Abstract

Fiber-optical sensors have some crucial advantages compared with rigid optical systems. They allow miniaturization and flexibility of system setups. Nevertheless, optical principles such as low-coherence interferometry can be realized by use of fiber optics. We developed and realized an approach for a fiber-optical sensor, which is based on the analysis of spatially modulated low-coherence interferograms. The system presented consists of three units, a miniaturized sensing probe, a broadband fiber-coupled light source, and an adapted Michelson interferometer, which is used as an optical receiver. Furthermore, the signal processing procedure, which was developed for the interferogram analysis in order to achieve nanometer measurement accuracy, is discussed. A system prototype has been validated thoroughly in different experiments. The results approve the accuracy of the sensor.

© 2007 Optical Society of America

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References

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  1. F. T. S. Yu, Fiber Optic Sensors (Dekker, 2002).
    [CrossRef]
  2. W. A. Reed, M. F. Yan, and M. J. Schnitzer, "Gradient-index fiber-optic microprobes for minimally invasive in vivo low-coherence interferometry," Opt. Lett. 27, 1794-1796 (2002).
    [CrossRef]
  3. F. Depiereux, S. Schmitz, and S. C. Lange, "Sensoren aus CFK," F&M Mechatronik 11-12, 22-24 (2003).
  4. B. E. Bouma and G. J. Tearney, eds., Handbook of Optical Coherence Tomography (Dekker, 2001).
  5. M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).
  6. M. Fleischer, R. Windecker, and H. J. Tiziani, "Fast algorithms for data reduction in modern optical three-dimensional profile measurement systems with MMX technology," Appl. Opt. 39, 1290-1297 (2000).
    [CrossRef]
  7. "Nano positioning and nano measuring machine (NMM-1)," Datasheet, Sios Messtechnik GmbH, Ilmenau, Germany (2006), http://www.sios.de.
  8. Rubert Ltd., ,i>Precision Reference Specimens, item 531 (2006), http://www.rubert.co.uk/Reference.htm.
  9. Geometrical Product Specifications (GPS)--Surface Texture: Profile Method--Nominal Characteristics of Contact (Stylus) Instruments, ANSI Doc. ISO 3274 (American National Standards Institute, 1996).

2003 (1)

F. Depiereux, S. Schmitz, and S. C. Lange, "Sensoren aus CFK," F&M Mechatronik 11-12, 22-24 (2003).

2002 (1)

2000 (1)

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Bouma, B. E.

B. E. Bouma and G. J. Tearney, eds., Handbook of Optical Coherence Tomography (Dekker, 2001).

Depiereux, F.

F. Depiereux, S. Schmitz, and S. C. Lange, "Sensoren aus CFK," F&M Mechatronik 11-12, 22-24 (2003).

Fleischer, M.

Lange, S. C.

F. Depiereux, S. Schmitz, and S. C. Lange, "Sensoren aus CFK," F&M Mechatronik 11-12, 22-24 (2003).

Reed, W. A.

Schmitz, S.

F. Depiereux, S. Schmitz, and S. C. Lange, "Sensoren aus CFK," F&M Mechatronik 11-12, 22-24 (2003).

Schnitzer, M. J.

Tearney, G. J.

B. E. Bouma and G. J. Tearney, eds., Handbook of Optical Coherence Tomography (Dekker, 2001).

Tiziani, H. J.

Windecker, R.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

Yan, M. F.

Yu, F. T. S.

F. T. S. Yu, Fiber Optic Sensors (Dekker, 2002).
[CrossRef]

Appl. Opt. (1)

F&M Mechatronik (1)

F. Depiereux, S. Schmitz, and S. C. Lange, "Sensoren aus CFK," F&M Mechatronik 11-12, 22-24 (2003).

Opt. Lett. (1)

Other (6)

F. T. S. Yu, Fiber Optic Sensors (Dekker, 2002).
[CrossRef]

B. E. Bouma and G. J. Tearney, eds., Handbook of Optical Coherence Tomography (Dekker, 2001).

M. Born and E. Wolf, Principles of Optics (Cambridge U. Press, 1999).

"Nano positioning and nano measuring machine (NMM-1)," Datasheet, Sios Messtechnik GmbH, Ilmenau, Germany (2006), http://www.sios.de.

Rubert Ltd., ,i>Precision Reference Specimens, item 531 (2006), http://www.rubert.co.uk/Reference.htm.

Geometrical Product Specifications (GPS)--Surface Texture: Profile Method--Nominal Characteristics of Contact (Stylus) Instruments, ANSI Doc. ISO 3274 (American National Standards Institute, 1996).

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Figures (12)

Fig. 1
Fig. 1

(Color online) System design.

Fig. 2
Fig. 2

(Color online) CFP-sensor prototype.

Fig. 3
Fig. 3

(Color online) Michelson interferometer used as a receiving unit.

Fig. 4
Fig. 4

Signal in 8 bit gray values.

Fig. 5
Fig. 5

Result of low-frequency elimination.

Fig. 6
Fig. 6

Original signal and contrast curve. In gray: Identified values that are necessary for further analyzing.

Fig. 7
Fig. 7

Original signal and Gaussian fit of the maximum contrast section.

Fig. 8
Fig. 8

Simulated interferograms (a) for a SLD with l c = 12 μ m emitting at 840   nm , (b) for a SLD with l c = 4 μ m emitting at 932   nm , and (c) for a superposition of interferograms (a) and (b).

Fig. 9
Fig. 9

Simulated interferograms for different SNRs. (a) For a SNR = 10   dB , (b) for a SNR = 5   dB , (c) for a SNR = 0   dB .

Fig. 10
Fig. 10

Results of repeatability measurements.

Fig. 11
Fig. 11

Result of measured sine wave standard (height: 1   μ m ).

Fig. 12
Fig. 12

Result of measured step (height: 5 .1   μ m ± 1% ).

Tables (2)

Tables Icon

Table 1 Standard Deviation of Distance Measurements Obtained From Envelope and Phase Evaluation of Simulated Noisy Signals for Different SNRs

Tables Icon

Table 2 Calculated Standard Deviation of Repeatability Measurements

Equations (8)

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

I ( x ) = I 1 + I 2 + 2 I 1 I 2 | γ ( x ) | cos ( k ¯ x + φ 0 ) ,
S 1 ( k ) = 2 ln   2 π Δ k 1   exp ( 4   ln ( 2 ) ( k k ¯ ) 2 ( Δ k 1 ) 2 ) ,
| γ 1 ( x ) | = exp ( x 2 ( Δ k 1 ) 2 / ( 4 ln ( 2 ) ) 2 ) .
S 2 ( k ) = 1 2 ( δ ( k k ¯ 1 ) + δ ( k k ¯ 2 ) ) ,
| γ 2 ( z ) | = cos ( Δ k 2 z / 2 ) ,
I ( x ) = I 1 + I 2 + 2 I 1 I 2 | γ 1 ( x ) | | γ 2 ( x ) | cos ( k ¯ x + φ 0 ) ,
l c 1 2 2   ln ( 2 ) λ ¯ 1 λ ¯ 2 λ ¯ 2 λ ¯ 1 ,
SNR = 10   log ( mean   square   amplitude   of   signal variance   of   noise ) .

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