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R. F. Lutomirski, H. T. Yura, Appl. Opt. 10, 1652 (1971).
[CrossRef]
[PubMed]
R. F. Lutomirski, H. T. Yura, J. Opt. Soc. Am. 61, 482 (1971).
[CrossRef]
Treatments that are restricted to include only the effects of turbulent eddies that are small compared to the laser beam diameter [e.g., A. M. Whitman, M. J. Beran, J. Opt. Soc. Am. 60, 1595 (1970); A. D. Varvastsis, M. I. Sancer, “Expansion of a Focused Laser Beam in the Turbulent Atmosphere,” Northrup Corporation Laboratories Report 70-36R14May1970] are led to the erroneous conclusion that the turbulence induced beam spread is independent of wavelength and always increases at a rate proportional to Cnz³/₂. The present analysis, which includes the effects of eddies of all sizes, shows that in the range zc ≲ z ≲ zi the beam diameter increases at a rate proportional to Cn⁶/₅k15z⁸/₅. This predicted wavelength dependence should be easily discernible by comparing the beam spread of a visible and ir laser beam that are simultaneously propagating over the same path (e.g., θ(0.53 μm)/θ(10.6 μm)=(20)15≈1.82).
[CrossRef]
R. S. Lawrence, G. R. Ochs, S. F. Clifford, J. Opt. Soc. Am. 60, 826 (1970).
[CrossRef]
C. E. Coulman, Solar Phys. 7, 122 (1969).
[CrossRef]
Treatments that are restricted to include only the effects of turbulent eddies that are small compared to the laser beam diameter [e.g., A. M. Whitman, M. J. Beran, J. Opt. Soc. Am. 60, 1595 (1970); A. D. Varvastsis, M. I. Sancer, “Expansion of a Focused Laser Beam in the Turbulent Atmosphere,” Northrup Corporation Laboratories Report 70-36R14May1970] are led to the erroneous conclusion that the turbulence induced beam spread is independent of wavelength and always increases at a rate proportional to Cnz³/₂. The present analysis, which includes the effects of eddies of all sizes, shows that in the range zc ≲ z ≲ zi the beam diameter increases at a rate proportional to Cn⁶/₅k15z⁸/₅. This predicted wavelength dependence should be easily discernible by comparing the beam spread of a visible and ir laser beam that are simultaneously propagating over the same path (e.g., θ(0.53 μm)/θ(10.6 μm)=(20)15≈1.82).
[CrossRef]
C. E. Coulman, Solar Phys. 7, 122 (1969).
[CrossRef]
R. F. Lutomirski, H. T. Yura, Appl. Opt. 10, 1652 (1971).
[CrossRef]
[PubMed]
R. F. Lutomirski, H. T. Yura, J. Opt. Soc. Am. 61, 482 (1971).
[CrossRef]
R. F. Lutomirski, J. Opt. Soc. Am.See also “Propagation of a Focused Laser Beam in a Turbulent Atmosphere,” Rand Corp. R-608 ARPA (June1971).
Treatments that are restricted to include only the effects of turbulent eddies that are small compared to the laser beam diameter [e.g., A. M. Whitman, M. J. Beran, J. Opt. Soc. Am. 60, 1595 (1970); A. D. Varvastsis, M. I. Sancer, “Expansion of a Focused Laser Beam in the Turbulent Atmosphere,” Northrup Corporation Laboratories Report 70-36R14May1970] are led to the erroneous conclusion that the turbulence induced beam spread is independent of wavelength and always increases at a rate proportional to Cnz³/₂. The present analysis, which includes the effects of eddies of all sizes, shows that in the range zc ≲ z ≲ zi the beam diameter increases at a rate proportional to Cn⁶/₅k15z⁸/₅. This predicted wavelength dependence should be easily discernible by comparing the beam spread of a visible and ir laser beam that are simultaneously propagating over the same path (e.g., θ(0.53 μm)/θ(10.6 μm)=(20)15≈1.82).
[CrossRef]
R. F. Lutomirski, H. T. Yura, J. Opt. Soc. Am. 61, 482 (1971).
[CrossRef]
Treatments that are restricted to include only the effects of turbulent eddies that are small compared to the laser beam diameter [e.g., A. M. Whitman, M. J. Beran, J. Opt. Soc. Am. 60, 1595 (1970); A. D. Varvastsis, M. I. Sancer, “Expansion of a Focused Laser Beam in the Turbulent Atmosphere,” Northrup Corporation Laboratories Report 70-36R14May1970] are led to the erroneous conclusion that the turbulence induced beam spread is independent of wavelength and always increases at a rate proportional to Cnz³/₂. The present analysis, which includes the effects of eddies of all sizes, shows that in the range zc ≲ z ≲ zi the beam diameter increases at a rate proportional to Cn⁶/₅k15z⁸/₅. This predicted wavelength dependence should be easily discernible by comparing the beam spread of a visible and ir laser beam that are simultaneously propagating over the same path (e.g., θ(0.53 μm)/θ(10.6 μm)=(20)15≈1.82).
[CrossRef]
R. S. Lawrence, G. R. Ochs, S. F. Clifford, J. Opt. Soc. Am. 60, 826 (1970).
[CrossRef]
C. E. Coulman, Solar Phys. 7, 122 (1969).
[CrossRef]
For example, ρo can be obtained by varying the slit separation in a Young’s interferometer and noting the separation where the fringe visibility is down by 1/e (as compared to its value for small slit separations).
The spot size is defined here as twice the distance from the z axis where the mean irradiance distribution is down by 1/e.
The mathematical expression used here to represent this aperture disturbance is given byUA(r)=Uo exp[-r2(wo-2+ikf-1)/2].
We note that the detailed computer calculations of Lutomirski on the propagation of a truncated Gaussian wavefront in a turbulent atmosphere8 show that the results for the nontruncated Gaussian are valid when the truncation diameter exceeds 2wo. Conversely, when 2wo exceeds the truncation diameter, the results obtained in Ref. 1 for a plane wave in a circular aperture are applicable.
R. F. Lutomirski, J. Opt. Soc. Am.See also “Propagation of a Focused Laser Beam in a Turbulent Atmosphere,” Rand Corp. R-608 ARPA (June1971).
S. Valley, ed., Handbook of Geophysics (Macmillan, New York, 1960), pp. 13–1, 13–2.
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Angular beam spread, normalized to that of a 15-cm diffraction limited 0.53-
Table I Summary of Spherical Wave Lateral Coherence Lengths and Beam Spreads for an Initially Gaussian Wavefront^{a}
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