Anhu Li,1
Liren Liu,1
Jianfeng Sun,1
Xianghong Zhong,1
Lijuan Wang,1
Dean Liu,1
and Zhu Luan1
1The authors are with the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, P.O. Box 800-211, Shanghai 201800, China. A. Li's e-mail address is yfliah@yahoo.com.cn.
The original scanner for tilting orthogonal double prisms is studied to test the tracking performance in intersatellite laser communications. With a reduction ratio of more than 100 times from the change rate of the angle of beam deviation to that of the tilting angle of each prism,
the theoretical analysis performed, as well as the verification experiment, indicates that the scanner can meet the requirements of the scanning accuracy superior to
with the scanning range greater than
and can facilitate the mechanical structure design.
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Different Wedge Angle α (°) to Beam Deviation Angle δ (mrad) and Change Rate ∂δ∕∂i (rad∕°)
α
Max δ
Min δ
Range δ
Max ∂δ∕∂i
Min ∂δ∕∂i
Mean ∂δ∕∂i
2
18.245
18.050
1.954 × 10−1
9.800 × 10−6
−1.900 × 10−5
−4.518 × 10−6
3
27.448
27.082
3.666 × 10−1
1.133 × 10−5
−3.209 × 10−5
−1.019 × 10−5
4
36.720
36.121
5.990 × 10−1
1.063 × 10−5
−4.768 × 10−5
−1.818 × 10−5
5
46.073
45.171
9.014 × 10−1
7.708 × 10−6
−6.587 × 10−5
−2.854 × 10−5
6
55.519
54.235
1.284
2.528 × 10−6
−8.677 × 10−5
−4.134 × 10−5
7
65.071
63.315
1.756
−4.933 × 10−6
−1.105 × 10−4
−5.665 × 10−5
8
74.744
72.433
2.312
−1.472 × 10−5
−1.373 × 10−4
−7.457 × 10−5
Table 2
Relation of Wedge Angle α (°) to Minimum Deviation Angle of Beam (°) and Required Tilting Angle of Double Prisms (°)
α1,2
3
4
5
6
7
δ1,2
1.5496
2.0668
2.5846
3.1032
3.6227
i1
−2.4333
−3.0613
−3.7097
−4.5806
−5.2903
i2
−0.7619
−0.93651
−1.129
−1.3871
−1.7419
θ1
−2.4333
−3.0613
−3.7092
−4.5806
−5.2903
7.1111
5.1111
2.8889
2.2222
0.88889
θ2
−0.7619
−0.93651
−1.129
−1.3871
−1.7419
8.7302
7.2063
6.1905
5.1746
4.6667
Table 3
Beam Scanning Errors Influenced by the Main Error Sources
(μrad)a
Main Errors
δθ1 (1 arcmin)
δθ2 (1 arcmin)
δn (1 × 10−6)
δα (1 arcsec)
δβ (1 arcsec)
Max
3.46
3.46
0.0712
2.638
0.4374
Min
1.45
1.45
0.0712
2.559
Style
Random error
System error
δθ1 and δθ2 are, respectively, the tilting angles of the first and second prisms, δn is the refractive index uniformity of glass; δα is the error of the wedge angle; and δβ is the perpendicularity between principal cross sections of double prisms.
Table 4
Results of Testing for Tilting Accuracy of Prism by the Autocollimation Measuring Methoda
Collimator (arcsec)
D-value (arcsec)
Coder Reading (°)
D-value (°)
Error ε (arcsec)
A
B
A
B
A
B
A
B
A
B
−258.5
−33.8
119.3
259.2
0.0527
−0.0112
0.0337
0.0733
2.02
4.68
−139.2
225.4
120.5
133.2
0.0190
−0.0845
0.0321
0.0377
4.94
2.52
18.7
92.2
124.8
121.9
−0.0131
−0.0508
0.0353
0.0352
2.28
4.82
143.5
−29.7
112.8
104.8
−0.0484
−0.0156
0.0315
0.0329
6.90
5.64
250.0
−142.5
−0.0799
0.0173
A is the result of testing for prism A, and B is for prism B.
Tables (4)
Table 1
Different Wedge Angle α (°) to Beam Deviation Angle δ (mrad) and Change Rate ∂δ∕∂i (rad∕°)
α
Max δ
Min δ
Range δ
Max ∂δ∕∂i
Min ∂δ∕∂i
Mean ∂δ∕∂i
2
18.245
18.050
1.954 × 10−1
9.800 × 10−6
−1.900 × 10−5
−4.518 × 10−6
3
27.448
27.082
3.666 × 10−1
1.133 × 10−5
−3.209 × 10−5
−1.019 × 10−5
4
36.720
36.121
5.990 × 10−1
1.063 × 10−5
−4.768 × 10−5
−1.818 × 10−5
5
46.073
45.171
9.014 × 10−1
7.708 × 10−6
−6.587 × 10−5
−2.854 × 10−5
6
55.519
54.235
1.284
2.528 × 10−6
−8.677 × 10−5
−4.134 × 10−5
7
65.071
63.315
1.756
−4.933 × 10−6
−1.105 × 10−4
−5.665 × 10−5
8
74.744
72.433
2.312
−1.472 × 10−5
−1.373 × 10−4
−7.457 × 10−5
Table 2
Relation of Wedge Angle α (°) to Minimum Deviation Angle of Beam (°) and Required Tilting Angle of Double Prisms (°)
α1,2
3
4
5
6
7
δ1,2
1.5496
2.0668
2.5846
3.1032
3.6227
i1
−2.4333
−3.0613
−3.7097
−4.5806
−5.2903
i2
−0.7619
−0.93651
−1.129
−1.3871
−1.7419
θ1
−2.4333
−3.0613
−3.7092
−4.5806
−5.2903
7.1111
5.1111
2.8889
2.2222
0.88889
θ2
−0.7619
−0.93651
−1.129
−1.3871
−1.7419
8.7302
7.2063
6.1905
5.1746
4.6667
Table 3
Beam Scanning Errors Influenced by the Main Error Sources
(μrad)a
Main Errors
δθ1 (1 arcmin)
δθ2 (1 arcmin)
δn (1 × 10−6)
δα (1 arcsec)
δβ (1 arcsec)
Max
3.46
3.46
0.0712
2.638
0.4374
Min
1.45
1.45
0.0712
2.559
Style
Random error
System error
δθ1 and δθ2 are, respectively, the tilting angles of the first and second prisms, δn is the refractive index uniformity of glass; δα is the error of the wedge angle; and δβ is the perpendicularity between principal cross sections of double prisms.
Table 4
Results of Testing for Tilting Accuracy of Prism by the Autocollimation Measuring Methoda
Collimator (arcsec)
D-value (arcsec)
Coder Reading (°)
D-value (°)
Error ε (arcsec)
A
B
A
B
A
B
A
B
A
B
−258.5
−33.8
119.3
259.2
0.0527
−0.0112
0.0337
0.0733
2.02
4.68
−139.2
225.4
120.5
133.2
0.0190
−0.0845
0.0321
0.0377
4.94
2.52
18.7
92.2
124.8
121.9
−0.0131
−0.0508
0.0353
0.0352
2.28
4.82
143.5
−29.7
112.8
104.8
−0.0484
−0.0156
0.0315
0.0329
6.90
5.64
250.0
−142.5
−0.0799
0.0173
A is the result of testing for prism A, and B is for prism B.
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