Table I
Spatial Frequencies of the Fringe Patterns and the Indices of the Four Interfering Beams at P00
a | Indices of the Four Interfering Beams | fx′ | fy′ |
---|
(m,n,m′,n′) |
---|
2 | (0,−1,0,2) | (−1,0,2,0) | (1,0,−2,0) | (0,1,0,−2) |
|
|
8 | (0,−2,0,4) | (−2,0,4,0) | (2,0,−4,0) | (0,2,0,−4) |
|
|
18 | (0,−3,0,6) | (−3,0,6,0) | (3,0,−6,0) | (0,3,0,−6) |
|
|
32 | (0,−4,0,8) | (−4,0,8,0) | (4,0,−8,0) | (0,4,0,−8) |
|
|
a | Indices of the Four Interfering Beams | fx | fy |
---|
(m,n,m′,n′) |
---|
4 | (−1,−1,2,2) | (1,−1,−2,2) | (−1,1,2,−2) | (1,1,−2−2) | 2f1 | 2f1 |
10 | (−1,−2,2,4) | (1,−2,−2,4) | (−1,2,2,−4) | (1,2,−2−4) | 2f1 | 4f1 |
10 | (−2,−1,4,2) | (−2,1,4,−2) | (2,−1,−4,2) | (2,1,−4−2) | 4f1 | 2f1 |
16 | (−2,−2,4,4) | (2,−2,−4,4) | (−2,2,4,−4) | (2,2,−4−4) | 4f1 | 4f1 |
20 | (−1,−3,2,6) | (1,−3,−2,6) | (−1,3,2,−6) | (1,3,−2−6) | 2f1 | 6f1 |
20 | (−3,−1,6,2) | (3,−1,−6,2) | (−3,1,6,−2) | (3,1,−6,−2) | 6f1 | 2f1 |
26 | (−2,−3,4,6) | (2,−3,−4,6) | (−2,3,4,−6) | (2,3,−4,−6) | 4f1 | 6f1 |
26 | (−3,−2,6,4) | (3,−2,−6,4) | (−3,2,6,−4) | (3,2,−6,−4) | 6f1 | 4f1 |
34 | (−1,−4,2,8) | (1,−4,−2,8) | (−1,4,2,−8) | (1,4,−2,−8) | 2f1 | 8f1 |
34 | (−4,−1,8,2) | (4,−1,−8,2) | (−4,1,8,−2) | (4,1,−8,−2) | 8f1 | 2f1 |
36 | (−3,−3,6,6) | (3,−3,−6,6) | (−3,3,6,−6) | (3,3,−6,−6) | 6f1 | 6f1 |
Table II
Spatial Frequencies of the Fringe Patterns and the Indices of the Four Interfering Beams at P01
a | Indices of the Four Interfering Beams | fx | fy |
---|
(m,n,m′,n′) |
---|
3 | (1,0,−2,1) | (−1,0,2,1) | (1,1,−2,−1) | (−1,1,2,−1) | 2f1 | f1 |
7 | (1,−1,−2,3) | (−1,−1,2,3) | (1,2,−2,−3) | (−1,2,2,−3) | 2f1 | 3f1 |
9 | (2,0,−4,1) | (−2,0,4,1) | (2,1,−4,−1) | (−2,1,4,−1) | 4f1 | f1 |
13 | (2,−1,−4,3) | (−2,−1,4,3) | (2,2,−4,−3) | (−2,2,4,−3) | 4f1 | 3f1 |
15 | (1,−2,−2,5) | (−1,−2,2,5) | (1,3,−2,−5) | (−1,3,2,−5) | 2f1 | 5f1 |
19 | (3,0,−6,1) | (−3,0,6,1) | (3,1,−6,1) | (−3,1,6,−1) | 6f1 | f1 |
21 | (2,−2,−4,5) | (−2,−2,4,5) | (2,3,−4,−5) | (−2,3,4,−5) | 4f1 | 5f1 |
23 | (3,−1,−6,3) | (−3,−1,6,3) | (3,2,−6,−3) | (−3,2,6,−3) | 6f1 | 3f1 |
27 | (1,−3,−2,7) | (−1,−3,2,7) | (1,4,−2,−7) | (−1,4,2,−7) | 2f1 | 7f1 |
