M. Loktev (m.loktev@ewi.tudelft.nl) and G. Vdovin are with the Electronic Instrumentation Laboratory, Delft University of Technology, Mekelweg 4, P.O. Box 5031, 2600 GA Delft, The Netherlands.
I. Guralnik is with the Department of Physics, Samara State University, Ac. Pavlova 1, 443011 Samara, Russia.
Liquid-crystal modal wave-front correctors provide much better wave-front correction than do piston correctors with the same number of actuators; moreover, use of additional degrees of freedom of the driving ac voltage signals may further improve device performance. Some practical aspects of the operation of liquid-crystal modal wave-front correctors are discussed. Special attention is paid to the interference of various contact responses and to the formation of required phase shapes through wider control of signal frequencies and electric phase shifts. The study is based on an analytic approach and numerical investigation; major theoretical conclusions are verified experimentally.
S. P. Kotova, M. Yu. Kvashnin, M. A. Rakhmatulin, O. A. Zayakin, I. R Guralnik, N. A. Klimov, P. Clark, G. D. Love, A. F. Naumov, C. D. Saunter, M. Yu. Loktev, G. V. Vdovin, and L. V. Toporkova Opt. Express 10(22) 1258-1272 (2002)
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E1 and E2 are EMFs generated in channels of the CU connected to contacts 1 and 2, respectively; U1 and U2 are voltages measured at these contacts; measured values of Zc and Zic were 27.4 and 45.6 kΩ, respectively. Fifth row, measurement results for the second contact disconnected from the CU. U1 = 7.07 in all cases.
Table 2
Approximation of Zernike Aberrations in a 38-Channel Modal LC Corrector by Use of SF-VACa
Aberration
Zernike Term
Amplitude (Wave)
Frequency (kHz)
1
20
50
100
150
Tilt
Z1,-1, Z1,1
-4, 4
0.064
0.061
0.094
0.349
0.801
Astigmatism
Z2,-2, Z2,2
-4, 4
0.088
0.086
0.107
0.340
0.780
Defocus
Z2,0
-4
0.333
0.324
0.276
0.171
0.385
Defocus
Z2,0
4
0.121
0.124
0.156
0.359
0.766
Coma
Z3,-1, Z3,1
-4, 4
0.312
0.309
0.298
0.373
0.706
Trifoil
Z3,-3, Z3,3
-4, 4
0.208
0.205
0.212
0.405
0.860
Spherical
Z4,0
-4
0.822
0.813
0.768
0.661
0.727
Spherical
Z4,0
4
0.546
0.545
0.546
0.585
0.779
Corrector parameters: diameter of pointlike contacts, 0.5 mm; aperture diameter, 30 mm; sheet resistance, ρ = 100 kΩ. Phenomenological characteristics of a 25-μm layer of Merck’s BL006 LC are used. rms residual aberrations are expressed as waves. The best result for each aberration is indicated by boldface type.
Improvement Owing to Optimization by Phase Shift (%)
Optimization by Amplitude (SF-VAC)
Optimization by Amplitude and Phase Shift
Tilt
Z1,-1, Z1,1
-4, 4
0.064
0.037
42.2
Astigmatism
Z2,-2, Z2,2
-4, 4
0.088
0.055
37.5
Defocus
Z2,0
-4
0.333
0.115
65.5
Defocus
Z2,0
4
0.121
0.119
1.6
Coma
Z3,-1, Z3,1
-4, 4
0.312
0.199
36.2
Trifoil
Z3,-3, Z3,3
-4, 4
0.208
0.110
47.1
Spherical
Z4,0
-4
0.822
0.355
56.8
Spherical
Z4,0
4
0.546
0.312
42.9
Comparison of the results of optimization by voltage amplitudes (SF-VAC) and by both amplitudes and phase shifts; signal frequency, 1 kHz. All conventions and corrector parameters are similar to those for Table
2.
