Abstract

Interference fringes with different periods are projected on an object surface. There is a constant phase point where the phase of the fringe is kept at a constant value while the period is scanning. Multiple optical fields with different periods on the object surface are made from detected phases of the fringes. The multiple optical fields are backpropagated to the constant phase point of the phase where all of the phases of the multiple backpropagated fields become the same value and the amplitude of the sum of the multiple backpropagated fields becomes maximum. The distance of the backpropagation provides the position of the object surface. Some experiments show that this method can measure an object surface with discontinuities of several millimeters with high accuracy of several micrometers.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2001 (1)

L. H. Jin, Y. Otani, and T. Yoshizawa, "Shadow moiré profilometry by frequency sweeping," Opt. Eng. 40, 1383-1386 (2001).
[CrossRef]

2000 (1)

C. Wagner, W. Osten, and S. Seebacher, "Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring," Opt. Eng. 39, 79-85 (2000).
[CrossRef]

1999 (1)

1997 (5)

H. J. Tiziani, B. Franze, and P. Haible, "Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser," J. Mod. Opt. 44, 1485-1496 (1997).
[CrossRef]

H. O. Saldner and J. M. Huntley, "Temporal phase unwrapping application to surface profiling of discontinuous objects," Appl. Opt. 36, 2770-2775 (1997).
[CrossRef] [PubMed]

J. M. Huntley and H. O. Saldner, "Error-reduction methods for shape measurement by temporal phase unwrapping," J. Opt. Soc. Am. A 14, 3188-3196 (1997).
[CrossRef]

J. M. Huntley and H. O. Saldner, "Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms," Meas. Sci. Technol. 8, 986-992 (1997).
[CrossRef]

S. Kuwamura and I. Yamaguchi, "Wavelength scanning profilometry for real-time surface shape measurement," Appl. Opt. 36, 4473-4482 (1997).
[CrossRef] [PubMed]

1994 (1)

1993 (1)

1990 (1)

O. Sasaki, T. Suzuki, and K. Takahashi, "Sinusoidal phase modulating laser diode interferometer with feedback control system to eliminate external disturbance," Opt. Eng. 29, 1511-1515 (1990).
[CrossRef]

1986 (1)

1982 (1)

Appl. Opt. (6)

J. Mod. Opt. (1)

H. J. Tiziani, B. Franze, and P. Haible, "Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser," J. Mod. Opt. 44, 1485-1496 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Meas. Sci. Technol. (1)

J. M. Huntley and H. O. Saldner, "Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms," Meas. Sci. Technol. 8, 986-992 (1997).
[CrossRef]

Opt. Eng. (3)

L. H. Jin, Y. Otani, and T. Yoshizawa, "Shadow moiré profilometry by frequency sweeping," Opt. Eng. 40, 1383-1386 (2001).
[CrossRef]

O. Sasaki, T. Suzuki, and K. Takahashi, "Sinusoidal phase modulating laser diode interferometer with feedback control system to eliminate external disturbance," Opt. Eng. 29, 1511-1515 (1990).
[CrossRef]

C. Wagner, W. Osten, and S. Seebacher, "Direct shape measurement by digital wavefront reconstruction and multiwavelength contouring," Opt. Eng. 39, 79-85 (2000).
[CrossRef]

Other (2)

K. Creath and J. C. Wyant, "Moire and fringe projection techniques," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 653-686.

J. E. Greivenkamp and J. H. Bruning, "Phase shifting interferometers," in Optical Shop Testing, D. Malacara, ed. (Wiley, 1992), pp. 501-598.

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Figures (10)

Fig. 1
Fig. 1

Schematic for multiperiod fringe projection and detection of the fringe patterns by sinusoidal phase-modulating interferometry.

Fig. 2
Fig. 2

Height h from standard plane AB in measurement of surface profile S.

Fig. 3
Fig. 3

Simulation results of the backpropagation method for one point object. (a) Amplitude distribution, (b) phase distribution.

Fig. 4
Fig. 4

Simulation results of the backpropagation method when the measured phase distribution contains a measurement error with standard deviation σ of 0 .36 rad . (a) Amplitude distribution, (b) phase distribution.

Fig. 5
Fig. 5

Unwrapped result of measured phase distribution α m , which contains a measurement error with standard deviation σ of 0.36 rad .

Fig. 6
Fig. 6

Experiment setup of the multiperiod fringe projection for surface profile measurement.

Fig. 7
Fig. 7

Backpropagation results for one point of x 0 = 1.45 mm , y = 1.79 mm on the object surface. (a) Amplitude distribution, (b) phase distribution.

Fig. 8
Fig. 8

Measured height distribution of the step profile made by two gauge blocks.

Fig. 9
Fig. 9

Cross section of the measured height distribution of Fig. 8 at y = 1.79 mm .

Fig. 10
Fig. 10

Measured height distributions of two rough surfaces forming the step profile.

Tables (1)

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Table 1 Standard Deviations of z g , z A , and z ϕ for Different Values of σ when z 0 = 1525 μm

Equations (18)

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α m ( z p , x p ) = k m x p + π 2 ,
α m ( x , z ) = k m ( x cos 2 β + z sin 2 β ) + π 2 .
I m ( x 0 , t ) = A m + B m cos [ a cos ω c t + α m ( x 0 , z 0 ) ] ,
m = 0 ,   …   ,   M 1.
α m z ( z 0 ) = k m z 0 sin 2 β .
D m ( x 0 , z 0 ) = B m exp [ j α m z ( z 0 ) ] .
U m ( x 0 , z ) = D m exp [ j α m z ( z ) ] , m = 0 ,   …   ,   M 1.
U R ( z ) = m = 0 M 1 U m ( z ) = m = 0 M 1 A m exp [ j S k m ( z z 0 ) ] ,
U R ( z ) = exp { j [ k 0 + ( M 1 ) 2 Δ k ] S z D } sin ( M 2 Δ k z D S ) sin ( 1 2 Δ k z D S ) = A R exp ( j ϕ R ) .
A R = sin ( B k 2 z D S ) sin ( Δ k 2 z D S ) ,
ϕ R = [ k 0 + ( M 1 ) 2 Δ k ] S z D = k C S z D ,
x r = x 0 cos β + z 0 sin β .
h ( x r , y r ) = ( z 0 x 0 tan β ) cos β .
Δ k = 2 π M 1 ( 1 P 0 1 P M 1 ) = ( k M 1 k 0 ) M 1 .
z max = 2 π Δ k S .
P C = 2 π k C S = 2 P 0 P M 1 ( P 0 + P M 1 ) S .
q = α m z k m = z 0 sin 2 β .
I m ( t , x f ) = A m + B m cos ( a cos ω c t + k m x f ) .

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