Abstract

We have calculated the efficiency with which starlight can be coupled into a single-mode fiber optic that is placed in the focal plane of a telescope. The calculations are performed for a wide range of seeing conditions, with and without rapid image stabilization, and for a wide range of wavelengths. The dependence of coupling efficiency on the f-ratio of the incident beam is explored. Also, we calculate the coupling efficiency as a function of displacement for a perfect Airy pattern. We have also used a computer program which simulates atmospheric wavefronts to determine the variance of instantaneous coupling efficiency as a function of seeing. In perfect conditions, the maximum efficiency at the LP11 mode cutoff is 78% due to the mismatch of the Airy pattern and the nearly Gaussian mode of the fiber. Maximum total coupled power is attained at d/r0 = 4 with rapid image stabilization.

© 1988 Optical Society of America

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References

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  1. P. Connes, C. Froehly, “A Fiber-Linked Version of Project TRIO,” in Proceedings, ESA Conference: Colloquium on Kilometric Optical Arrays in Space, 23–25 Oct. 1984 (Cargese, Corsica, France), pp. 49–61.
  2. P. Connes, S. Shaklan, F. Roddier, “A Fiber-Linked Ground-Based Array,” in Proceedings, NOAO-ESO Workshop on Interferometric Imaging in Astronomy, 12–15 Jan. 1987 (Oracle, AZ).
  3. P. Connes, F. Roddier, S. Shaklan, E. Ribak, “Ground and Space Fiber Arrays,” in Proceedings, ESA Workshop on Optical Interferometry in Space, 16–18 June 1987 (Granada, Spain).
  4. S. B. Shaklan, F. Roddier, “Single-Mode Fiber Optics in a Long-Baseline Interferometer,” Appl. Opt. 26, 2159 (1987).
    [CrossRef] [PubMed]
  5. R. E. Wagner, W. J. Tomlinson, “Coupling Efficiency of Optics in Single-Mode Fiber Components,” Appl. Opt. 21, 2671 (1982).
    [CrossRef] [PubMed]
  6. L. Jeunhomme, Single-Mode Fiber Optics (Marcel Dekker, New York, 1983).
  7. D. Marcuse, “Loss Analysis of Single-Mode Fiber Splices,” Bell Syst. Tech. J. 56, 703 (1977).
  8. F. Roddier, “The Effects of Atmospheric Turbulence in Optical Astronomy,” Prog. Opt. 19, 281 (1981).
    [CrossRef]
  9. D. L. Fried, “Optical Resolution Through a Randomly Inhomogeneous Medium for Very Long and Very Short Exposures,” J. Opt. Soc. Am. 56, 1372 (1966).
    [CrossRef]
  10. J. R. Stern, R. B. Dyott, “Off-Axis Launching into a Fibre-Optical Waveguide,” Electron. Lett. 7, 52 (1971).
    [CrossRef]
  11. J. R. Stern, M. Peace, R. B. Dyott, “Launching into Optical Fiber Waveguide,” Electron. Lett. 6, 160 (1970).
    [CrossRef]
  12. B. J. McGlamery, “Computer Simulation Studies of Compensation of Turbulence Degraded Images,” Proc. Soc. Photo-Opt. Instrum. Eng. 74, 225 (1976).

1987 (1)

1982 (1)

1981 (1)

F. Roddier, “The Effects of Atmospheric Turbulence in Optical Astronomy,” Prog. Opt. 19, 281 (1981).
[CrossRef]

1977 (1)

D. Marcuse, “Loss Analysis of Single-Mode Fiber Splices,” Bell Syst. Tech. J. 56, 703 (1977).

1976 (1)

B. J. McGlamery, “Computer Simulation Studies of Compensation of Turbulence Degraded Images,” Proc. Soc. Photo-Opt. Instrum. Eng. 74, 225 (1976).

1971 (1)

J. R. Stern, R. B. Dyott, “Off-Axis Launching into a Fibre-Optical Waveguide,” Electron. Lett. 7, 52 (1971).
[CrossRef]

1970 (1)

J. R. Stern, M. Peace, R. B. Dyott, “Launching into Optical Fiber Waveguide,” Electron. Lett. 6, 160 (1970).
[CrossRef]

1966 (1)

Connes, P.

P. Connes, C. Froehly, “A Fiber-Linked Version of Project TRIO,” in Proceedings, ESA Conference: Colloquium on Kilometric Optical Arrays in Space, 23–25 Oct. 1984 (Cargese, Corsica, France), pp. 49–61.

P. Connes, S. Shaklan, F. Roddier, “A Fiber-Linked Ground-Based Array,” in Proceedings, NOAO-ESO Workshop on Interferometric Imaging in Astronomy, 12–15 Jan. 1987 (Oracle, AZ).

