Abstract

A general focal length function is proposed to design microlenses with long extended focal depth and high lateral resolution. The focal performance of the designed microlenses, including the actual focal depth, the focal spot size, and the diffraction efficiency, is calculated by rigorous electromagnetic theory and the boundary-element method for several f-numbers. In contrast to conventional microlenses, the numerical results indicate that the designed microlenses can exhibit long extended focal depth and good focal performance. It is expected that the long focal length function will be widely used to design microlenses with long focal depth characteristics.

© 2007 Optical Society of America

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References

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  1. B.-Z. Dong, J. Liu, G.-Z. Yang, B.-Y. Gu, and O. K. Ersoy, "Interative optimization approach for designing an axicon with long focal depth and high transverse resolution," J. Opt. Soc. Am. A 13, 97-103 (1996).
    [CrossRef]
  2. P. Varga, "Use of confocal microscopes in conoscopy and ellipsometry. 1. Electromagnetic theory," Appl. Opt. 39, 6360-6365 (2000).
    [CrossRef]
  3. R. Kant, "Superresolution and increased depth of focus: an inverse problem of vector diffraction," J. Mod. Opt. 47, 905-916 (2000).
    [CrossRef]
  4. N. Davidson, A. A. Friesem, and E. Hasman, "Holographic axilens: high resolution and long focal depth," Opt. Lett. 16, 523-525 (1991).
    [CrossRef] [PubMed]
  5. J. Sochacki, S. Bará, Z. Jaroszewicz, and A. Kolodziejczyk, "Phase retardation of the uniform-intensity axilens," Opt. Lett. 17, 7-9 (1992).
    [CrossRef] [PubMed]
  6. J. Sochacki, A. Kolodziejczyk, Z. Jaroszewicz, and S. Bará, "Nonparaxial design of generalized axicons," Appl. Opt. 31, 5326-5330 (1993).
    [CrossRef]
  7. Z. Jaroszewicz, J. Sochacki, A. Kolodziejczyk, and L. R. Staronski, "Apodized annular-aperture logarithmic axicon: smoothness and uniformity of intensity distributions," Opt. Lett. 18, 1893-1895 (1993).
    [CrossRef] [PubMed]
  8. J. Sochacki, Z. Jaroszewicz, L. R. Staronski, and A. Kolodziejczyk, "Annular-aperture logarithmic axicon," J. Opt. Soc. Am. A 10, 1765-1768 (1993).
    [CrossRef]
  9. B.-Z. Dong, J. Liu, B.-Y. Gu, G.-Z. Yang, and J. Wang, "Rigorous electromagnetic analysis of a microcylindrical axilens with long focal depth and high transverse resolution," J. Opt. Soc. Am. A 18, 1465-1470 (2001).
    [CrossRef]
  10. J.-S. Ye, B.-Z. Dong, B.-Y. Gu, G.-Z. Yang, and S.-T. Liu, "Analysis of a closed-boundary axilens with long focal depth and high transverse resolution based on rigorous electromagnetic theory," J. Opt. Soc. Am. A 19, 2030-2035 (2002).
    [CrossRef]
  11. F. Di, Y. Yingbai, J. Guofan, and W. Minxian, "Rigorous concept for the analysis of diffractive lenses with different axial resolution and high lateral resolution," Opt. Express 11, 1987-1994 (2003).
    [CrossRef] [PubMed]
  12. J.-S. Ye, B.-Z. Dong, B.-Y. Gu, and S.-T. Liu, "Analysis of a cylindrical microlens array with long focal depth by a rigorous boundary-element method and scalar approximations," Appl. Opt. 43, 5183-5192 (2004).
    [PubMed]
  13. S.-Q. Wang, J. Liu, B.-Y. Gu, Y.-Q. Wang, B. Hu, X.-D. Sun, and S. Di, "Rigorous electromagnetic analysis of the common focusing characteristics of cylindrical microlens with long focal depth under multi-wavelength illumination," J. Opt. Soc. Am. A 24, 512-516 (2007).
    [CrossRef]
  14. K. Yashiro and S. Ohkawa, "Boundary element method for electromagnetic scattering from cylinders," IEEE Trans. Antennas Propag. AP-33, 383-389 (1985).
    [CrossRef]
  15. K. Hirayama, E. N. Glytsis, T. K. Gaylord, and D. W. Wilson, "Rigorous electromagnetic analysis of diffractive cylindrical lenses," J. Opt. Soc. Am. A 13, 2219-2231 (1996).
    [CrossRef]
  16. J. M. Bendickson, E. N. Glytsis, and T. K. Gaylord, "Scalar integral diffraction methods: unification, accuracy, and comparison with a rigorous boundary element method with application to diffractive cylindrical lenses," J. Opt. Soc. Am. A 15, 1822-1837 (1998).
    [CrossRef]

