Table I
Expressions of fj and Associated S for Some Frequently Used Sets
Set | fj | S = (N − p − 1)σ2 |
---|
Δ, ψ | Δj + iψj |
|
tanψ, cosΔ | tanψj + icosΔj |
|
ρ | Re(ρ)j + i Im(ρ)j |
|
α, β | αj + iβj |
|
Table II
Variance–Covariance Matrices of a Few Optical Parameter Sets for Gold Film; Au Film: Variance–Covariance Matrix Element (×108) Table of α, β
| | 350 nm | 400 nm | 450 nm | 500 nm | 550 nm | 600 nm | 650 nm |
---|
| |
|
---|
(nm) | | α | β | α | β | α | β | α | β | α | β | α | β | α | β |
---|
350 | α | 42 | −1 | 1 | 3 | 2 | −5 | −3 | −5 | −2 | 0 | 0 | 3 | 0 | 0 |
| β | −1 | 50 | 2 | −2 | −2 | 0 | −1 | 1 | −2 | 1 | −2 | 0 | −1 | 0 |
400 | α | 1 | 2 | 24 | −2 | 2 | 4 | 1 | −2 | 0 | 4 | 1 | 2 | 1 | 1 |
| β | 3 | −2 | −2 | 33 | 2 | −1 | 4 | 6 | 0 | −3 | 0 | 1 | 0 | 3 |
450 | α | 2 | −2 | 2 | 2 | 18 | 0 | 0 | 0 | 1 | −3 | 0 | 2 | 2 | 1 |
| β | −5 | 0 | 4 | −1 | 0 | 23 | 0 | −1 | 0 | 4 | 0 | 0 | 2 | 1 |
500 | α | −3 | −1 | 1 | 4 | 0 | 0 | 18 | 1 | 0 | 1 | −1 | 0 | 1 | 0 |
| β | −5 | 1 | −2 | 6 | 0 | −1 | 1 | 27 | 2 | 1 | 0 | 1 | 1 | 7 |
550 | α | −2 | −2 | 0 | 0 | 1 | 0 | 0 | 2 | 16 | 0 | 1 | 0 | 2 | 1 |
| β | 0 | 1 | 4 | −3 | −3 | 4 | 1 | 1 | 0 | 24 | 2 | −3 | −2 | −3 |
600 | α | 0 | −2 | 1 | 0 | 0 | 0 | −1 | 0 | 1 | 2 | 12 | −1 | 0 | 0 |
| β | 3 | 0 | 2 | 1 | 2 | 0 | 0 | 1 | 0 | −3 | −1 | 18 | 2 | 4 |
650 | α | 0 | −1 | 1 | 0 | 2 | 2 | 1 | 1 | 2 | −2 | 0 | 2 | 11 | 3 |
| β | 0 | 0 | 1 | 3 | 1 | 1 | 0 | 7 | 1 | −3 | 0 | 4 | 3 | 27 |
Table III
Variance–Covariance Matrices of a Few Optical Parameter Sets for Gold Film; Au Film: Variance–Covariance Matrix Element (×108) Table of Δ, ψ
| | 350 nm | 400 nm | 450 nm | 500 nm | 550 nm | 600 nm | 650 nm |
---|
| |
|
---|
(nm) | | Δ | ψ | Δ | ψ | Δ | ψ | Δ | ψ | Δ | ψ | Δ | ψ | Δ | ψ |
---|
350 | Δ | 54 | 1 | −3 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 |
| ψ | 1 | 7 | −1 | 0 | 2 | 0 | 2 | 0 | 0 | 0 | −1 | 0 | 0 | 0 |
400 | Δ | −3 | −1 | 35 | 1 | −1 | −1 | 7 | −2 | −4 | 0 | 1 | 0 | 4 | 0 |
