Abstract

Orthogonal projection sampling mode was proposed to reconstruct the incomplete-data flow field in optical computerized tomography (OCT). With numerical simulation technique, a two-peak plane symmetric flow field was reconstructed in different sampling modes and discussed in simulated results is the reconstructive accuracy with error indexes, such as mean square error (MSE) and peak error (PE). The corresponding experiments were researched with a Fabry–Perot rotary interferometer. The results indicated that the errors were drastically reduced and the precision was improved when orthogonal projection sampling mode was adopted in the reconstruction of the incomplete data field. The MSE obtained with orthogonal sampling mode was decreased 72.81% from that of the sequential projection sampling mode (the difference between the MSE obtained with the orthogonal sampling mode and that with the sequential sampling mode divided by the MSE of the sequential sampling mode) and the PE was decreased by 73.97%. The precision obtained from the experimental results reached 10%, which showed the orthogonal projection sampling could be a practicable sampling mode for the incomplete data field reconstruction in OCT and could provide some guidance for the flow-field measurement and apparatus design in the practical situation.

© 2008 Optical Society of America

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References

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2006

B. Zhang, Y. Song, Y. Song, and A. He, “New reconstruction algorithm for moire tomography in flow field measurements,” Opt. Eng. 45, 117002 (2006).
[CrossRef]

H. Yao, X. Ye, J. Zhou, and A. He, “Orthogonal projection sampling method used in reconstruction of incomplete data field,” Microw. Opt. Technol. Lett. 48, 2333-2336 (2006).
[CrossRef]

Y. Song, B. Zhang, and A. He, “Algebraic iterative algorithm for deflection tomography and its application to density flow fields in a hypersonic wind tunnel,” Appl. Opt. 45, 8092-8101(2006).
[CrossRef] [PubMed]

2003

N. Saxena, G. L. Baheti, P. K. Khatri, K. C. Songara, L. R. Meghwal, and V. L. Meena, “Computed tomography reconstructions using multiple discrete detectors,” Insight: Non-Destructive Testing and Condition Monitoring 45, 682-685(2003).
[CrossRef]

H. Yao and A. He, “Application of optical computerized tomography in the heat elimination of an aeroengine blade,” Microw. Opt. Technol. Lett. 38, 117-119 (2003).
[CrossRef]

H. Koizumi, T. Yamamoto, A. Maki, Y. Yamashita, H. Sato, H. Kawaguchi, and N. Ichikawa, “Optical topography: practical problems and new applications,” Appl. Opt. 42, 3054-3062(2003).
[CrossRef] [PubMed]

Z. Chen and R. Ning, “Filling the radon domain in computed tomography by local convex combination,” Appl. Opt. 42, 7043-7051 (2003).
[CrossRef] [PubMed]

1999

1994

Baheti, G. L.

N. Saxena, G. L. Baheti, P. K. Khatri, K. C. Songara, L. R. Meghwal, and V. L. Meena, “Computed tomography reconstructions using multiple discrete detectors,” Insight: Non-Destructive Testing and Condition Monitoring 45, 682-685(2003).
[CrossRef]

Chen, Z.

He, A.

B. Zhang, Y. Song, Y. Song, and A. He, “New reconstruction algorithm for moire tomography in flow field measurements,” Opt. Eng. 45, 117002 (2006).
[CrossRef]

H. Yao, X. Ye, J. Zhou, and A. He, “Orthogonal projection sampling method used in reconstruction of incomplete data field,” Microw. Opt. Technol. Lett. 48, 2333-2336 (2006).
[CrossRef]

Y. Song, B. Zhang, and A. He, “Algebraic iterative algorithm for deflection tomography and its application to density flow fields in a hypersonic wind tunnel,” Appl. Opt. 45, 8092-8101(2006).
[CrossRef] [PubMed]

H. Yao and A. He, “Application of optical computerized tomography in the heat elimination of an aeroengine blade,” Microw. Opt. Technol. Lett. 38, 117-119 (2003).
[CrossRef]

D. Wu and A. He, “Measurement of three-dimensional temperature fields with interferometric tomography,” Appl. Opt. 38, 3468-3473 (1999).
[CrossRef]

W. Yao and A. He, “Application of Gabor transformation to the two-dimensional projection extraction in interferometric tomography,” J. Opt. Soc. Am. A 16, 258-263 (1999).
[CrossRef]

Ichikawa, N.