31 | (3,−2,−6,5) | (−3,−2,6,5) | (3,3,−6,−5) | (−3,3,6,−5) | 6f1 | 5f1 |
33 | (4,0,−8,1) | (−4,0,8,1) | (4,1,−8,−1) | (−4,1,8,−1) | 8f1 | f1 |
33 | (2,−3,−4,7) | (−2,−3,4,7) | (2,4,−4,−7) | (−2,4,4,−7) | 4f1 | 7f1 |
37 | (4,−1,−8,3) | (−4,−1,8,3) | (4,2,−8,−3) | (−4,2,8,−3) | 8f1 | 3f1 |
43 | (3,−3,−6,7) | (−3,−3,6,7) | (3,4,−6,−7) | (−3,4,6,−7) | 6f1 | 7f1 |
Table III
Spatial Frequencies of the Fringe Patterns and the Indices of the Four Interfering Beams at P02
a | Indices of the Four Interfering Beams | fx′ | fy′ |
---|
(m,n,m′,n′) |
---|
4 | (0,0,0,2) | (−1,1,2,0) | (1,1,−2,0) | (0,2,0,−2) |
|
|
10 | (0,−1,0,4) | (−2,1,4,0) | (2,1,−4,0) | (0,3,0,−4) |
|
|
20 | (0,−2,0,6) | (−3,1,6,0) | (3,1,−6,0) | (0,4,0,−6) |
|
|
34 | (0,−3,0,8) | (−4,1,8,0) | (4,1,−8,0) | (0,5,0,−8) |
|
|
a | Indices of the Four Interfering Beams | fx | fy |
---|
(m,n,m′,n′) |
---|
6 | (−1,0,2,2) | (1,0,−2,2) | (−1,2,2,−2) | (1,2,−2,−2) | 2f1 | 2f1 |
12 | (−1,−1,2,4) | (1,−1,−2,4) | (−1,3,2,−4) | (1,3,−2,−4) | 2f1 | 4f1 |
12 | (−2,0,4,2) | (2,0,−4,2) | (−2,2,4,−2) | (2,2,−4,−2) | 4f1 | 2f1 |
18 | (−2,−1,4,4) | (2,−1,−4,4) | (−2,3,4,−4) | (2,3,−4,−4) | 4f1 | 4f1 |
22 | (−1,−2,2,6) | (1,−2,−2,6) | (−1,4,2,−6) | (1,4,−2,−6) | 2f1 | 6f1 |
22 | (−3,0,6,2) | (3,0,−6,2) | (−3,2,6,−2) | (3,2,−6,−2) | 6f1 | 2f1 |
28 | (−2,−2,4,6) | (2,−2,−4,6) | (−2,4,4,−6) | (2,4,−4,−6) | 4f1 | 6f1 |
28 | (−3,−1,6,4) | (3,−1,−6,4) | (−3,3,6,−4) | (3,3,−6,−4) | 6f1 | 4f1 |
36 | (−1,−3,2,8) | (1,−3,−2,8) | (−1,5,2,−8) | (1,5,−2,−8) | 2f1 | 8f1 |
36 | (−4,0,8,2) | (4,0,−8,2) | (−4,2,8,−2) | (4,2,−8,−2) | 8f1 | 2f1 |
38 | (−3,−2,6,6) | (3,−2,−6,6) | (−3,4,6,−6) | (3,4,−6,−6) | 6f1 | 6f1 |
Table IV
Spatial Frequencies of the Fringe Patterns and the Indices of the Four Interfering Beams at P03
a | Indices of the Four Interfering Beams | fx | fy |
---|
(m,n,m′,n′) |
---|
7 | (−1,1,2,1) | (1,1,−2,1) | (−1,2,2,−1) | (1,2,−2,−1) | 2f1 | f1 |
11 | (−1,0,2,3) | (1,0,−2,3) | (−1,3,2,−3) | (1,3,−2,−3) | 2f1 | 3f1 |
13 | (−2,1,4,1) | (2,1,−4,1) | (−2,2,4,−1) | (2,2,−4,−1) | 4f1 | f1 |