| ψ | 0 | 0 | 1 | 4 | −1 | 0 | 1 | 0 | −2 | 0 | −1 | 0 | 0 | 0 |
450 | Δ | 0 | 2 | −1 | −1 | 25 | 0 | −1 | 0 | 5 | 0 | 0 | 0 | 2 | −1 |
| ψ | 1 | 0 | −1 | 0 | 0 | 3 | 0 | 0 | 1 | 0 | −1 | 0 | 0 | 0 |
500 | Δ | 1 | 2 | 7 | 1 | −1 | 0 | 31 | −1 | 1 | −1 | 2 | 0 | 9 | 0 |
| ψ | 0 | 0 | −2 | 0 | 0 | 0 | −1 | 4 | 0 | 0 | 0 | 0 | 0 | 0 |
550 | Δ | 1 | 0 | −4 | −2 | 5 | 1 | 1 | 0 | 30 | 0 | −4 | −1 | −3 | 1 |
| ψ | 1 | 0 | 0 | 0 | 0 | 0 | −1 | 0 | 0 | 6 | 0 | 0 | 0 | 0 |
600 | Δ | 0 | −1 | 1 | −1 | 0 | −1 | 2 | 0 | −4 | 0 | 24 | 1 | 5 | −1 |
| ψ | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | −1 | 0 | 1 | 5 | 0 | 0 |
650 | Δ | 0 | 0 | 4 | 0 | 2 | 0 | 9 | 0 | −3 | 0 | 5 | 0 | 39 | −1 |
| ψ | 1 | 0 | 0 | 0 | −1 | 0 | 0 | 0 | 1 | 0 | −1 | 0 | −1 | 4 |
Table IV
Variance–Covariance Matrices of a Few Optical Parameter Sets for Gold Film; Au Film: Variance–Covariance Matrix Element (×108) Table of tanψ, cosΔ
| | 350 nm | 400 nm | 450 nm | 500 nm | 550 nm | 600 nm | 650 nm |
---|
| |
|
---|
(nm) | | tanψ | cosΔ | tanψ | cosΔ | tanψ | cosΔ | tanψ | cosΔ | tanψ | cosΔ | tanψ | cosΔ | tanψ | cosΔ |
---|
350 | tanψ | 12 | −1 | 0 | 1 | 0 | −2 | −1 | −3 | −1 | 0 | 0 | 2 | 0 | 0 |
| cosΔ | −1 | 53 | 1 | −3 | −1 | 0 | 0 | 1 | −2 | 1 | −3 | 0 | −2 | 0 |
400 | tanψ | 0 | 1 | 7 | −1 | 0 | 2 | 0 | −1 | 0 | 2 | 0 | 1 | 0 | 0 |
| cosΔ | 1 | −3 | −1 | 35 | 1 | −1 | 3 | 7 | 0 | −4 | 0 | 1 | 0 | 3 |
450 | tanψ | 0 | −1 | 0 | 1 | 6 | 0 | 0 | 0 | 0 | −1 | 0 | 1 | 2 | 0 |
| cosΔ | −2 | 0 | 2 | −1 | 0 | 24 | 0 | −1 | 0 | 5 | 0 | 0 | 2 | 1 |
500 | tanψ | −1 | 0 | 0 | 3 | 0 | 0 | 10 | 1 | 0 | 1 | −1 | 0 | 1 | 0 |
| cosΔ | −3 | 1 | −1 | 7 | 0 | −1 | 1 | 29 | 2 | 1 | 0 | 2 | 1 | 8 |
550 | tanψ | −1 | −2 | 0 | 0 | 0 | 0 | 0 | 2 | 18 | 0 | 1 | 0 | 2 | 1 |
| cosΔ | 0 | 1 | 2 | −4 | −1 | 5 | 1 | 1 | 0 | 30 | 3 | −4 | −3 | −3 |
600 | tanψ | 0 | −3 | 0 | 0 | 0 | 0 | −1 | 0 | 1 | 3 | 17 | −2 | 0 | 0 |
| cosΔ | 2 | 0 | 1 | 1 | 1 | 0 | 0 | 2 | 0 | −4 | −2 | 24 | 2 | 5 |
