Abstract

The principle of stroboscopic motion freezing of oscillating objects extends directly to interference microscopes that use coherence as part of the measurement principle. Analysis shows, however, that the fringe contrast loss for out-of-plane motion in stroboscopic interferometry is a wavelength-dependent phenomenon, which can alter the apparent nominal center wavelength of the white-light source. As in monochromatic systems, the key adjustable parameter is the duty cycle, equal to the product of the vibrational frequency and the pulse width. This theoretical study provides detailed graphs of expected errors as a function of the duty cycle, including fringe contrast loss, apparent wavelength shift, and measurement error.

© 2006 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. T. Eguchi and S. Okuma, "Apparatus for measuring fine periodic vibration displacement," Japanese patent 3150239 (1995).
  4. K. Nakano, H. Yoshida, K. Hane, S. Okuma, and T. Eguchi, "Fringe scanning interferometric imaging of small vibration using pulsed laser diode," Trans. SICE 31, 454-460 (1995).
  5. R. Gutierrez, K. Shcheglov, and T. Tang, "Interferometric system for precision imaging of vibrating structures," U.S. patent 6,291,145 (2001).
  6. E. Novak, M. B. Krell, and T. Browne, "Template-based software for accurate MEMS characterization," in Proc. SPIE 4980, 75-80 (2003).
    [CrossRef]
  7. A. Bosseboeuf and S. Petigrand, "Application of microscopic interferometry techniques in the MEMS field," in Proc. SPIE 5145, 1-16 (2003).
    [CrossRef]
  8. C. Gorecki, ed., "Microsystems engineering: metrology and inspection III," in Proc. SPIE 5145 (2003).
  9. P. de Groot and X. Colonna de Lega, "Signal modeling for low coherence height-scanning interference microscopy," Appl. Opt. 43, 4821-4830 (2004).
    [CrossRef] [PubMed]
  10. H.-C. Hsu, C.-H. Tung, C.-F. Kao, and C. C. Chang, "A white-light profiling algorithm adopting the multiwavelength interferometric technique," in Proc. SPIE 5531, 244-249 (2004).
    [CrossRef]
  11. E. Novak and F. Pasop, "Three-dimensional characterization of MEMS devices," in IMAPS Conference Microtech (Cambridge, U.K., 2004).

2004

P. de Groot and X. Colonna de Lega, "Signal modeling for low coherence height-scanning interference microscopy," Appl. Opt. 43, 4821-4830 (2004).
[CrossRef] [PubMed]

H.-C. Hsu, C.-H. Tung, C.-F. Kao, and C. C. Chang, "A white-light profiling algorithm adopting the multiwavelength interferometric technique," in Proc. SPIE 5531, 244-249 (2004).
[CrossRef]

2003

E. Novak, M. B. Krell, and T. Browne, "Template-based software for accurate MEMS characterization," in Proc. SPIE 4980, 75-80 (2003).
[CrossRef]

A. Bosseboeuf and S. Petigrand, "Application of microscopic interferometry techniques in the MEMS field," in Proc. SPIE 5145, 1-16 (2003).
[CrossRef]

1995

K. Nakano, H. Yoshida, K. Hane, S. Okuma, and T. Eguchi, "Fringe scanning interferometric imaging of small vibration using pulsed laser diode," Trans. SICE 31, 454-460 (1995).

1987

1979

Bosseboeuf, A.

A. Bosseboeuf and S. Petigrand, "Application of microscopic interferometry techniques in the MEMS field," in Proc. SPIE 5145, 1-16 (2003).
[CrossRef]

Browne, T.

E. Novak, M. B. Krell, and T. Browne, "Template-based software for accurate MEMS characterization," in Proc. SPIE 4980, 75-80 (2003).
[CrossRef]

Chang, C. C.

H.-C. Hsu, C.-H. Tung, C.-F. Kao, and C. C. Chang, "A white-light profiling algorithm adopting the multiwavelength interferometric technique," in Proc. SPIE 5531, 244-249 (2004).
[CrossRef]

de Groot, P.

de Lega, X. Colonna

Eguchi, T.

K. Nakano, H. Yoshida, K. Hane, S. Okuma, and T. Eguchi, "Fringe scanning interferometric imaging of small vibration using pulsed laser diode," Trans. SICE 31, 454-460 (1995).

