Abstract

A technique has been developed for the measurement of a component of the position of a small target within a laser beam and used to measure atmospherically induced beam-pointing fluctuations. A modulation is impressed on the beam in a manner such that the modulation phase varies with position across the beam, so the relative modulation phase of the signal returned from a remote retroreflector is indicative of the position of the retroreflector within the beam. The far-field modulation phase distribution is shown to be relatively unaffected by turbulence, and results are given for a series of experimental measurements of beam-pointing fluctuations.

© 1971 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
    [CrossRef]
  2. G. R. Ochs, R. S. Lawrence, J. Opt. Soc. Am. 59, 226 (1969).
    [CrossRef]
  3. J. I. Davis, Appl. Opt. 5, 139 (1966).
    [CrossRef] [PubMed]
  4. V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961) (Trans. by R. A. Silverman).

1969 (1)

1966 (2)

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

J. I. Davis, Appl. Opt. 5, 139 (1966).
[CrossRef] [PubMed]

Davis, J. I.

Kogelnik, H.

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Lawrence, R. S.

Li, T.

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Ochs, G. R.

Tatarski, V. I.

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961) (Trans. by R. A. Silverman).

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Proc. IEEE (1)

H. Kogelnik, T. Li, Proc. IEEE 54, 1312 (1966).
[CrossRef]

Other (1)

V. I. Tatarski, Wave Propagation in a Turbulent Medium (McGraw-Hill, New York, 1961) (Trans. by R. A. Silverman).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1
Fig. 1

Curves of modulation phase vs normalized distance from the beam axis for various values of γ for w0 = 3.4 mm, a = −257 rad/m, and β = 0.55.

Fig. 2
Fig. 2

Curves of modulation phase vs normalized distance from the beam axis for various values of initial phase shift variation and w0 = 3.4 mm, β = 0.55, γ = 62.7 (z = 3613 m).

Fig. 3
Fig. 3

Block diagram of transmitter–receiver unit and associated equipment.

Fig. 4
Fig. 4

Block diagram of the signal-processing electronics.

Fig. 5
Fig. 5

Initial modulation phase pattern for modulator alignment used for all remote-target measurements.

Fig. 6
Fig. 6

Far-field modulation phase pattern measured under relatively quiet atmospheric conditions for an initially collimated beam with the source rotated to produce approximately horizontal phase contours.

Fig. 7
Fig. 7

Far-field modulation phase pattern measured with moderately strong atmospheric turbulence for an initially collimated beam with the source rotated to produce approximately horizontal constant phase contours.

Fig. 8
Fig. 8

Far-field modulation phase pattern measured under low turbulence conditions for an initially diverging beam with the source rotated to produce approximately horizontal contours.

Fig. 9
Fig. 9

Far-field modulation phase pattern measured under very strong turbulence conditions for an initially diverging beam with the source rotated to produce approximately horizontal contours.

Fig. 10
Fig. 10

Cumulative distribution of modulation phase fluctuations for data of 12:00 noon, 30 November 1970.

Fig. 11
Fig. 11

Cumulative distribution of modulation phase fluctuations for data of 11:30 p.m., 23 December 1970.

Fig. 12
Fig. 12

Scatter diagram plotting rms beam angular fluctuations against 〈χ2〉.

Fig. 13
Fig. 13

Behavior of scintillation parameter and modulation phase variance near sunset, 23 December 1970.

Equations (6)

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

e out ( t ) = { - [ 1 + J 0 2 ( β ) ] 1 2 / 2 } ( cos { ω t - tan - 1 J 0 ( β ) ] + { J 1 ( β ) / [ 1 + J 0 2 ( β ) ] 1 2 } { cos [ ( ω + ω m ) t + α ( x , y ) - ( π / 2 ) ] + cos [ ( ω - ω m ) t - α ( x y ) + ( π / 2 ) ] } + { J 2 ( β ) / [ 1 + J 0 2 ( β ) ] 1 2 } × { cos [ ( ω + 2 ω m ) t + 2 α ( x , y ) + ( π / 2 ) ] + cos [ ( ω - 2 ω m ) t - 2 α ( x , y ) + ( π / 2 ) ] } + { J 3 ( β ) / [ 1 + J 0 2 ( β ) ] 1 2 } × { cos [ ( ω + 3 ω m ) t + 3 α ( x , y ) - ( π / 2 ) ] + cos [ ( ω + 3 ω m ) t - 3 α ( x , y ) + ( π / 2 ) ] } + ) ,
e sig ( t ) = ( K / 2 ) J 1 ( β ) sin [ ω m t + α ( x , y ) ] ,
- exp ( - { [ ( x ) 2 + ( y ) 2 ] / w 0 2 } + j α ( x , y ) - ( j k / 2 z ) [ ( x - x ) 2 + ( y - y ) 2 ] ) d x d y ,
α ( x , y ) = - a x ,
A re 1 = exp [ - 2 ( x 2 + y 2 ) / w 0 2 ( 1 + γ 2 ) ] ( cosh [ 2 a x γ / ( 1 + γ 2 ) ] + cos { 2 tan - 1 J 0 ( β ) + ( a 2 w 0 2 / 2 ) [ γ / ( 1 + γ 2 ) ] } 1 2 ,
φ re 1 = tan - 1 ( tanh [ a x γ / ( 1 + γ 2 ) ] tan { tan - 1 J 0 ( β ) + ( a 2 w 0 2 ) / 4 ) × [ γ / ( 1 + γ 2 ) ] } ) - [ a x / ( 1 + γ 2 ) ] .

Metrics