650 | tanψ | 0 | −2 | 0 | 0 | 2 | 2 | 1 | 1 | 2 | −3 | 0 | 2 | 17 | 2 |
| cosΔ | 0 | 0 | 0 | 3 | 0 | 1 | 0 | 8 | 1 | −3 | 0 | 5 | 2 | 35 |
Table V
Variance–Covariance Matrices of a Few Optical Parameter Sets for Gold Film; Au Film: Variance–Covariance Matrix Element (×108) Table of Re(ρ), Im(ρ)
| | 350 nm | 400 nm | 450 nm | 500 nm | 550 nm | 600 nm | 650 nm |
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| |
|
---|
(nm) | | Re(ρ) | Im(ρ) | Re(ρ) | Im(ρ) | Re(ρ) | Im(ρ) | Re(ρ) | Im(ρ) | Re(ρ) | Im(ρ) | Re(ρ) | Im(ρ) | Re(ρ) | Im(ρ) |
---|
350 | Re(ρ) | 14 | −1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | −1 | 0 | −1 | 0 | 0 |
| Im(ρ) | −1 | 12 | 1 | 0 | −1 | 1 | −2 | 0 | 0 | −1 | 2 | 0 | 0 | 0 |
400 | Re(ρ) | 0 | 1 | 10 | −1 | 0 | 0 | 2 | 1 | −1 | 0 | 1 | 0 | 1 | 1 |
| Im(ρ) | 0 | 0 | −1 | 7 | 1 | 0 | −1 | 0 | 2 | 0 | 1 | 0 | 0 | 0 |
450 | Re(ρ) | 0 | −1 | 0 | 1 | 7 | 0 | 0 | 0 | 2 | 0 | 0 | 0 | 0 | 2 |
| Im(ρ) | 0 | 1 | 0 | 0 | 0 | 6 | 0 | 0 | −2 | 0 | 1 | 0 | 0 | 1 |
500 | Re(ρ) | 0 | −2 | 2 | −1 | 0 | 0 | 15 | 0 | 1 | 1 | 1 | 0 | 5 | 3 |
| Im(ρ) | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 9 | 0 | 0 | 0 | −1 | −2 | 0 |
550 | Re(ρ) | 0 | 0 | −1 | 2 | 2 | −2 | 1 | 0 | 23 | 0 | −4 | 2 | −2 | −3 |
| Im(ρ) | −1 | −1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 18 | 0 | 1 | 0 | 3 |
600 | Re(ρ) | 0 | 2 | 1 | 1 | 0 | 1 | 1 | 0 | −4 | 0 | 22 | −2 | 4 | 4 |
| Im(ρ) | −1 | 0 | 0 | 0 | 0 | 0 | 0 | −1 | 2 | 1 | −2 | 17 | 0 | 0 |
650 | Re(ρ) | 0 | 0 | 1 | 0 | 0 | 0 | 5 | −2 | −2 | 0 | 4 | 0 | 32 | 7 |
| Im(ρ) | 0 | 0 | 1 | 0 | 2 | 1 | 3 | 0 | −3 | 3 | 4 | 0 | 7 | 20 |
Table VI
Variance–Covariance Matrices of a Few Optical Parameter Sets for Crystalline Silicon; c-Si: Variance–Covariance Matrix Element (×108) Table of α, β
| | 350 nm | 400 nm | 450 nm | 500 nm | 550 nm | 600 nm | 650 nm |
---|
| |
|
---|
(nm) | | α | β | α | β | α | β | α | β | α | β | α | β | α | β |
---|
350 | α | 31 | 3 | −2 | 2 | 2 | 0 | 0 | 0 | 3 | 0 | 1 | 0 | −1 | 1 |
