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Mutual alignment errors due to the variation of wave-front aberrations in a free-space laser communication link

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Abstract

Optical devices in free-space laser communication systems are affected by their environment, particularly in relation to the effects of temperature while in orbit. The mutual alignment error between the transmitted and received optical axes is caused by deformation of the optics due to temperature variation in spite of the common optics used for transmission and reception of the optical beams. When a Gaussian beam wave for transmission is aligned at the center of a received plane wave, 3rd-order Coma aberrations have the most influence on the mutual alignment error, which is an inevitable open pointing error under only the Tip/Tilt tracking control. As an example, a mutual alignment error of less than 0.2 µrad is predicted for a laser communication terminal in orbit using the results from space chamber thermal vacuum tests. The relative power penalty due to aberration is estimated to be about 0.4 dB. The results will mitigate surface quality in an optical antenna and contribute to the design of free-space laser communication systems.

©2001 Optical Society of America

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Supplementary Material (4)

Media 1: MOV (906 KB)     
Media 2: MOV (846 KB)     
Media 3: MOV (1696 KB)     
Media 4: MOV (1527 KB)     

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Figures (17)

Fig. 1.
Fig. 1. Definition of the coordinate systems.
Fig. 2.
Fig. 2. Definition of the received optical axis.
Fig. 3.
Fig. 3. Definition of the transmitted optical axis.
Fig. 4.
Fig. 4. X-axis mutual alignment error due to wave-front aberration (F 0=α, γ=0.0 and α=1.579).
Fig. 5.
Fig. 5. Y-axis mutual alignment error due to wave-front aberration (F 0=α, γ=0.0 and α=1.579).
Fig. 6.
Fig. 6. Phase displacement of the Coma aberration (Z7).
Fig. 7.
Fig. 7. Movie of the received intensity distribution due to the Coma aberration (Z7) generated from the plane wave on the optical sensor as the Zernike coefficient a7 varies with time (γ=0.0 and α=1.579). (906 KB)
Fig. 8.
Fig. 8. Movie of the transmitted intensity distribution due to the Coma aberration (Z7) generated from the Gaussian beam wave at the far-field as the Zernike coefficient a7 varies with time (F 0=α, γ=0.0 and α=1.579). (847 KB)
Fig. 9.
Fig. 9. X-axis mutual alignment error due to the Coma aberration (Z7) as a function of the truncation ratio α (F 0=α and γ=0.0).
Fig. 10.
Fig. 10. X-axis mutual alignment error due to wave-front aberrations for the OICETS optical antenna (F 0=α, γ=0.2889 and α=1.579).
Fig. 11.
Fig. 11. Y-axis mutual alignment error due to wave-front aberrations for the OICETS optical antenna (F 0=α, γ=0.2889 and α=1.579).
Fig. 12.
Fig. 12. Movie of the wave-front variation of LD1 onboard the OICETS laser terminal measured during the thermal vacuum test. (1.70 MB)
Fig. 13.
Fig. 13. Movie of the wave-front variation of LD2 for the OICETS laser terminal measured during the thermal vacuum test. (1.53 MB)
Fig. 14.
Fig. 14. Trend of wave-front errors of LD1 onboard the OICETS laser terminal measured during the thermal vacuum test.
Fig. 15.
Fig. 15. Trend of wave-front errors of LD2 onboard the OICETS laser terminal measured during the thermal vacuum test.
Fig. 16.
Fig. 16. Degradation of the transmitted optical power due to wave-front aberrations at the counter terminal for the OICETS laser terminal (F 0=α, γ=0.2889 and α=1.579).
Fig. 17.
Fig. 17. Trends in the relative peak intensities of the far-field pattern transmitted from LD1 and LD2 onboard the OICETS laser terminal measured during the thermal vacuum test.

Equations (14)

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Φ ( ρ , θ ) = i = 1 a i Z i ( 2 ρ D , θ ) ,
Z i ( r , θ ) = { Z even i = n + 1 R n m ( r ) 2 cos m θ , m 0 Z odd i = n + 1 R n m ( r ) 2 sin m θ , m 0 , Z i = n + 1 R n 0 ( r ) , m = 0
R n m ( r ) = s = 0 ( n m ) 2 ( 1 ) s ( n s ) ! s ! [ ( n + m ) 2 s ] ! [ ( n m ) 2 s ] ! r n 2 s ,
Φ rms 2 = 1 π d 2 r W ( Dr 2 , θ ) Φ 2 ( Dr 2 , θ ) ,
= 1 π d 2 r W ( Dr 2 , θ ) [ i = 1 a i Z i ( r , θ ) ] 2 ,
= 1 π i = 1 { d 2 r W ( Dr 2 , θ ) [ a i Z i ( r , θ ) ] 2 } ,
= Φ rms , 1 2 + Φ rms , 2 2 + Φ rms , 3 2 + ,
{ W ( ρ , θ ) = 4 π D 2 for ρ D 2 W ( ρ , θ ) = 0 for D 2 < ρ .
U f ( x , y ) = A j λ f e j k 2 f ( x 2 + y 2 ) U l ( u , v ) exp [ j 2 π λ f ( xu + yv ) ] dudv ,
U l ( u , v ) = W ( ρ , θ ) exp [ j Φ ( ρ , θ ) ] ,
I f ( x , y ) = A 2 λ 2 f 2 U l ( u , v ) exp [ j 2 π λ f ( xu + yv ) ] dudv 2 .
{ 0 I f ( x X , y ) dxdy 0 I f ( x X , y ) dxdy I f ( x , y ) dxdy = 0 0 I f ( x , y Y ) dxdy 0 I f ( x , y Y ) dxdy I f ( x , y ) dxdy = 0 .
I ffp ( η , ξ ) = A 2 λ 2 z 2 W ( ρ , θ ) exp [ ρ 2 W 0 2 j k ρ 2 2 F 0
+ j Φ ( ρ , θ ) ] exp [ j 2 π λ z ( η u + ξ v ) ] dudv 2 ,
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