Abstract

In a technique reminiscent of the classic autocollimation method, we demonstrate that focal lengths of micro-optic lenses may be measured precisely by the use of a mirror and a 2 × 1 fiber coupler.

© 1996 Optical Society of America

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References

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  1. G. S. Monk, Light: Principles and Experiments (McGraw-Hill, New York, 1937), pp. 343–346.
  2. D. L. MacFarlane, V. Narayan, W. R. Cox, T. Chen, D. J. Hayes, “Microjet fabrication of microlens arrays,” IEEE Photon. Technol. Lett. 6, 1112–1114 (1994).
    [CrossRef]
  3. W. R. Cox, D. J. Hayes, T. Chen, D. W. Ussery, D. L. MacFarlane, E. Wilson, “Fabrication of micro-optics by microjet printing,” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Motamedi, L. Beiser, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2383, 110–115 (1995).
  4. K. Iga, Y. Kokubura, M. Okawa, Fundamentals of Micro-Optics: Distributed Index, Microlens, and Stacked Planar Optics (Academic, Tokyo, 1984).
  5. M. C. Hutley, “Optical techniques for the generation of microlens arrays,” J. Mod. Opt. 37, 253–265 (1990).
    [CrossRef]
  6. M. Kubo, H. Hanabusa, “Fabrication of microlenses by laser chemical vapor deposition,” Appl. Opt. 32, 6211–6218 (1993).
  7. A. J. Cantor, M. M. Abou el leil, R. H. Hobbs, “Theory of 2-D ion exchange in glass: optimization of microlens arrays,” Appl. Opt. 30, 2704–2713 (1991).
    [CrossRef] [PubMed]
  8. D. Marcuse, “Loss analysis of single mode fiber splices,” Bell Sys. Tech. J 56, 703–718 (1977).
  9. H. Kogelnik, T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
    [CrossRef] [PubMed]
  10. W. B. Joyce, B. C. DeLoach, “Alignment of Gaussian beams,” Appl. Opt. 23, 4187–4196 (1984).
    [CrossRef] [PubMed]
  11. K. S. Lee, “Focusing characteristics of a truncated and aberrated Gaussian beam through a hemispherical microlens,” Appl. Opt. 25, 3671–3675 (1986).
    [CrossRef] [PubMed]
  12. C. A. Edwards, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
    [CrossRef]

1994 (1)

D. L. MacFarlane, V. Narayan, W. R. Cox, T. Chen, D. J. Hayes, “Microjet fabrication of microlens arrays,” IEEE Photon. Technol. Lett. 6, 1112–1114 (1994).
[CrossRef]

1993 (2)

M. Kubo, H. Hanabusa, “Fabrication of microlenses by laser chemical vapor deposition,” Appl. Opt. 32, 6211–6218 (1993).

C. A. Edwards, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
[CrossRef]

1991 (1)

1990 (1)

M. C. Hutley, “Optical techniques for the generation of microlens arrays,” J. Mod. Opt. 37, 253–265 (1990).
[CrossRef]

1986 (1)

1984 (1)

1977 (1)

D. Marcuse, “Loss analysis of single mode fiber splices,” Bell Sys. Tech. J 56, 703–718 (1977).

1966 (1)

Abou el leil, M. M.

Cantor, A. J.

Chen, T.

D. L. MacFarlane, V. Narayan, W. R. Cox, T. Chen, D. J. Hayes, “Microjet fabrication of microlens arrays,” IEEE Photon. Technol. Lett. 6, 1112–1114 (1994).
[CrossRef]

W. R. Cox, D. J. Hayes, T. Chen, D. W. Ussery, D. L. MacFarlane, E. Wilson, “Fabrication of micro-optics by microjet printing,” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Motamedi, L. Beiser, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2383, 110–115 (1995).

Cox, W. R.

D. L. MacFarlane, V. Narayan, W. R. Cox, T. Chen, D. J. Hayes, “Microjet fabrication of microlens arrays,” IEEE Photon. Technol. Lett. 6, 1112–1114 (1994).
[CrossRef]

W. R. Cox, D. J. Hayes, T. Chen, D. W. Ussery, D. L. MacFarlane, E. Wilson, “Fabrication of micro-optics by microjet printing,” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Motamedi, L. Beiser, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2383, 110–115 (1995).

DeLoach, B. C.

Dragone, C.

C. A. Edwards, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
[CrossRef]

Edwards, C. A.

C. A. Edwards, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
[CrossRef]

Hanabusa, H.

Hayes, D. J.

D. L. MacFarlane, V. Narayan, W. R. Cox, T. Chen, D. J. Hayes, “Microjet fabrication of microlens arrays,” IEEE Photon. Technol. Lett. 6, 1112–1114 (1994).
[CrossRef]

W. R. Cox, D. J. Hayes, T. Chen, D. W. Ussery, D. L. MacFarlane, E. Wilson, “Fabrication of micro-optics by microjet printing,” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Motamedi, L. Beiser, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2383, 110–115 (1995).

Hobbs, R. H.

Hutley, M. C.

M. C. Hutley, “Optical techniques for the generation of microlens arrays,” J. Mod. Opt. 37, 253–265 (1990).
[CrossRef]

Iga, K.

K. Iga, Y. Kokubura, M. Okawa, Fundamentals of Micro-Optics: Distributed Index, Microlens, and Stacked Planar Optics (Academic, Tokyo, 1984).

Joyce, W. B.

Kogelnik, H.

Kokubura, Y.

K. Iga, Y. Kokubura, M. Okawa, Fundamentals of Micro-Optics: Distributed Index, Microlens, and Stacked Planar Optics (Academic, Tokyo, 1984).

Kubo, M.

Lee, K. S.

