Table 1
Fully Connected Versus LimitedFanOut SV Systems
System Type  SubDOE Array
 Propagation Length Z
 Aspect Ratio W/Z
 Lens fNumber  Number of Connections NI
 System Volume ZW
^{
2
}
 Connection Density NI/ZW
^{
2
}


SBWP
 Width W


Fully connected 
C
^{2}
B
^{2}
N
^{4}
 CBΔN^{2}

$$\left(\frac{C}{\mathrm{\lambda}}\right){\left(\mathit{BN}\mathrm{\Delta}\right)}^{2}$$

$$\left(\frac{1}{B}\right)\left(\frac{\mathrm{\lambda}}{\mathrm{\Delta}}\right)$$

$$B\left(\frac{\mathrm{\Delta}}{\mathrm{\lambda}}\right)$$

N
^{4}

$$\frac{{C}^{3}{B}^{4}{N}^{6}{\mathrm{\Delta}}^{4}}{\mathrm{\lambda}}$$

$$\left(\frac{\mathrm{\lambda}}{{C}^{3}{B}^{4}{\mathrm{\Delta}}^{4}}\right)\left(\frac{1}{{N}^{2}}\right)$$

Limited fanout 
C
^{2}
B
^{2}
N
^{2}
M
^{2}
 CBΔMN

$$\left(\frac{C}{\mathrm{\lambda}}\right)\left(\mathit{BM}{\mathrm{\Delta}}^{2}\right)$$

$$\left(\frac{1}{B}\right)\left(\frac{\mathrm{\lambda}}{\mathrm{\Delta}}\right)\left(\frac{N}{M}\right)$$

$$\mathit{MB}\left(\frac{\mathrm{\Delta}}{\mathrm{\lambda}}\right)$$

M
^{2}
N
^{2}

$$\frac{{C}^{3}{B}^{4}{N}^{2}{M}^{4}{\mathrm{\Delta}}^{4}}{\mathrm{\lambda}}$$

$$\left(\frac{\mathrm{\lambda}}{{C}^{3}{B}^{4}{\mathrm{\Delta}}^{4}}\right)\left(\frac{1}{{M}^{2}}\right)$$

Table 2
Comparison of Fully Connected and LimitedFanOut SV
Systems with Parameters of N = 100, λ = 850 nm, Δ
= 2 μm, B = 2, C = 2, and
M = 10
System Type  SubDOE Array
 Propagation Length Z (mm)  Aspect Ratio W/Z
 Lens fNumber  Number of Connections NI
 System Volume (mm^{3})  Connection Density (connections/mm^{3}) 

SBWP
 Width W (mm) 

Fully connected  1.6 × 10^{9}
 80  376  0.21  4.7  10^{8}
 2.4 × 10^{6}
 4.2 × 10^{1}

Limited fanout
 1.6 × 10^{7}
 8
 3.76
 2.1
 47
 10^{6}
 2.4 × 10^{2}
 4.2 × 10^{3}

Table 3
LimitedFanOut SV Systems with the CrossTalk Reduction
Parameter Y
System Type  SubDOE Array
 Propagation Length Z
 Aspect Ratio W/Z
 Lens fNumber  Number of Connections NI
 System Volume ZW
^{
2
}
 Connection Density NI/ZW
^{
2
}


SBWP
 Width W


Limited fanout 
$$\frac{{N}^{2}{S}^{2}}{{\mathrm{\Delta}}^{2}}$$

NS

$$\frac{S\left(\mathit{BM}\mathrm{\Delta}\right)}{\mathrm{\lambda}Y}$$

$$\left(\frac{Y}{B}\right)\left(\frac{\mathrm{\lambda}}{\mathrm{\Delta}}\right)\left(\frac{N}{M}\right)$$

$$M\left(\frac{B}{Y}\right)\left(\frac{\mathrm{\Delta}}{\mathrm{\lambda}}\right)$$

M
^{
2
}
N
^{
2
}

$$\frac{{S}^{3}\left(\mathit{BM}\mathrm{\Delta}\right){N}^{2}}{\mathrm{\lambda}Y}$$

$$\frac{\mathrm{\lambda}\mathit{MY}}{{S}^{3}\left(B\mathrm{\Delta}\right)}$$

Table 4
LimitedFanOut Systems with Different Values of the
Oversampling Ratio B and the CrossTalk Reduction Parameter
Y for N = 128, M = 5, λ
= 850 nm, Δ = 2 μm, S = 96 μm, and
P = 32 μm
Phase Elements Per SubDOE Period
 Detector Width P (μm)
 Oversampling Ratio B
 CrossTalk Reduction Parameter Y
 SubDOE Array Width W (mm)
 Propagation Length Z (mm)
 Compression Ratio C
 Normalized Detector Width K
 Cross Talk β


8 × 8  32  1.6  1  12.3  1.81  6.0  1.0  0.1889 
16 × 16  32  3.2  2  12.3  1.81  3.0  1.0  0.1746 
22 × 22  32  4.4  3  12.3  1.67  2.2  1.1  0.0736 
22 × 22
 16
 4.4
 3
 12.3
 1.67
 2.2
 0.55
 0.0316

Table 5
Same Example and Parameters as Given in Table 4 Except
with a Larger SubDOE Width of S = 192 μm
Phase Elements Per SubDOE Period
 Detector Width P (μm)
 Oversampling Ratio B
 CrossTalk Reduction Parameter Y
 SubDOE Array Width W (mm)
 Propagation Length Z (mm)
 Compression Ratio C
 Normalized Detector Width K
 Cross Talk β


8 × 8  32  1.6  1  24.6  3.6  12.0  1.0  0.1572 
16 × 16  32  3.2  2  24.6  3.6  6.0  1.0  0.1287 
22 × 22
 32
 4.4
 3
 24.6
 3.3
 4.4
 1.1
 0.0214

Table 6
Parameters and Average Performances for Each Set of the
Nine SubDOE’s Designed with Different Values of Y
Y

J

Z
 Average SNR (dB)
 Average Diffraction Efficiency (%)
 SRMSE
 Scale Factor


1  8  16  17.8  77.1  0.0076  1.3 
2  16  16  15.8  58.8  0.0020  1.7 
3
 22
 16
 16.8
 51.6
 0.0011
 1.9