| β | 3 | 18 | −2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | −2 | 2 | 1 |
400 | α | −2 | −2 | 21 | −6 | 0 | −2 | −3 | 2 | 0 | −4 | 4 | 0 | −5 | 3 |
| β | 2 | 0 | −6 | 14 | 1 | 1 | 1 | 0 | 1 | 0 | −1 | 2 | 1 | 1 |
450 | α | 2 | 0 | 0 | 1 | 17 | −4 | 1 | −3 | 0 | 0 | 2 | 0 | 0 | 2 |
| β | 0 | 0 | −2 | 1 | −4 | 12 | 0 | −1 | −2 | 3 | −2 | 2 | 0 | 1 |
500 | α | 0 | 0 | −3 | 1 | 1 | 0 | 14 | −8 | −1 | −1 | 1 | 0 | 1 | 2 |
| β | 0 | 0 | 2 | 0 | −3 | −1 | −8 | 23 | 0 | 1 | 2 | −5 | 2 | −2 |
550 | α | 3 | 0 | 0 | 1 | 0 | −2 | −1 | 0 | 14 | −5 | 0 | 1 | 0 | 0 |
| β | 0 | 1 | −4 | 0 | 0 | 3 | −1 | 1 | −5 | 25 | −1 | 2 | 0 | −4 |
600 | α | 1 | 0 | 4 | −1 | 2 | −2 | 1 | 2 | 0 | −1 | 22 | −5 | 0 | 0 |
| β | 0 | −2 | 0 | 2 | 0 | 2 | 0 | −5 | 1 | 2 | −5 | 38 | −5 | −3 |
650 | α | −1 | 2 | −5 | 1 | 0 | 0 | 1 | 2 | 0 | 0 | 0 | −5 | 39 | −6 |
| β | 1 | 1 | 3 | 1 | 2 | 1 | 2 | −2 | 0 | −4 | 0 | −3 | −6 | 42 |
Table VII
Variance–Covariance Matrices of a Few Optical Parameter Sets for Crystalline Silicon; c-Si: Variance–Covariance Matrix Element (×108) Table of Δ, ψ
| | 350 nm | 400 nm | 450 nm | 500 nm | 550 nm | 600 nm | 650 nm |
---|
| |
|
---|
(nm) | | Δ | ψ | Δ | ψ | Δ | ψ | Δ | ψ | Δ | ψ | Δ | ψ | Δ | ψ |
---|
350 | Δ | 76 | −6 | −22 | 2 | 3 | 0 | −8 | 0 | 26 | 0 | −54 | 0 | 77 | −2 |
| ψ | −6 | 5 | −4 | 0 | −3 | 0 | 0 | 0 | −12 | 0 | −4 | 0 | 0 | 0 |
400 | Δ | −22 | −4 | 461 | −8 | 48 | −3 | 7 | 1 | 22 | −6 | 127 | −1 | 123 | 1 |
| ψ | 2 | 0 | −8 | 3 | 8 | 0 | 5 | 0 | 14 | 0 | −16 | 0 | 12 | −1 |
450 | Δ | 3 | −3 | 48 | 8 | 1216 | −36 | −281 | −2 | 81 | 7 | 188 | 0 | 198 | 1 |
| ψ | 0 | 0 | −3 | 0 | −36 | 3 | 11 | 0 | −3 | 0 | −13 | 0 | −6 | 0 |
500 | Δ | −8 | 0 | 7 | 5 | −281 | 11 | 1868 | −30 | −226 | 10 | 66 | −24 | 439 | −21 |
| ψ | 0 | 0 | 1 | 0 | −2 | 0 | −30 | 3 | 13 | 0 | −11 | 0 | −16 | 0 |
550 | Δ | 26 | −12 | 22 | 14 | 81 | −3 | −226 | 13 | 2903 | −61 | 202 | 8 | −235 | −5 |
| ψ | 0 | 0 | −6 | 0 | 7 | 0 | 10 | 0 | −61 | 3 | −6 | 0 | 0 | 0 |