2007

2004

2003

2002

2001

2000

P. Varga, "Use of confocal microscopes in conoscopy and ellipsometry. 1. Electromagnetic theory," Appl. Opt. 39, 6360-6365 (2000).
[CrossRef]

R. Kant, "Superresolution and increased depth of focus: an inverse problem of vector diffraction," J. Mod. Opt. 47, 905-916 (2000).
[CrossRef]

1998

1996

1993

1992

1991

1985

K. Yashiro and S. Ohkawa, "Boundary element method for electromagnetic scattering from cylinders," IEEE Trans. Antennas Propag. AP-33, 383-389 (1985).
[CrossRef]

Bará, S.

Bendickson, J. M.

Davidson, N.

Di, F.

Di, S.

Dong, B.-Z.

Ersoy, O. K.

Friesem, A. A.

Gaylord, T. K.

Glytsis, E. N.

Gu, B.-Y.

Guofan, J.

Hasman, E.

Hirayama, K.

Hu, B.

Jaroszewicz, Z.

Kant, R.

R. Kant, "Superresolution and increased depth of focus: an inverse problem of vector diffraction," J. Mod. Opt. 47, 905-916 (2000).
[CrossRef]

Kolodziejczyk, A.

Liu, J.

Liu, S.-T.

Minxian, W.

Ohkawa, S.

K. Yashiro and S. Ohkawa, "Boundary element method for electromagnetic scattering from cylinders," IEEE Trans. Antennas Propag. AP-33, 383-389 (1985).
[CrossRef]

Sochacki, J.

Staronski, L. R.

Sun, X.-D.

Varga, P.

Wang, J.

Wang, S.-Q.

Wang, Y.-Q.

Wilson, D. W.

Yang, G.-Z.

Yashiro, K.

K. Yashiro and S. Ohkawa, "Boundary element method for electromagnetic scattering from cylinders," IEEE Trans. Antennas Propag. AP-33, 383-389 (1985).
[CrossRef]

Ye, J.-S.

Yingbai, Y.

Appl. Opt.

IEEE Trans. Antennas Propag.

K. Yashiro and S. Ohkawa, "Boundary element method for electromagnetic scattering from cylinders," IEEE Trans. Antennas Propag. AP-33, 383-389 (1985).
[CrossRef]

J. Mod. Opt.

R. Kant, "Superresolution and increased depth of focus: an inverse problem of vector diffraction," J. Mod. Opt. 47, 905-916 (2000).
[CrossRef]

J. Opt. Soc. Am. A

J. Sochacki, Z. Jaroszewicz, L. R. Staronski, and A. Kolodziejczyk, "Annular-aperture logarithmic axicon," J. Opt. Soc. Am. A 10, 1765-1768 (1993).
[CrossRef]

B.-Z. Dong, J. Liu, B.-Y. Gu, G.-Z. Yang, and J. Wang, "Rigorous electromagnetic analysis of a microcylindrical axilens with long focal depth and high transverse resolution," J. Opt. Soc. Am. A 18, 1465-1470 (2001).
[CrossRef]

J.-S. Ye, B.-Z. Dong, B.-Y. Gu, G.-Z. Yang, and S.-T. Liu, "Analysis of a closed-boundary axilens with long focal depth and high transverse resolution based on rigorous electromagnetic theory," J. Opt. Soc. Am. A 19, 2030-2035 (2002).
[CrossRef]

