Abstract

We establish theoretically the relationship between the lateral magnification m and the object distance L0 for a gradient refractive index (GRIN) square lens and a GRIN rod lens. Through the linear fit of the object distance and the reciprocal of the magnification for different image locations, we use the imaging method to measure the central refractive index n0 and focusing constant α of the GRIN square lens and the GRIN rod lens. The center refractive indices and focusing constant α of the GRIN square lens and the GRIN rod lens are 1.611 and 1.609, 0.0926 and 0.100, respectively. For the GRIN square lens and the GRIN rod lens, the measured central refractive indices are accurate to 103.

© 2009 Optical Society of America

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References

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  1. H. Lv, A. Liu, X. Yi, and Q. Li, “Numerical analysis of low chromatic aberration of a gradient refractive index rod lens,” Appl. Opt. 48, 584-590 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. C. Ye and R. R. McLeod, “GRIN lens and lens array fabrication with diffusion-driven photopolymer,” Opt. Lett. 33, 2575-2577 (2008).
    [CrossRef] [PubMed]
  5. X. Chen and N. George, “Study of a GRIN array imaging system: resolution analysis and extended depth-of-field,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper FWX8.
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    [CrossRef]
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    [CrossRef]
  8. Y. C. Lin, “Characteristics of lensed fiber collimator with larger gradient-index lens diameter,” Microwave Opt. Technol. Lett. 51, 1137-1139 (2008).
    [CrossRef]
  9. E. Acosta, D. Vazquez, L. Garner, and G. Smith, “Tomographic method for measurement of the gradient refractive index of the crystalline lens. I. The spherical fish lens,” J. Opt. Soc. Am. A 22, 424-433 (2005).
    [CrossRef]
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    [CrossRef]
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2009

2008

H. Kobayashi and T. Horiuchi, “Novel projection exposure system using gradient-index lens array,” Jpn. J. Appl. Phys., Part 1 47, 5702-5707 (2008).
[CrossRef]

Y. C. Lin, “Characteristics of lensed fiber collimator with larger gradient-index lens diameter,” Microwave Opt. Technol. Lett. 51, 1137-1139 (2008).
[CrossRef]

H. Lv, B. Shi, L. Guo, and A. Liu, “Fabrication of Maxwell fish-eye spherical lenses and research on distribution profiles of gradient refractive index,” J. Opt. Soc. Am. A 25, 609-611 (2008).
[CrossRef]

C. Ye and R. R. McLeod, “GRIN lens and lens array fabrication with diffusion-driven photopolymer,” Opt. Lett. 33, 2575-2577 (2008).
[CrossRef] [PubMed]

2005

1986

Acosta, E.

Bao, C.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer, 2002).

Chen, X.

X. Chen and N. George, “Study of a GRIN array imaging system: resolution analysis and extended depth-of-field,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper FWX8.

Fu, Q. Y.

Q. Y. Fu, Gradient Index Optics (Kexue Publishing Company, Beijing, 1991).

Garner, L.

George, N.

X. Chen and N. George, “Study of a GRIN array imaging system: resolution analysis and extended depth-of-field,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper FWX8.

Gomez-Reino, C.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer, 2002).

Guo, L.

Horiuchi, T.

H. Kobayashi and T. Horiuchi, “Novel projection exposure system using gradient-index lens array,” Jpn. J. Appl. Phys., Part 1 47, 5702-5707 (2008).
[CrossRef]

Ichikawa, H.

Kitano, I.

Kobayashi, H.

H. Kobayashi and T. Horiuchi, “Novel projection exposure system using gradient-index lens array,” Jpn. J. Appl. Phys., Part 1 47, 5702-5707 (2008).
[CrossRef]

Li, Q.

Lin, Y. C.

Y. C. Lin, “Characteristics of lensed fiber collimator with larger gradient-index lens diameter,” Microwave Opt. Technol. Lett. 51, 1137-1139 (2008).
[CrossRef]

Liu, A.

Lv, H.

Marchand, E. W.

E. W. Marchand, Gradient Index Optics (Academic, 1978).

McLeod, R. R.

Nishi, H.

Perez, M. V.

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer, 2002).

Shi, B.

Smith, G.

Tong, J.

Toyama, M.

Vazquez, D.

Ye, C.

Yi, X.

Appl. Opt.

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys., Part 1

H. Kobayashi and T. Horiuchi, “Novel projection exposure system using gradient-index lens array,” Jpn. J. Appl. Phys., Part 1 47, 5702-5707 (2008).
[CrossRef]

Microwave Opt. Technol. Lett.

Y. C. Lin, “Characteristics of lensed fiber collimator with larger gradient-index lens diameter,” Microwave Opt. Technol. Lett. 51, 1137-1139 (2008).
[CrossRef]

Opt. Lett.

Other

C. Gomez-Reino, M. V. Perez, and C. Bao, Gradient-Index Optics: Fundamentals and Applications (Springer, 2002).

Q. Y. Fu, Gradient Index Optics (Kexue Publishing Company, Beijing, 1991).

E. W. Marchand, Gradient Index Optics (Academic, 1978).

X. Chen and N. George, “Study of a GRIN array imaging system: resolution analysis and extended depth-of-field,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper FWX8.

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Figures (5)

Fig. 1
Fig. 1

Imaging formation of (a) the GRIN square lens and (b) the GRIN rod lens.

Fig. 2
Fig. 2

Experimental setup of imaging measurement of a GRIN lens.

Fig. 3
Fig. 3

Linear fit of object distance L 0 and the reciprocal of magnification 1 m of (a) the GRIN square lens and (b) the GRIN rod lens.

Fig. 4
Fig. 4

Imaging of the mesh object through (a) the GRIN square lens and (b) the GRIN rod lens.

Fig. 5
Fig. 5

Interferogram of (a) the GRIN square lens and (b) the GRIN rod lens.

Equations (7)

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L 1 = cos ( L α ) ( 1 n 0 L 0 α ) sin ( L α ) ( 1 L 0 ) cos ( L α ) + n 0 α sin ( L α ) ,
m = 1 cos ( L α ) + n 0 L 0 α sin ( L α ) .
L 0 = cos ( L α ) n 0 α sin ( L α ) 1 n 0 α sin ( L α ) 1 m ,
L 0 = C + D 1 m
C D = cos ( L α ) , D = 1 n 0 α sin ( L α ) .
α = 0.0926 , n 0 = 1.611 for the GRIN square lens ,
α = 0.1000 , n 0 = 1.609 for the GRIN rod lens ,

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