600 | Δ | −54 | −4 | 127 | −16 | 188 | −13 | 66 | −11 | 202 | −6 | 4469 | −111 | −826 | 29 |
| ψ | 0 | 0 | −1 | 0 | 0 | 0 | −24 | 0 | 8 | 0 | −111 | 6 | 6 | 0 |
650 | Δ | 77 | 0 | 123 | 12 | 198 | −6 | 439 | −16 | −235 | 0 | −826 | 6 | 6024 | −213 |
| ψ | −2 | 0 | 1 | −1 | 1 | 0 | −21 | 0 | −5 | 0 | 29 | 0 | −213 | 12 |
Table VIII
Variance–Covariance Matrices of a Few Optical Parameter Sets for Crystalline Silicon; c-Si: Variance–Covariance Matrix Element (×108) Table of tanψ, cosΔ
| | 350 nm | 400 nm | 450 nm | 500 nm | 550 nm | 600 nm | 650 nm |
---|
| |
|
---|
(nm) | | tanψ | cosΔ | tanψ | cosΔ | tanψ | cosΔ | tanψ | cosΔ | tanψ | cosΔ | tanψ | cosΔ | tanψ | cosΔ |
---|
350 | tanψ | 8 | 4 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | 1 | 0 | 0 |
| cosΔ | 4 | 22 | −1 | −2 | 0 | 0 | 0 | 0 | 0 | 2 | 0 | −5 | 1 | 9 |
400 | tanψ | 0 | −1 | 4 | 1 | 0 | −1 | 0 | −1 | 0 | −2 | 1 | 3 | −1 | −3 |
| cosΔ | 1 | −2 | 1 | 15 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 4 | 0 | 5 |
450 | tanψ | 0 | 0 | 0 | 0 | 4 | 6 | 0 | −1 | 0 | 0 | 0 | 2 | 0 | 1 |
| cosΔ | 0 | 0 | −1 | 1 | 6 | 28 | 0 | −6 | −1 | 2 | 0 | 5 | 0 | 7 |
500 | tanψ | 0 | 0 | 0 | 0 | 0 | 0 | 3 | 5 | 0 | −2 | 0 | 2 | 0 | 4 |
| cosΔ | 0 | 0 | −1 | 0 | −1 | −6 | 5 | 45 | −1 | −6 | 3 | 2 | 3 | 16 |
550 | tanψ | 0 | 0 | 0 | 1 | 0 | −1 | 0 | −1 | 4 | 11 | 0 | 1 | 0 | 0 |
| cosΔ | 2 | 2 | −2 | 0 | 0 | 2 | −2 | −6 | 11 | 86 | −1 | 6 | 0 | −9 |
600 | tanψ | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 3 | 0 | −1 | 7 | 23 | 0 | −1 |
| cosΔ | 1 | −5 | 3 | 4 | 2 | 5 | 2 | 2 | 1 | 6 | 23 | 178 | −6 | −39 |
650 | tanψ | 0 | 1 | −1 | 0 | 0 | 0 | 0 | 3 | 0 | 0 | 0 | −6 | 13 | 51 |
| cosΔ | 0 | 9 | −3 | 5 | 1 | 7 | 4 | 16 | 0 | −9 | −1 | −39 | 51 | 327 |
Table IX
Variance–Covariance Matrices of a Few Optical Parameter Sets for Crystalline Silicon; c-Si: Variance–Covariance Matrix Element (×108) Table of Re(ρ), Im(ρ)
| | 350 nm | 400 nm | 450 nm | 500 nm | 550 nm | 600 nm | 650 nm |