17 | (−2,0,4,3) | (2,0,−4,3) | (−2,3,4,−3) | (2,3,−4,−3) | 4f1 | 3f1 |
19 | (−1,−1,2,5) | (1,−1,−2,5) | (−1,4,2,−5) | (1,4,−2,−5) | 2f1 | 5f1 |
23 | (−3,1,6,1) | (3,1,−6,1) | (−3,2,6,−1) | (3,2,−6,−1) | 6f1 | f1 |
25 | (−2,−1,4,5) | (2,−1,−4,5) | (−2,4,4,−5) | (2,4,−4,−5) | 4f1 | 5f1 |
27 | (−3,0,6,3) | (3,0,−6,3) | (−3,3,6,−3) | (3,3,−6,−3) | 6f1 | 3f1 |
31 | (−1,−2,2,7) | (1,−2,−2,7) | (−1,5,2,−7) | (1,5,−2,−7) | 2f1 | 7f1 |
35 | (−3,−1,6,5) | (3,−1,−6,5) | (−3,4,6,−5) | (3,4,−6,−5) | 6f1 | 5f1 |
37 | (−2,−2,4,7) | (2,−2,−4,7) | (−2,5,4,−7) | (2,5,−4,−7) | 4f1 | 7f1 |
37 | (−4,1,8,1) | (4,1,−8,1) | (−4,2,8,−1) | (4,2,−8,−1) | 8f1 | f1 |
41 | (−4,0,8,3) | (4,0,−8,3) | (−4,3,8,−3) | (4,3,−8,−3) | 8f1 | 3f1 |
Table V
Spatial Frequencies of the Fringe Patterns and the Indices of the Four Interfering Beams at P11
a | Indices of the Four Interfering Beams | fx | fy |
---|
(m,n,m′,n′) |
---|
2 | (0,0,1,1) | (1,0,−1,1) | (0,1,1,−1) | (1,1,−1,−1) | f1 | f1 |
6 | (0,−1,1,3) | (0,−1,−1,3) | (0,2,1,−3) | (1,2,−1,−3) | f1 | 3f1 |
6 | (−1,0,3,1) | (2,0,−3,1) | (−1,0,3,−1) | (2,1,−3,−1) | 3f1 | f1 |
10 | (−1,−1,3,3) | (2,−1,−3,3) | (−1,2,3,−3) | (2,2,−3,−3) | 3f1 | 3f1 |
14 | (0,−2,1,5) | (1,−2,−1,5) | (0,3,1,−5) | (1,3,−1,−5) | f1 | 5f1 |
14 | (−2,0,5,1) | (3,0,−5,1) | (−2,1,5,−1) | (3,1,−5,−1) | 5f1 | f1 |
18 | (−1,−2,3,5) | (2,−2,−3,5) | (−1,3,3,−5) | (2,3,−3,−5) | 3f1 | 5f1 |
18 | (−2,−1,5,3) | (3,−1,−5,3) | (−2,2,5,−3) | (3,2,−5,−3) | 5f1 | 3f1 |
26 | (0,−3,1,7) | (1,−3,−1,7) | (0,4,1,−7) | (1,4,−1,−7) | f1 | 7f1 |
26 | (−3,0,7,1) | (4,0,−7,1) | (−3,1,7,−1) | (4,1,−7,−1) | 7f1 | f1 |
26 | (−2,−2,5,5) | (3,−2,−5,5) | (−2,3,5,−5) | (3,3,−5,−5) | 5f1 | 5f1 |
30 | (−1,−3,3,7) | (2,−3,−3,7) | (−1,4,3,−7) | (2,4,−3,−7) | 3f1 | 7f1 |
30 | (−3,−1,7,3) | (4,−1,−7,3) | (−3,2,7,−3) | (4,2,−7,−3) | 7f1 | 3f1 |
38 | (−2,−3,5,7) | (3,−3,−5,7) | (−2,4,5,−7) | (3,4,−5,−7) | 5f1 | 7f1 |
38 | (−3,−2,7,5) | (4,−2,−7,5) | (−3,3,7,−5) | (4,3,−7,−5) | 7f1 | 5f1 |
Table VI
Spatial Frequencies of the Fringe Patterns and the Indices of the Interfering Beams at P12
a | Indices of the Four Interfering Beams | fx | fy |
---|
(m,n,m′,n′) |
