A new method of aligning the optical components has been proposed for the polarizer–specimen–compensator–analyzer ellipsometer configuration. By carrying out the measurements at four different pairs of azimuths of the polarizer and the compensator, we can simultaneously determine the orientation of the optical components with respect to the plane of incidence and the phase retardation of the compensator. The method is fundamentally based on the fact that all the linearly polarized light is transferred on the same great circle on the Poincaré sphere that passes through the p and s directions after reflection from the isotropic surface.
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Experimental Results Obtained by Varying the Azimuth of the Polarizer by 1°a
Azimuth of the Optical Component (degrees)
Phase Retardation of the Compensator (degrees)
Ellipsometric Parameters of the Reflecting Surface
Polarizer
Compensator
Analyzer
tan Ψ
Δ (degrees)
42.82
2.69
−17.28
85.07
0.4893
114.22
43.98
2.70
−17.37
85.10
0.4926
114.09
44.84
2.69
−17.20
85.12
0.4889
114.03
45.80
2.69
−17.18
85.14
0.4892
114.08
46.80
2.68
−17.16
85.07
0.4888
114.06
_–
(2.69)
(−17.24)
(85.10)
(0.4898)
(114.10)
Figures in parentheses represent the average values. Reflecting surface, MgF2/Si. Angle of incidence, 65°. Wavelength, 632.8 nm.
Table 2
Experimental Results Obtained by Varying the Azimuth of the Compensator by 1°a
Azimuth of the Optical Component (degrees)
Phase Retardation of the Compensator (degrees)
Ellipsometric Parameters of the Reflecting Surface
Polarizer
Compensator
Analyzer
tan Ψ
Δ (degrees)
44.76
0.81
−17.15
85.01
0.4890
114.15
44.79
1.75
−17.17
85.02
0.4889
114.13
44.79
2.73
−17.18
85.05
0.4888
114.16
44.78
3.71
−17.16
85.00
0.4891
114.13
(44.78)
–
(−17.17)
(85.02)
(0.4889)
(114.14)
Figures in parentheses represent the average values. Reflecting surface, MgF2/Si. Angle of incidence, 65°. Wavelength, 632.8 nm.
Table 3
Results of the Computer Simulation Taking into Account the Incomplete Rotation of the Compensatora
Rotation Angle of the Compensator (degrees)
Azimuth of the Optical Component (degrees)
Phase Retardation of the Compensator (86.06°) (degrees)
Polarizer (44.78°)
Compensator (2.69°)
Analyzer (−17.56°)
δC
δC*
(δC + δC*)/2
89.5
44.44
2.53
−17.35
84.66
85.43
85.05
89.6
44.51
2.56
−17.40
84.73
85.36
85.05
89.7
44.57
2.59
−17.44
84.82
85.28
85.05
89.8
44.63
2.62
−17.48
84.89
85.21
85.05
89.9
44.71
2.65
−17.52
84.97
85.14
85.06
90.0
44.78
2.69
−17.56
85.05
85.06
85.06
90.1
44.85
2.73
−17.60
85.14
84.98
85.06
90.2
44.92
2.76
−17.64
85.21
84.91
85.06
90.3
44.97
2.79
−17.68
85.29
84.83
85.06
90.4
45.06
2.83
−17.72
85.38
84.77
85.07
90.5
45.12
2.86
−17.76
85.47
84.69
85.08
The input data of the calculation are shown in the parentheses. δC and δC* represent the phase retardation of the compensator derived from Eqs. (11) and (15), respectively.
Table 4
Results of the Computer Simulation Taking into Account a Defect of the Compensatora
Transmission Ratio of the Compensator
Azimuth of the Optical Component (degrees)
Average Retardation (85.06°) (degrees)
Relative Azimuth of the Compensator (degrees)
Polarizer (44.78°)
Compensator (2.69°)
Analyzer (−17.56°)
(δC − χA)
(δC − χA)*
0.95
44.78
2.69
−17.49
85.86
21.46
18.90
0.96
44.78
2.69
−17.50
85.68
21.21
19.18
0.97
44.78
2.69
−17.52
85.53
20.97
19.45
0.98
44.78
2.69
−17.53
85.38
20.73
19.72
0.99
44.78
2.69
−17.55
85.22
20.49
19.99
1.00
44.78
2.69
−17.56
85.06
20.25
20.25
1.01
44.78
2.69
−17.58
84.91
20.02
20.51
1.02
44.78
2.69
−17.59
84.76
19.78
20.77
1.03
44.78
2.69
−17.61
84.61
19.55
21.03
1.04
44.79
2.67
−17.63
84.46
19.32
21.28
1.05
44.79
2.68
−17.63
84.32
19.10
21.54
The input data of the calculation are shown in the parentheses. (θC − χA) and (θC − χA)* represent the relative azimuth of the compensator with respect to the initial azimuth of the rotating analyzer derived from Eqs. (10) and (14), respectively.