Table 4
Approximation of Zernike Aberrations in a LC MWC by Use of MFC and Current-Addressing Modea
Aberration
Zernike Term
Amplitude (Wave)
Base Frequency (kHz)
1
10
20
50
100
Tilt
Z1,-1, Z1,1
-4, 4
0.153
0.220
0.410
1.500
2.893
Astigmatism
Z2,-2, Z2,2
-4, 4
0.171
0.246
0.438
1.806
2.862
Defocus
Z2,0
-4
1.231
1.107
0.891
0.213
2.067
Defocus
Z2,0
4
0.275
0.359
0.569
2.440
2.613
Coma
Z3,-1, Z3,1
-4, 4
0.562
0.530
0.577
1.571
2.813
Trifoil
Z3,-3, Z3,3
-4, 4
0.272
0.351
0.513
1.756
2.865
Spherical
Z4,0
-4
1.101
1.049
0.954
0.902
2.480
Spherical
Z4,0
4
1.018
0.992
1.021
2.239
2.772
All conventions and corrector parameters are similar to those for Table
2.
Tables (4)
Table 1
Experimental Investigation of the Screening Effect in a 38-Channel 80-mm LC MWC for Several CU Series Resistances Ra
E1 and E2 are EMFs generated in channels of the CU connected to contacts 1 and 2, respectively; U1 and U2 are voltages measured at these contacts; measured values of Zc and Zic were 27.4 and 45.6 kΩ, respectively. Fifth row, measurement results for the second contact disconnected from the CU. U1 = 7.07 in all cases.
Table 2
Approximation of Zernike Aberrations in a 38-Channel Modal LC Corrector by Use of SF-VACa
Aberration
Zernike Term
Amplitude (Wave)
Frequency (kHz)
1
20
50
100
150
Tilt
Z1,-1, Z1,1
-4, 4
0.064
0.061
0.094
0.349
0.801
Astigmatism
Z2,-2, Z2,2
-4, 4
0.088
0.086
0.107
0.340
0.780
Defocus
Z2,0
-4
0.333
0.324
0.276
0.171
0.385
Defocus
Z2,0
4
0.121
0.124
0.156
0.359
0.766
Coma
Z3,-1, Z3,1
-4, 4
0.312
0.309
0.298
0.373
0.706
Trifoil
Z3,-3, Z3,3
-4, 4
0.208
0.205
0.212
0.405
0.860
Spherical
Z4,0
-4
0.822
0.813
0.768
0.661
0.727
Spherical
Z4,0
4
0.546
0.545
0.546
0.585
0.779
Corrector parameters: diameter of pointlike contacts, 0.5 mm; aperture diameter, 30 mm; sheet resistance, ρ = 100 kΩ. Phenomenological characteristics of a 25-μm layer of Merck’s BL006 LC are used. rms residual aberrations are expressed as waves. The best result for each aberration is indicated by boldface type.
Improvement Owing to Optimization by Phase Shift (%)
Optimization by Amplitude (SF-VAC)
Optimization by Amplitude and Phase Shift
Tilt
Z1,-1, Z1,1
-4, 4
0.064
0.037
42.2
Astigmatism
Z2,-2, Z2,2
-4, 4
0.088
0.055
37.5
Defocus
Z2,0
-4
0.333
0.115
65.5
Defocus
Z2,0
4
0.121
0.119
1.6
Coma
Z3,-1, Z3,1
-4, 4
0.312
0.199
36.2
Trifoil
Z3,-3, Z3,3
-4, 4
0.208
0.110
47.1
Spherical
Z4,0
-4
0.822
0.355
56.8
Spherical
Z4,0
4
0.546
0.312
42.9
Comparison of the results of optimization by voltage amplitudes (SF-VAC) and by both amplitudes and phase shifts; signal frequency, 1 kHz. All conventions and corrector parameters are similar to those for Table
2.
Table 4
Approximation of Zernike Aberrations in a LC MWC by Use of MFC and Current-Addressing Modea
Aberration
Zernike Term
Amplitude (Wave)
Base Frequency (kHz)
1
10
20
50
100
Tilt
Z1,-1, Z1,1
-4, 4
0.153
0.220
0.410
1.500
2.893
Astigmatism
Z2,-2, Z2,2
-4, 4
0.171
0.246
0.438
1.806
2.862
Defocus
Z2,0
-4
1.231
1.107
0.891
0.213
2.067
Defocus
Z2,0
4
0.275
0.359
0.569
2.440
2.613
Coma
Z3,-1, Z3,1
-4, 4
0.562
0.530
0.577
1.571
2.813
Trifoil
Z3,-3, Z3,3
-4, 4
0.272
0.351
0.513
1.756
2.865
Spherical
Z4,0
-4
1.101
1.049
0.954
0.902
2.480
Spherical
Z4,0
4
1.018
0.992
1.021
2.239
2.772
All conventions and corrector parameters are similar to those for Table
2.
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