Abstract

An evaluating method is proposed for aligning fiber-optic image bundles finely to detector arrays with coupled contrast transfer function (CTF). The mathematical expression of coupled CTF is deduced based on the definition of the CTF. The paper discusses the characteristics and variation law of coupled CTF at the Nyquist frequency domain. The results show that the value of coupled CTF is closely related with aligning accuracy. According to the value of coupled CTF, it can accurately determine the situation of aligning between fiber-optic image bundles and detector pixels. Accordingly, this paper proposes a new method to evaluate the aligning accuracy between fiber-optic image bundles and detector pixels using the coupled CTF.

© 2011 Optical Society of America

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2010

J. He, Z. Zhou, H. Dong, G. Zhang, and J. Ou, “Design of coefficient-adjustable FBG strain sensors,” Opt. Precis. Eng. 18, 2339–2346 (2010).

2004

C. Latry, V. Despringre, and C. Valorge, “Automatic MTF measurement through a least square method,” Proc. SPIE 5570, 233–244 (2004).
[CrossRef]

2002

E. Rave and A. Katzir, “Ordered bundles of infrared transmitting silver halide fibers: attenuation, resolution and crosstalk in long and flexible bundles,” Opt. Eng. 41, 1467–1468(2002).
[CrossRef]

1999

B. Dekel, A. Katzir, and A. Inberg, “A simple thermal imaging system based on hollow glass waveguides or silver halide fibers as scanning elements for medical applications,” Proc. SPIE 3596, 82–90 (1999).
[CrossRef]

1998

K. Muarta, H. Fujiwara, and R. Sato, “Two-dimensional measurement of optical transfer function by holographic techniques,” Proc. SPIE 46, 104–114 (1998).

1990

J. Feltz, “Development of the modulation transfer function and contrast transfer function for discrete systems, particularly charge-coupled devices,” Opt. Eng. 29, 893–904(1990).
[CrossRef]

1986

D. D. Babrc, J. J. Lowe, C. Sheldon, E. S. D’Ippoltto, A. G. Osler, and W. F. Mogran, “A description of the focal plane/detector test and evaluation lab at MDAC-HB,” Proc. SPIE 685, 80–87 (1986).

1983

A. A. Friesem, L. U. Silberg, and Y. Parallel, “transmission of images through single optical fibers,” Proc. IEEE 71, 208–221 (1983).
[CrossRef]

1975

1974

D. H. Seib, “Carrier diffusion degradation of modulation transfer function in charge coupled imager,” IEEE Trans. Electron Devices 21, 210–217 (1974).
[CrossRef]

1964

Babrc, D. D.

D. D. Babrc, J. J. Lowe, C. Sheldon, E. S. D’Ippoltto, A. G. Osler, and W. F. Mogran, “A description of the focal plane/detector test and evaluation lab at MDAC-HB,” Proc. SPIE 685, 80–87 (1986).

D’Ippoltto, E. S.

D. D. Babrc, J. J. Lowe, C. Sheldon, E. S. D’Ippoltto, A. G. Osler, and W. F. Mogran, “A description of the focal plane/detector test and evaluation lab at MDAC-HB,” Proc. SPIE 685, 80–87 (1986).

Dekel, B.

B. Dekel, A. Katzir, and A. Inberg, “A simple thermal imaging system based on hollow glass waveguides or silver halide fibers as scanning elements for medical applications,” Proc. SPIE 3596, 82–90 (1999).
[CrossRef]

Despringre, V.

C. Latry, V. Despringre, and C. Valorge, “Automatic MTF measurement through a least square method,” Proc. SPIE 5570, 233–244 (2004).
[CrossRef]

Dong, H.

J. He, Z. Zhou, H. Dong, G. Zhang, and J. Ou, “Design of coefficient-adjustable FBG strain sensors,” Opt. Precis. Eng. 18, 2339–2346 (2010).

Drougard, R.

Feltz, J.

J. Feltz, “Development of the modulation transfer function and contrast transfer function for discrete systems, particularly charge-coupled devices,” Opt. Eng. 29, 893–904(1990).
[CrossRef]

Friesem, A. A.

A. A. Friesem, L. U. Silberg, and Y. Parallel, “transmission of images through single optical fibers,” Proc. IEEE 71, 208–221 (1983).
[CrossRef]

Fujiwara, H.