---|
5 | (0,0,1,2) | (1,0,−1,2) | (0,2,1,−2) | (1,2,−1,−2) | f1 | 2f1 |
9 | (−1,0,3,2) | (2,0,−3,2) | (−1,2,3,−2) | (2,2,−3,−2) | 3f1 | 2f1 |
11 | (0,−1,1,4) | (1,−1,−1,4) | (0,3,1,−4) | (1,3,−1,−4) | f1 | 4f1 |
15 | (−1,−1,3,4) | (2,−1,−3,4) | (−1,3,3,−4) | (2,3,−3,−4) | 3f1 | 4f1 |
17 | (−2,0,5,2) | (3,0,−5,2) | (−2,2,5,−2) | (3,2,−5,−2) | 5f1 | 2f1 |
21 | (0,−2,1,6) | (1,−2,−1,6) | (0,4,1,−6) | (1,4,−1,−6) | f1 | 6f1 |
23 | (−2,−1,5,4) | (3,−1,−5,4) | (−2,3,5,−4) | (3,3,−5,−4) | 5f1 | 4f1 |
25 | (−1,−2,3,6) | (2,−2,−3,6) | (−1,4,3,−6) | (2,4,−3,−6) | 3f1 | 6f1 |
29 | (−3,0,7,2) | (4,0,−7,2) | (−3,2,7,−2) | (4,2,−7,−2) | 7f1 | 2f1 |
33 | (−2,−2,5,6) | (3,−2,−5,6) | (−2,4,5,−6) | (3,4,−5,−6) | 5f1 | 6f1 |
35 | (0,−3,1,8) | (0,−3,−1,8) | (0,5,1,−8) | (1,5,−1,−8) | f1 | 8f1 |
35 | (−3,−1,7,4) | (4,−1,−7,4) | (−3,3,7,−4) | (4,3,−7,−4) | 7f1 | 4f1 |
39 | (−1,−3,3,8) | (2,−3,−3,8) | (−1,5,3,−8) | (2,5,−3,−8) | 3f1 | 8f1 |
Table VII
Spatial Frequencies of the Fringe Patterns and the Indices of the Interfering Beams at P13
a | Indices of the Four Interfering Beams | fx | fy |
---|
(m,n,m′,n′) |
---|
6 | (0,1,1,1) | (1,1,−1,1) | (0,2,1,−1) | (1,2,−1,−1) | f1 | f1 |
10 | (0,0,1,3) | (1,0,−1,3) | (0,3,1,−3) | (1,3,−1,−3) | f1 | 3f1 |
10 | (−1,1,3,1) | (2,1,−3,1) | (−1,2,3,−1) | (2,2,−3,−1) | 3f1 | f1 |
14 | (−1,0,3,3) | (2,0,−3,3) | (−1,3,3,−3) | (2,3,−3,−3) | 3f1 | 3f1 |
18 | (0,−1,1,5) | (1,−1,−1,5) | (0,4,1,−5) | (1,4,−1,−5) | f1 | 5f1 |
18 | (−2,1,5,1) | (3,1,−5,1) | (−2,2,5,−1) | (3,2,−5,−1) | 5f1 | f1 |
22 | (−1,−1,3,5) | (2,−1,−3,5) | (−1,4,3,−5) | (2,4,−3,−5) | 3f1 | 5f1 |
22 | (−2,0,5,3) | (3,0,−5,3) | (−2,3,5,−3) | (3,3,−5,−3) | 5f1 | 3f1 |
30 | (0,−2,1,7) | (1,−2,−1,7) | (0,5,1,−7) | (1,5,−1,−7) | f1 | 7f1 |
30 | (−3,1,7,1) | (4,1,−7,1) | (−3,2,7,−1) | (4,2,−7,−1) | 7f1 | f1 |
30 | (−2,−1,5,5) | (3,−1,−5,5) | (−2,4,5,−5) | (3,4,−5,−5) | 5f1 | 5f1 |
34 | (−1,−2,3,7) | (2,−2,−3,7) | (−1,5,3,−7) | (2,5,−3,−7) | 3f1 | 7f1 |
34 | (−3,0,7,3) | (4,0,−7,3) | (−3,3,7,−3) | (4,3,−7,−3) | 7f1 | 3f1 |
42 | (−2,−2,5,7) | (3,−2,−5,7) | (−2,5,5,−7) | (3,5,−5,−7) | 5f1 | 7f1 |