P. Connes, F. Roddier, S. Shaklan, E. Ribak, “Ground and Space Fiber Arrays,” in Proceedings, ESA Workshop on Optical Interferometry in Space, 16–18 June 1987 (Granada, Spain).

Dyott, R. B.

J. R. Stern, R. B. Dyott, “Off-Axis Launching into a Fibre-Optical Waveguide,” Electron. Lett. 7, 52 (1971).
[CrossRef]

J. R. Stern, M. Peace, R. B. Dyott, “Launching into Optical Fiber Waveguide,” Electron. Lett. 6, 160 (1970).
[CrossRef]

Fried, D. L.

Froehly, C.

P. Connes, C. Froehly, “A Fiber-Linked Version of Project TRIO,” in Proceedings, ESA Conference: Colloquium on Kilometric Optical Arrays in Space, 23–25 Oct. 1984 (Cargese, Corsica, France), pp. 49–61.

Jeunhomme, L.

L. Jeunhomme, Single-Mode Fiber Optics (Marcel Dekker, New York, 1983).

Marcuse, D.

D. Marcuse, “Loss Analysis of Single-Mode Fiber Splices,” Bell Syst. Tech. J. 56, 703 (1977).

McGlamery, B. J.

B. J. McGlamery, “Computer Simulation Studies of Compensation of Turbulence Degraded Images,” Proc. Soc. Photo-Opt. Instrum. Eng. 74, 225 (1976).

Peace, M.

J. R. Stern, M. Peace, R. B. Dyott, “Launching into Optical Fiber Waveguide,” Electron. Lett. 6, 160 (1970).
[CrossRef]

Ribak, E.

P. Connes, F. Roddier, S. Shaklan, E. Ribak, “Ground and Space Fiber Arrays,” in Proceedings, ESA Workshop on Optical Interferometry in Space, 16–18 June 1987 (Granada, Spain).

Roddier, F.

S. B. Shaklan, F. Roddier, “Single-Mode Fiber Optics in a Long-Baseline Interferometer,” Appl. Opt. 26, 2159 (1987).
[CrossRef] [PubMed]

F. Roddier, “The Effects of Atmospheric Turbulence in Optical Astronomy,” Prog. Opt. 19, 281 (1981).
[CrossRef]

P. Connes, S. Shaklan, F. Roddier, “A Fiber-Linked Ground-Based Array,” in Proceedings, NOAO-ESO Workshop on Interferometric Imaging in Astronomy, 12–15 Jan. 1987 (Oracle, AZ).

P. Connes, F. Roddier, S. Shaklan, E. Ribak, “Ground and Space Fiber Arrays,” in Proceedings, ESA Workshop on Optical Interferometry in Space, 16–18 June 1987 (Granada, Spain).

Shaklan, S.

P. Connes, F. Roddier, S. Shaklan, E. Ribak, “Ground and Space Fiber Arrays,” in Proceedings, ESA Workshop on Optical Interferometry in Space, 16–18 June 1987 (Granada, Spain).

P. Connes, S. Shaklan, F. Roddier, “A Fiber-Linked Ground-Based Array,” in Proceedings, NOAO-ESO Workshop on Interferometric Imaging in Astronomy, 12–15 Jan. 1987 (Oracle, AZ).

Shaklan, S. B.

Stern, J. R.

J. R. Stern, R. B. Dyott, “Off-Axis Launching into a Fibre-Optical Waveguide,” Electron. Lett. 7, 52 (1971).
[CrossRef]

J. R. Stern, M. Peace, R. B. Dyott, “Launching into Optical Fiber Waveguide,” Electron. Lett. 6, 160 (1970).
[CrossRef]

Tomlinson, W. J.

Wagner, R. E.

Appl. Opt. (2)

Bell Syst. Tech. J. (1)

D. Marcuse, “Loss Analysis of Single-Mode Fiber Splices,” Bell Syst. Tech. J. 56, 703 (1977).

Electron. Lett. (2)

J. R. Stern, R. B. Dyott, “Off-Axis Launching into a Fibre-Optical Waveguide,” Electron. Lett. 7, 52 (1971).
[CrossRef]

J. R. Stern, M. Peace, R. B. Dyott, “Launching into Optical Fiber Waveguide,” Electron. Lett. 6, 160 (1970).
[CrossRef]

J. Opt. Soc. Am. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

B. J. McGlamery, “Computer Simulation Studies of Compensation of Turbulence Degraded Images,” Proc. Soc. Photo-Opt. Instrum. Eng. 74, 225 (1976).

Prog. Opt. (1)

F. Roddier, “The Effects of Atmospheric Turbulence in Optical Astronomy,” Prog. Opt. 19, 281 (1981).
[CrossRef]

Other (4)

L. Jeunhomme, Single-Mode Fiber Optics (Marcel Dekker, New York, 1983).

P. Connes, C. Froehly, “A Fiber-Linked Version of Project TRIO,” in Proceedings, ESA Conference: Colloquium on Kilometric Optical Arrays in Space, 23–25 Oct. 1984 (Cargese, Corsica, France), pp. 49–61.