T. Eguchi and S. Okuma, "Apparatus for measuring fine periodic vibration displacement," Japanese patent 3150239 (1995).

Fusek, R. L.

Gorecki, C.

C. Gorecki, ed., "Microsystems engineering: metrology and inspection III," in Proc. SPIE 5145 (2003).

Gutierrez, R.

R. Gutierrez, K. Shcheglov, and T. Tang, "Interferometric system for precision imaging of vibrating structures," U.S. patent 6,291,145 (2001).

Hane, K.

K. Nakano, H. Yoshida, K. Hane, S. Okuma, and T. Eguchi, "Fringe scanning interferometric imaging of small vibration using pulsed laser diode," Trans. SICE 31, 454-460 (1995).

Harris, J. S.

Hsu, H.-C.

H.-C. Hsu, C.-H. Tung, C.-F. Kao, and C. C. Chang, "A white-light profiling algorithm adopting the multiwavelength interferometric technique," in Proc. SPIE 5531, 244-249 (2004).
[CrossRef]

Kao, C.-F.

H.-C. Hsu, C.-H. Tung, C.-F. Kao, and C. C. Chang, "A white-light profiling algorithm adopting the multiwavelength interferometric technique," in Proc. SPIE 5531, 244-249 (2004).
[CrossRef]

Krell, M. B.

E. Novak, M. B. Krell, and T. Browne, "Template-based software for accurate MEMS characterization," in Proc. SPIE 4980, 75-80 (2003).
[CrossRef]

Kwon, O. Y.

Marcheski, J. S.

Nakano, K.

K. Nakano, H. Yoshida, K. Hane, S. Okuma, and T. Eguchi, "Fringe scanning interferometric imaging of small vibration using pulsed laser diode," Trans. SICE 31, 454-460 (1995).

Novak, E.

E. Novak, M. B. Krell, and T. Browne, "Template-based software for accurate MEMS characterization," in Proc. SPIE 4980, 75-80 (2003).
[CrossRef]

E. Novak and F. Pasop, "Three-dimensional characterization of MEMS devices," in IMAPS Conference Microtech (Cambridge, U.K., 2004).

Okuma, S.

K. Nakano, H. Yoshida, K. Hane, S. Okuma, and T. Eguchi, "Fringe scanning interferometric imaging of small vibration using pulsed laser diode," Trans. SICE 31, 454-460 (1995).

T. Eguchi and S. Okuma, "Apparatus for measuring fine periodic vibration displacement," Japanese patent 3150239 (1995).

Pasop, F.

E. Novak and F. Pasop, "Three-dimensional characterization of MEMS devices," in IMAPS Conference Microtech (Cambridge, U.K., 2004).

Petigrand, S.

A. Bosseboeuf and S. Petigrand, "Application of microscopic interferometry techniques in the MEMS field," in Proc. SPIE 5145, 1-16 (2003).
[CrossRef]

Shcheglov, K.

R. Gutierrez, K. Shcheglov, and T. Tang, "Interferometric system for precision imaging of vibrating structures," U.S. patent 6,291,145 (2001).

Shough, D. M.

Tang, T.

R. Gutierrez, K. Shcheglov, and T. Tang, "Interferometric system for precision imaging of vibrating structures," U.S. patent 6,291,145 (2001).

Tung, C.-H.

H.-C. Hsu, C.-H. Tung, C.-F. Kao, and C. C. Chang, "A white-light profiling algorithm adopting the multiwavelength interferometric technique," in Proc. SPIE 5531, 244-249 (2004).
[CrossRef]

Williams, R. A.

Yoshida, H.

K. Nakano, H. Yoshida, K. Hane, S. Okuma, and T. Eguchi, "Fringe scanning interferometric imaging of small vibration using pulsed laser diode," Trans. SICE 31, 454-460 (1995).

Appl. Opt.

Opt. Lett.