K. Muarta, H. Fujiwara, and R. Sato, “Two-dimensional measurement of optical transfer function by holographic techniques,” Proc. SPIE 46, 104–114 (1998).

He, J.

J. He, Z. Zhou, H. Dong, G. Zhang, and J. Ou, “Design of coefficient-adjustable FBG strain sensors,” Opt. Precis. Eng. 18, 2339–2346 (2010).

Inberg, A.

B. Dekel, A. Katzir, and A. Inberg, “A simple thermal imaging system based on hollow glass waveguides or silver halide fibers as scanning elements for medical applications,” Proc. SPIE 3596, 82–90 (1999).
[CrossRef]

Katzir, A.

E. Rave and A. Katzir, “Ordered bundles of infrared transmitting silver halide fibers: attenuation, resolution and crosstalk in long and flexible bundles,” Opt. Eng. 41, 1467–1468(2002).
[CrossRef]

B. Dekel, A. Katzir, and A. Inberg, “A simple thermal imaging system based on hollow glass waveguides or silver halide fibers as scanning elements for medical applications,” Proc. SPIE 3596, 82–90 (1999).
[CrossRef]

Latry, C.

C. Latry, V. Despringre, and C. Valorge, “Automatic MTF measurement through a least square method,” Proc. SPIE 5570, 233–244 (2004).
[CrossRef]

Lowe, J. J.

D. D. Babrc, J. J. Lowe, C. Sheldon, E. S. D’Ippoltto, A. G. Osler, and W. F. Mogran, “A description of the focal plane/detector test and evaluation lab at MDAC-HB,” Proc. SPIE 685, 80–87 (1986).

Mogran, W. F.

D. D. Babrc, J. J. Lowe, C. Sheldon, E. S. D’Ippoltto, A. G. Osler, and W. F. Mogran, “A description of the focal plane/detector test and evaluation lab at MDAC-HB,” Proc. SPIE 685, 80–87 (1986).

Montgomery, W. D.

Muarta, K.

K. Muarta, H. Fujiwara, and R. Sato, “Two-dimensional measurement of optical transfer function by holographic techniques,” Proc. SPIE 46, 104–114 (1998).

Osler, A. G.

D. D. Babrc, J. J. Lowe, C. Sheldon, E. S. D’Ippoltto, A. G. Osler, and W. F. Mogran, “A description of the focal plane/detector test and evaluation lab at MDAC-HB,” Proc. SPIE 685, 80–87 (1986).

Ou, J.

J. He, Z. Zhou, H. Dong, G. Zhang, and J. Ou, “Design of coefficient-adjustable FBG strain sensors,” Opt. Precis. Eng. 18, 2339–2346 (2010).

Parallel, Y.

A. A. Friesem, L. U. Silberg, and Y. Parallel, “transmission of images through single optical fibers,” Proc. IEEE 71, 208–221 (1983).
[CrossRef]

Rave, E.

E. Rave and A. Katzir, “Ordered bundles of infrared transmitting silver halide fibers: attenuation, resolution and crosstalk in long and flexible bundles,” Opt. Eng. 41, 1467–1468(2002).
[CrossRef]

Sato, R.

K. Muarta, H. Fujiwara, and R. Sato, “Two-dimensional measurement of optical transfer function by holographic techniques,” Proc. SPIE 46, 104–114 (1998).

Seib, D. H.

D. H. Seib, “Carrier diffusion degradation of modulation transfer function in charge coupled imager,” IEEE Trans. Electron Devices 21, 210–217 (1974).
[CrossRef]

Sheldon, C.

D. D. Babrc, J. J. Lowe, C. Sheldon, E. S. D’Ippoltto, A. G. Osler, and W. F. Mogran, “A description of the focal plane/detector test and evaluation lab at MDAC-HB,” Proc. SPIE 685, 80–87 (1986).

Silberg, L. U.

A. A. Friesem, L. U. Silberg, and Y. Parallel, “transmission of images through single optical fibers,” Proc. IEEE 71, 208–221 (1983).
[CrossRef]

Valorge, C.

C. Latry, V. Despringre, and C. Valorge, “Automatic MTF measurement through a least square method,” Proc. SPIE 5570, 233–244 (2004).
[CrossRef]

Zhang, G.