P. Connes, S. Shaklan, F. Roddier, “A Fiber-Linked Ground-Based Array,” in Proceedings, NOAO-ESO Workshop on Interferometric Imaging in Astronomy, 12–15 Jan. 1987 (Oracle, AZ).

P. Connes, F. Roddier, S. Shaklan, E. Ribak, “Ground and Space Fiber Arrays,” in Proceedings, ESA Workshop on Optical Interferometry in Space, 16–18 June 1987 (Granada, Spain).

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Figures (6)

Fig. 1
Fig. 1

Coupling efficiency vs normalized frequency V. Curves for several different seeing conditions are plotted: (1) ideal seeing; (2) d/r0 = 0.5; (3) d/r0 = 1; (4) d/r0 = 2; (5) d/r0 = 4. The dashed lines show the coupling efficiency obtained if, by proper choice of fiber core, the plotted frequency was forced to become the cutoff frequency.

Fig. 2
Fig. 2

Coupling efficiency vs seeing at V = 2.2. The upper curve is the image stabilization case; the lower curve is for no stabilization. The dashed curve goes with the scale on the right and is the ratio of the two solid curves.

Fig. 3
Fig. 3

Comparison of the optimized f-ratio to the fixed f-ratio · coupling. The upper curve is identical to curve 4 of Fig. 1; the f-ratio varies from 5.2 to 7.4. The dashed curve has a fixed f-ratio = 5.1.

Fig. 4
Fig. 4

Relative fluctuations in ρ vs seeing at V = 2.4 for the case of rapid image stabilization. The nonstabilized case could not be simulated due to limitations in the wavefront simulation program

Fig. 5
Fig. 5

Normalized total coupled power vs seeing at V = 2.2. Upper curve is image stabilization case. The maximum shows that power is maximized by using a pupil which has d = 4r0. The peak corresponds to 18% efficiency.

Fig. 6
Fig. 6

Coupling efficiency vs image displacement for perfect imaging. The dashed curve is the amplitude mode profile of the fiber.

Equations (20)

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E ( r ) = E 0 Ψ ( r ) P ( r ) .
ρ = { 1 2 [ E ˜ x ( r λ f ) × H y * ( r a ) ] · z ^ d r } 2 [ 1 2 E ˜ x ( r λ f ) H y * ( r a ) d r ] 2 ,
E 0 2 = 8 π d 2 μ 0 1 n clad
H y ( r a ) = c H 2 W J 0 ( U ) a V J 1 ( U ) { J 0 ( U / a ) J 0 ( U ) r a K 0 ( W r a ) K 0 ( W ) r a ,
c H = 2 n clad π ( 0 μ ) 1 / 4 .
ρ ψ ( r ) ψ * ( r ) P ( r ) P * ( r ) H ˜ ( a r λ f ) H ˜ * ( a r λ f ) d r d r .
ρ ψ ( r ) ψ * ( r + s ) P a ( r ) P a * ( r + s ) d r d s .
ρ ψ ( r ) ψ * ( r + s ) P a ( r ) P a * ( r + s ) d r d s .
B ( s ) = exp - 3.44 ( s r 0 ) 5 / 3 .
B s ( s ) = exp - 3.44 ( s r 0 ) 5 / 3 [ 1 - ( s d ) 1 / 3 ] .
ρ = E 0 2 B ( s ) ( s ) P a ( r ) P a ( r + s ) d r d s .
H ( r w ) = c H w exp - ( r w ) 2 ,
w = a ( 0.65 + 1.619 V 3 / 2 + 2.879 V 6 ) .
E ( r , α ) = E 0 π d 2 4 λ f 2 J 1 [ π d ( r - α f ) / λ f ] π d ( r - α f ) / λ f ,
ρ ( α f ) [ J 1 ( π d r / λ f ) π d / λ f exp - ( r + α f / w ) 2 r d r d ϕ ] 2 .
r + α f 2 = r 2 + ( α f ) 2 - 2 r α f cos ϕ .
I 0 ( 2 r α f / w 2 ) = 1 2 π 0 2 π exp [ 2 r α f cos ( ϕ ) / w 2 d ϕ .
ρ ( α f ) = 8 w 2 exp - 2 ( α f / w ) 2 × [ ( exp - ( r / w ) 2 ) I 0 ( 2 r α f / w 2 ) J 1 ( π d r / λ f ) d r ] 2 .
ρ [ P ( r ) H ˜ ( r ) d r ] 2 .
ρ [ P ˜ ( r ) H ( r ) d r ] 2 .

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