David C. Tilotta, Robert M. Hammaker, and William G. Fateley, "Multiplex advantage in Hadamard transform spectrometry utilizing solid-state encoding masks with uniform, bistable optical transmission defects," Appl. Opt. 26, 4285-4292 (1987)
The effect of a uniform bistable optical transmission defect in the encoding mask on the multiplex efficiency is investigated for solid-state Hadamard transform spectrometry with thermal detection. It is demonstrated that encoding masks which possess nonideal optical transmission properties, i.e., bistable transmission defects, need not impare the multiplex capability provided a sufficient number of resolution elements are multiplexed. Application to the SNR of a general algorithm for the calculation of the average mean square error in the estimate of the spectrum shows that reasonable SNR improvements can be expected when compared to conventional dispersive instruments.
You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.
The average deviation of the values in this table from the values obtained via the exact equation [i.e., Eq. (15)] from all values of N as listed in Table I.
Table IV
SNR Improvementa Calculated from the Approximate Equation
for Various Values of ΔT and N
Compared to a scanning dispersive spectrometer.
Average deviation of the values in this table from the values obtained via the exact equation [i.e., Eq. (16)] from all values of N as listed in Table II.
Tables (4)
Table I
Multiplex Efficiency Evaluated as ∊/σ2 for Selected Values of N, Tt and T0 using Eg. (15)
Tt
T0
N =
3
15
63
255
1023
4095
1.000
1.000
∞
∞
∞
∞
∞
∞
1.000
0.9000
66.71
23.33
6.151
1.556
0.3902
0.09763
1.000
0.8000
16.71
5.834
1.538
0.3891
0.09756
0.02441
1.000
0.7000
7.453
2.593
0.6834
0.1729
0.04336
0.01085
1.000
0.6000
4.216
1.459
0.3844
0.09727
0.02439
0.006102
1.000
0.5000
2.720
0.9338
0.2460
0.06226
0.01561
0.003905
1.000
0.4000
1.910
0.6487
0.1709
0.04323
0.01084
0.002712
1.000
0.3000
1.424
0.4768
0.1255
0.03176
0.007964
0.001993
1.000
0.2000
1.111
0.3653
0.09612
0.02432
0.006098
0.001526
1.000
0.1000
0.8986
0.2889
0.07595
0.01922
0.004818
0.001205
1.000
0.000
0.7500
0.2344
0.06152
0.01556
0.003902
0.0009763
0.9500
0.0500
0.9107
0.2891
0.07595
0.01922
0.004818
0.001205
0.8500
0.05000
1.151
0.3659
0.09613
0.02432
0.006098
0.001526
0.7500
0.05000
1.499
0.4778
0.1256
0.03176
0.007964
0.001993
0.6500
0.05000
2.035
0.6503
0.1709
0.04323
0.01084
0.002712
0.5500
0.05000
2.919
0.9363
0.2461
0.06226
0.01561
0.003905
0.4500
0.05000
4.536
1.463
0.3845
0.09727
0.02439
0.006102
0.3500
0.05000
8.000
2.599
0.6835
0.1729
0.04336
0.01085
0.2500
0.05000
17.77
5.845
1.538
0.3891
0.09756
0.02441
0.1500
0.05000
69.39
23.36
6.151
1.556
0.3902
0.09763
0.000
0.000
∞
∞
∞
∞
∞
∞
Table II
SNR Improvementa for Selected Values of N, Tt, and T0 using Eq. (16)
Tt
T0
N =
3
15
63
255
1023
4095
1.000
1.000
0.000
0.000
0.000
0.000
0.000
0.000
1.000
0.9000
0.1224
0.2070
0.4032
0.8016
1.601
3.200
1.000
0.8000
0.2446
0.4140
0.8064
1.603
3.202
6.401
1.000
0.7000
0.3663
0.6210
1.210
2.405
4.802
9.601
1.000
0.6000
0.4870
0.8280
1.613
3.206
6.403
12.80
1.000
0.5000
0.6063
1.035
2.016
4.008
8.004
16.00
1.000
0.4000
0.7236
1.242
2.419
4.809
9.605
19.20
1.000
0.3000
0.8381
1.448
2.822
5.611
11.21
22.40
1.000
0.2000
0.9489
1.654
3.226
6.413
12.81
25.60
1.000
0.1000
1.055
1.860
3.629
7.214
14.41
28.80
1.000
0.000
1.155
2.066
4.032
8.016
16.01
32.00
0.9500
0.05000
1.048
1.860
3.629
7.214
14.41
28.80
0.8500
0.05000
0.9323
1.653
3.225
6.413
12.81
25.60
0.7500
0.05000
0.8167
1.447
2.822
5.612
11.21
22.40
0.6500
0.05000
0.7010
1.240
2.419
4.809
9.605
19.20
0.5500
0.05000
0.5853
1.033
2.016
4.008
8.004
16.00
0.4500
0.05000
0.4695
0.8269
1.613
3.206
6.403
12.80
0.3500
0.05000
0.3536
0.6203
1.210
2.405
4.802
9.601
0.2500
0.05000
0.2372
0.4136
0.8064
1.603
3.202
6.401
0.1500
0.05000
0.1200
0.2069
0.4032
0.8016
1.601
3.200
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
Compared to a scanning dispersive spectrometer.
Table III
Multiplex Efficiency Evaluated as ∊/σ2 from the Approximate Equation ∊/σ2 = [1/(ΔT)2][4N/(N + 1)2] for Various Values of ΔT and N
The average deviation of the values in this table from the values obtained via the exact equation [i.e., Eq. (15)] from all values of N as listed in Table I.
Table IV
SNR Improvementa Calculated from the Approximate Equation
for Various Values of ΔT and N
Compared to a scanning dispersive spectrometer.
Average deviation of the values in this table from the values obtained via the exact equation [i.e., Eq. (16)] from all values of N as listed in Table II.