Table I
Performance of Three Algorithms for the Design of 1-D Screens
| Algorithm |
---|
|
|
---|
Nonlinearity | DS | DSMOD | pairfit |
---|
Linear | 5.29 × 10−5 | 3.67 × 10−5 | 1.04 × 10−5 |
NV = 64, N = 256 | 1.56 × 10−2 | 1.24 × 10−2 | 7.29 × 10−3 |
Triangle | 3.33 × 10−5 | 2.01 × 10−5 | 6.05 × 10−5 |
NV = 64, N = 256 | 1.16 × 10−2 | 8.72 × 10−3 | 5.30 × 10−3 |
Triangle | 1.09 × 10−5 | 8.63 × 10−6 | 1.69 × 10−6 |
NV = 64, N = 512 | 7.74 × 10−3 | 6.58 × 10−3 | 2.66 × 10−3 |
|sinc| | 8.32 × 10−4 | 4.18 × 10−4 | 1.02 × 10−4 |
NV = 50, N = 128 | 4.54 × 10−2 | 1.46 × 10−2 | 1.17 × 10−2 |
Note: NV = number of output values;
N = number of vectors. Each entry consists of the mean-squared error, followed by the maximum error.
Table II
Performance of the DS and pairfit Algorithms on Worst-Case Nonlinearities as Shown in Figs. 5(a) and 5(b)
| Algorithm |
---|
|
|
---|
Nonlinearity | DS | pairfit |
---|
(a) | 1.21 × 10−4 | 5.86 × 10−6 |
NV = 64, N = 256 | 1.23 × 10−2 | 2.59 × 10−3 |
(b) | 1.35 × 10−4 | 5.19 × 10−6 |
NV = 64, N = 256 | 1.23 × 10−2 | 2.73 × 10−3 |
(a) | 1.16 × 10−3 | 2.12 × 10−4 |
NV = 21, N = 80 | 3.92 × 10−2 | 2.50 × 10−2 |
(b) | 1.27 × 10−3 | 3.26 × 10−4 |
NV = 21, N = 80 | 3.92 × 10−2 | 4.10 × 10−2 |
Note: NV = number of output values;
N = number of vectors. Each entry consists of the mean-squared error, followed by the maximum error.
Table III
Aliasing Coefficients for the DS Algorithm in 1-D (N = 64) and 2-D (N = 8)
| | Diffraction order (m) |
---|
| |
|
---|
| Nonlinearity | −2 | −1 | 0 | 1 | 2 | 3 | 4 |
---|
| Parabolic | 1.42 | 1.00 | 3.33 | — | 1.42 | 0.47 | 0.36 |
1-D | |sinc| | 1.08 | 1.00 | 4.11 | — | 1.08 | 0.45 | 0.68 |
| Expsin | 1.02 | 1.00 | 3.12 | — | 1.02 | 0.42 | 0.55 |
| | | n |
---|
| | |
|
---|
| Nonlinearity | m | 0 | 1 | 2 |
---|
2-D | Parabolic | 2 | 0.10 | 0.18 | 1.53 |
1 | 0.18 | — | 0.18 |
0 | 3.25 | 0.18 | 0.10 |
|sinc| | 2 | 0.15 | 0.17 | 1.15 |
1 | 0.18 | — | 0.17 |
0 | 4.08 | 0.22 | 0.15 |
Expsin | 2 | 0.15 | 0.23 | 1.28 |
1 | 0.32 | — | 0.29 |
0 | 3.09 | 0.29 | 0.15 |
Table IV
Aliasing Coefficients for the Stack Vector Orderings of Fig. 9, for the |Sinc| Nonlinearity
| n |
---|
|
|
---|
m | −1 | 0 | 1 | 2 | 3 |
---|
3 | 0.09 | 0.13 | 0.09 | 0.17 | 0.46 |
| 0.25 | 0.60 | 0.47 | 0.21 | 0.46 |
2 | 0.11 | 0.15 | 0.17 | 1.15 | 0.16 |
| 0.21 | 1.02 | 0.82 | 0.21 | 0.27 |
1 | 0.15 | 0.18 | — | 0.17 | 0.12 |
| 0.27 | 1.65 | — | 0.23 | 0.16 |
0 | 0.22 | 4.08 | 0.22 | 0.15 | 0.12 |
| 0.56 | 5.93 | 0.56 | 0.21 | 0.13 |
−1 | 1.00 | 0.21 | 0.15 | 0.13 | 0.12 |
| 1.00 | 1.65 | 0.27 | 0.23 | 0.10 |
Note: Each entry consists of the coefficient for the ordering of
Fig. 9(a), followed by the coefficient for the ordering of 9(b).
Table V
Allasing Coefficients for the Stack Vector Orderings of Fig. 9, for the Parabolic Nonlinearity
| n |
---|
|
|
---|
m | −1 | 0 | 1 | 2 | 3 |
---|
3 | 0.07 | 0.07 | 0.10 | 0.18 | 0.54 |
| 0.23 | 0.83 | 0.40 | 0.14 | 0.41 |
2 | 0.07 | 0.10 | 0.18 | 1.53 | 0.18 |
| 0.27 | 0.54 | 0.74 | 0.14 | 0.31 |
1 | 0.10 | 0.18 | — | 0.18 | 0.10 |
| 0.35 | 2.00 | — | 0.14 | 0.16 |
0 | 0.18 | 3.25 | 0.18 | 0.10 | 0.07 |
| 0.65 | 4.59 | 0.65 | 0.14 | 0.13 |
−1 | 1.00 | 0.18 | 0.10 | 0.07 | 0.07 |
| 1.00 | 2.10 | 0.27 | 0.14 | 0.10 |
Table VI
Allasing Coefficients for the Stack Vector Orderings of Fig. 9, for the Expsin Nonlinearity
| n |
---|
|
|
---|
m | −1 | 0 | 1 | 2 | 3 |
---|
3 | 0.09 | 0.13 | 0.13 | 0.23 | 0.53 |
| 0.17 | 0.44 | 0.32 | 0.12 | 0.40 |
2 | 0.10 | 0.15 | 0.23 | 1.28 | 0.28 |
| 0.15 | 0.65 | 0.56 | 0.15 | 0.18 |
1 | 0.15 | 0.32 | — | 0.29 | 0.16 |
| 0.18 | 0.89 | — | 0.13 | 0.10 |
0 | 0.29 | 3.09 | 0.29 | 0.15 | 0.13 |
| 0.35 | 3.78 | 0.35 | 0.15 | 0.06 |
−1 | 1.00 | 0.32 | 0.15 | 0.10 | 0.12 |
| 1.00 | 0.89 | 0.18 | 0.16 | 0.07 |
Note: Each entry consists of the coefficient for the ordering of
Fig. 9(a), followed by the coefficient for the ordering of 9(b).