K. Hirayama, E. N. Glytsis, T. K. Gaylord, and D. W. Wilson, "Rigorous electromagnetic analysis of diffractive cylindrical lenses," J. Opt. Soc. Am. A 13, 2219-2231 (1996).
[CrossRef]

J. M. Bendickson, E. N. Glytsis, and T. K. Gaylord, "Scalar integral diffraction methods: unification, accuracy, and comparison with a rigorous boundary element method with application to diffractive cylindrical lenses," J. Opt. Soc. Am. A 15, 1822-1837 (1998).
[CrossRef]

B.-Z. Dong, J. Liu, G.-Z. Yang, B.-Y. Gu, and O. K. Ersoy, "Interative optimization approach for designing an axicon with long focal depth and high transverse resolution," J. Opt. Soc. Am. A 13, 97-103 (1996).
[CrossRef]

S.-Q. Wang, J. Liu, B.-Y. Gu, Y.-Q. Wang, B. Hu, X.-D. Sun, and S. Di, "Rigorous electromagnetic analysis of the common focusing characteristics of cylindrical microlens with long focal depth under multi-wavelength illumination," J. Opt. Soc. Am. A 24, 512-516 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of an open-boundary microlens with extended focal depth.

Fig. 2
Fig. 2

Axial intensity distributions of the microlenses designed according to different values of b. The f-number is f 1.0 , and the preset focal depth is 10 μ m . Curves I, II, and III correspond to b = 0.5 , 2, and 6, respectively. Curve IV represents the axial intensity distribution of the conventional microlens with same parameters. Dashed lines mark the long focal depth ranges of the designed microlenses.

Fig. 3
Fig. 3

Lateral intensity distributions of the focused field on the three observation planes, corresponding to Fig. 2: (a) for b = 0.5 , (b) for b = 2 , (c) for b = 6 , and (d) for the conventional microlens. The solid curves represent the field intensity distributions on the real focal planes. The dashed, solid, and dotted–dashed curves correspond to the observation planes at (a) y = 21.76 , 25.53 , and 30.57 μ m , respectively; (b) y = 20.41 , 24.10 , and 28.77 μ m , respectively; (c) y = 16.99 , 20.61 , and 24.69 , respectively; (d) y = 13.83 , 15.92 , and 18.54 μ m , respectively.

Fig. 4
Fig. 4

Electric field intensity distributions of the microlenses in region S 2 , corresponding to Fig. 2: (a) for b = 0.5 , (b) for b = 2 , (c) for b = 6 , and (d) for the conventional microlens. The bright (dark) areas indicate the regions with high (low) electric intensities.

Fig. 5
Fig. 5

Same as Fig. 2 except for f 1.5 . Curves I, II, and III correspond to b = 0.5 , 2, and 6, respectively, while curve IV corresponds to the conventional microlens.

Fig. 6
Fig. 6

Lateral intensity distributions of the focused field on the three observation planes, corresponding to Fig. 5: (a) for b = 0.5 , (b) for b = 2 , (c) for b = 6 , and (d) for the conventional microlens.

Tables (2)

Tables Icon

Table 1 Focal Performance of Open Boundary Microlenses with Long Focal Depth Designed According to Different b for f 1.0 a

Tables Icon

Table 2 Focal Performance of the Open Boundary Microlenses with Long Focal Depth Designed According to Different b for f 1.5

Equations (5)

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

ϕ ( r ) = 2 π λ n 2 n 1 n 2 [ f 2 ( r ) + r 2 f ( r ) ] ,
f ( r ) = f 0 + a r b ,
a = δ f R b .
f ( r ) = f 0 + δ f ( r R ) b .
E ( r 2 ) = Γ [ E Γ ( r Γ ) G 2 ( r 2 , r Γ ) n ̂ G 2 ( r 2 , r Γ ) E Γ ( r Γ ) n ̂ ] d l ,

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