Proc. SPIE

H.-C. Hsu, C.-H. Tung, C.-F. Kao, and C. C. Chang, "A white-light profiling algorithm adopting the multiwavelength interferometric technique," in Proc. SPIE 5531, 244-249 (2004).
[CrossRef]

E. Novak, M. B. Krell, and T. Browne, "Template-based software for accurate MEMS characterization," in Proc. SPIE 4980, 75-80 (2003).
[CrossRef]

A. Bosseboeuf and S. Petigrand, "Application of microscopic interferometry techniques in the MEMS field," in Proc. SPIE 5145, 1-16 (2003).
[CrossRef]

C. Gorecki, ed., "Microsystems engineering: metrology and inspection III," in Proc. SPIE 5145 (2003).

Trans. SICE

K. Nakano, H. Yoshida, K. Hane, S. Okuma, and T. Eguchi, "Fringe scanning interferometric imaging of small vibration using pulsed laser diode," Trans. SICE 31, 454-460 (1995).

Other

R. Gutierrez, K. Shcheglov, and T. Tang, "Interferometric system for precision imaging of vibrating structures," U.S. patent 6,291,145 (2001).

T. Eguchi and S. Okuma, "Apparatus for measuring fine periodic vibration displacement," Japanese patent 3150239 (1995).

E. Novak and F. Pasop, "Three-dimensional characterization of MEMS devices," in IMAPS Conference Microtech (Cambridge, U.K., 2004).

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Figures (4)

Fig. 1
Fig. 1

(a) Variation in fringe contrast with vibrational phase φ. (b) Variation in measurement error with vibrational phase φ. Duty cycle of D = 10 % , vibrational amplitude of Λ = 250   nm .

Fig. 2
Fig. 2

(a) Dependence of the fringe contrast on interference spatial frequency. (b) Resultant distortion in the frequency domain of an interferometer signal, showing, in particular, a shift in the peak wavelength. Vibrational amplitude of 250   nm , vibrational phase of 0, and three different pulse duty cycles.

Fig. 3
Fig. 3

(a) Dependence on interference spatial frequency K of the phase error (argument of u) attributable to stroboscopic interferometry for a vibrational amplitude of Λ = 250   nm and a vibrational phase of φ 0 = π / 2 . (b) Resultant measurement error as a function of vibrational amplitude.

Fig. 4
Fig. 4

(a) Dependence on duty cycle D of the fringe contrast at a vibrational phase of φ 0 = 0 . (b) Dependence on D of the relative measurement error (which equals the error divided by the vibrational amplitude Λ) at a vibrational phase of φ 0 = π / 2 .

Equations (24)

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I ( ζ ) = 0 q ( K ) cos [ ( ζ h ) K + ω ( K ) ] d K ,
I ( ζ ) = q ( K ) exp ( i ζ K ) d K ,
q ( K ) = q ( K ) 2 exp [ i ω ( K ) i h K ] ,
q ( K ) = q ( K ) 2 exp [ i ω ( K ) i h K ] .
ξ = Λ sin ( 2 π f t ) .
I ( ζ , ξ ) = q ( K ) exp [ i ( ζ + ξ ) K ] d K .
I ( ζ ) = 1 δ t t 1 t 2 q ( K ) exp ( i ζ K ) exp ( i ξ K ) d K d t ,
I ( ζ ) = [ 1 δ t t 1 t 2 exp ( i ξ K ) d t ] q ( K ) exp ( i ζ K ) d K .
I ( ζ ) = u ( K ) q ( K ) exp ( i ζ K ) d K ,
u ( K ) = 1 δ t t 1 t 2 exp [ i Λ K sin ( 2 π f t ) ] d t .
u ( K ) = 1 2 π D π D π D exp [ i Λ K sin ( φ + φ 0 ) ] d φ ,
D = f δ t .
φ 0 = 0 , 2 π , 4 π .
sin ( φ ) φ
u ( K ) = 1 2 π D π D π D exp ( i Λ K φ ) d φ ,
u ( K ) sin ( Λ K π D ) Λ K πD ( object   deflection   ξ = 0 ) .
2 π f t = π / 2 , 5 π / 2 , 9 π / 2 .
u ( K ) = 1 2 π D π D π D exp [ i Λ K cos ( φ ) ] d φ .
u ( K ) exp [ i Λ K cos ( φ ) ¯ ]
cos ( φ ) ¯ = 1 2 π D π D π D cos ( φ ) d φ .
cos ( φ ) ¯ = sin ( π D ) π D ,
u ( K ) exp [ i Λ K sin ( π D ) π D ]
( object   deflection   ξ Λ ) .
Δ ξ ξ = sin ( π D ) π D

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