---|
| |
|
---|
(nm) | | Re(ρ) | Im(ρ) | Re(ρ) | Im(ρ) | Re(ρ) | Im(ρ) | Re(ρ) | Im(ρ) | Re(ρ) | Im(ρ) | Re(ρ) | Im(ρ) | Re(ρ) | Im(ρ) |
---|
350 | Re(ρ) | 7 | 2 | 0 | −3 | 0 | 0 | 0 | 0 | 0 | −1 | 0 | −3 | 0 | 4 |
| Im(ρ) | 2 | 18 | 1 | −2 | 0 | 1 | 0 | 0 | 0 | 4 | 0 | −3 | 0 | 5 |
400 | Re(ρ) | 0 | 1 | 5 | 7 | 0 | 3 | 0 | 1 | 0 | 3 | 0 | −1 | 0 | 4 |
| Im(ρ) | −3 | −2 | 7 | 63 | 0 | 4 | 0 | 0 | −2 | 1 | 1 | 9 | 2 | 7 |
450 | Re(ρ) | 0 | 0 | 0 | 0 | 2 | 3 | 0 | 0 | 0 | 0 | 0 | −1 | 0 | 0 |
| Im(ρ) | 0 | 1 | 3 | 4 | 3 | 97 | −3 | −18 | 2 | 4 | 2 | 10 | 2 | 9 |
500 | Re(ρ) | 0 | 0 | 0 | 0 | 0 | −3 | 3 | 8 | 0 | 1 | 0 | −1 | 0 | 0 |
| Im(ρ) | 0 | 0 | 1 | 0 | 0 | −18 | 8 | 106 | 0 | −12 | −5 | 4 | 0 | 20 |
550 | Re(ρ) | 0 | 0 | 0 | −2 | 0 | 2 | 0 | 0 | 3 | 8 | 0 | 0 | 0 | −1 |
| Im(ρ) | −1 | 4 | 3 | 1 | 0 | 4 | 1 | −12 | 8 | 132 | 3 | 7 | −3 | −8 |
600 | Re(ρ) | 0 | 0 | 0 | 1 | 0 | 2 | 0 | −5 | 0 | 3 | 4 | 11 | 0 | −4 |
| Im(ρ) | −3 | −3 | −1 | 9 | −1 | 10 | −1 | 4 | 0 | 7 | 11 | 174 | −1 | −30 |
650 | Re(ρ) | 0 | 0 | 0 | 2 | 0 | 2 | 0 | 0 | 0 | −3 | 0 | −1 | 5 | 7 |
| Im(ρ) | 4 | 5 | 4 | 7 | 0 | 9 | 0 | 20 | −1 | −8 | −4 | −30 | 7 | 213 |
Table X
Summary of the Variance–Covariance Matrices
c-Si | M ratios | Mmax/Mmin | Correlations between parameters at λ = λi |
---|
|
---|
max | min |
---|
α, β | 1.7 | 0.93 | 3.5 | Weak, anticorrelation |
Δ, ψ | 970 | 15 | 2000 | Strong, anticorrelation |
tanψ, cosΔ | 0.36 | 0.04 | 109 | Strong correlation |
∊′, ∊Prime; | 2.7 | 0.08 | 24 | Very strong correlation |
n, k | 1.9 | 0.04 | 29 | Strong correlation |
Re(ρ), Im(ρ) | 0.39 | 0.02 | 107 | Strong correlation |
Au film | M ratios | Mmax/Mmin | Correlations between parameters at λ = λI |
---|
|
---|
max | min |
---|
α, β | 0.84 | 0.41 | 4.5 | Very weak |
Δ, ψ | 9.8 | 4.8 | 18 | Very weak |
tanψ, cosΔ | 0.71 | 0.20 | 8.8 | Very weak |
∊′, ∊Prime; | 1.9 | 0.94 | 14 | Very weak |
n, k | 0.83 | 0.50 | 6.9 | Very weak |
Re(ρ), Im(ρ) | 1.7 | 1.2 | 5.3 | Very weak |