Kawaguchi, H.

Khatri, P. K.

N. Saxena, G. L. Baheti, P. K. Khatri, K. C. Songara, L. R. Meghwal, and V. L. Meena, “Computed tomography reconstructions using multiple discrete detectors,” Insight: Non-Destructive Testing and Condition Monitoring 45, 682-685(2003).
[CrossRef]

Koizumi, H.

Maki, A.

Meena, V. L.

N. Saxena, G. L. Baheti, P. K. Khatri, K. C. Songara, L. R. Meghwal, and V. L. Meena, “Computed tomography reconstructions using multiple discrete detectors,” Insight: Non-Destructive Testing and Condition Monitoring 45, 682-685(2003).
[CrossRef]

Meghwal, L. R.

N. Saxena, G. L. Baheti, P. K. Khatri, K. C. Songara, L. R. Meghwal, and V. L. Meena, “Computed tomography reconstructions using multiple discrete detectors,” Insight: Non-Destructive Testing and Condition Monitoring 45, 682-685(2003).
[CrossRef]

Meier, G. E. A.

Middendorf, P.

Ning, R.

Obermeir, F.

Sato, H.

Saxena, N.

N. Saxena, G. L. Baheti, P. K. Khatri, K. C. Songara, L. R. Meghwal, and V. L. Meena, “Computed tomography reconstructions using multiple discrete detectors,” Insight: Non-Destructive Testing and Condition Monitoring 45, 682-685(2003).
[CrossRef]

Soller, C.

Song, Y.

Y. Song, B. Zhang, and A. He, “Algebraic iterative algorithm for deflection tomography and its application to density flow fields in a hypersonic wind tunnel,” Appl. Opt. 45, 8092-8101(2006).
[CrossRef] [PubMed]

B. Zhang, Y. Song, Y. Song, and A. He, “New reconstruction algorithm for moire tomography in flow field measurements,” Opt. Eng. 45, 117002 (2006).
[CrossRef]

B. Zhang, Y. Song, Y. Song, and A. He, “New reconstruction algorithm for moire tomography in flow field measurements,” Opt. Eng. 45, 117002 (2006).
[CrossRef]

Songara, K. C.

N. Saxena, G. L. Baheti, P. K. Khatri, K. C. Songara, L. R. Meghwal, and V. L. Meena, “Computed tomography reconstructions using multiple discrete detectors,” Insight: Non-Destructive Testing and Condition Monitoring 45, 682-685(2003).
[CrossRef]

Wenskus, R.

Wu, D.

Yamamoto, T.

Yamashita, Y.

Yao, H.

H. Yao, X. Ye, J. Zhou, and A. He, “Orthogonal projection sampling method used in reconstruction of incomplete data field,” Microw. Opt. Technol. Lett. 48, 2333-2336 (2006).
[CrossRef]

H. Yao and A. He, “Application of optical computerized tomography in the heat elimination of an aeroengine blade,” Microw. Opt. Technol. Lett. 38, 117-119 (2003).
[CrossRef]

Yao, W.

Ye, X.

H. Yao, X. Ye, J. Zhou, and A. He, “Orthogonal projection sampling method used in reconstruction of incomplete data field,” Microw. Opt. Technol. Lett. 48, 2333-2336 (2006).
[CrossRef]

Zhang, B.

B. Zhang, Y. Song, Y. Song, and A. He, “New reconstruction algorithm for moire tomography in flow field measurements,” Opt. Eng. 45, 117002 (2006).
[CrossRef]

Y. Song, B. Zhang, and A. He, “Algebraic iterative algorithm for deflection tomography and its application to density flow fields in a hypersonic wind tunnel,” Appl. Opt. 45, 8092-8101(2006).
[CrossRef] [PubMed]

Zhou, J.