42 | (−3,−1,7,5) | (4,−1,−7,5) | (−3,4,7,−5) | (4,4,−7,−5) | 7f1 | 5f1 |
Table VIII
Spatial Frequencies of the Fringe Patterns and the Indices of the Interfering Beams at P22
a | Indices of the Four Interfering Beams | fx′ | fy′ |
---|
(m,n,m′,n′) |
---|
6 | (1,0,0,2) | (0,1,2,0) | (2,1,−2,0) | (1,2,0,−2) |
|
|
12 | (1,−1,0,4) | (−1,1,4,0) | (3,1,−4,0) | (1,3,0,−4) |
|
|
22 | (1,−2,0,6) | (−2,1,6,0) | (4,1,−6,0) | (1,4,0,−6) |
|
|
36 | (1,−3,0,8) | (−3,1,8,0) | (5,1,−8,0) | (1,5,0,−8) |
|
|
a | Indices of the Four Interfering Beams | fx | fy |
---|
(m,n,m′,n′) |
---|
8 | (0,0,2,2) | (2,0,−2,2) | (0,2,2,−2) | (2,2,−2,−2) | 2f1 | 2f1 |
14 | (0,−1,2,4) | (2,−1,−2,4) | (0,3,2,−4) | (2,3,−2,−4) | 2f1 | 4f1 |
14 | (−1,0,4,2) | (−1,2,4,−2) | (3,0,−4,2) | (3,2,−4,−2) | 4f1 | 2f1 |
20 | (−1,−1,4,4) | (−1,3,4,−4) | (3,−1,−4,4) | (3,3,−4,−4) | 4f1 | 4f1 |
24 | (0,−2,2,6) | (0,4,2,−6) | (2,−2,−2,6) | (2,4,−2,−6) | 2f1 | 6f1 |
24 | (−2,0,6,2) | (−2,2,6,−2) | (4,0,−6,2) | (4,2,−6,−2) | 6f1 | 2f1 |
30 | (−2,−1,6,4) | (−2,3,6,−4) | (4,−1,−6,4) | (4,3,−6,−4) | 6f1 | 4f1 |
30 | (−1,−2,4,6) | (−1,4,4,−6) | (3,−2,−4,6) | (3,4,−4,−6) | 4f1 | 6f1 |
38 | (0,−3,2,8) | (0,5,2,−8) | (2,−3,−2,8) | (2,5,−2,−8) | 2f1 | 8f1 |
38 | (−3,0,8,2) | (−3,2,8,−2) | (5,0,−8,2) | (5,2,−8,−2) | 8f1 | 2f1 |
40 | (−2,−2,6,6) | (−2,4,6,−6) | (4,−2,−6,6) | (4,4,−6,−6) | 6f1 | 6f1 |
Table IX
Spatial Frequencies of the Fringe Patterns and the Indices of the Interfering Beams at P23
a | Indices of the Four Interfering Beams | fx | fy |
---|
(m,n,m′,n′) |
---|
9 | (0,1,2,1) | (2,1,−2,1) | (0,2,2,−1) | (2,2,−2,−1) | 2f1 | f1 |
13 | (0,0,2,3) | (2,0,−2,3) | (0,3,2,−3) | (2,3,−2,−3) | 2f1 | 3f1 |
15 | (−1,1,4,1) | (3,1,−4,1) | (−1,2,4,−1) | (3,2,−4,−1) | 4f1 | f1 |
19 | (−1,0,4,3) | (3,0,−4,3) | (−1,3,4,−3) | (3,3,−4,−3) | 4f1 | 3f |
21 | (0,−1,2,5) | (2,−1,−2,5) | (0,4,2,−5) | (2,4,−2,−5) | 2f1 | 5f1 |
25 | (−2,1,6,1) | (4,1,−6,1) | (−2,2,6,−1) | (4,2,−6,−1) | 6f1 | f1 |
27 | (−1,−1,4,5) | (3,−1,−4,5) | (−1,4,4,−5) | (3,4,−4,−5) | 4f1 | 5f1 |
29 | (−2,0,6,3) | (4,0,−6,3) | (−2,3,6,−3) | (4,3,−6,−3) | 6f1 | 3f1 |
