( x 3 + y 3 ) ] , | x | L / 2 , | y | L / 2 0 , o t h e r w i s e ,
H ( f x , f y , ψ ) { π 12 α 1 | f x f y | exp [ j α 4 ( f x 3 + f y 3 ) ] exp [ j ψ 2 3 α ( f x + f y ) ] , i f f x f y 0 1 , i f f x f y = 0 .
H ( f x , f y , ψ ) H ( f x , f y , 0 ) = { π 12 α 1 | f x f y | exp [ j α 4 ( f x 3 + f y 3 ) ] , i f f x f y 0 1 , i f f x f y = 0 .
z ( φ ) = n = 0 N c n φ n ,
{ x = a 1 z + a o y = b 1 z + b o ,

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