Peter D. Gianino, Charles L. Woods, and Joseph L. Horner, "Analysis of spatial light modulator contrast ratios and optical correlation," Appl. Opt. 34, 6682-6694 (1995)
We have performed a general analysis of optical correlators with spatal light modulators (SLM’s) whose primary defect is a finite contrast ratio (CR). Our mathematical analysis identifies three noise terms that appear in addition to the correlation term. The filter SLM contains either a phase-only filter (POF) or a binary-phase-only filter (BPOF). Insertion of a dc block at the center of the filter SLM decreases the noise background in the correlator plane; this dc block is larger than that required for the same level of performance in a correlator whose SLM’s have transmissive (or reflective) dead zones. With a noise-free input and the dc block, our computer simulations that show the peak intensity falling off as the CR decreases are in quantitative agreement with the correlation term of the mathematical model. For a cluttered, disjoint noise input this agreement is only qualitative, and at low CR’s the dc block is definitely required for the BPOF correlator if the secondary peaks in the output are to be brought below the correlation peak.
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Operating Values of Various Metrics when a 3 × 3 Pixel dc Block Is Added to Filter SLMa
Input
Filter
Case
R
Opaque dcB Operation
Improvement Factors
PNR
PSR
PNR
PSR
Ip
Opaque dcB
Gray dcB
Opaque dcB
Gray dcB
Woman’s face
POF
All
∞
59.2
17.4
16.3
1.4
1.3
1.6
1.4
A
5
26.2
3.0
1.6
2.9
1.6
0.91
0.70
B
5
33.0
3.8
5.1
2.1
1.5
1.1
1.0
C
5
45.6
7.9
5.2
1.5
1.3
1.4
1.2
BPOF
All
∞
47.3
9.0
6.5
1.3
1.2
1.3
1.3
A
5
17.0
2.6
0.6
4.9
2.0
1.7
1.5
B
5
23.8
3.6
2.0
3.7
1.9
1.6
1.6
C
5
31.0
4.0
2.1
1.5
1.3
1.2
1.1
Tank
POF
All
∞
15.6
3.4
1.7
1.8
1.1
1.2
0.9
A
5
6.5
1.4
0.16
1.9
0.8
1.0
0.8
B
5
5.8
1.2
0.41
1.3
0.8
0.7
0.6
C
5
15.0
3.4
0.55
2.4
1.0
1.6
0.9
BPOF
All
∞
9.9
2.3
0.71
2.4
1.6
2.3
1.5
A
5
4.8
1.2
0.83
[1.7]
[1.2]
B
5
0.8
0.17
[1.4]
[1.2]
C
5
10.3
1.2
0.83
[2.4]
[1.4]
Square brackets indicate values for which the correlation peak was not at the maximum. Blank entries indicate that measurements are not possible under those circumstances.
Table 3
Energy Partitioning in Percent throughout the Correlator with and without the Use of a dc Block for the Input of the Woman’s Face
This light loss occurs for all phases of F* that are different from zero.
This light loss occurs because SLM2 diffracts the incident light at too large an angle to permit it to be captured at the detector.
Table 4
Energy Partitioning in Percent throughout the Correlator with and without the Use of a dc Block for the Input of the Tank
This light loss occurs for all phases of F* that are different from zero.
This light loss occurs because SLM2 diffracts the incident light at too large an angle to permit it to be captured at the detector.
Operating Values of Various Metrics when a 3 × 3 Pixel dc Block Is Added to Filter SLMa
Input
Filter
Case
R
Opaque dcB Operation
Improvement Factors
PNR
PSR
PNR
PSR
Ip
Opaque dcB
Gray dcB
Opaque dcB
Gray dcB
Woman’s face
POF
All
∞
59.2
17.4
16.3
1.4
1.3
1.6
1.4
A
5
26.2
3.0
1.6
2.9
1.6
0.91
0.70
B
5
33.0
3.8
5.1
2.1
1.5
1.1
1.0
C
5
45.6
7.9
5.2
1.5
1.3
1.4
1.2
BPOF
All
∞
47.3
9.0
6.5
1.3
1.2
1.3
1.3
A
5
17.0
2.6
0.6
4.9
2.0
1.7
1.5
B
5
23.8
3.6
2.0
3.7
1.9
1.6
1.6
C
5
31.0
4.0
2.1
1.5
1.3
1.2
1.1
Tank
POF
All
∞
15.6
3.4
1.7
1.8
1.1
1.2
0.9
A
5
6.5
1.4
0.16
1.9
0.8
1.0
0.8
B
5
5.8
1.2
0.41
1.3
0.8
0.7
0.6
C
5
15.0
3.4
0.55
2.4
1.0
1.6
0.9
BPOF
All
∞
9.9
2.3
0.71
2.4
1.6
2.3
1.5
A
5
4.8
1.2
0.83
[1.7]
[1.2]
B
5
0.8
0.17
[1.4]
[1.2]
C
5
10.3
1.2
0.83
[2.4]
[1.4]
Square brackets indicate values for which the correlation peak was not at the maximum. Blank entries indicate that measurements are not possible under those circumstances.
Table 3
Energy Partitioning in Percent throughout the Correlator with and without the Use of a dc Block for the Input of the Woman’s Face
This light loss occurs for all phases of F* that are different from zero.
This light loss occurs because SLM2 diffracts the incident light at too large an angle to permit it to be captured at the detector.
Table 4
Energy Partitioning in Percent throughout the Correlator with and without the Use of a dc Block for the Input of the Tank
This light loss occurs for all phases of F* that are different from zero.
This light loss occurs because SLM2 diffracts the incident light at too large an angle to permit it to be captured at the detector.
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