33 | (0,−2,2,7) | (2,−2,−2,7) | (0,5,2,−7) | (2,5,−2,−7) | 2f1 | 7f1 |
37 | (−2,−1,6,5) | (4,−1,−6,5) | (−2,4,6,−5) | (4,4,−6,−5) | 6f1 | 5f1 |
39 | (−1,−2,4,7) | (3,−2,−4,7) | (−1,5,4,−7) | (3,5,−4,−7) | 4f1 | 7f1 |
39 | (−3,1,8,1) | (5,1,−8,1) | (−3,2,8,−1) | (5,2,−8,−1) | 8f1 | f1 |
43 | (−3,0,8,3) | (5,0,−8,3) | (−3,3,8,−3) | (5,3,−8,−3) | 8f1 | 3f1 |
Table X
Spatial Frequencies of the Fringe Patterns and the Indices of the Interfering Beams at P33
a | Indices of the Four Interfering Beams | fx | fy |
---|
(m,n,m′,n′) |
---|
10 | (1,1,1,1) | (2,1,−1,1) | (1,2,1,−1) | (2,2,−1,−1) | f1 | f1 |
14 | (1,0,1,3) | (2,0,−1,3) | (1,3,1,−3) | (2,3,−1,−3) | f1 | 3f1 |
14 | (0,1,3,1) | (3,1,−3,1) | (0,2,3,−1) | (3,2,−3,−1) | 3f1 | f1 |
18 | (0,0,3,3) | (3,0,−3,3) | (0,3,3,−3) | (3,3,−3,−3) | 3f1 | 3f1 |
22 | (1,−1,1,5) | (2,−1,−1,5) | (1,4,1,−5) | (2,4,−1,−5) | f1 | 5f1 |
22 | (−1,1,5,1) | (4,1,−5,1) | (−1,2,5,−1) | (4,2,−5,−1) | 5f1 | f1 |
26 | (0,−1,3,5) | (3,−1,−3,5) | (0,4,3,−5) | (3,4,−3,−5) | 3f1 | 5f1 |
26 | (−1,0,5,3) | (4,0,−5,3) | (−1,3,5,−3) | (4,3,−5,−3) | 5f1 | 3f1 |
34 | (1,−2,1,7) | (2,−2,−1,7) | (1,5,1,−7) | (2,5,−1,−7) | f1 | 7f1 |
34 | (−1,−1,5,5) | (4,−1,−5,5) | (−1,4,5,−5) | (4,4,−5,−5) | 5f1 | 5f1 |
34 | (−2,1,7,1) | (5,1,−7,1) | (−2,2,7,−1) | (5,2,−7,−1) | 7f1 | f1 |
38 | (0,−2,3,7) | (3,−2,−3,7) | (0,5,3,−7) | (3,5,−3,−7) | 3f1 | 7f1 |
38 | (−2,0,7,3) | (5,0,−7,3) | (−2,3,7,−3) | (5,3,−7,−3) | 7f1 | 3f1 |
Table XI
Indices of the Four Interfering Beams In the Three-Cross-Grating Interferometer
(a) M = 0, N = 0, α = 2 |
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|
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m1 | n1 | m2 | n2 | m3 | n3 |
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1 | 0 | −1 | 0 | −1 | 0 |
0 | 1 | 0 | −1 | 0 | −1 |
−1 | 0 | 1 | 0 | 1 | 0 |
0 | −1 | 0 | 1 | 0 | 1 |
(b) M = 1, N = 1, α = 2 |
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|
---|
m1 | n1 | m2 | n2 | m3 | n3 |
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1 | 1 | −1 | −1 | 0 | 0 |
1 | 0 | −1 | 0 | 0 | 1 |
0 | 1 | 0 | −1 | 1 | 0 |
0 | 0 | 0 | 0 | 1 | 1 |