J. He, Z. Zhou, H. Dong, G. Zhang, and J. Ou, “Design of coefficient-adjustable FBG strain sensors,” Opt. Precis. Eng. 18, 2339–2346 (2010).

Zhou, Z.

J. He, Z. Zhou, H. Dong, G. Zhang, and J. Ou, “Design of coefficient-adjustable FBG strain sensors,” Opt. Precis. Eng. 18, 2339–2346 (2010).

IEEE Trans. Electron Devices

D. H. Seib, “Carrier diffusion degradation of modulation transfer function in charge coupled imager,” IEEE Trans. Electron Devices 21, 210–217 (1974).
[CrossRef]

J. Opt. Soc. Am.

Opt. Eng.

E. Rave and A. Katzir, “Ordered bundles of infrared transmitting silver halide fibers: attenuation, resolution and crosstalk in long and flexible bundles,” Opt. Eng. 41, 1467–1468(2002).
[CrossRef]

J. Feltz, “Development of the modulation transfer function and contrast transfer function for discrete systems, particularly charge-coupled devices,” Opt. Eng. 29, 893–904(1990).
[CrossRef]

Opt. Precis. Eng.

J. He, Z. Zhou, H. Dong, G. Zhang, and J. Ou, “Design of coefficient-adjustable FBG strain sensors,” Opt. Precis. Eng. 18, 2339–2346 (2010).

Proc. IEEE

A. A. Friesem, L. U. Silberg, and Y. Parallel, “transmission of images through single optical fibers,” Proc. IEEE 71, 208–221 (1983).
[CrossRef]

Proc. SPIE

C. Latry, V. Despringre, and C. Valorge, “Automatic MTF measurement through a least square method,” Proc. SPIE 5570, 233–244 (2004).
[CrossRef]

K. Muarta, H. Fujiwara, and R. Sato, “Two-dimensional measurement of optical transfer function by holographic techniques,” Proc. SPIE 46, 104–114 (1998).

D. D. Babrc, J. J. Lowe, C. Sheldon, E. S. D’Ippoltto, A. G. Osler, and W. F. Mogran, “A description of the focal plane/detector test and evaluation lab at MDAC-HB,” Proc. SPIE 685, 80–87 (1986).

B. Dekel, A. Katzir, and A. Inberg, “A simple thermal imaging system based on hollow glass waveguides or silver halide fibers as scanning elements for medical applications,” Proc. SPIE 3596, 82–90 (1999).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Coupled situation between fiber-optic image bundles and the detector pixels. (a) The R is outer radius of fiber in fiber-optic image bundles. (b) The dimension of pixel is 2 R × 2 R , and the alignment error of pixels between fiber-optic image bundles is expressed as α.

Fig. 2
Fig. 2

Sketch of square wave signal transfor mation. (a) The square wave signal sampled by input side of the fiber-optic image bundles. (b) Signal export from output side of the bundles. (c) Detector pixels sampled the output signal from fiber-optic image bundles.

Fig. 3
Fig. 3

Simulation of the relationship of coupled contrast transfer function with coupling deviation based on Eq. (7): (a)  f = f N , (b)  f = 0.999 f N , (c)  f = 0.997 f N , (d)  f = 0.995 f N , (e)  f = 0.993 f N .

Equations (7)

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

I j = I m · ( π r 2 S j ) π r 2 ,
S j = 2 2 j R r + Δ 2 j R + r ( r 2 ( x 2 j R ) 2 ) 1 / 2 d x = r 2 arccos ( Δ r ) Δ r 2 Δ 2 , Δ = { δ α .
I j ( f , α ) = ( π r 2 S j ) π r 2 I j ( f ) + S j π r 2 I j + 1 ( f ) .
C ( f , α ) = I ¯ max ( f , α ) I ¯ min ( f , α ) I ¯ max ( f , α ) + I ¯ min ( f , α ) .
{ I ¯ max ( f , α ) = 1 N n = 1 N I ¯ max n ( f , α ) , I ¯ min ( f , α ) = 1 M m = 1 M I ¯ min m ( f , α ) .
C T F ( f , α ) = C ( f ) C o ( f ) .
C T F ( f , α ) = 1 N n = 1 N I max n ( f , α ) 1 M m = 1 M I min m ( f , α ) 1 N n = 1 N I max m ( f , α ) + 1 M m = 1 M I min m ( f , α ) .

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