Tables (4)
Table 1
Experimental Results Obtained by Varying the Azimuth of the Polarizer by 1°a
Azimuth of the Optical Component (degrees)
Phase Retardation of the Compensator (degrees)
Ellipsometric Parameters of the Reflecting Surface
Polarizer
Compensator
Analyzer
tan Ψ
Δ (degrees)
42.82
2.69
−17.28
85.07
0.4893
114.22
43.98
2.70
−17.37
85.10
0.4926
114.09
44.84
2.69
−17.20
85.12
0.4889
114.03
45.80
2.69
−17.18
85.14
0.4892
114.08
46.80
2.68
−17.16
85.07
0.4888
114.06
_–
(2.69)
(−17.24)
(85.10)
(0.4898)
(114.10)
Figures in parentheses represent the average values. Reflecting surface, MgF2/Si. Angle of incidence, 65°. Wavelength, 632.8 nm.
Table 2
Experimental Results Obtained by Varying the Azimuth of the Compensator by 1°a
Azimuth of the Optical Component (degrees)
Phase Retardation of the Compensator (degrees)
Ellipsometric Parameters of the Reflecting Surface
Polarizer
Compensator
Analyzer
tan Ψ
Δ (degrees)
44.76
0.81
−17.15
85.01
0.4890
114.15
44.79
1.75
−17.17
85.02
0.4889
114.13
44.79
2.73
−17.18
85.05
0.4888
114.16
44.78
3.71
−17.16
85.00
0.4891
114.13
(44.78)
–
(−17.17)
(85.02)
(0.4889)
(114.14)
Figures in parentheses represent the average values. Reflecting surface, MgF2/Si. Angle of incidence, 65°. Wavelength, 632.8 nm.
Table 3
Results of the Computer Simulation Taking into Account the Incomplete Rotation of the Compensatora
Rotation Angle of the Compensator (degrees)
Azimuth of the Optical Component (degrees)
Phase Retardation of the Compensator (86.06°) (degrees)
Polarizer (44.78°)
Compensator (2.69°)
Analyzer (−17.56°)
δC
δC*
(δC + δC*)/2
89.5
44.44
2.53
−17.35
84.66
85.43
85.05
89.6
44.51
2.56
−17.40
84.73
85.36
85.05
89.7
44.57
2.59
−17.44
84.82
85.28
85.05
89.8
44.63
2.62
−17.48
84.89
85.21
85.05
89.9
44.71
2.65
−17.52
84.97
85.14
85.06
90.0
44.78
2.69
−17.56
85.05
85.06
85.06
90.1
44.85
2.73
−17.60
85.14
84.98
85.06
90.2
44.92
2.76
−17.64
85.21
84.91
85.06
90.3
44.97
2.79
−17.68
85.29
84.83
85.06
90.4
45.06
2.83
−17.72
85.38
84.77
85.07
90.5
45.12
2.86
−17.76
85.47
84.69
85.08
The input data of the calculation are shown in the parentheses. δC and δC* represent the phase retardation of the compensator derived from Eqs. (11) and (15), respectively.
Table 4
Results of the Computer Simulation Taking into Account a Defect of the Compensatora
Transmission Ratio of the Compensator
Azimuth of the Optical Component (degrees)
Average Retardation (85.06°) (degrees)
Relative Azimuth of the Compensator (degrees)
Polarizer (44.78°)
Compensator (2.69°)
Analyzer (−17.56°)
(δC − χA)
(δC − χA)*
0.95
44.78
2.69
−17.49
85.86
21.46
18.90
0.96
44.78
2.69
−17.50
85.68
21.21
19.18
0.97
44.78
2.69
−17.52
85.53
20.97
19.45
0.98
44.78
2.69
−17.53
85.38
20.73
19.72
0.99
44.78
2.69
−17.55
85.22
20.49
19.99
1.00
44.78
2.69
−17.56
85.06
20.25
20.25
1.01
44.78
2.69
−17.58
84.91
20.02
20.51
1.02
44.78
2.69
−17.59
84.76
19.78
20.77
1.03
44.78
2.69
−17.61
84.61
19.55
21.03
1.04
44.79
2.67
−17.63
84.46
19.32
21.28
1.05
44.79
2.68
−17.63
84.32
19.10
21.54
The input data of the calculation are shown in the parentheses. (θC − χA) and (θC − χA)* represent the relative azimuth of the compensator with respect to the initial azimuth of the rotating analyzer derived from Eqs. (10) and (14), respectively.
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