Li, T.

MacFarlane, D. L.

D. L. MacFarlane, V. Narayan, W. R. Cox, T. Chen, D. J. Hayes, “Microjet fabrication of microlens arrays,” IEEE Photon. Technol. Lett. 6, 1112–1114 (1994).
[CrossRef]

W. R. Cox, D. J. Hayes, T. Chen, D. W. Ussery, D. L. MacFarlane, E. Wilson, “Fabrication of micro-optics by microjet printing,” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Motamedi, L. Beiser, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2383, 110–115 (1995).

Marcuse, D.

D. Marcuse, “Loss analysis of single mode fiber splices,” Bell Sys. Tech. J 56, 703–718 (1977).

Monk, G. S.

G. S. Monk, Light: Principles and Experiments (McGraw-Hill, New York, 1937), pp. 343–346.

Narayan, V.

D. L. MacFarlane, V. Narayan, W. R. Cox, T. Chen, D. J. Hayes, “Microjet fabrication of microlens arrays,” IEEE Photon. Technol. Lett. 6, 1112–1114 (1994).
[CrossRef]

Okawa, M.

K. Iga, Y. Kokubura, M. Okawa, Fundamentals of Micro-Optics: Distributed Index, Microlens, and Stacked Planar Optics (Academic, Tokyo, 1984).

Presby, H. M.

C. A. Edwards, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
[CrossRef]

Ussery, D. W.

W. R. Cox, D. J. Hayes, T. Chen, D. W. Ussery, D. L. MacFarlane, E. Wilson, “Fabrication of micro-optics by microjet printing,” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Motamedi, L. Beiser, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2383, 110–115 (1995).

Wilson, E.

W. R. Cox, D. J. Hayes, T. Chen, D. W. Ussery, D. L. MacFarlane, E. Wilson, “Fabrication of micro-optics by microjet printing,” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Motamedi, L. Beiser, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2383, 110–115 (1995).

Appl. Opt. (5)

Bell Sys. Tech. J (1)

D. Marcuse, “Loss analysis of single mode fiber splices,” Bell Sys. Tech. J 56, 703–718 (1977).

IEEE Photon. Technol. Lett. (1)

D. L. MacFarlane, V. Narayan, W. R. Cox, T. Chen, D. J. Hayes, “Microjet fabrication of microlens arrays,” IEEE Photon. Technol. Lett. 6, 1112–1114 (1994).
[CrossRef]

J. Lightwave Technol. (1)

C. A. Edwards, H. M. Presby, C. Dragone, “Ideal microlenses for laser to fiber coupling,” J. Lightwave Technol. 11, 252–257 (1993).
[CrossRef]

J. Mod. Opt. (1)

M. C. Hutley, “Optical techniques for the generation of microlens arrays,” J. Mod. Opt. 37, 253–265 (1990).
[CrossRef]

Other (3)

G. S. Monk, Light: Principles and Experiments (McGraw-Hill, New York, 1937), pp. 343–346.

W. R. Cox, D. J. Hayes, T. Chen, D. W. Ussery, D. L. MacFarlane, E. Wilson, “Fabrication of micro-optics by microjet printing,” in Micro-Optics/Micromechanics and Laser Scanning and Shaping, M. E. Motamedi, L. Beiser, eds., Proc. Soc. Photo-Opt. Instrum. Eng.2383, 110–115 (1995).

K. Iga, Y. Kokubura, M. Okawa, Fundamentals of Micro-Optics: Distributed Index, Microlens, and Stacked Planar Optics (Academic, Tokyo, 1984).

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Figures (9)

Fig. 1
Fig. 1

Schematic of (a) a traditional method for measuring the focal length of a lens by the use of an autocollimator, (b) the experimental setup of the method discussed herein.

Fig. 2
Fig. 2

Theoretical and experimental results of the fiber-coupler focal length measurement technique for a 136-μm-diameter F-1.8 lenslet. The solid curve is theory, which is in reasonable agreement with the data points plotted as discrete asterisks.

Fig. 3
Fig. 3

Theoretical and experimental results of the fiber-coupler focal length measurement technique for a 248-μm-diameter F-1.9 lenslet. The solid curve is theory, which is in reasonable agreement with the data points plotted as discrete asterisks.

Fig. 4
Fig. 4

Theoretical and experimental results of the fiber-coupler focal length measurement technique for a 416-μm-diameter F-2.2 lenslet. The solid curve is theory, which is in reasonable agreement with the data points plotted as discrete asterisks.

Fig. 5
Fig. 5

Theoretical and experimental results of the fiber-coupler focal length measurement technique for a 1300-μm-diameter F-2.6 lenselt. The solid curve is theory, which is in reasonable agreement with the data points plotted as discrete asterisks.

Fig. 6
Fig. 6

Uncertainty, Δf/f, plotted as a function of lenslet diameter for different f-number lenslets.

Fig. 7
Fig. 7

Uncertainty, Δf/f, plotted as a function of fiber-core diameter for different f-number lenslets.

Fig. 8
Fig. 8

Theoretically calculated curve of signal versus distance for an F-1.5 lens and a tilt of 0.005 rad.

Fig. 9
Fig. 9

Sensitivity, Δf/f, plotted as a function of mirror-fiber tilt for different f-number lenslets.

Equations (3)

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w 0 = a ( 0.65 + 1.619 V 3 / 2 + 2.879 V 6 ) ,
w 1 2 = w 0 2 [ ( A + B / R 0 ) 2 + ( B λ / π w 0 2 ) 2 ] ,
1 / R 1 = ( w 0 / w 1 ) 2 [ ( C + D / R 0 ) ( A + B / R 0 ) + D B ( λ / π w 0 2 ) 2 ] .

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