H. Yao, X. Ye, J. Zhou, and A. He, “Orthogonal projection sampling method used in reconstruction of incomplete data field,” Microw. Opt. Technol. Lett. 48, 2333-2336 (2006).
[CrossRef]

Appl. Opt.

Insight: Non-Destructive Testing and Condition Monitoring

N. Saxena, G. L. Baheti, P. K. Khatri, K. C. Songara, L. R. Meghwal, and V. L. Meena, “Computed tomography reconstructions using multiple discrete detectors,” Insight: Non-Destructive Testing and Condition Monitoring 45, 682-685(2003).
[CrossRef]

J. Opt. Soc. Am. A

Microw. Opt. Technol. Lett.

H. Yao, X. Ye, J. Zhou, and A. He, “Orthogonal projection sampling method used in reconstruction of incomplete data field,” Microw. Opt. Technol. Lett. 48, 2333-2336 (2006).
[CrossRef]

H. Yao and A. He, “Application of optical computerized tomography in the heat elimination of an aeroengine blade,” Microw. Opt. Technol. Lett. 38, 117-119 (2003).
[CrossRef]

Opt. Eng.

B. Zhang, Y. Song, Y. Song, and A. He, “New reconstruction algorithm for moire tomography in flow field measurements,” Opt. Eng. 45, 117002 (2006).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Model of the simulated two-peak plane symmetric flow field.

Fig. 2
Fig. 2

The simulated original field.

Fig. 3
Fig. 3

Three-dimensional reconstructed results of the original simulated field in different sampling modes: (a) result of eight projections in orthogonal sampling mode, (b) result of eight projections in sequential sampling mode, (c) result of four projections in orthogonal sampling mode, (d) result of four projections in sequential sampling mode, (e) result of two projections in orthogonal sampling mode, and (f) result of two projections in sequential sampling mode.

Fig. 4
Fig. 4

Two projection interferograms at 1 ° and 45 ° viewing angles.

Fig. 5
Fig. 5

Three-dimensional temperature distribution and temperature topography of the cross section: (a) 3D temperature distribution reconstructed in complete data sampling mode, (b) temperature topography reconstructed in complete data sampling mode; (c) 3D temperature distribution reconstructed in orthogonal sampling mode, sampling angular ranges [ 0 ° 45 ° ] and [ 90 ° 135 ° ] ; (d) temperature topography reconstructed in orthogonal sampling mode, sampling angular ranges [ 0 ° 45 ° ] and [ 90 ° 135 ° ] ; (e) 3D temperature distribution reconstructed in sequential sampling mode, sampling angular range [ 0 ° 90 ° ] ; (f) temperature topography reconstructed in sequential sampling mode, sampling angular range [ 0 ° 90 ° ] .

Fig. 6
Fig. 6

Comparison between reconstructed temperatures and measured temperature: series 1, measured temperature results; series 2, reconstructed results in complete data sampling mode; series 3, reconstructed results in orthogonal sampling mode; series 4, reconstructed results in sequential sampling mode.

Tables (1)

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Table 1 Mean Square Error and Peak Error of Each Reconstructed Field

Equations (7)

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Φ = 2 π λ L [ n ( x , y , z 0 ) n 0 ] d s ,
m ( p , θ ) = 1 λ ( n ( x , y ) n 0 ) · δ ( p x cos θ y sin θ ) d x d y = 1 λ Δ n ( x , y ) d s ,
m i ( p , θ ) = j = 1 n Δ n j A i j ,
Δ n j ( k ) = Δ n j ( k 1 ) + ω m i ( p , θ ) j = 1 n Δ n j A i j ( j = 1 n A i j ) A i j · A i j i = 1 , 2 , , I ,
Δ n j = R s , if     i , j S Δ n j = Δ n j , if     i , j S ,
n 1 ρ = k ,
ρ = M P R T ,

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